id	sid	tid	token	lemma	pos
ejpam-6089	1	1	european	european	PROPN
ejpam-6089	1	2	journal	journal	PROPN
ejpam-6089	1	3	of	of	ADP
ejpam-6089	1	4	pure	pure	ADJ
ejpam-6089	1	5	and	and	CCONJ
ejpam-6089	1	6	applied	applied	ADJ
ejpam-6089	1	7	mathematics	mathematic	NOUN
ejpam-6089	1	8	2025	2025	NUM
ejpam-6089	1	9	,	,	PUNCT
ejpam-6089	1	10	vol	vol	NOUN
ejpam-6089	1	11	.	.	PROPN
ejpam-6089	1	12	18	18	NUM
ejpam-6089	1	13	,	,	PUNCT
ejpam-6089	1	14	issue	issue	NOUN
ejpam-6089	1	15	2	2	NUM
ejpam-6089	1	16	,	,	PUNCT
ejpam-6089	1	17	article	article	NOUN
ejpam-6089	1	18	number	number	NOUN
ejpam-6089	1	19	6089	6089	NUM
ejpam-6089	1	20	issn	issn	VERB
ejpam-6089	1	21	1307	1307	NUM
ejpam-6089	1	22	-	-	SYM
ejpam-6089	1	23	5543	5543	NUM
ejpam-6089	1	24	–	–	PUNCT
ejpam-6089	1	25	ejpam.com	ejpam.com	X
ejpam-6089	1	26	published	publish	VERB
ejpam-6089	1	27	by	by	ADP
ejpam-6089	1	28	new	new	PROPN
ejpam-6089	1	29	york	york	PROPN
ejpam-6089	1	30	business	business	PROPN
ejpam-6089	1	31	global	global	ADJ
ejpam-6089	1	32	generalized	generalize	VERB
ejpam-6089	1	33	fractional	fractional	ADJ
ejpam-6089	1	34	integral	integral	ADJ
ejpam-6089	1	35	extensions	extension	NOUN
ejpam-6089	1	36	of	of	ADP
ejpam-6089	1	37	hermite	hermite	PROPN
ejpam-6089	1	38	-	-	PUNCT
ejpam-6089	1	39	hadamard	hadamard	ADJ
ejpam-6089	1	40	inequalities	inequality	NOUN
ejpam-6089	1	41	saima	saima	PROPN
ejpam-6089	1	42	naheed1,∗	naheed1,∗	PROPN
ejpam-6089	1	43	,	,	PUNCT
ejpam-6089	1	44	adeeba	adeeba	PROPN
ejpam-6089	1	45	rafi1	rafi1	PROPN
ejpam-6089	1	46	,	,	PUNCT
ejpam-6089	1	47	gauhar	gauhar	PROPN
ejpam-6089	1	48	rahman2	rahman2	PROPN
ejpam-6089	1	49	,	,	PUNCT
ejpam-6089	1	50	irshad	irshad	VERB
ejpam-6089	1	51	ayoob3	ayoob3	PROPN
ejpam-6089	1	52	,	,	PUNCT
ejpam-6089	1	53	nabil	nabil	PROPN
ejpam-6089	1	54	mlaiki3	mlaiki3	PROPN
ejpam-6089	1	55	1	1	NUM
ejpam-6089	1	56	department	department	NOUN
ejpam-6089	1	57	of	of	ADP
ejpam-6089	1	58	mathematics	mathematics	PROPN
ejpam-6089	1	59	,	,	PUNCT
ejpam-6089	1	60	university	university	PROPN
ejpam-6089	1	61	of	of	ADP
ejpam-6089	1	62	sargodha	sargodha	PROPN
ejpam-6089	1	63	p.o	p.o	PROPN
ejpam-6089	1	64	.	.	PROPN
ejpam-6089	1	65	box	box	PROPN
ejpam-6089	1	66	40100	40100	PROPN
ejpam-6089	1	67	,	,	PUNCT
ejpam-6089	1	68	sargodha	sargodha	PROPN
ejpam-6089	1	69	,	,	PUNCT
ejpam-6089	1	70	pakistan	pakistan	PROPN
ejpam-6089	1	71	2	2	NUM
ejpam-6089	1	72	department	department	NOUN
ejpam-6089	1	73	of	of	ADP
ejpam-6089	1	74	mathematics	mathematic	NOUN
ejpam-6089	1	75	and	and	CCONJ
ejpam-6089	1	76	statistics	statistic	NOUN
ejpam-6089	1	77	,	,	PUNCT
ejpam-6089	1	78	hazara	hazara	PROPN
ejpam-6089	1	79	university	university	PROPN
ejpam-6089	1	80	,	,	PUNCT
ejpam-6089	1	81	mansehra	mansehra	PROPN
ejpam-6089	1	82	21300	21300	NUM
ejpam-6089	1	83	,	,	PUNCT
ejpam-6089	1	84	pakistan	pakistan	PROPN
ejpam-6089	1	85	3	3	NUM
ejpam-6089	1	86	department	department	NOUN
ejpam-6089	1	87	of	of	ADP
ejpam-6089	1	88	mathematics	mathematic	NOUN
ejpam-6089	1	89	and	and	CCONJ
ejpam-6089	1	90	sciences	science	NOUN
ejpam-6089	1	91	,	,	PUNCT
ejpam-6089	1	92	prince	prince	PROPN
ejpam-6089	1	93	sultan	sultan	PROPN
ejpam-6089	1	94	university	university	PROPN
ejpam-6089	1	95	,	,	PUNCT
ejpam-6089	1	96	riyadh	riyadh	PROPN
ejpam-6089	1	97	11586	11586	NUM
ejpam-6089	1	98	,	,	PUNCT
ejpam-6089	1	99	saudi	saudi	PROPN
ejpam-6089	1	100	arabia	arabia	PROPN
ejpam-6089	1	101	abstract	abstract	NOUN
ejpam-6089	1	102	.	.	PUNCT
ejpam-6089	2	1	in	in	ADP
ejpam-6089	2	2	this	this	DET
ejpam-6089	2	3	article	article	NOUN
ejpam-6089	2	4	,	,	PUNCT
ejpam-6089	2	5	we	we	PRON
ejpam-6089	2	6	provide	provide	VERB
ejpam-6089	2	7	a	a	DET
ejpam-6089	2	8	number	number	NOUN
ejpam-6089	2	9	of	of	ADP
ejpam-6089	2	10	hermite	hermite	ADJ
ejpam-6089	2	11	-	-	PUNCT
ejpam-6089	2	12	hadamard	hadamard	ADJ
ejpam-6089	2	13	type	type	NOUN
ejpam-6089	2	14	fractional	fractional	ADJ
ejpam-6089	2	15	integral	integral	ADJ
ejpam-6089	2	16	inequalities	inequality	NOUN
ejpam-6089	2	17	for	for	ADP
ejpam-6089	2	18	the	the	DET
ejpam-6089	2	19	atangana	atangana	PROPN
ejpam-6089	2	20	-	-	PUNCT
ejpam-6089	2	21	baleanu	baleanu	PROPN
ejpam-6089	2	22	and	and	CCONJ
ejpam-6089	2	23	prabhakar	prabhakar	PROPN
ejpam-6089	2	24	fractional	fractional	PROPN
ejpam-6089	2	25	operators	operator	NOUN
ejpam-6089	2	26	,	,	PUNCT
ejpam-6089	2	27	using	use	VERB
ejpam-6089	2	28	extended	extended	ADJ
ejpam-6089	2	29	generalized	generalize	VERB
ejpam-6089	2	30	mittag	mittag	ADJ
ejpam-6089	2	31	-	-	PUNCT
ejpam-6089	2	32	leffler	leffler	NOUN
ejpam-6089	2	33	functions	function	NOUN
ejpam-6089	2	34	as	as	ADP
ejpam-6089	2	35	their	their	PRON
ejpam-6089	2	36	kernel	kernel	NOUN
ejpam-6089	2	37	.	.	PUNCT
ejpam-6089	3	1	significant	significant	ADJ
ejpam-6089	3	2	findings	finding	NOUN
ejpam-6089	3	3	are	be	AUX
ejpam-6089	3	4	provided	provide	VERB
ejpam-6089	3	5	for	for	ADP
ejpam-6089	3	6	the	the	DET
ejpam-6089	3	7	integral	integral	ADJ
ejpam-6089	3	8	inequalities	inequality	NOUN
ejpam-6089	3	9	involving	involve	VERB
ejpam-6089	3	10	fractional	fractional	ADJ
ejpam-6089	3	11	integrals	integral	NOUN
ejpam-6089	3	12	of	of	ADP
ejpam-6089	3	13	the	the	DET
ejpam-6089	3	14	type	type	NOUN
ejpam-6089	3	15	(	(	PUNCT
ejpam-6089	3	16	ℑ1+,ℑ2−	ℑ1+,ℑ2−	PROPN
ejpam-6089	3	17	)	)	PUNCT
ejpam-6089	3	18	and	and	CCONJ
ejpam-6089	3	19	(	(	PUNCT
ejpam-6089	3	20	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	3	21	2	2	NUM
ejpam-6089	3	22	)	)	PUNCT
ejpam-6089	3	23	.	.	PUNCT
ejpam-6089	4	1	by	by	ADP
ejpam-6089	4	2	employing	employ	VERB
ejpam-6089	4	3	certain	certain	ADJ
ejpam-6089	4	4	functions	function	NOUN
ejpam-6089	4	5	to	to	PART
ejpam-6089	4	6	create	create	VERB
ejpam-6089	4	7	visual	visual	ADJ
ejpam-6089	4	8	graphs	graph	NOUN
ejpam-6089	4	9	with	with	ADP
ejpam-6089	4	10	matching	match	VERB
ejpam-6089	4	11	numerical	numerical	ADJ
ejpam-6089	4	12	entries	entry	NOUN
ejpam-6089	4	13	that	that	PRON
ejpam-6089	4	14	depict	depict	VERB
ejpam-6089	4	15	the	the	DET
ejpam-6089	4	16	inequalities	inequality	NOUN
ejpam-6089	4	17	,	,	PUNCT
ejpam-6089	4	18	we	we	PRON
ejpam-6089	4	19	show	show	VERB
ejpam-6089	4	20	the	the	DET
ejpam-6089	4	21	veracity	veracity	NOUN
ejpam-6089	4	22	of	of	ADP
ejpam-6089	4	23	our	our	PRON
ejpam-6089	4	24	findings	finding	NOUN
ejpam-6089	4	25	.	.	PUNCT
ejpam-6089	5	1	2020	2020	NUM
ejpam-6089	5	2	mathematics	mathematic	NOUN
ejpam-6089	5	3	subject	subject	NOUN
ejpam-6089	5	4	classifications	classification	NOUN
ejpam-6089	5	5	:	:	PUNCT
ejpam-6089	5	6	33e12	33e12	NUM
ejpam-6089	5	7	,	,	PUNCT
ejpam-6089	5	8	26a33	26a33	NUM
ejpam-6089	5	9	,	,	PUNCT
ejpam-6089	5	10	26d15	26d15	PRON
ejpam-6089	5	11	key	key	ADJ
ejpam-6089	5	12	words	word	NOUN
ejpam-6089	5	13	and	and	CCONJ
ejpam-6089	5	14	phrases	phrase	NOUN
ejpam-6089	5	15	:	:	PUNCT
ejpam-6089	5	16	atangana	atangana	PROPN
ejpam-6089	5	17	-	-	PUNCT
ejpam-6089	5	18	baleanu	baleanu	ADJ
ejpam-6089	5	19	fractional	fractional	ADJ
ejpam-6089	5	20	calculus	calculus	NOUN
ejpam-6089	5	21	,	,	PUNCT
ejpam-6089	5	22	fractional	fractional	ADJ
ejpam-6089	5	23	calculus	calculus	NOUN
ejpam-6089	5	24	,	,	PUNCT
ejpam-6089	5	25	hermitehadamard	hermitehadamard	NOUN
ejpam-6089	5	26	inequality	inequality	NOUN
ejpam-6089	5	27	,	,	PUNCT
ejpam-6089	5	28	generalized	generalize	VERB
ejpam-6089	5	29	fractional	fractional	ADJ
ejpam-6089	5	30	integral	integral	ADJ
ejpam-6089	5	31	operators	operator	NOUN
ejpam-6089	5	32	,	,	PUNCT
ejpam-6089	5	33	mittag	mittag	ADJ
ejpam-6089	5	34	-	-	PUNCT
ejpam-6089	5	35	leffler	leffler	NOUN
ejpam-6089	5	36	function	function	NOUN
ejpam-6089	5	37	1	1	NUM
ejpam-6089	5	38	.	.	PUNCT
ejpam-6089	6	1	introduction	introduction	VERB
ejpam-6089	6	2	the	the	DET
ejpam-6089	6	3	expansion	expansion	NOUN
ejpam-6089	6	4	of	of	ADP
ejpam-6089	6	5	differentiation	differentiation	NOUN
ejpam-6089	6	6	and	and	CCONJ
ejpam-6089	6	7	integration	integration	NOUN
ejpam-6089	6	8	to	to	ADP
ejpam-6089	6	9	non	non	ADJ
ejpam-6089	6	10	-	-	ADJ
ejpam-6089	6	11	integer	integer	ADJ
ejpam-6089	6	12	orders	order	NOUN
ejpam-6089	6	13	is	be	AUX
ejpam-6089	6	14	the	the	DET
ejpam-6089	6	15	work	work	NOUN
ejpam-6089	6	16	of	of	ADP
ejpam-6089	6	17	fractional	fractional	ADJ
ejpam-6089	6	18	calculus	calculus	NOUN
ejpam-6089	6	19	,	,	PUNCT
ejpam-6089	6	20	a	a	DET
ejpam-6089	6	21	subfield	subfield	NOUN
ejpam-6089	6	22	of	of	ADP
ejpam-6089	6	23	mathematics	mathematic	NOUN
ejpam-6089	6	24	,	,	PUNCT
ejpam-6089	6	25	making	make	VERB
ejpam-6089	6	26	it	it	PRON
ejpam-6089	6	27	possible	possible	ADJ
ejpam-6089	6	28	to	to	PART
ejpam-6089	6	29	represent	represent	VERB
ejpam-6089	6	30	complex	complex	ADJ
ejpam-6089	6	31	processes	process	NOUN
ejpam-6089	6	32	more	more	ADV
ejpam-6089	6	33	intricately	intricately	ADV
ejpam-6089	7	1	[	[	X
ejpam-6089	7	2	1	1	NUM
ejpam-6089	7	3	,	,	PUNCT
ejpam-6089	7	4	2	2	NUM
ejpam-6089	7	5	]	]	PUNCT
ejpam-6089	7	6	.	.	PUNCT
ejpam-6089	8	1	fractional	fractional	ADJ
ejpam-6089	8	2	integral	integral	ADJ
ejpam-6089	8	3	operators	operator	NOUN
ejpam-6089	8	4	are	be	AUX
ejpam-6089	8	5	utilized	utilize	VERB
ejpam-6089	8	6	as	as	ADP
ejpam-6089	8	7	mathematical	mathematical	ADJ
ejpam-6089	8	8	tools	tool	NOUN
ejpam-6089	8	9	in	in	ADP
ejpam-6089	8	10	the	the	DET
ejpam-6089	8	11	study	study	NOUN
ejpam-6089	8	12	of	of	ADP
ejpam-6089	8	13	fractional	fractional	ADJ
ejpam-6089	8	14	calculus	calculus	NOUN
ejpam-6089	8	15	because	because	SCONJ
ejpam-6089	8	16	they	they	PRON
ejpam-6089	8	17	are	be	AUX
ejpam-6089	8	18	integrals	integral	NOUN
ejpam-6089	8	19	of	of	ADP
ejpam-6089	8	20	a	a	DET
ejpam-6089	8	21	certain	certain	ADJ
ejpam-6089	8	22	order	order	NOUN
ejpam-6089	8	23	,	,	PUNCT
ejpam-6089	8	24	which	which	PRON
ejpam-6089	8	25	is	be	AUX
ejpam-6089	8	26	not	not	PART
ejpam-6089	8	27	limited	limit	VERB
ejpam-6089	8	28	to	to	ADP
ejpam-6089	8	29	integer	integer	NOUN
ejpam-6089	8	30	values	value	NOUN
ejpam-6089	8	31	but	but	CCONJ
ejpam-6089	8	32	can	can	AUX
ejpam-6089	8	33	be	be	AUX
ejpam-6089	8	34	any	any	DET
ejpam-6089	8	35	real	real	ADJ
ejpam-6089	8	36	or	or	CCONJ
ejpam-6089	8	37	complex	complex	ADJ
ejpam-6089	8	38	number	number	NOUN
ejpam-6089	8	39	.	.	PUNCT
ejpam-6089	9	1	in	in	ADP
ejpam-6089	9	2	the	the	DET
ejpam-6089	9	3	solution	solution	NOUN
ejpam-6089	9	4	of	of	ADP
ejpam-6089	9	5	fractional	fractional	ADJ
ejpam-6089	9	6	differential	differential	ADJ
ejpam-6089	9	7	equations	equation	NOUN
ejpam-6089	9	8	,	,	PUNCT
ejpam-6089	9	9	fractional	fractional	ADJ
ejpam-6089	9	10	integral	integral	ADJ
ejpam-6089	9	11	operators	operator	NOUN
ejpam-6089	9	12	are	be	AUX
ejpam-6089	9	13	crucial	crucial	ADJ
ejpam-6089	9	14	because	because	SCONJ
ejpam-6089	9	15	they	they	PRON
ejpam-6089	9	16	generalize	generalize	VERB
ejpam-6089	9	17	several	several	ADJ
ejpam-6089	9	18	classical	classical	ADJ
ejpam-6089	9	19	operators	operator	NOUN
ejpam-6089	9	20	,	,	PUNCT
ejpam-6089	9	21	including	include	VERB
ejpam-6089	9	22	the	the	DET
ejpam-6089	9	23	integral	integral	ADJ
ejpam-6089	9	24	and	and	CCONJ
ejpam-6089	9	25	derivative	derivative	ADJ
ejpam-6089	9	26	[	[	X
ejpam-6089	9	27	3	3	NUM
ejpam-6089	9	28	]	]	PUNCT
ejpam-6089	9	29	,	,	PUNCT
ejpam-6089	9	30	and	and	CCONJ
ejpam-6089	9	31	they	they	PRON
ejpam-6089	9	32	aid	aid	VERB
ejpam-6089	9	33	in	in	ADP
ejpam-6089	9	34	describing	describe	VERB
ejpam-6089	9	35	processes	process	NOUN
ejpam-6089	9	36	that	that	PRON
ejpam-6089	9	37	are	be	AUX
ejpam-6089	9	38	not	not	PART
ejpam-6089	9	39	fully	fully	ADV
ejpam-6089	9	40	represented	represent	VERB
ejpam-6089	9	41	by	by	ADP
ejpam-6089	9	42	traditional	traditional	ADJ
ejpam-6089	9	43	calculus	calculus	NOUN
ejpam-6089	9	44	,	,	PUNCT
ejpam-6089	9	45	which	which	PRON
ejpam-6089	9	46	is	be	AUX
ejpam-6089	9	47	limited	limit	VERB
ejpam-6089	9	48	to	to	ADP
ejpam-6089	9	49	integer	integer	NOUN
ejpam-6089	9	50	orders	order	NOUN
ejpam-6089	9	51	.	.	PUNCT
ejpam-6089	10	1	fractional	fractional	ADJ
ejpam-6089	10	2	calculus	calculus	NOUN
ejpam-6089	10	3	uses	use	VERB
ejpam-6089	10	4	definitions	definition	NOUN
ejpam-6089	10	5	such	such	ADJ
ejpam-6089	10	6	as	as	ADP
ejpam-6089	10	7	riemann	riemann	PROPN
ejpam-6089	10	8	-	-	PUNCT
ejpam-6089	10	9	liouville	liouville	NOUN
ejpam-6089	10	10	to	to	PART
ejpam-6089	10	11	extend	extend	VERB
ejpam-6089	10	12	these	these	DET
ejpam-6089	10	13	operations	operation	NOUN
ejpam-6089	10	14	to	to	ADP
ejpam-6089	10	15	arbitrary	arbitrary	ADJ
ejpam-6089	10	16	real	real	ADJ
ejpam-6089	10	17	or	or	CCONJ
ejpam-6089	10	18	complex	complex	ADJ
ejpam-6089	10	19	numbers	number	NOUN
ejpam-6089	10	20	[	[	X
ejpam-6089	10	21	4	4	NUM
ejpam-6089	10	22	,	,	PUNCT
ejpam-6089	10	23	5	5	NUM
ejpam-6089	10	24	]	]	PUNCT
ejpam-6089	10	25	.	.	PUNCT
ejpam-6089	11	1	moreover	moreover	ADV
ejpam-6089	11	2	,	,	PUNCT
ejpam-6089	11	3	fractional	fractional	ADJ
ejpam-6089	11	4	∗corresponding	∗corresponding	NOUN
ejpam-6089	11	5	author	author	NOUN
ejpam-6089	11	6	.	.	PUNCT
ejpam-6089	12	1	doi	doi	NOUN
ejpam-6089	12	2	:	:	PUNCT
ejpam-6089	12	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6089	https://doi.org/10.29020/nybg.ejpam.v18i2.6089	ADJ
ejpam-6089	12	4	email	email	NOUN
ejpam-6089	12	5	addresses	address	NOUN
ejpam-6089	12	6	:	:	PUNCT
ejpam-6089	12	7	saima.naheed@uos.edu.pk	saima.naheed@uos.edu.pk	PROPN
ejpam-6089	12	8	(	(	PUNCT
ejpam-6089	12	9	s.	s.	PROPN
ejpam-6089	12	10	naheed	naheed	PROPN
ejpam-6089	12	11	)	)	PUNCT
ejpam-6089	12	12	,	,	PUNCT
ejpam-6089	12	13	osa436rj@gmail.com	osa436rj@gmail.com	PROPN
ejpam-6089	12	14	(	(	PUNCT
ejpam-6089	12	15	a.	a.	PROPN
ejpam-6089	12	16	rafi	rafi	PROPN
ejpam-6089	12	17	)	)	PUNCT
ejpam-6089	12	18	,	,	PUNCT
ejpam-6089	12	19	gauhar55uom@gmail.com	gauhar55uom@gmail.com	X
ejpam-6089	12	20	(	(	PUNCT
ejpam-6089	12	21	g.	g.	PROPN
ejpam-6089	12	22	rehman	rehman	PROPN
ejpam-6089	12	23	)	)	PUNCT
ejpam-6089	12	24	,	,	PUNCT
ejpam-6089	12	25	iayoub@psu.edu.sa	iayoub@psu.edu.sa	NOUN
ejpam-6089	12	26	(	(	PUNCT
ejpam-6089	12	27	i.	i.	PROPN
ejpam-6089	12	28	ayoob	ayoob	PROPN
ejpam-6089	12	29	)	)	PUNCT
ejpam-6089	12	30	,	,	PUNCT
ejpam-6089	12	31	nmlaiki@psu.edu.sa	nmlaiki@psu.edu.sa	NOUN
ejpam-6089	12	32	(	(	PUNCT
ejpam-6089	12	33	n.	n.	PROPN
ejpam-6089	12	34	mlaiki	mlaiki	PROPN
ejpam-6089	12	35	)	)	PUNCT
ejpam-6089	12	36	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6089	13	1	1	1	NUM
ejpam-6089	13	2	copyright	copyright	NOUN
ejpam-6089	13	3	:	:	PUNCT
ejpam-6089	13	4	©	©	PROPN
ejpam-6089	13	5	2025	2025	NUM
ejpam-6089	13	6	the	the	DET
ejpam-6089	13	7	author(s	author(s	NOUN
ejpam-6089	13	8	)	)	PUNCT
ejpam-6089	13	9	.	.	PUNCT
ejpam-6089	14	1	(	(	PUNCT
ejpam-6089	14	2	cc	cc	NOUN
ejpam-6089	14	3	by	by	ADP
ejpam-6089	14	4	-	-	PUNCT
ejpam-6089	14	5	nc	nc	PROPN
ejpam-6089	14	6	4.0	4.0	NUM
ejpam-6089	14	7	)	)	PUNCT
ejpam-6089	14	8	s.	s.	PROPN
ejpam-6089	14	9	naheed	nahee	VERB
ejpam-6089	14	10	et	et	PROPN
ejpam-6089	14	11	al	al	PROPN
ejpam-6089	14	12	.	.	PUNCT
ejpam-6089	14	13	/	/	SYM
ejpam-6089	14	14	eur	eur	PROPN
ejpam-6089	14	15	.	.	PUNCT
ejpam-6089	15	1	j.	j.	PROPN
ejpam-6089	15	2	pure	pure	PROPN
ejpam-6089	15	3	appl	appl	PROPN
ejpam-6089	15	4	.	.	PROPN
ejpam-6089	15	5	math	math	PROPN
ejpam-6089	15	6	,	,	PUNCT
ejpam-6089	15	7	18	18	NUM
ejpam-6089	15	8	(	(	PUNCT
ejpam-6089	15	9	2	2	NUM
ejpam-6089	15	10	)	)	PUNCT
ejpam-6089	15	11	(	(	PUNCT
ejpam-6089	15	12	2025	2025	NUM
ejpam-6089	15	13	)	)	PUNCT
ejpam-6089	15	14	,	,	PUNCT
ejpam-6089	15	15	6089	6089	NUM
ejpam-6089	15	16	2	2	NUM
ejpam-6089	15	17	of	of	ADP
ejpam-6089	15	18	34	34	NUM
ejpam-6089	15	19	calculus	calculus	NOUN
ejpam-6089	15	20	intersects	intersect	NOUN
ejpam-6089	15	21	with	with	ADP
ejpam-6089	15	22	concepts	concept	NOUN
ejpam-6089	15	23	like	like	ADP
ejpam-6089	15	24	convex	convex	NOUN
ejpam-6089	15	25	functions	function	NOUN
ejpam-6089	15	26	[	[	X
ejpam-6089	15	27	6	6	NUM
ejpam-6089	15	28	]	]	PUNCT
ejpam-6089	15	29	,	,	PUNCT
ejpam-6089	15	30	leading	lead	VERB
ejpam-6089	15	31	to	to	ADP
ejpam-6089	15	32	advancements	advancement	NOUN
ejpam-6089	15	33	in	in	ADP
ejpam-6089	15	34	optimization	optimization	NOUN
ejpam-6089	15	35	and	and	CCONJ
ejpam-6089	15	36	engineering	engineering	NOUN
ejpam-6089	15	37	[	[	X
ejpam-6089	15	38	7	7	NUM
ejpam-6089	15	39	,	,	PUNCT
ejpam-6089	15	40	8	8	NUM
ejpam-6089	15	41	]	]	PUNCT
ejpam-6089	15	42	.	.	PUNCT
ejpam-6089	16	1	overall	overall	ADJ
ejpam-6089	16	2	,	,	PUNCT
ejpam-6089	16	3	fractional	fractional	ADJ
ejpam-6089	16	4	calculus	calculus	NOUN
ejpam-6089	16	5	offers	offer	VERB
ejpam-6089	16	6	a	a	DET
ejpam-6089	16	7	robust	robust	ADJ
ejpam-6089	16	8	framework	framework	NOUN
ejpam-6089	16	9	for	for	ADP
ejpam-6089	16	10	understanding	understanding	NOUN
ejpam-6089	16	11	and	and	CCONJ
ejpam-6089	16	12	analyzing	analyze	VERB
ejpam-6089	16	13	complex	complex	ADJ
ejpam-6089	16	14	phenomena	phenomenon	NOUN
ejpam-6089	16	15	.	.	PUNCT
ejpam-6089	17	1	giving	give	VERB
ejpam-6089	17	2	complex	complex	ADJ
ejpam-6089	17	3	functions	function	NOUN
ejpam-6089	17	4	boundaries	boundary	NOUN
ejpam-6089	17	5	and	and	CCONJ
ejpam-6089	17	6	approximations	approximation	NOUN
ejpam-6089	17	7	is	be	AUX
ejpam-6089	17	8	an	an	DET
ejpam-6089	17	9	essential	essential	ADJ
ejpam-6089	17	10	part	part	NOUN
ejpam-6089	17	11	that	that	PRON
ejpam-6089	17	12	inequalities	inequality	NOUN
ejpam-6089	17	13	play	play	VERB
ejpam-6089	17	14	in	in	ADP
ejpam-6089	17	15	providing	provide	VERB
ejpam-6089	17	16	important	important	ADJ
ejpam-6089	17	17	insights	insight	NOUN
ejpam-6089	17	18	into	into	ADP
ejpam-6089	17	19	their	their	PRON
ejpam-6089	17	20	behavior	behavior	NOUN
ejpam-6089	17	21	.	.	PUNCT
ejpam-6089	18	1	integral	integral	ADJ
ejpam-6089	18	2	inequalities	inequality	NOUN
ejpam-6089	18	3	are	be	AUX
ejpam-6089	18	4	a	a	DET
ejpam-6089	18	5	key	key	ADJ
ejpam-6089	18	6	area	area	NOUN
ejpam-6089	18	7	in	in	ADP
ejpam-6089	18	8	mathematical	mathematical	ADJ
ejpam-6089	18	9	analysis	analysis	NOUN
ejpam-6089	18	10	,	,	PUNCT
ejpam-6089	18	11	crucial	crucial	ADJ
ejpam-6089	18	12	for	for	ADP
ejpam-6089	18	13	studying	study	VERB
ejpam-6089	18	14	integral	integral	ADJ
ejpam-6089	18	15	equations	equation	NOUN
ejpam-6089	18	16	and	and	CCONJ
ejpam-6089	18	17	differential	differential	ADJ
ejpam-6089	18	18	equations	equation	NOUN
ejpam-6089	18	19	[	[	X
ejpam-6089	18	20	9	9	NUM
ejpam-6089	18	21	,	,	PUNCT
ejpam-6089	18	22	10	10	NUM
ejpam-6089	18	23	]	]	PUNCT
ejpam-6089	18	24	.	.	PUNCT
ejpam-6089	19	1	they	they	PRON
ejpam-6089	19	2	play	play	VERB
ejpam-6089	19	3	a	a	DET
ejpam-6089	19	4	crucial	crucial	ADJ
ejpam-6089	19	5	role	role	NOUN
ejpam-6089	19	6	in	in	ADP
ejpam-6089	19	7	fractional	fractional	ADJ
ejpam-6089	19	8	differential	differential	ADJ
ejpam-6089	19	9	equations	equation	NOUN
ejpam-6089	19	10	,	,	PUNCT
ejpam-6089	19	11	where	where	SCONJ
ejpam-6089	19	12	fractional	fractional	ADJ
ejpam-6089	19	13	integral	integral	ADJ
ejpam-6089	19	14	inequalities	inequality	NOUN
ejpam-6089	19	15	help	help	VERB
ejpam-6089	19	16	to	to	PART
ejpam-6089	19	17	establish	establish	VERB
ejpam-6089	19	18	the	the	DET
ejpam-6089	19	19	uniqueness	uniqueness	NOUN
ejpam-6089	19	20	of	of	ADP
ejpam-6089	19	21	solutions	solution	NOUN
ejpam-6089	19	22	and	and	CCONJ
ejpam-6089	19	23	provide	provide	VERB
ejpam-6089	19	24	bounds	bound	NOUN
ejpam-6089	19	25	for	for	ADP
ejpam-6089	19	26	fractional	fractional	ADJ
ejpam-6089	19	27	boundary	boundary	ADJ
ejpam-6089	19	28	value	value	NOUN
ejpam-6089	19	29	problems	problem	NOUN
ejpam-6089	19	30	.	.	PUNCT
ejpam-6089	20	1	inequalities	inequality	NOUN
ejpam-6089	20	2	involving	involve	VERB
ejpam-6089	20	3	fractional	fractional	ADJ
ejpam-6089	20	4	derivatives	derivative	NOUN
ejpam-6089	20	5	are	be	AUX
ejpam-6089	20	6	especially	especially	ADV
ejpam-6089	20	7	valuable	valuable	ADJ
ejpam-6089	20	8	in	in	ADP
ejpam-6089	20	9	determining	determine	VERB
ejpam-6089	20	10	solutions	solution	NOUN
ejpam-6089	20	11	for	for	ADP
ejpam-6089	20	12	cauchy	cauchy	NOUN
ejpam-6089	20	13	problems	problem	NOUN
ejpam-6089	20	14	as	as	ADV
ejpam-6089	20	15	well	well	ADV
ejpam-6089	20	16	as	as	ADP
ejpam-6089	20	17	their	their	PRON
ejpam-6089	20	18	upper	upper	ADJ
ejpam-6089	20	19	limits	limit	NOUN
ejpam-6089	20	20	[	[	X
ejpam-6089	20	21	11	11	NUM
ejpam-6089	20	22	,	,	PUNCT
ejpam-6089	20	23	12	12	NUM
ejpam-6089	20	24	]	]	PUNCT
ejpam-6089	20	25	.	.	PUNCT
ejpam-6089	21	1	the	the	DET
ejpam-6089	21	2	goal	goal	NOUN
ejpam-6089	21	3	of	of	ADP
ejpam-6089	21	4	expanding	expand	VERB
ejpam-6089	21	5	the	the	DET
ejpam-6089	21	6	theory	theory	NOUN
ejpam-6089	21	7	of	of	ADP
ejpam-6089	21	8	integral	integral	ADJ
ejpam-6089	21	9	inequalities	inequality	NOUN
ejpam-6089	21	10	through	through	ADP
ejpam-6089	21	11	the	the	DET
ejpam-6089	21	12	use	use	NOUN
ejpam-6089	21	13	of	of	ADP
ejpam-6089	21	14	fractional	fractional	ADJ
ejpam-6089	21	15	integral	integral	ADJ
ejpam-6089	21	16	operators	operator	NOUN
ejpam-6089	21	17	to	to	PART
ejpam-6089	21	18	generalize	generalize	VERB
ejpam-6089	21	19	classical	classical	ADJ
ejpam-6089	21	20	inequalities	inequality	NOUN
ejpam-6089	21	21	has	have	AUX
ejpam-6089	21	22	been	be	AUX
ejpam-6089	21	23	spurred	spur	VERB
ejpam-6089	21	24	by	by	ADP
ejpam-6089	21	25	this	this	DET
ejpam-6089	21	26	significance	significance	NOUN
ejpam-6089	21	27	[	[	X
ejpam-6089	21	28	13	13	NUM
ejpam-6089	21	29	]	]	PUNCT
ejpam-6089	21	30	,	,	PUNCT
ejpam-6089	21	31	which	which	PRON
ejpam-6089	21	32	improves	improve	VERB
ejpam-6089	21	33	theoretical	theoretical	ADJ
ejpam-6089	21	34	comprehension	comprehension	NOUN
ejpam-6089	21	35	and	and	CCONJ
ejpam-6089	21	36	real	real	ADJ
ejpam-6089	21	37	-	-	PUNCT
ejpam-6089	21	38	world	world	NOUN
ejpam-6089	21	39	applications	application	NOUN
ejpam-6089	21	40	[	[	X
ejpam-6089	21	41	14	14	NUM
ejpam-6089	21	42	,	,	PUNCT
ejpam-6089	21	43	15	15	NUM
ejpam-6089	21	44	]	]	PUNCT
ejpam-6089	21	45	.	.	PUNCT
ejpam-6089	22	1	sajid	sajid	PROPN
ejpam-6089	22	2	et	et	PROPN
ejpam-6089	22	3	al	al	PROPN
ejpam-6089	22	4	.	.	PROPN
ejpam-6089	22	5	have	have	AUX
ejpam-6089	22	6	discussed	discuss	VERB
ejpam-6089	22	7	some	some	DET
ejpam-6089	22	8	new	new	ADJ
ejpam-6089	22	9	grüss	grüss	PROPN
ejpam-6089	22	10	type	type	NOUN
ejpam-6089	22	11	inequalities	inequality	NOUN
ejpam-6089	22	12	associated	associate	VERB
ejpam-6089	22	13	with	with	ADP
ejpam-6089	22	14	generalized	generalized	ADJ
ejpam-6089	22	15	fractional	fractional	ADJ
ejpam-6089	22	16	derivatives	derivative	NOUN
ejpam-6089	22	17	in	in	ADP
ejpam-6089	22	18	[	[	X
ejpam-6089	22	19	16	16	NUM
ejpam-6089	22	20	]	]	PUNCT
ejpam-6089	22	21	.	.	PUNCT
ejpam-6089	23	1	special	special	ADJ
ejpam-6089	23	2	functions	function	NOUN
ejpam-6089	23	3	are	be	AUX
ejpam-6089	23	4	closely	closely	ADV
ejpam-6089	23	5	related	relate	VERB
ejpam-6089	23	6	to	to	ADP
ejpam-6089	23	7	fractional	fractional	ADJ
ejpam-6089	23	8	calculus	calculus	NOUN
ejpam-6089	23	9	in	in	ADP
ejpam-6089	23	10	many	many	ADJ
ejpam-6089	23	11	ways	way	NOUN
ejpam-6089	23	12	[	[	X
ejpam-6089	23	13	9	9	NUM
ejpam-6089	23	14	,	,	PUNCT
ejpam-6089	23	15	17	17	NUM
ejpam-6089	23	16	]	]	PUNCT
ejpam-6089	23	17	,	,	PUNCT
ejpam-6089	23	18	like	like	ADP
ejpam-6089	23	19	the	the	DET
ejpam-6089	23	20	mittag	mittag	ADJ
ejpam-6089	23	21	-	-	PUNCT
ejpam-6089	23	22	leffler	leffler	NOUN
ejpam-6089	23	23	function	function	NOUN
ejpam-6089	23	24	,	,	PUNCT
ejpam-6089	23	25	which	which	PRON
ejpam-6089	23	26	extends	extend	VERB
ejpam-6089	23	27	the	the	DET
ejpam-6089	23	28	concepts	concept	NOUN
ejpam-6089	23	29	of	of	ADP
ejpam-6089	23	30	fractional	fractional	ADJ
ejpam-6089	23	31	operators	operator	NOUN
ejpam-6089	23	32	[	[	X
ejpam-6089	23	33	18	18	NUM
ejpam-6089	23	34	,	,	PUNCT
ejpam-6089	23	35	19	19	NUM
ejpam-6089	23	36	]	]	PUNCT
ejpam-6089	23	37	and	and	CCONJ
ejpam-6089	23	38	plays	play	VERB
ejpam-6089	23	39	a	a	DET
ejpam-6089	23	40	crucial	crucial	ADJ
ejpam-6089	23	41	role	role	NOUN
ejpam-6089	23	42	in	in	ADP
ejpam-6089	23	43	fractional	fractional	ADJ
ejpam-6089	23	44	calculus	calculus	NOUN
ejpam-6089	23	45	[	[	X
ejpam-6089	23	46	20	20	NUM
ejpam-6089	23	47	,	,	PUNCT
ejpam-6089	23	48	21	21	NUM
ejpam-6089	23	49	]	]	PUNCT
ejpam-6089	23	50	.	.	PUNCT
ejpam-6089	24	1	named	name	VERB
ejpam-6089	24	2	after	after	ADP
ejpam-6089	24	3	gösta	gösta	ADJ
ejpam-6089	24	4	mittag	mittag	ADJ
ejpam-6089	24	5	-	-	PUNCT
ejpam-6089	24	6	leffler	leffler	NOUN
ejpam-6089	24	7	,	,	PUNCT
ejpam-6089	24	8	this	this	DET
ejpam-6089	24	9	function	function	NOUN
ejpam-6089	24	10	is	be	AUX
ejpam-6089	24	11	essential	essential	ADJ
ejpam-6089	24	12	for	for	ADP
ejpam-6089	24	13	solving	solve	VERB
ejpam-6089	24	14	fractional	fractional	ADJ
ejpam-6089	24	15	differential	differential	ADJ
ejpam-6089	24	16	equations	equation	NOUN
ejpam-6089	24	17	.	.	PUNCT
ejpam-6089	25	1	usually	usually	ADV
ejpam-6089	25	2	accomplished	accomplish	VERB
ejpam-6089	25	3	by	by	ADP
ejpam-6089	25	4	adding	add	VERB
ejpam-6089	25	5	more	more	ADJ
ejpam-6089	25	6	parameters	parameter	NOUN
ejpam-6089	25	7	to	to	ADP
ejpam-6089	25	8	its	its	PRON
ejpam-6089	25	9	definition	definition	NOUN
ejpam-6089	25	10	,	,	PUNCT
ejpam-6089	25	11	the	the	DET
ejpam-6089	25	12	extended	extended	ADJ
ejpam-6089	25	13	generalized	generalize	VERB
ejpam-6089	25	14	mittag	mittag	ADJ
ejpam-6089	25	15	-	-	PUNCT
ejpam-6089	25	16	leffler	leffler	NOUN
ejpam-6089	25	17	function	function	NOUN
ejpam-6089	25	18	is	be	AUX
ejpam-6089	25	19	a	a	DET
ejpam-6089	25	20	further	far	ADV
ejpam-6089	25	21	expanded	expand	VERB
ejpam-6089	25	22	form	form	NOUN
ejpam-6089	25	23	of	of	ADP
ejpam-6089	25	24	the	the	DET
ejpam-6089	25	25	standard	standard	ADJ
ejpam-6089	25	26	mittag	mittag	ADJ
ejpam-6089	25	27	-	-	PUNCT
ejpam-6089	25	28	leffler	leffler	NOUN
ejpam-6089	25	29	function	function	NOUN
ejpam-6089	25	30	that	that	PRON
ejpam-6089	25	31	provides	provide	VERB
ejpam-6089	25	32	more	more	ADJ
ejpam-6089	25	33	flexibility	flexibility	NOUN
ejpam-6089	25	34	in	in	ADP
ejpam-6089	25	35	modeling	model	VERB
ejpam-6089	25	36	complex	complex	ADJ
ejpam-6089	25	37	phenomena	phenomenon	NOUN
ejpam-6089	25	38	[	[	X
ejpam-6089	25	39	22	22	NUM
ejpam-6089	25	40	]	]	PUNCT
ejpam-6089	25	41	.	.	PUNCT
ejpam-6089	26	1	two	two	NUM
ejpam-6089	26	2	prominent	prominent	ADJ
ejpam-6089	26	3	models	model	NOUN
ejpam-6089	26	4	in	in	ADP
ejpam-6089	26	5	this	this	DET
ejpam-6089	26	6	area	area	NOUN
ejpam-6089	26	7	that	that	PRON
ejpam-6089	26	8	incorporate	incorporate	VERB
ejpam-6089	26	9	mittag	mittag	ADJ
ejpam-6089	26	10	-	-	PUNCT
ejpam-6089	26	11	leffler	leffler	NOUN
ejpam-6089	26	12	functions	function	NOUN
ejpam-6089	26	13	are	be	AUX
ejpam-6089	26	14	the	the	DET
ejpam-6089	26	15	atangana	atangana	PROPN
ejpam-6089	26	16	-	-	PUNCT
ejpam-6089	26	17	baleanu	baleanu	PROPN
ejpam-6089	27	1	[	[	X
ejpam-6089	27	2	23	23	NUM
ejpam-6089	27	3	]	]	PUNCT
ejpam-6089	27	4	and	and	CCONJ
ejpam-6089	27	5	prabhakar	prabhakar	NOUN
ejpam-6089	27	6	models	model	NOUN
ejpam-6089	27	7	[	[	X
ejpam-6089	27	8	24	24	NUM
ejpam-6089	27	9	,	,	PUNCT
ejpam-6089	27	10	25	25	NUM
ejpam-6089	27	11	]	]	PUNCT
ejpam-6089	27	12	.	.	PUNCT
ejpam-6089	28	1	these	these	DET
ejpam-6089	28	2	models	model	NOUN
ejpam-6089	28	3	advance	advance	VERB
ejpam-6089	28	4	fractional	fractional	ADJ
ejpam-6089	28	5	calculus	calculus	NOUN
ejpam-6089	28	6	by	by	ADP
ejpam-6089	28	7	offering	offer	VERB
ejpam-6089	28	8	refined	refined	ADJ
ejpam-6089	28	9	tools	tool	NOUN
ejpam-6089	28	10	for	for	ADP
ejpam-6089	28	11	describing	describe	VERB
ejpam-6089	28	12	systems	system	NOUN
ejpam-6089	28	13	with	with	ADP
ejpam-6089	28	14	memory	memory	NOUN
ejpam-6089	28	15	,	,	PUNCT
ejpam-6089	28	16	non	non	ADJ
ejpam-6089	28	17	-	-	ADJ
ejpam-6089	28	18	singular	singular	ADJ
ejpam-6089	28	19	and	and	CCONJ
ejpam-6089	28	20	non	non	ADJ
ejpam-6089	28	21	-	-	ADJ
ejpam-6089	28	22	local	local	ADJ
ejpam-6089	28	23	effects	effect	NOUN
ejpam-6089	28	24	[	[	X
ejpam-6089	28	25	26	26	NUM
ejpam-6089	28	26	,	,	PUNCT
ejpam-6089	28	27	27	27	NUM
ejpam-6089	28	28	]	]	PUNCT
ejpam-6089	28	29	,	,	PUNCT
ejpam-6089	28	30	making	make	VERB
ejpam-6089	28	31	them	they	PRON
ejpam-6089	28	32	valuable	valuable	ADJ
ejpam-6089	28	33	in	in	ADP
ejpam-6089	28	34	various	various	ADJ
ejpam-6089	28	35	scientific	scientific	ADJ
ejpam-6089	28	36	and	and	CCONJ
ejpam-6089	28	37	engineering	engineering	NOUN
ejpam-6089	28	38	fields	field	NOUN
ejpam-6089	28	39	[	[	X
ejpam-6089	28	40	28	28	NUM
ejpam-6089	28	41	,	,	PUNCT
ejpam-6089	28	42	29	29	NUM
ejpam-6089	28	43	]	]	PUNCT
ejpam-6089	28	44	while	while	SCONJ
ejpam-6089	28	45	tackling	tackle	VERB
ejpam-6089	28	46	practical	practical	ADJ
ejpam-6089	28	47	issues	issue	NOUN
ejpam-6089	28	48	in	in	ADP
ejpam-6089	28	49	a	a	DET
ejpam-6089	28	50	variety	variety	NOUN
ejpam-6089	28	51	of	of	ADP
ejpam-6089	28	52	fields	field	NOUN
ejpam-6089	28	53	[	[	X
ejpam-6089	28	54	30	30	NUM
ejpam-6089	28	55	,	,	PUNCT
ejpam-6089	28	56	31	31	NUM
ejpam-6089	28	57	]	]	PUNCT
ejpam-6089	28	58	.	.	PUNCT
ejpam-6089	29	1	the	the	DET
ejpam-6089	29	2	modified	modified	ADJ
ejpam-6089	29	3	(	(	PUNCT
ejpam-6089	29	4	k	k	X
ejpam-6089	29	5	,	,	PUNCT
ejpam-6089	29	6	s	s	X
ejpam-6089	29	7	)	)	PUNCT
ejpam-6089	29	8	fractional	fractional	ADJ
ejpam-6089	29	9	integral	integral	ADJ
ejpam-6089	29	10	operator	operator	NOUN
ejpam-6089	29	11	involving	involve	VERB
ejpam-6089	29	12	k	k	ADJ
ejpam-6089	29	13	-	-	ADJ
ejpam-6089	29	14	mittag	mittag	ADJ
ejpam-6089	29	15	-	-	PUNCT
ejpam-6089	29	16	leffler	leffler	NOUN
ejpam-6089	29	17	function	function	NOUN
ejpam-6089	29	18	along	along	ADP
ejpam-6089	29	19	with	with	ADP
ejpam-6089	29	20	its	its	PRON
ejpam-6089	29	21	properties	property	NOUN
ejpam-6089	29	22	is	be	AUX
ejpam-6089	29	23	discussed	discuss	VERB
ejpam-6089	29	24	in	in	ADP
ejpam-6089	29	25	[	[	X
ejpam-6089	29	26	32	32	NUM
ejpam-6089	29	27	]	]	PUNCT
ejpam-6089	29	28	.	.	PUNCT
ejpam-6089	30	1	in	in	ADP
ejpam-6089	30	2	this	this	DET
ejpam-6089	30	3	research	research	NOUN
ejpam-6089	30	4	,	,	PUNCT
ejpam-6089	30	5	the	the	DET
ejpam-6089	30	6	hermite	hermite	PROPN
ejpam-6089	30	7	-	-	PUNCT
ejpam-6089	30	8	hadamard	hadamard	ADJ
ejpam-6089	30	9	(	(	PUNCT
ejpam-6089	30	10	h−h	h−h	NOUN
ejpam-6089	30	11	)	)	PUNCT
ejpam-6089	30	12	inequality	inequality	NOUN
ejpam-6089	30	13	[	[	X
ejpam-6089	30	14	33	33	NUM
ejpam-6089	30	15	]	]	PUNCT
ejpam-6089	30	16	by	by	ADP
ejpam-6089	30	17	applying	apply	VERB
ejpam-6089	30	18	generalized	generalize	VERB
ejpam-6089	30	19	fractional	fractional	ADJ
ejpam-6089	30	20	integral	integral	ADJ
ejpam-6089	30	21	operators	operator	NOUN
ejpam-6089	30	22	through	through	ADP
ejpam-6089	30	23	the	the	DET
ejpam-6089	30	24	extended	extended	ADJ
ejpam-6089	30	25	generalized	generalize	VERB
ejpam-6089	30	26	mittag	mittag	ADJ
ejpam-6089	30	27	-	-	PUNCT
ejpam-6089	30	28	leffler	leffler	NOUN
ejpam-6089	30	29	function	function	NOUN
ejpam-6089	30	30	will	will	AUX
ejpam-6089	30	31	be	be	AUX
ejpam-6089	30	32	studied	study	VERB
ejpam-6089	30	33	.	.	PUNCT
ejpam-6089	31	1	the	the	DET
ejpam-6089	31	2	goal	goal	NOUN
ejpam-6089	31	3	is	be	AUX
ejpam-6089	31	4	to	to	PART
ejpam-6089	31	5	derive	derive	VERB
ejpam-6089	31	6	new	new	ADJ
ejpam-6089	31	7	inequalities	inequality	NOUN
ejpam-6089	31	8	that	that	PRON
ejpam-6089	31	9	not	not	PART
ejpam-6089	31	10	only	only	ADV
ejpam-6089	31	11	generalize	generalize	VERB
ejpam-6089	31	12	but	but	CCONJ
ejpam-6089	31	13	also	also	ADV
ejpam-6089	31	14	enhance	enhance	VERB
ejpam-6089	31	15	the	the	DET
ejpam-6089	31	16	classical	classical	ADJ
ejpam-6089	31	17	(	(	PUNCT
ejpam-6089	31	18	h−h	h−h	NOUN
ejpam-6089	31	19	)	)	PUNCT
ejpam-6089	31	20	inequality	inequality	NOUN
ejpam-6089	31	21	[	[	X
ejpam-6089	31	22	34	34	NUM
ejpam-6089	31	23	]	]	PUNCT
ejpam-6089	31	24	,	,	PUNCT
ejpam-6089	31	25	utilizing	utilize	VERB
ejpam-6089	31	26	fractional	fractional	ADJ
ejpam-6089	31	27	calculus	calculus	NOUN
ejpam-6089	31	28	and	and	CCONJ
ejpam-6089	31	29	special	special	ADJ
ejpam-6089	31	30	function	function	NOUN
ejpam-6089	31	31	methodologies	methodology	NOUN
ejpam-6089	31	32	.	.	PUNCT
ejpam-6089	32	1	as	as	SCONJ
ejpam-6089	32	2	we	we	PRON
ejpam-6089	32	3	continue	continue	VERB
ejpam-6089	32	4	our	our	PRON
ejpam-6089	32	5	work	work	NOUN
ejpam-6089	32	6	,	,	PUNCT
ejpam-6089	32	7	it	it	PRON
ejpam-6089	32	8	is	be	AUX
ejpam-6089	32	9	crucial	crucial	ADJ
ejpam-6089	32	10	to	to	PART
ejpam-6089	32	11	remember	remember	VERB
ejpam-6089	32	12	important	important	ADJ
ejpam-6089	32	13	definitions	definition	NOUN
ejpam-6089	32	14	to	to	PART
ejpam-6089	32	15	ensure	ensure	VERB
ejpam-6089	32	16	clarity	clarity	NOUN
ejpam-6089	32	17	and	and	CCONJ
ejpam-6089	32	18	consistency	consistency	NOUN
ejpam-6089	32	19	.	.	PUNCT
ejpam-6089	33	1	these	these	DET
ejpam-6089	33	2	concepts	concept	NOUN
ejpam-6089	33	3	help	help	VERB
ejpam-6089	33	4	to	to	PART
ejpam-6089	33	5	manage	manage	VERB
ejpam-6089	33	6	complex	complex	ADJ
ejpam-6089	33	7	activities	activity	NOUN
ejpam-6089	33	8	and	and	CCONJ
ejpam-6089	33	9	initiatives	initiative	NOUN
ejpam-6089	33	10	by	by	ADP
ejpam-6089	33	11	providing	provide	VERB
ejpam-6089	33	12	a	a	DET
ejpam-6089	33	13	strong	strong	ADJ
ejpam-6089	33	14	foundation	foundation	NOUN
ejpam-6089	33	15	.	.	PUNCT
ejpam-6089	34	1	definition	definition	NOUN
ejpam-6089	34	2	1	1	NUM
ejpam-6089	34	3	.	.	PUNCT
ejpam-6089	35	1	[	[	X
ejpam-6089	35	2	7	7	X
ejpam-6089	35	3	]	]	X
ejpam-6089	35	4	a	a	DET
ejpam-6089	35	5	function	function	NOUN
ejpam-6089	35	6	υ	υ	NOUN
ejpam-6089	35	7	:	:	PUNCT
ejpam-6089	35	8	i	i	PRON
ejpam-6089	35	9	→	→	SYM
ejpam-6089	35	10	ℜ	ℜ	PROPN
ejpam-6089	35	11	is	be	AUX
ejpam-6089	35	12	known	know	VERB
ejpam-6089	35	13	as	as	ADP
ejpam-6089	35	14	a	a	DET
ejpam-6089	35	15	convex	convex	NOUN
ejpam-6089	35	16	function	function	NOUN
ejpam-6089	35	17	if	if	SCONJ
ejpam-6089	35	18	it	it	PRON
ejpam-6089	35	19	satisfies	satisfy	VERB
ejpam-6089	35	20	the	the	DET
ejpam-6089	35	21	following	follow	VERB
ejpam-6089	35	22	inequality	inequality	NOUN
ejpam-6089	35	23	υ(cℑ1	υ(cℑ1	PUNCT
ejpam-6089	35	24	+	+	CCONJ
ejpam-6089	35	25	(	(	PUNCT
ejpam-6089	35	26	1−	1−	NUM
ejpam-6089	35	27	c)ℑ2	c)ℑ2	PROPN
ejpam-6089	35	28	)	)	PUNCT
ejpam-6089	35	29	≤	≤	NUM
ejpam-6089	35	30	cυ(ℑ1	cυ(ℑ1	NOUN
ejpam-6089	35	31	)	)	PUNCT
ejpam-6089	36	1	+	+	CCONJ
ejpam-6089	36	2	(	(	PUNCT
ejpam-6089	36	3	1−	1−	NUM
ejpam-6089	36	4	c)υ(ℑ2	c)υ(ℑ2	NOUN
ejpam-6089	36	5	)	)	PUNCT
ejpam-6089	36	6	,	,	PUNCT
ejpam-6089	36	7	where	where	SCONJ
ejpam-6089	36	8	c	c	PROPN
ejpam-6089	36	9	∈	∈	PROPN
ejpam-6089	37	1	[	[	X
ejpam-6089	37	2	0	0	NUM
ejpam-6089	37	3	,	,	PUNCT
ejpam-6089	37	4	1	1	NUM
ejpam-6089	37	5	]	]	PUNCT
ejpam-6089	37	6	and	and	CCONJ
ejpam-6089	37	7	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	37	8	∈	∈	PROPN
ejpam-6089	37	9	i.	i.	PROPN
ejpam-6089	37	10	s.	s.	PROPN
ejpam-6089	37	11	naheed	nahee	VERB
ejpam-6089	37	12	et	et	PROPN
ejpam-6089	37	13	al	al	PROPN
ejpam-6089	37	14	.	.	PUNCT
ejpam-6089	37	15	/	/	SYM
ejpam-6089	37	16	eur	eur	PROPN
ejpam-6089	37	17	.	.	PUNCT
ejpam-6089	38	1	j.	j.	PROPN
ejpam-6089	38	2	pure	pure	PROPN
ejpam-6089	38	3	appl	appl	PROPN
ejpam-6089	38	4	.	.	PROPN
ejpam-6089	38	5	math	math	PROPN
ejpam-6089	38	6	,	,	PUNCT
ejpam-6089	38	7	18	18	NUM
ejpam-6089	38	8	(	(	PUNCT
ejpam-6089	38	9	2	2	NUM
ejpam-6089	38	10	)	)	PUNCT
ejpam-6089	38	11	(	(	PUNCT
ejpam-6089	38	12	2025	2025	NUM
ejpam-6089	38	13	)	)	PUNCT
ejpam-6089	38	14	,	,	PUNCT
ejpam-6089	38	15	6089	6089	NUM
ejpam-6089	38	16	3	3	NUM
ejpam-6089	38	17	of	of	ADP
ejpam-6089	38	18	34	34	NUM
ejpam-6089	38	19	definition	definition	NOUN
ejpam-6089	38	20	2	2	NUM
ejpam-6089	38	21	.	.	PUNCT
ejpam-6089	39	1	[	[	X
ejpam-6089	39	2	4	4	X
ejpam-6089	39	3	]	]	PUNCT
ejpam-6089	39	4	let	let	VERB
ejpam-6089	39	5	υ	υ	PRON
ejpam-6089	39	6	be	be	AUX
ejpam-6089	39	7	a	a	DET
ejpam-6089	39	8	function	function	NOUN
ejpam-6089	39	9	in	in	ADP
ejpam-6089	39	10	l1	l1	PROPN
ejpam-6089	39	11	on	on	ADP
ejpam-6089	39	12	the	the	DET
ejpam-6089	39	13	interval	interval	NOUN
ejpam-6089	39	14	[	[	X
ejpam-6089	39	15	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	39	16	]	]	PUNCT
ejpam-6089	39	17	.	.	PUNCT
ejpam-6089	40	1	the	the	DET
ejpam-6089	40	2	g	g	NOUN
ejpam-6089	40	3	-	-	PUNCT
ejpam-6089	40	4	th	th	VERB
ejpam-6089	40	5	order	order	NOUN
ejpam-6089	40	6	left	leave	VERB
ejpam-6089	40	7	and	and	CCONJ
ejpam-6089	40	8	right	right	ADJ
ejpam-6089	40	9	sided	sided	ADJ
ejpam-6089	40	10	reimann	reimann	NOUN
ejpam-6089	40	11	-	-	PUNCT
ejpam-6089	40	12	liouville	liouville	NOUN
ejpam-6089	40	13	integrals	integral	NOUN
ejpam-6089	40	14	for	for	ADP
ejpam-6089	40	15	any	any	DET
ejpam-6089	40	16	c	c	PROPN
ejpam-6089	40	17	∈	∈	PROPN
ejpam-6089	41	1	[	[	X
ejpam-6089	41	2	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	41	3	]	]	PUNCT
ejpam-6089	41	4	,	,	PUNCT
ejpam-6089	41	5	applied	apply	VERB
ejpam-6089	41	6	to	to	ADP
ejpam-6089	41	7	υ(c	υ(c	PROPN
ejpam-6089	41	8	)	)	PUNCT
ejpam-6089	41	9	are	be	AUX
ejpam-6089	41	10	defined	define	VERB
ejpam-6089	41	11	as	as	ADP
ejpam-6089	41	12	,	,	PUNCT
ejpam-6089	41	13	provided	provide	VERB
ejpam-6089	41	14	that	that	SCONJ
ejpam-6089	41	15	ℜ(g	ℜ(g	ADJ
ejpam-6089	41	16	)	)	PUNCT
ejpam-6089	41	17	>	>	SYM
ejpam-6089	42	1	0	0	NUM
ejpam-6089	42	2	r−ligℑ1+υ(c	r−ligℑ1+υ(c	NOUN
ejpam-6089	42	3	)	)	PUNCT
ejpam-6089	42	4	=	=	SYM
ejpam-6089	42	5	1	1	NUM
ejpam-6089	42	6	γ(g	γ(g	PROPN
ejpam-6089	42	7	)	)	PUNCT
ejpam-6089	42	8	∫	∫	PROPN
ejpam-6089	42	9	c	c	PROPN
ejpam-6089	42	10	ℑ1	ℑ1	PROPN
ejpam-6089	42	11	(	(	PUNCT
ejpam-6089	42	12	c−	c−	ADJ
ejpam-6089	42	13	ψ)g−1υ(ψ)dψ	ψ)g−1υ(ψ)dψ	NOUN
ejpam-6089	42	14	,	,	PUNCT
ejpam-6089	42	15	(	(	PUNCT
ejpam-6089	42	16	1	1	NUM
ejpam-6089	42	17	)	)	PUNCT
ejpam-6089	42	18	and	and	CCONJ
ejpam-6089	42	19	r−ligℑ2−υ(c	r−ligℑ2−υ(c	NOUN
ejpam-6089	42	20	)	)	PUNCT
ejpam-6089	42	21	=	=	SYM
ejpam-6089	42	22	1	1	NUM
ejpam-6089	42	23	γ(g	γ(g	PROPN
ejpam-6089	42	24	)	)	PUNCT
ejpam-6089	42	25	∫	∫	PROPN
ejpam-6089	42	26	ℑ2	ℑ2	PROPN
ejpam-6089	42	27	c	c	PROPN
ejpam-6089	42	28	(	(	PUNCT
ejpam-6089	42	29	ψ	ψ	X
ejpam-6089	42	30	−	−	NOUN
ejpam-6089	42	31	c)g−1υ(ψ)dψ	c)g−1υ(ψ)dψ	NOUN
ejpam-6089	42	32	.	.	PUNCT
ejpam-6089	43	1	(	(	PUNCT
ejpam-6089	43	2	2	2	X
ejpam-6089	43	3	)	)	PUNCT
ejpam-6089	43	4	definition	definition	NOUN
ejpam-6089	43	5	3	3	NUM
ejpam-6089	43	6	.	.	PUNCT
ejpam-6089	44	1	[	[	X
ejpam-6089	44	2	23	23	NUM
ejpam-6089	44	3	]	]	PUNCT
ejpam-6089	44	4	let	let	VERB
ejpam-6089	44	5	υ	υ	PRON
ejpam-6089	44	6	be	be	AUX
ejpam-6089	44	7	a	a	DET
ejpam-6089	44	8	function	function	NOUN
ejpam-6089	44	9	in	in	ADP
ejpam-6089	44	10	l1	l1	PROPN
ejpam-6089	44	11	on	on	ADP
ejpam-6089	44	12	the	the	DET
ejpam-6089	44	13	interval	interval	NOUN
ejpam-6089	44	14	[	[	X
ejpam-6089	44	15	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	44	16	]	]	PUNCT
ejpam-6089	44	17	.	.	PUNCT
ejpam-6089	45	1	the	the	DET
ejpam-6089	45	2	g	g	NOUN
ejpam-6089	45	3	-	-	PUNCT
ejpam-6089	45	4	th	th	VERB
ejpam-6089	45	5	order	order	NOUN
ejpam-6089	45	6	left	leave	VERB
ejpam-6089	45	7	and	and	CCONJ
ejpam-6089	45	8	right	right	ADV
ejpam-6089	45	9	sided	sided	ADJ
ejpam-6089	45	10	atangana	atangana	PROPN
ejpam-6089	45	11	-	-	PUNCT
ejpam-6089	45	12	baleanu	baleanu	PROPN
ejpam-6089	45	13	integrals	integral	NOUN
ejpam-6089	45	14	for	for	ADP
ejpam-6089	45	15	any	any	DET
ejpam-6089	45	16	c	c	PROPN
ejpam-6089	45	17	∈	∈	PROPN
ejpam-6089	46	1	[	[	X
ejpam-6089	46	2	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	46	3	]	]	PUNCT
ejpam-6089	46	4	,	,	PUNCT
ejpam-6089	46	5	applied	apply	VERB
ejpam-6089	46	6	to	to	ADP
ejpam-6089	46	7	υ(c	υ(c	PROPN
ejpam-6089	46	8	)	)	PUNCT
ejpam-6089	46	9	and	and	CCONJ
ejpam-6089	46	10	for	for	ADP
ejpam-6089	46	11	1	1	NUM
ejpam-6089	46	12	>	>	PART
ejpam-6089	46	13	g	g	PROPN
ejpam-6089	46	14	>	>	X
ejpam-6089	46	15	0	0	PROPN
ejpam-6089	46	16	,	,	PUNCT
ejpam-6089	46	17	written	write	VERB
ejpam-6089	46	18	as	as	ADP
ejpam-6089	46	19	a−bigℑ1+υ(c	a−bigℑ1+υ(c	NOUN
ejpam-6089	46	20	)	)	PUNCT
ejpam-6089	47	1	=	=	SYM
ejpam-6089	47	2	g	g	PROPN
ejpam-6089	47	3	b(g	b(g	PROPN
ejpam-6089	47	4	)	)	PUNCT
ejpam-6089	47	5	(	(	PUNCT
ejpam-6089	47	6	r−ligℑ1+υ(c	r−ligℑ1+υ(c	NOUN
ejpam-6089	47	7	)	)	PUNCT
ejpam-6089	47	8	)	)	PUNCT
ejpam-6089	48	1	+	+	CCONJ
ejpam-6089	48	2	(	(	PUNCT
ejpam-6089	48	3	1−g	1−g	NUM
ejpam-6089	48	4	)	)	PUNCT
ejpam-6089	48	5	b(g	b(g	PROPN
ejpam-6089	48	6	)	)	PUNCT
ejpam-6089	48	7	υ(c	υ(c	PROPN
ejpam-6089	48	8	)	)	PUNCT
ejpam-6089	48	9	,	,	PUNCT
ejpam-6089	48	10	(	(	PUNCT
ejpam-6089	48	11	3	3	X
ejpam-6089	48	12	)	)	PUNCT
ejpam-6089	48	13	and	and	CCONJ
ejpam-6089	48	14	a−bigℑ2−υ(c	a−bigℑ2−υ(c	NOUN
ejpam-6089	48	15	)	)	PUNCT
ejpam-6089	48	16	=	=	SYM
ejpam-6089	48	17	g	g	PROPN
ejpam-6089	48	18	b(g	b(g	PROPN
ejpam-6089	48	19	)	)	PUNCT
ejpam-6089	48	20	(	(	PUNCT
ejpam-6089	48	21	r−ligℑ2−υ(c	r−ligℑ2−υ(c	NOUN
ejpam-6089	48	22	)	)	PUNCT
ejpam-6089	48	23	)	)	PUNCT
ejpam-6089	49	1	+	+	CCONJ
ejpam-6089	49	2	(	(	PUNCT
ejpam-6089	49	3	1−g	1−g	NUM
ejpam-6089	49	4	)	)	PUNCT
ejpam-6089	49	5	b(g	b(g	PROPN
ejpam-6089	49	6	)	)	PUNCT
ejpam-6089	49	7	υ(c	υ(c	PROPN
ejpam-6089	49	8	)	)	PUNCT
ejpam-6089	49	9	,	,	PUNCT
ejpam-6089	49	10	(	(	PUNCT
ejpam-6089	49	11	4	4	X
ejpam-6089	49	12	)	)	PUNCT
ejpam-6089	49	13	where	where	SCONJ
ejpam-6089	49	14	b(g	b(g	PROPN
ejpam-6089	49	15	)	)	PUNCT
ejpam-6089	49	16	is	be	AUX
ejpam-6089	49	17	a	a	DET
ejpam-6089	49	18	normalization	normalization	NOUN
ejpam-6089	49	19	function	function	NOUN
ejpam-6089	49	20	that	that	PRON
ejpam-6089	49	21	is	be	AUX
ejpam-6089	49	22	both	both	PRON
ejpam-6089	49	23	real	real	ADJ
ejpam-6089	49	24	and	and	CCONJ
ejpam-6089	49	25	positive	positive	ADJ
ejpam-6089	49	26	,	,	PUNCT
ejpam-6089	49	27	having	have	VERB
ejpam-6089	49	28	properties	property	NOUN
ejpam-6089	49	29	b(0	b(0	VERB
ejpam-6089	49	30	)	)	PUNCT
ejpam-6089	49	31	=	=	SYM
ejpam-6089	49	32	b(1	b(1	PROPN
ejpam-6089	49	33	)	)	PUNCT
ejpam-6089	49	34	=	=	NOUN
ejpam-6089	50	1	1	1	X
ejpam-6089	50	2	.	.	X
ejpam-6089	50	3	definition	definition	NOUN
ejpam-6089	50	4	4	4	NUM
ejpam-6089	50	5	.	.	PUNCT
ejpam-6089	51	1	[	[	X
ejpam-6089	51	2	24	24	NUM
ejpam-6089	51	3	,	,	PUNCT
ejpam-6089	51	4	25	25	NUM
ejpam-6089	51	5	]	]	PUNCT
ejpam-6089	51	6	given	give	VERB
ejpam-6089	51	7	a	a	DET
ejpam-6089	51	8	function	function	NOUN
ejpam-6089	51	9	υ	υ	NOUN
ejpam-6089	51	10	that	that	PRON
ejpam-6089	51	11	belongs	belong	VERB
ejpam-6089	51	12	to	to	ADP
ejpam-6089	51	13	l1	l1	PROPN
ejpam-6089	51	14	on	on	ADP
ejpam-6089	51	15	the	the	DET
ejpam-6089	51	16	interval	interval	NOUN
ejpam-6089	51	17	[	[	X
ejpam-6089	51	18	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	51	19	]	]	PUNCT
ejpam-6089	51	20	and	and	CCONJ
ejpam-6089	51	21	for	for	ADP
ejpam-6089	51	22	any	any	DET
ejpam-6089	51	23	c	c	PROPN
ejpam-6089	51	24	∈	∈	PROPN
ejpam-6089	52	1	[	[	X
ejpam-6089	52	2	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	52	3	]	]	PUNCT
ejpam-6089	52	4	,	,	PUNCT
ejpam-6089	52	5	then	then	ADV
ejpam-6089	52	6	the	the	DET
ejpam-6089	52	7	left	left	ADJ
ejpam-6089	52	8	and	and	CCONJ
ejpam-6089	52	9	right	right	ADJ
ejpam-6089	52	10	sided	sided	ADJ
ejpam-6089	52	11	prabhakar	prabhakar	NOUN
ejpam-6089	52	12	fractional	fractional	ADJ
ejpam-6089	52	13	integral	integral	ADJ
ejpam-6089	52	14	operators	operator	NOUN
ejpam-6089	52	15	applied	apply	VERB
ejpam-6089	52	16	to	to	ADP
ejpam-6089	52	17	υ(c	υ(c	PROPN
ejpam-6089	52	18	)	)	PUNCT
ejpam-6089	52	19	with	with	ADP
ejpam-6089	52	20	ℜ(α∗	ℜ(α∗	PROPN
ejpam-6089	52	21	)	)	PUNCT
ejpam-6089	52	22	>	>	X
ejpam-6089	52	23	0	0	NUM
ejpam-6089	52	24	,	,	PUNCT
ejpam-6089	52	25	ℜ(β∗	ℜ(β∗	NUM
ejpam-6089	52	26	)	)	PUNCT
ejpam-6089	52	27	>	>	X
ejpam-6089	52	28	0	0	PUNCT
ejpam-6089	52	29	and	and	CCONJ
ejpam-6089	52	30	γ	γ	PROPN
ejpam-6089	52	31	,	,	PUNCT
ejpam-6089	52	32	♭	♭	PROPN
ejpam-6089	52	33	∈	∈	PROPN
ejpam-6089	52	34	c	c	NOUN
ejpam-6089	52	35	,	,	PUNCT
ejpam-6089	52	36	given	give	VERB
ejpam-6089	52	37	as	as	ADP
ejpam-6089	52	38	piα	piα	PROPN
ejpam-6089	52	39	∗,β∗,γ	∗,β∗,γ	PROPN
ejpam-6089	52	40	,	,	PUNCT
ejpam-6089	52	41	♭	♭	PROPN
ejpam-6089	52	42	ℑ1	ℑ1	PROPN
ejpam-6089	52	43	+	+	CCONJ
ejpam-6089	52	44	υ(c	υ(c	PROPN
ejpam-6089	52	45	)	)	PUNCT
ejpam-6089	52	46	=	=	PUNCT
ejpam-6089	53	1	∫	∫	PROPN
ejpam-6089	53	2	c	c	PROPN
ejpam-6089	53	3	ℑ1	ℑ1	PROPN
ejpam-6089	53	4	(	(	PUNCT
ejpam-6089	53	5	c−	c−	NOUN
ejpam-6089	53	6	ψ)β	ψ)β	PUNCT
ejpam-6089	53	7	∗−1eγα∗,β∗	∗−1eγα∗,β∗	PROPN
ejpam-6089	53	8	(	(	PUNCT
ejpam-6089	53	9	♭	♭	PROPN
ejpam-6089	53	10	(	(	PUNCT
ejpam-6089	53	11	c−	c−	X
ejpam-6089	53	12	ψ)α	ψ)α	NOUN
ejpam-6089	53	13	∗	∗	NOUN
ejpam-6089	53	14	)	)	PUNCT
ejpam-6089	53	15	υ(ψ)dψ	υ(ψ)dψ	NOUN
ejpam-6089	53	16	,	,	PUNCT
ejpam-6089	53	17	(	(	PUNCT
ejpam-6089	53	18	5	5	NUM
ejpam-6089	53	19	)	)	PUNCT
ejpam-6089	53	20	and	and	CCONJ
ejpam-6089	53	21	piα	piα	PROPN
ejpam-6089	53	22	∗,β∗,γ	∗,β∗,γ	PROPN
ejpam-6089	53	23	,	,	PUNCT
ejpam-6089	53	24	♭	♭	PROPN
ejpam-6089	53	25	ℑ2−	ℑ2−	NUM
ejpam-6089	53	26	υ(c	υ(c	PROPN
ejpam-6089	53	27	)	)	PUNCT
ejpam-6089	53	28	=	=	SYM
ejpam-6089	54	1	∫	∫	PROPN
ejpam-6089	54	2	ℑ2	ℑ2	PROPN
ejpam-6089	54	3	c	c	PROPN
ejpam-6089	54	4	(	(	PUNCT
ejpam-6089	54	5	ψ	ψ	X
ejpam-6089	54	6	−	−	PROPN
ejpam-6089	54	7	c)β	c)β	X
ejpam-6089	54	8	∗−1eγα∗,β∗	∗−1eγα∗,β∗	PROPN
ejpam-6089	54	9	(	(	PUNCT
ejpam-6089	54	10	♭	♭	PROPN
ejpam-6089	54	11	(	(	PUNCT
ejpam-6089	54	12	ψ	ψ	NOUN
ejpam-6089	54	13	−	−	NOUN
ejpam-6089	54	14	c)α	c)α	NOUN
ejpam-6089	54	15	∗	∗	NOUN
ejpam-6089	54	16	)	)	PUNCT
ejpam-6089	54	17	υ(ψ)dψ	υ(ψ)dψ	NOUN
ejpam-6089	54	18	,	,	PUNCT
ejpam-6089	54	19	(	(	PUNCT
ejpam-6089	54	20	6	6	NUM
ejpam-6089	54	21	)	)	PUNCT
ejpam-6089	54	22	where	where	SCONJ
ejpam-6089	54	23	eγα∗,β∗(z	eγα∗,β∗(z	NOUN
ejpam-6089	54	24	)	)	PUNCT
ejpam-6089	54	25	symbolizes	symbolize	VERB
ejpam-6089	54	26	the	the	DET
ejpam-6089	54	27	three	three	NUM
ejpam-6089	54	28	parameters	parameter	NOUN
ejpam-6089	54	29	mittag	mittag	ADJ
ejpam-6089	54	30	-	-	PUNCT
ejpam-6089	54	31	leffler	leffler	NOUN
ejpam-6089	54	32	function	function	NOUN
ejpam-6089	54	33	.	.	PUNCT
ejpam-6089	55	1	definition	definition	NOUN
ejpam-6089	55	2	5	5	NUM
ejpam-6089	55	3	.	.	PUNCT
ejpam-6089	56	1	[	[	X
ejpam-6089	56	2	29	29	NUM
ejpam-6089	56	3	]	]	PUNCT
ejpam-6089	56	4	for	for	ADP
ejpam-6089	56	5	any	any	DET
ejpam-6089	56	6	function	function	NOUN
ejpam-6089	56	7	υ	υ	PROPN
ejpam-6089	56	8	∈	∈	PROPN
ejpam-6089	56	9	l1	l1	PROPN
ejpam-6089	56	10	on	on	ADP
ejpam-6089	56	11	the	the	DET
ejpam-6089	56	12	interval	interval	NOUN
ejpam-6089	56	13	[	[	X
ejpam-6089	56	14	ℑ1,ℑ2	ℑ1,ℑ2	X
ejpam-6089	56	15	]	]	X
ejpam-6089	56	16	⊂	⊂	X
ejpam-6089	56	17	r	r	NOUN
ejpam-6089	56	18	and	and	CCONJ
ejpam-6089	56	19	c	c	NOUN
ejpam-6089	56	20	∈	∈	PROPN
ejpam-6089	57	1	[	[	X
ejpam-6089	57	2	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	57	3	]	]	PUNCT
ejpam-6089	57	4	,	,	PUNCT
ejpam-6089	57	5	then	then	ADV
ejpam-6089	57	6	the	the	DET
ejpam-6089	57	7	infinite	infinite	ADJ
ejpam-6089	57	8	series	series	NOUN
ejpam-6089	57	9	formula	formula	NOUN
ejpam-6089	57	10	for	for	ADP
ejpam-6089	57	11	left	left	ADJ
ejpam-6089	57	12	and	and	CCONJ
ejpam-6089	57	13	right	right	ADJ
ejpam-6089	57	14	prabhakar	prabhakar	NOUN
ejpam-6089	57	15	integrals	integral	NOUN
ejpam-6089	57	16	applied	apply	VERB
ejpam-6089	57	17	to	to	ADP
ejpam-6089	57	18	υ(c	υ(c	PROPN
ejpam-6089	57	19	)	)	PUNCT
ejpam-6089	57	20	,	,	PUNCT
ejpam-6089	57	21	stated	state	VERB
ejpam-6089	57	22	as	as	ADP
ejpam-6089	57	23	piℵ,℘,γ,	piℵ,℘,γ,	NOUN
ejpam-6089	57	24	♭	♭	NOUN
ejpam-6089	57	25	ℑ1	ℑ1	NOUN
ejpam-6089	57	26	+	+	CCONJ
ejpam-6089	57	27	υ(c	υ(c	PROPN
ejpam-6089	57	28	)	)	PUNCT
ejpam-6089	57	29	=	=	PUNCT
ejpam-6089	58	1	∞∑	∞∑	NUM
ejpam-6089	58	2	ð=0	ð=0	PUNCT
ejpam-6089	58	3	γ(γ	γ(γ	PROPN
ejpam-6089	58	4	+	+	CCONJ
ejpam-6089	58	5	ð)	ð)	PUNCT
ejpam-6089	58	6	♭	♭	PROPN
ejpam-6089	58	7	ð	ð	X
ejpam-6089	58	8	γ(γ)ð	γ(γ)ð	PROPN
ejpam-6089	58	9	!	!	PUNCT
ejpam-6089	59	1	r−li	r−li	NOUN
ejpam-6089	59	2	(	(	PUNCT
ejpam-6089	59	3	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	59	4	)	)	PUNCT
ejpam-6089	59	5	ℑ1	ℑ1	NOUN
ejpam-6089	59	6	+	+	CCONJ
ejpam-6089	59	7	υ(c	υ(c	PROPN
ejpam-6089	59	8	)	)	PUNCT
ejpam-6089	59	9	,	,	PUNCT
ejpam-6089	59	10	(	(	PUNCT
ejpam-6089	59	11	7	7	X
ejpam-6089	59	12	)	)	PUNCT
ejpam-6089	59	13	and	and	CCONJ
ejpam-6089	59	14	piℵ,℘,γ,	piℵ,℘,γ,	VERB
ejpam-6089	59	15	♭	♭	PROPN
ejpam-6089	59	16	ℑ2−	ℑ2−	NUM
ejpam-6089	59	17	υ(c	υ(c	PROPN
ejpam-6089	59	18	)	)	PUNCT
ejpam-6089	59	19	=	=	PUNCT
ejpam-6089	60	1	∞∑	∞∑	NUM
ejpam-6089	60	2	ð=0	ð=0	PUNCT
ejpam-6089	60	3	γ(γ	γ(γ	PROPN
ejpam-6089	60	4	+	+	CCONJ
ejpam-6089	60	5	ð)	ð)	PUNCT
ejpam-6089	60	6	♭	♭	PROPN
ejpam-6089	60	7	ð	ð	X
ejpam-6089	60	8	γ(γ)ð	γ(γ)ð	PROPN
ejpam-6089	60	9	!	!	PUNCT
ejpam-6089	61	1	r−li	r−li	NOUN
ejpam-6089	61	2	(	(	PUNCT
ejpam-6089	61	3	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	61	4	)	)	PUNCT
ejpam-6089	61	5	ℑ2−	ℑ2−	NUM
ejpam-6089	61	6	υ(c	υ(c	PROPN
ejpam-6089	61	7	)	)	PUNCT
ejpam-6089	61	8	.	.	PUNCT
ejpam-6089	62	1	(	(	PUNCT
ejpam-6089	62	2	8)	8)	NUM
ejpam-6089	62	3	s.	s.	PROPN
ejpam-6089	62	4	naheed	nahee	VERB
ejpam-6089	62	5	et	et	PROPN
ejpam-6089	62	6	al	al	PROPN
ejpam-6089	62	7	.	.	PUNCT
ejpam-6089	62	8	/	/	SYM
ejpam-6089	62	9	eur	eur	PROPN
ejpam-6089	62	10	.	.	PUNCT
ejpam-6089	63	1	j.	j.	PROPN
ejpam-6089	63	2	pure	pure	PROPN
ejpam-6089	63	3	appl	appl	PROPN
ejpam-6089	63	4	.	.	PROPN
ejpam-6089	63	5	math	math	PROPN
ejpam-6089	63	6	,	,	PUNCT
ejpam-6089	63	7	18	18	NUM
ejpam-6089	63	8	(	(	PUNCT
ejpam-6089	63	9	2	2	NUM
ejpam-6089	63	10	)	)	PUNCT
ejpam-6089	63	11	(	(	PUNCT
ejpam-6089	63	12	2025	2025	NUM
ejpam-6089	63	13	)	)	PUNCT
ejpam-6089	63	14	,	,	PUNCT
ejpam-6089	63	15	6089	6089	NUM
ejpam-6089	63	16	4	4	NUM
ejpam-6089	63	17	of	of	ADP
ejpam-6089	63	18	34	34	NUM
ejpam-6089	63	19	definition	definition	NOUN
ejpam-6089	63	20	6	6	NUM
ejpam-6089	63	21	.	.	PUNCT
ejpam-6089	64	1	[	[	X
ejpam-6089	64	2	18	18	NUM
ejpam-6089	64	3	]	]	PUNCT
ejpam-6089	64	4	the	the	DET
ejpam-6089	64	5	mittag	mittag	ADJ
ejpam-6089	64	6	-	-	PUNCT
ejpam-6089	64	7	leffler	leffler	NOUN
ejpam-6089	64	8	function	function	NOUN
ejpam-6089	64	9	with	with	ADP
ejpam-6089	64	10	one	one	NUM
ejpam-6089	64	11	parameter	parameter	NOUN
ejpam-6089	64	12	can	can	AUX
ejpam-6089	64	13	be	be	AUX
ejpam-6089	64	14	defined	define	VERB
ejpam-6089	64	15	as	as	ADP
ejpam-6089	64	16	eℵ(z	eℵ(z	NOUN
ejpam-6089	64	17	)	)	PUNCT
ejpam-6089	64	18	=	=	SYM
ejpam-6089	65	1	∞∑	∞∑	NUM
ejpam-6089	65	2	ð=0	ð=0	X
ejpam-6089	65	3	zð	zð	NOUN
ejpam-6089	65	4	γ(ℵð+	γ(ℵð+	PROPN
ejpam-6089	65	5	1	1	NUM
ejpam-6089	65	6	)	)	PUNCT
ejpam-6089	65	7	,	,	PUNCT
ejpam-6089	65	8	(	(	PUNCT
ejpam-6089	65	9	z	z	NOUN
ejpam-6089	65	10	∈	∈	PROPN
ejpam-6089	65	11	c,ℜ(ℵ	c,ℜ(ℵ	PROPN
ejpam-6089	65	12	)	)	PUNCT
ejpam-6089	65	13	>	>	X
ejpam-6089	65	14	0	0	NUM
ejpam-6089	65	15	)	)	PUNCT
ejpam-6089	65	16	.	.	PUNCT
ejpam-6089	66	1	the	the	DET
ejpam-6089	66	2	first	first	ADJ
ejpam-6089	66	3	generalization	generalization	NOUN
ejpam-6089	66	4	of	of	ADP
ejpam-6089	66	5	mittag	mittag	ADJ
ejpam-6089	66	6	-	-	PUNCT
ejpam-6089	66	7	leffler	leffler	NOUN
ejpam-6089	66	8	function	function	NOUN
ejpam-6089	66	9	for	for	ADP
ejpam-6089	66	10	two	two	NUM
ejpam-6089	66	11	parameters	parameter	NOUN
ejpam-6089	66	12	,	,	PUNCT
ejpam-6089	66	13	is	be	AUX
ejpam-6089	66	14	given	give	VERB
ejpam-6089	66	15	as	as	ADP
ejpam-6089	66	16	eℵ,℘(z	eℵ,℘(z	ADJ
ejpam-6089	66	17	)	)	PUNCT
ejpam-6089	66	18	=	=	PUNCT
ejpam-6089	67	1	∞∑	∞∑	NUM
ejpam-6089	67	2	ð=0	ð=0	X
ejpam-6089	67	3	zð	zð	NOUN
ejpam-6089	67	4	γ(ℵð+	γ(ℵð+	NOUN
ejpam-6089	67	5	℘	℘	PROPN
ejpam-6089	67	6	)	)	PUNCT
ejpam-6089	67	7	,	,	PUNCT
ejpam-6089	67	8	(	(	PUNCT
ejpam-6089	67	9	z,ℵ	z,ℵ	PROPN
ejpam-6089	67	10	,	,	PUNCT
ejpam-6089	67	11	℘	℘	PROPN
ejpam-6089	67	12	∈	∈	PROPN
ejpam-6089	67	13	c,ℜ(ℵ	c,ℜ(ℵ	NOUN
ejpam-6089	67	14	)	)	PUNCT
ejpam-6089	67	15	>	>	X
ejpam-6089	67	16	0	0	NUM
ejpam-6089	67	17	)	)	PUNCT
ejpam-6089	67	18	.	.	PUNCT
ejpam-6089	68	1	prabhakar	prabhakar	PROPN
ejpam-6089	68	2	defined	define	VERB
ejpam-6089	68	3	the	the	DET
ejpam-6089	68	4	mittag	mittag	ADJ
ejpam-6089	68	5	-	-	PUNCT
ejpam-6089	68	6	leffler	leffler	NOUN
ejpam-6089	68	7	function	function	NOUN
ejpam-6089	68	8	of	of	ADP
ejpam-6089	68	9	three	three	NUM
ejpam-6089	68	10	parameters	parameter	NOUN
ejpam-6089	68	11	[	[	X
ejpam-6089	68	12	25	25	NUM
ejpam-6089	68	13	]	]	PUNCT
ejpam-6089	68	14	as	as	ADP
ejpam-6089	68	15	eδℵ,℘(z	eδℵ,℘(z	X
ejpam-6089	68	16	)	)	PUNCT
ejpam-6089	68	17	=	=	PUNCT
ejpam-6089	69	1	∞∑	∞∑	NUM
ejpam-6089	69	2	ð=0	ð=0	X
ejpam-6089	69	3	(	(	PUNCT
ejpam-6089	69	4	δ)ð	δ)ð	VERB
ejpam-6089	69	5	γ(ℵð+	γ(ℵð+	NOUN
ejpam-6089	69	6	℘	℘	NOUN
ejpam-6089	69	7	)	)	PUNCT
ejpam-6089	69	8	zð	zð	NOUN
ejpam-6089	69	9	ð	ð	NUM
ejpam-6089	69	10	!	!	PUNCT
ejpam-6089	69	11	,	,	PUNCT
ejpam-6089	69	12	(	(	PUNCT
ejpam-6089	69	13	z,ℵ	z,ℵ	PROPN
ejpam-6089	69	14	,	,	PUNCT
ejpam-6089	69	15	℘	℘	PROPN
ejpam-6089	69	16	,	,	PUNCT
ejpam-6089	69	17	δ	δ	PROPN
ejpam-6089	69	18	∈	∈	PROPN
ejpam-6089	69	19	c,ℜ(ℵ	c,ℜ(ℵ	PROPN
ejpam-6089	69	20	)	)	PUNCT
ejpam-6089	69	21	>	>	X
ejpam-6089	69	22	0	0	NUM
ejpam-6089	69	23	)	)	PUNCT
ejpam-6089	69	24	.	.	PUNCT
ejpam-6089	70	1	definition	definition	NOUN
ejpam-6089	70	2	7	7	NUM
ejpam-6089	70	3	.	.	PUNCT
ejpam-6089	71	1	[	[	X
ejpam-6089	71	2	22	22	NUM
ejpam-6089	71	3	]	]	PUNCT
ejpam-6089	71	4	let	let	VERB
ejpam-6089	71	5	ℵ	ℵ	NOUN
ejpam-6089	71	6	,	,	PUNCT
ejpam-6089	71	7	℘	℘	PROPN
ejpam-6089	71	8	,	,	PUNCT
ejpam-6089	71	9	τ	τ	PROPN
ejpam-6089	71	10	,	,	PUNCT
ejpam-6089	71	11	δ	δ	PROPN
ejpam-6089	71	12	,	,	PUNCT
ejpam-6089	71	13	c	c	PROPN
ejpam-6089	71	14	∈	∈	PROPN
ejpam-6089	72	1	c	c	NOUN
ejpam-6089	72	2	,	,	PUNCT
ejpam-6089	72	3	with	with	ADP
ejpam-6089	72	4	ℜ(ℵ),ℜ(℘),ℜ(τ	ℜ(ℵ),ℜ(℘),ℜ(τ	PROPN
ejpam-6089	72	5	)	)	PUNCT
ejpam-6089	72	6	>	>	X
ejpam-6089	72	7	0	0	NUM
ejpam-6089	72	8	and	and	CCONJ
ejpam-6089	72	9	ℜ(b	ℜ(b	NOUN
ejpam-6089	72	10	)	)	PUNCT
ejpam-6089	72	11	>	>	X
ejpam-6089	72	12	ℜ(δ	ℜ(δ	X
ejpam-6089	72	13	)	)	PUNCT
ejpam-6089	72	14	>	>	X
ejpam-6089	72	15	0	0	PUNCT
ejpam-6089	72	16	with	with	ADP
ejpam-6089	72	17	0	0	NUM
ejpam-6089	72	18	≤	≤	NUM
ejpam-6089	72	19	g	g	NOUN
ejpam-6089	72	20	,	,	PUNCT
ejpam-6089	72	21	1	1	NUM
ejpam-6089	72	22	>	>	SYM
ejpam-6089	72	23	0	0	NUM
ejpam-6089	72	24	and	and	CCONJ
ejpam-6089	72	25	l	l	NOUN
ejpam-6089	72	26	+	+	CCONJ
ejpam-6089	72	27	ℜ(ℵ	ℜ(ℵ	NOUN
ejpam-6089	72	28	)	)	PUNCT
ejpam-6089	72	29	≥	≥	X
ejpam-6089	72	30	s	s	NOUN
ejpam-6089	72	31	>	>	X
ejpam-6089	72	32	0	0	NUM
ejpam-6089	72	33	.	.	PUNCT
ejpam-6089	73	1	then	then	ADV
ejpam-6089	73	2	the	the	DET
ejpam-6089	73	3	extended	extended	ADJ
ejpam-6089	73	4	generalized	generalize	VERB
ejpam-6089	73	5	mittag	mittag	ADJ
ejpam-6089	73	6	-	-	PUNCT
ejpam-6089	73	7	leffler	leffler	NOUN
ejpam-6089	73	8	function	function	NOUN
ejpam-6089	73	9	eδ	eδ	ADP
ejpam-6089	73	10	,	,	PUNCT
ejpam-6089	73	11	b	b	NOUN
ejpam-6089	73	12	,	,	PUNCT
ejpam-6089	73	13	s	s	NOUN
ejpam-6089	73	14	,	,	PUNCT
ejpam-6089	73	15	lℵ,℘,τ	lℵ,℘,τ	NOUN
ejpam-6089	73	16	(	(	PUNCT
ejpam-6089	73	17	z	z	NOUN
ejpam-6089	73	18	;	;	PUNCT
ejpam-6089	73	19	g	g	NOUN
ejpam-6089	73	20	)	)	PUNCT
ejpam-6089	73	21	is	be	AUX
ejpam-6089	73	22	defined	define	VERB
ejpam-6089	73	23	by	by	ADP
ejpam-6089	73	24	eδ	eδ	NOUN
ejpam-6089	73	25	,	,	PUNCT
ejpam-6089	73	26	b	b	NOUN
ejpam-6089	73	27	,	,	PUNCT
ejpam-6089	73	28	s	s	NOUN
ejpam-6089	73	29	,	,	PUNCT
ejpam-6089	73	30	lℵ,℘,τ	lℵ,℘,τ	NOUN
ejpam-6089	73	31	(	(	PUNCT
ejpam-6089	73	32	z	z	NOUN
ejpam-6089	73	33	;	;	PUNCT
ejpam-6089	73	34	g	g	NOUN
ejpam-6089	73	35	)	)	PUNCT
ejpam-6089	73	36	=	=	PUNCT
ejpam-6089	74	1	∞∑	∞∑	NUM
ejpam-6089	74	2	ð=0	ð=0	X
ejpam-6089	74	3	bg(δ	bg(δ	NOUN
ejpam-6089	74	4	+	+	CCONJ
ejpam-6089	74	5	ðs	ðs	CCONJ
ejpam-6089	74	6	,	,	PUNCT
ejpam-6089	74	7	b−	b−	PROPN
ejpam-6089	74	8	δ	δ	PROPN
ejpam-6089	74	9	)	)	PUNCT
ejpam-6089	74	10	b(δ	b(δ	PROPN
ejpam-6089	74	11	,	,	PUNCT
ejpam-6089	74	12	b−	b−	PROPN
ejpam-6089	74	13	δ	δ	PROPN
ejpam-6089	74	14	)	)	PUNCT
ejpam-6089	74	15	(	(	PUNCT
ejpam-6089	74	16	b)ðs	b)ðs	PROPN
ejpam-6089	74	17	γ(ℵð+	γ(ℵð+	VERB
ejpam-6089	74	18	℘	℘	PROPN
ejpam-6089	74	19	)	)	PUNCT
ejpam-6089	74	20	zð	zð	NOUN
ejpam-6089	74	21	(	(	PUNCT
ejpam-6089	74	22	τ)ðl	τ)ðl	PROPN
ejpam-6089	74	23	,	,	PUNCT
ejpam-6089	74	24	(	(	PUNCT
ejpam-6089	74	25	9	9	NUM
ejpam-6089	74	26	)	)	PUNCT
ejpam-6089	74	27	where	where	SCONJ
ejpam-6089	74	28	(	(	PUNCT
ejpam-6089	74	29	b)ðs	b)ðs	PROPN
ejpam-6089	74	30	=	=	PUNCT
ejpam-6089	74	31	γ(b+ðs	γ(b+ðs	X
ejpam-6089	74	32	)	)	PUNCT
ejpam-6089	74	33	γ(b	γ(b	NOUN
ejpam-6089	74	34	)	)	PUNCT
ejpam-6089	74	35	,	,	PUNCT
ejpam-6089	74	36	is	be	AUX
ejpam-6089	74	37	the	the	DET
ejpam-6089	74	38	generalized	generalized	ADJ
ejpam-6089	74	39	pochhammer	pochhammer	NOUN
ejpam-6089	74	40	symbol	symbol	NOUN
ejpam-6089	74	41	and	and	CCONJ
ejpam-6089	74	42	bg(i	bg(i	PROPN
ejpam-6089	74	43	,	,	PUNCT
ejpam-6089	74	44	j	j	NOUN
ejpam-6089	74	45	)	)	PUNCT
ejpam-6089	75	1	=	=	SYM
ejpam-6089	75	2	∫	∫	PROPN
ejpam-6089	75	3	1	1	NUM
ejpam-6089	75	4	0	0	NUM
ejpam-6089	75	5	t	t	PROPN
ejpam-6089	76	1	i−1	i−1	PROPN
ejpam-6089	76	2	(	(	PUNCT
ejpam-6089	76	3	1−	1−	NUM
ejpam-6089	76	4	t)j−1e	t)j−1e	NOUN
ejpam-6089	76	5	−	−	ADP
ejpam-6089	76	6	g	g	PROPN
ejpam-6089	76	7	t(1−t)dt	t(1−t)dt	NOUN
ejpam-6089	76	8	with	with	ADP
ejpam-6089	76	9	ℜ(i),ℜ(j),ℜ(g	ℜ(i),ℜ(j),ℜ(g	NOUN
ejpam-6089	76	10	)	)	PUNCT
ejpam-6089	76	11	>	>	X
ejpam-6089	76	12	0	0	NUM
ejpam-6089	76	13	,	,	PUNCT
ejpam-6089	76	14	is	be	AUX
ejpam-6089	76	15	an	an	DET
ejpam-6089	76	16	extended	extended	ADJ
ejpam-6089	76	17	beta	beta	NOUN
ejpam-6089	76	18	function	function	NOUN
ejpam-6089	76	19	.	.	PUNCT
ejpam-6089	77	1	definition	definition	NOUN
ejpam-6089	77	2	8	8	NUM
ejpam-6089	77	3	.	.	PUNCT
ejpam-6089	78	1	[	[	X
ejpam-6089	78	2	22	22	NUM
ejpam-6089	78	3	]	]	PUNCT
ejpam-6089	78	4	let	let	VERB
ejpam-6089	78	5	♭	♭	PRON
ejpam-6089	78	6	,	,	PUNCT
ejpam-6089	78	7	ℵ	ℵ	NOUN
ejpam-6089	78	8	,	,	PUNCT
ejpam-6089	78	9	℘	℘	PROPN
ejpam-6089	78	10	,	,	PUNCT
ejpam-6089	78	11	τ	τ	PROPN
ejpam-6089	78	12	,	,	PUNCT
ejpam-6089	78	13	δ	δ	PROPN
ejpam-6089	78	14	,	,	PUNCT
ejpam-6089	78	15	b	b	PROPN
ejpam-6089	78	16	∈	∈	PROPN
ejpam-6089	78	17	c	c	NOUN
ejpam-6089	78	18	with	with	ADP
ejpam-6089	78	19	ℜ(ℵ),ℜ(℘),ℜ(τ	ℜ(ℵ),ℜ(℘),ℜ(τ	PROPN
ejpam-6089	78	20	)	)	PUNCT
ejpam-6089	78	21	>	>	X
ejpam-6089	78	22	0	0	NUM
ejpam-6089	78	23	and	and	CCONJ
ejpam-6089	78	24	ℜ(b	ℜ(b	NOUN
ejpam-6089	78	25	)	)	PUNCT
ejpam-6089	78	26	>	>	X
ejpam-6089	79	1	ℜ(δ	ℜ(δ	X
ejpam-6089	79	2	)	)	PUNCT
ejpam-6089	79	3	>	>	X
ejpam-6089	79	4	0	0	PUNCT
ejpam-6089	80	1	and	and	CCONJ
ejpam-6089	80	2	let	let	VERB
ejpam-6089	80	3	g	g	PROPN
ejpam-6089	80	4	≥	≥	NOUN
ejpam-6089	80	5	0	0	NUM
ejpam-6089	80	6	,	,	PUNCT
ejpam-6089	80	7	l	l	NOUN
ejpam-6089	80	8	>	>	X
ejpam-6089	80	9	0	0	PUNCT
ejpam-6089	80	10	and	and	CCONJ
ejpam-6089	80	11	l+ℜ(ℵ	l+ℜ(ℵ	ADJ
ejpam-6089	80	12	)	)	PUNCT
ejpam-6089	80	13	≥	≥	NOUN
ejpam-6089	80	14	s	s	NOUN
ejpam-6089	80	15	>	>	X
ejpam-6089	80	16	0	0	NUM
ejpam-6089	80	17	.	.	PUNCT
ejpam-6089	81	1	for	for	ADP
ejpam-6089	81	2	a	a	DET
ejpam-6089	81	3	function	function	NOUN
ejpam-6089	81	4	υ	υ	X
ejpam-6089	81	5	∈	∈	PROPN
ejpam-6089	81	6	l1[ℑ1,ℑ2	l1[ℑ1,ℑ2	PROPN
ejpam-6089	81	7	]	]	PUNCT
ejpam-6089	81	8	and	and	CCONJ
ejpam-6089	81	9	c	c	NOUN
ejpam-6089	81	10	∈	∈	PROPN
ejpam-6089	81	11	[	[	X
ejpam-6089	81	12	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	81	13	]	]	PUNCT
ejpam-6089	81	14	,	,	PUNCT
ejpam-6089	81	15	the	the	DET
ejpam-6089	81	16	left	left	ADJ
ejpam-6089	81	17	and	and	CCONJ
ejpam-6089	81	18	right	right	ADJ
ejpam-6089	81	19	sided	sided	ADJ
ejpam-6089	81	20	generalized	generalized	ADJ
ejpam-6089	81	21	fractional	fractional	ADJ
ejpam-6089	81	22	integral	integral	ADJ
ejpam-6089	81	23	operators	operator	NOUN
ejpam-6089	81	24	ε	ε	VERB
ejpam-6089	81	25	♭	♭	PROPN
ejpam-6089	81	26	,δ	,δ	PUNCT
ejpam-6089	81	27	,	,	PUNCT
ejpam-6089	81	28	b	b	NOUN
ejpam-6089	81	29	,	,	PUNCT
ejpam-6089	81	30	s	s	NOUN
ejpam-6089	81	31	,	,	PUNCT
ejpam-6089	81	32	lℑ1+,ℵ,℘,τυ	lℑ1+,ℵ,℘,τυ	NOUN
ejpam-6089	81	33	,	,	PUNCT
ejpam-6089	81	34	ε	ε	PROPN
ejpam-6089	81	35	♭	♭	PROPN
ejpam-6089	81	36	,δ	,δ	PUNCT
ejpam-6089	81	37	,	,	PUNCT
ejpam-6089	81	38	b	b	NOUN
ejpam-6089	81	39	,	,	PUNCT
ejpam-6089	81	40	s	s	NOUN
ejpam-6089	81	41	,	,	PUNCT
ejpam-6089	81	42	lℑ2−,ℵ,℘,τυ	lℑ2−,ℵ,℘,τυ	NOUN
ejpam-6089	81	43	given	give	VERB
ejpam-6089	81	44	as	as	ADP
ejpam-6089	81	45	ε	ε	PROPN
ejpam-6089	81	46	♭	♭	PROPN
ejpam-6089	81	47	,δ	,δ	PUNCT
ejpam-6089	81	48	,	,	PUNCT
ejpam-6089	81	49	b	b	NOUN
ejpam-6089	81	50	,	,	PUNCT
ejpam-6089	81	51	s	s	X
ejpam-6089	81	52	,	,	PUNCT
ejpam-6089	81	53	lℑ1+,ℵ,℘,τυ(c	lℑ1+,ℵ,℘,τυ(c	PROPN
ejpam-6089	81	54	;	;	PUNCT
ejpam-6089	81	55	g	g	NOUN
ejpam-6089	81	56	)	)	PUNCT
ejpam-6089	81	57	=	=	SYM
ejpam-6089	81	58	∫	∫	PROPN
ejpam-6089	81	59	c	c	PROPN
ejpam-6089	81	60	ℑ1	ℑ1	PROPN
ejpam-6089	81	61	(	(	PUNCT
ejpam-6089	81	62	c−	c−	X
ejpam-6089	81	63	ψ)℘−1eδ	ψ)℘−1eδ	NOUN
ejpam-6089	81	64	,	,	PUNCT
ejpam-6089	81	65	b	b	NOUN
ejpam-6089	81	66	,	,	PUNCT
ejpam-6089	81	67	s	s	NOUN
ejpam-6089	81	68	,	,	PUNCT
ejpam-6089	81	69	lℵ,℘,τ	lℵ,℘,τ	NOUN
ejpam-6089	81	70	(	(	PUNCT
ejpam-6089	81	71	♭	♭	PROPN
ejpam-6089	81	72	(	(	PUNCT
ejpam-6089	81	73	c−	c−	NOUN
ejpam-6089	81	74	ψ)ℵ	ψ)ℵ	NOUN
ejpam-6089	81	75	;	;	PUNCT
ejpam-6089	81	76	g	g	NOUN
ejpam-6089	81	77	)	)	PUNCT
ejpam-6089	81	78	υ(ψ)dψ	υ(ψ)dψ	PROPN
ejpam-6089	81	79	,	,	PUNCT
ejpam-6089	81	80	(	(	PUNCT
ejpam-6089	81	81	10	10	NUM
ejpam-6089	81	82	)	)	PUNCT
ejpam-6089	81	83	and	and	CCONJ
ejpam-6089	81	84	ε	ε	PROPN
ejpam-6089	81	85	♭	♭	PROPN
ejpam-6089	81	86	,δ	,δ	PUNCT
ejpam-6089	81	87	,	,	PUNCT
ejpam-6089	81	88	b	b	NOUN
ejpam-6089	81	89	,	,	PUNCT
ejpam-6089	81	90	s	s	NOUN
ejpam-6089	81	91	,	,	PUNCT
ejpam-6089	81	92	lℑ2−,ℵ,℘,τυ(c	lℑ2−,ℵ,℘,τυ(c	NOUN
ejpam-6089	81	93	;	;	PUNCT
ejpam-6089	81	94	g	g	NOUN
ejpam-6089	81	95	)	)	PUNCT
ejpam-6089	81	96	=	=	SYM
ejpam-6089	81	97	∫	∫	PROPN
ejpam-6089	81	98	ℑ2	ℑ2	PROPN
ejpam-6089	81	99	c	c	PROPN
ejpam-6089	81	100	(	(	PUNCT
ejpam-6089	81	101	ψ	ψ	X
ejpam-6089	81	102	−	−	PROPN
ejpam-6089	81	103	c)℘−1eδ	c)℘−1eδ	NOUN
ejpam-6089	81	104	,	,	PUNCT
ejpam-6089	81	105	b	b	PROPN
ejpam-6089	81	106	,	,	PUNCT
ejpam-6089	81	107	s	s	NOUN
ejpam-6089	81	108	,	,	PUNCT
ejpam-6089	81	109	lℵ,℘,τ	lℵ,℘,τ	NOUN
ejpam-6089	81	110	(	(	PUNCT
ejpam-6089	81	111	♭	♭	PROPN
ejpam-6089	81	112	(	(	PUNCT
ejpam-6089	81	113	ψ	ψ	X
ejpam-6089	81	114	−	−	NOUN
ejpam-6089	81	115	c)ℵ	c)ℵ	ADJ
ejpam-6089	81	116	;	;	PUNCT
ejpam-6089	81	117	g	g	NOUN
ejpam-6089	81	118	)	)	PUNCT
ejpam-6089	81	119	υ(ψ)dψ	υ(ψ)dψ	NOUN
ejpam-6089	81	120	.	.	PUNCT
ejpam-6089	82	1	(	(	PUNCT
ejpam-6089	82	2	11	11	NUM
ejpam-6089	82	3	)	)	PUNCT
ejpam-6089	82	4	to	to	PART
ejpam-6089	82	5	derive	derive	VERB
ejpam-6089	82	6	the	the	DET
ejpam-6089	82	7	main	main	ADJ
ejpam-6089	82	8	results	result	NOUN
ejpam-6089	82	9	,	,	PUNCT
ejpam-6089	82	10	we	we	PRON
ejpam-6089	82	11	relied	rely	VERB
ejpam-6089	82	12	on	on	ADP
ejpam-6089	82	13	theorems	theorem	NOUN
ejpam-6089	82	14	and	and	CCONJ
ejpam-6089	82	15	lemmas	lemma	NOUN
ejpam-6089	82	16	provided	provide	VERB
ejpam-6089	82	17	in	in	ADP
ejpam-6089	82	18	references	reference	NOUN
ejpam-6089	82	19	[	[	X
ejpam-6089	82	20	35	35	NUM
ejpam-6089	82	21	]	]	PUNCT
ejpam-6089	82	22	,	,	PUNCT
ejpam-6089	82	23	[	[	X
ejpam-6089	82	24	36	36	NUM
ejpam-6089	82	25	]	]	PUNCT
ejpam-6089	82	26	and	and	CCONJ
ejpam-6089	82	27	[	[	X
ejpam-6089	82	28	37	37	NUM
ejpam-6089	82	29	]	]	PUNCT
ejpam-6089	82	30	.	.	PUNCT
ejpam-6089	83	1	theorem	theorem	NOUN
ejpam-6089	83	2	1	1	NUM
ejpam-6089	83	3	.	.	X
ejpam-6089	84	1	for	for	ADP
ejpam-6089	84	2	an	an	DET
ejpam-6089	84	3	l1	l1	PROPN
ejpam-6089	84	4	continuous	continuous	ADJ
ejpam-6089	84	5	convex	convex	NOUN
ejpam-6089	84	6	function	function	NOUN
ejpam-6089	84	7	υ	υ	NOUN
ejpam-6089	84	8	:	:	PUNCT
ejpam-6089	84	9	[	[	X
ejpam-6089	84	10	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	84	11	]	]	PUNCT
ejpam-6089	84	12	→	→	SYM
ejpam-6089	84	13	ℜ	ℜ	PROPN
ejpam-6089	84	14	,	,	PUNCT
ejpam-6089	84	15	with	with	ADP
ejpam-6089	84	16	ℑ2	ℑ2	PROPN
ejpam-6089	84	17	>	>	SYM
ejpam-6089	84	18	ℑ1	ℑ1	PROPN
ejpam-6089	84	19	,	,	PUNCT
ejpam-6089	84	20	the	the	DET
ejpam-6089	84	21	standard	standard	ADJ
ejpam-6089	84	22	(	(	PUNCT
ejpam-6089	84	23	h−h	h−h	NOUN
ejpam-6089	84	24	)	)	PUNCT
ejpam-6089	84	25	inequality	inequality	NOUN
ejpam-6089	84	26	is	be	AUX
ejpam-6089	84	27	stated	state	VERB
ejpam-6089	84	28	as	as	ADP
ejpam-6089	84	29	υ	υ	PROPN
ejpam-6089	84	30	(	(	PUNCT
ejpam-6089	84	31	ℑ1	ℑ1	PROPN
ejpam-6089	84	32	+	+	CCONJ
ejpam-6089	84	33	ℑ2	ℑ2	PROPN
ejpam-6089	84	34	2	2	NUM
ejpam-6089	84	35	)	)	PUNCT
ejpam-6089	84	36	≤	≤	NUM
ejpam-6089	84	37	1	1	NUM
ejpam-6089	84	38	ℑ2	ℑ2	NOUN
ejpam-6089	84	39	−ℑ1	−ℑ1	PROPN
ejpam-6089	84	40	∫	∫	PROPN
ejpam-6089	84	41	ℑ2	ℑ2	PROPN
ejpam-6089	84	42	ℑ1	ℑ1	PROPN
ejpam-6089	84	43	υ(c)dc	υ(c)dc	PROPN
ejpam-6089	84	44	≤	≤	NUM
ejpam-6089	84	45	(	(	PUNCT
ejpam-6089	84	46	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	84	47	)	)	PUNCT
ejpam-6089	84	48	+	+	CCONJ
ejpam-6089	84	49	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	84	50	)	)	PUNCT
ejpam-6089	84	51	2	2	NUM
ejpam-6089	84	52	)	)	PUNCT
ejpam-6089	84	53	.	.	PUNCT
ejpam-6089	85	1	s.	s.	PROPN
ejpam-6089	85	2	naheed	nahee	VERB
ejpam-6089	85	3	et	et	PROPN
ejpam-6089	85	4	al	al	PROPN
ejpam-6089	85	5	.	.	PUNCT
ejpam-6089	85	6	/	/	SYM
ejpam-6089	85	7	eur	eur	PROPN
ejpam-6089	85	8	.	.	PUNCT
ejpam-6089	86	1	j.	j.	PROPN
ejpam-6089	86	2	pure	pure	PROPN
ejpam-6089	86	3	appl	appl	PROPN
ejpam-6089	86	4	.	.	PROPN
ejpam-6089	86	5	math	math	PROPN
ejpam-6089	86	6	,	,	PUNCT
ejpam-6089	86	7	18	18	NUM
ejpam-6089	86	8	(	(	PUNCT
ejpam-6089	86	9	2	2	NUM
ejpam-6089	86	10	)	)	PUNCT
ejpam-6089	86	11	(	(	PUNCT
ejpam-6089	86	12	2025	2025	NUM
ejpam-6089	86	13	)	)	PUNCT
ejpam-6089	86	14	,	,	PUNCT
ejpam-6089	86	15	6089	6089	NUM
ejpam-6089	86	16	5	5	NUM
ejpam-6089	86	17	of	of	ADP
ejpam-6089	86	18	34	34	NUM
ejpam-6089	86	19	theorem	theorem	NOUN
ejpam-6089	86	20	2	2	NUM
ejpam-6089	86	21	.	.	X
ejpam-6089	87	1	for	for	ADP
ejpam-6089	87	2	υ	υ	NOUN
ejpam-6089	87	3	:	:	PUNCT
ejpam-6089	87	4	[	[	X
ejpam-6089	87	5	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	87	6	]	]	X
ejpam-6089	87	7	→	→	PUNCT
ejpam-6089	87	8	ℜ	ℜ	PROPN
ejpam-6089	87	9	be	be	AUX
ejpam-6089	87	10	a	a	DET
ejpam-6089	87	11	positive	positive	ADJ
ejpam-6089	87	12	convex	convex	NOUN
ejpam-6089	87	13	function	function	NOUN
ejpam-6089	87	14	with	with	ADP
ejpam-6089	87	15	0	0	NUM
ejpam-6089	87	16	≤	≤	NUM
ejpam-6089	87	17	ℑ1	ℑ1	NOUN
ejpam-6089	87	18	<	<	X
ejpam-6089	87	19	ℑ2	ℑ2	PROPN
ejpam-6089	87	20	and	and	CCONJ
ejpam-6089	87	21	υ	υ	PRON
ejpam-6089	87	22	∈	∈	PROPN
ejpam-6089	88	1	l1[ℑ1,ℑ2	l1[ℑ1,ℑ2	PROPN
ejpam-6089	88	2	]	]	PUNCT
ejpam-6089	88	3	,	,	PUNCT
ejpam-6089	88	4	then	then	ADV
ejpam-6089	88	5	we	we	PRON
ejpam-6089	88	6	have	have	VERB
ejpam-6089	88	7	υ	υ	NOUN
ejpam-6089	88	8	(	(	PUNCT
ejpam-6089	88	9	ℑ1	ℑ1	PROPN
ejpam-6089	88	10	+	+	CCONJ
ejpam-6089	88	11	ℑ2	ℑ2	PROPN
ejpam-6089	88	12	2	2	NUM
ejpam-6089	88	13	)	)	PUNCT
ejpam-6089	88	14	≤	≤	NOUN
ejpam-6089	88	15	γ(α∗	γ(α∗	X
ejpam-6089	89	1	+	+	CCONJ
ejpam-6089	89	2	1	1	NUM
ejpam-6089	89	3	)	)	PUNCT
ejpam-6089	89	4	2(ℑ2	2(ℑ2	NUM
ejpam-6089	90	1	−ℑ1)α	−ℑ1)α	ADP
ejpam-6089	90	2	∗	∗	NOUN
ejpam-6089	90	3	(	(	PUNCT
ejpam-6089	90	4	r−liα	r−liα	NOUN
ejpam-6089	90	5	∗	∗	NOUN
ejpam-6089	90	6	ℑ1+υ(ℑ2	ℑ1+υ(ℑ2	NOUN
ejpam-6089	90	7	)	)	PUNCT
ejpam-6089	90	8	+	+	NUM
ejpam-6089	90	9	r−liα	r−liα	NOUN
ejpam-6089	90	10	∗	∗	NOUN
ejpam-6089	90	11	ℑ2−υ(ℑ1	ℑ2−υ(ℑ1	NOUN
ejpam-6089	90	12	)	)	PUNCT
ejpam-6089	90	13	)	)	PUNCT
ejpam-6089	90	14	≤	≤	NOUN
ejpam-6089	90	15	(	(	PUNCT
ejpam-6089	90	16	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	90	17	)	)	PUNCT
ejpam-6089	90	18	+	+	CCONJ
ejpam-6089	90	19	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	90	20	)	)	PUNCT
ejpam-6089	90	21	2	2	NUM
ejpam-6089	90	22	)	)	PUNCT
ejpam-6089	90	23	.	.	PUNCT
ejpam-6089	91	1	theorem	theorem	VERB
ejpam-6089	91	2	3	3	NUM
ejpam-6089	91	3	.	.	PUNCT
ejpam-6089	92	1	if	if	SCONJ
ejpam-6089	92	2	υ	υ	PRON
ejpam-6089	92	3	:	:	PUNCT
ejpam-6089	92	4	[	[	X
ejpam-6089	92	5	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	92	6	]	]	PUNCT
ejpam-6089	92	7	→	→	SYM
ejpam-6089	92	8	ℜ	ℜ	PROPN
ejpam-6089	92	9	is	be	AUX
ejpam-6089	92	10	l1	l1	PROPN
ejpam-6089	92	11	and	and	CCONJ
ejpam-6089	92	12	convex	convex	NOUN
ejpam-6089	92	13	,	,	PUNCT
ejpam-6089	92	14	and	and	CCONJ
ejpam-6089	92	15	α∗	α∗	VERB
ejpam-6089	92	16	∈	∈	PROPN
ejpam-6089	92	17	(	(	PUNCT
ejpam-6089	92	18	0	0	NUM
ejpam-6089	92	19	,	,	PUNCT
ejpam-6089	92	20	1	1	NUM
ejpam-6089	92	21	)	)	PUNCT
ejpam-6089	92	22	,	,	PUNCT
ejpam-6089	92	23	then	then	ADV
ejpam-6089	92	24	we	we	PRON
ejpam-6089	92	25	have	have	VERB
ejpam-6089	92	26	the	the	DET
ejpam-6089	92	27	following	follow	VERB
ejpam-6089	92	28	inequality	inequality	NOUN
ejpam-6089	92	29	υ	υ	PROPN
ejpam-6089	92	30	(	(	PUNCT
ejpam-6089	92	31	ℑ1	ℑ1	PROPN
ejpam-6089	92	32	+	+	CCONJ
ejpam-6089	92	33	ℑ2	ℑ2	PROPN
ejpam-6089	92	34	2	2	NUM
ejpam-6089	92	35	)	)	PUNCT
ejpam-6089	92	36	≤	≤	NOUN
ejpam-6089	92	37	b(α∗)γ(α∗	b(α∗)γ(α∗	NOUN
ejpam-6089	92	38	)	)	PUNCT
ejpam-6089	92	39	2	2	NUM
ejpam-6089	92	40	(	(	PUNCT
ejpam-6089	92	41	(	(	PUNCT
ejpam-6089	92	42	ℑ2	ℑ2	PROPN
ejpam-6089	92	43	−ℑ1)α	−ℑ1)α	ADP
ejpam-6089	92	44	∗	∗	NOUN
ejpam-6089	92	45	+	+	CCONJ
ejpam-6089	92	46	(	(	PUNCT
ejpam-6089	92	47	1−	1−	NUM
ejpam-6089	92	48	α∗)γ(α∗	α∗)γ(α∗	NUM
ejpam-6089	92	49	)	)	PUNCT
ejpam-6089	92	50	)	)	PUNCT
ejpam-6089	92	51	×	×	NOUN
ejpam-6089	92	52	(	(	PUNCT
ejpam-6089	92	53	a−biα	a−biα	NOUN
ejpam-6089	92	54	∗	∗	NOUN
ejpam-6089	92	55	ℑ1+υ(ℑ2	ℑ1+υ(ℑ2	NOUN
ejpam-6089	92	56	)	)	PUNCT
ejpam-6089	92	57	+	+	NUM
ejpam-6089	92	58	a−biα	a−biα	ADJ
ejpam-6089	92	59	∗	∗	NOUN
ejpam-6089	92	60	ℑ2−υ(ℑ1	ℑ2−υ(ℑ1	NOUN
ejpam-6089	92	61	)	)	PUNCT
ejpam-6089	92	62	)	)	PUNCT
ejpam-6089	92	63	≤	≤	NOUN
ejpam-6089	92	64	(	(	PUNCT
ejpam-6089	92	65	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	92	66	)	)	PUNCT
ejpam-6089	93	1	+	+	CCONJ
ejpam-6089	93	2	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	93	3	)	)	PUNCT
ejpam-6089	93	4	2	2	NUM
ejpam-6089	93	5	)	)	PUNCT
ejpam-6089	93	6	.	.	PUNCT
ejpam-6089	94	1	theorem	theorem	ADJ
ejpam-6089	94	2	4	4	NUM
ejpam-6089	94	3	.	.	X
ejpam-6089	95	1	for	for	ADP
ejpam-6089	95	2	υ	υ	NOUN
ejpam-6089	95	3	:	:	PUNCT
ejpam-6089	95	4	[	[	X
ejpam-6089	95	5	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	95	6	]	]	X
ejpam-6089	95	7	→	→	PUNCT
ejpam-6089	95	8	ℜ	ℜ	PROPN
ejpam-6089	95	9	be	be	AUX
ejpam-6089	95	10	a	a	DET
ejpam-6089	95	11	positive	positive	ADJ
ejpam-6089	95	12	function	function	NOUN
ejpam-6089	95	13	with	with	ADP
ejpam-6089	95	14	0	0	NUM
ejpam-6089	95	15	≤	≤	NUM
ejpam-6089	95	16	ℑ1	ℑ1	NOUN
ejpam-6089	95	17	<	<	X
ejpam-6089	95	18	ℑ2	ℑ2	PROPN
ejpam-6089	95	19	and	and	CCONJ
ejpam-6089	95	20	υ	υ	PRON
ejpam-6089	95	21	∈	∈	PROPN
ejpam-6089	96	1	l1[ℑ1,ℑ2	l1[ℑ1,ℑ2	AUX
ejpam-6089	96	2	]	]	PUNCT
ejpam-6089	96	3	be	be	AUX
ejpam-6089	96	4	convex	convex	ADJ
ejpam-6089	96	5	function	function	NOUN
ejpam-6089	96	6	,	,	PUNCT
ejpam-6089	96	7	then	then	ADV
ejpam-6089	96	8	we	we	PRON
ejpam-6089	96	9	have	have	VERB
ejpam-6089	96	10	υ	υ	NOUN
ejpam-6089	96	11	(	(	PUNCT
ejpam-6089	96	12	ℑ1	ℑ1	PROPN
ejpam-6089	96	13	+	+	CCONJ
ejpam-6089	96	14	ℑ2	ℑ2	PROPN
ejpam-6089	96	15	2	2	NUM
ejpam-6089	96	16	)	)	PUNCT
ejpam-6089	96	17	≤	≤	NOUN
ejpam-6089	96	18	2α	2α	NOUN
ejpam-6089	96	19	∗−1γ(α∗	∗−1γ(α∗	NOUN
ejpam-6089	97	1	+	+	CCONJ
ejpam-6089	97	2	1	1	X
ejpam-6089	97	3	)	)	PUNCT
ejpam-6089	97	4	(	(	PUNCT
ejpam-6089	97	5	ℑ2	ℑ2	PROPN
ejpam-6089	97	6	−ℑ1)α	−ℑ1)α	ADP
ejpam-6089	97	7	∗	∗	NOUN
ejpam-6089	97	8	(	(	PUNCT
ejpam-6089	97	9	r−liα	r−liα	NOUN
ejpam-6089	97	10	∗	∗	NOUN
ejpam-6089	97	11	(	(	PUNCT
ejpam-6089	97	12	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	97	13	2	2	NUM
ejpam-6089	97	14	)	)	PUNCT
ejpam-6089	97	15	+	+	CCONJ
ejpam-6089	97	16	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	97	17	)	)	PUNCT
ejpam-6089	97	18	+	+	NUM
ejpam-6089	97	19	r−liα	r−liα	NOUN
ejpam-6089	97	20	∗	∗	NOUN
ejpam-6089	97	21	(	(	PUNCT
ejpam-6089	97	22	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	97	23	2	2	NUM
ejpam-6089	97	24	)	)	PUNCT
ejpam-6089	97	25	−	−	PROPN
ejpam-6089	97	26	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	97	27	)	)	PUNCT
ejpam-6089	97	28	)	)	PUNCT
ejpam-6089	97	29	≤	≤	NOUN
ejpam-6089	97	30	(	(	PUNCT
ejpam-6089	97	31	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	97	32	)	)	PUNCT
ejpam-6089	97	33	+	+	CCONJ
ejpam-6089	97	34	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	97	35	)	)	PUNCT
ejpam-6089	97	36	2	2	NUM
ejpam-6089	97	37	)	)	PUNCT
ejpam-6089	97	38	.	.	PUNCT
ejpam-6089	98	1	lemma	lemma	PROPN
ejpam-6089	98	2	1	1	NUM
ejpam-6089	98	3	.	.	PUNCT
ejpam-6089	99	1	for	for	ADP
ejpam-6089	99	2	υ	υ	NOUN
ejpam-6089	99	3	:	:	PUNCT
ejpam-6089	99	4	[	[	X
ejpam-6089	99	5	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	99	6	]	]	PUNCT
ejpam-6089	99	7	→	→	PUNCT
ejpam-6089	99	8	ℜ	ℜ	PROPN
ejpam-6089	99	9	in	in	ADP
ejpam-6089	99	10	l1	l1	PROPN
ejpam-6089	99	11	and	and	CCONJ
ejpam-6089	99	12	have	have	VERB
ejpam-6089	99	13	a	a	DET
ejpam-6089	99	14	differentiable	differentiable	ADJ
ejpam-6089	99	15	mapping	mapping	NOUN
ejpam-6089	99	16	on	on	ADP
ejpam-6089	99	17	(	(	PUNCT
ejpam-6089	99	18	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	99	19	)	)	PUNCT
ejpam-6089	99	20	with	with	ADP
ejpam-6089	99	21	ℑ1	ℑ1	NOUN
ejpam-6089	99	22	<	<	X
ejpam-6089	99	23	ℑ2	ℑ2	PROPN
ejpam-6089	99	24	and	and	CCONJ
ejpam-6089	99	25	if	if	SCONJ
ejpam-6089	99	26	υ′	υ′	DET
ejpam-6089	99	27	∈	∈	NOUN
ejpam-6089	99	28	l1[ℑ1,ℑ2	l1[ℑ1,ℑ2	NOUN
ejpam-6089	99	29	]	]	PUNCT
ejpam-6089	99	30	with	with	ADP
ejpam-6089	99	31	α	α	PROPN
ejpam-6089	99	32	∗	∗	NOUN
ejpam-6089	99	33	>	>	X
ejpam-6089	99	34	0	0	PUNCT
ejpam-6089	99	35	then	then	ADV
ejpam-6089	99	36	the	the	DET
ejpam-6089	99	37	following	follow	VERB
ejpam-6089	99	38	equality	equality	NOUN
ejpam-6089	99	39	for	for	ADP
ejpam-6089	99	40	fractional	fractional	ADJ
ejpam-6089	99	41	integrals	integral	NOUN
ejpam-6089	99	42	holds	hold	VERB
ejpam-6089	99	43	(	(	PUNCT
ejpam-6089	99	44	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	99	45	)	)	PUNCT
ejpam-6089	100	1	+	+	CCONJ
ejpam-6089	100	2	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	100	3	)	)	PUNCT
ejpam-6089	100	4	2	2	NUM
ejpam-6089	100	5	)	)	PUNCT
ejpam-6089	101	1	−	−	NOUN
ejpam-6089	102	1	γ(α∗	γ(α∗	NOUN
ejpam-6089	102	2	+	+	CCONJ
ejpam-6089	102	3	1	1	NUM
ejpam-6089	102	4	)	)	PUNCT
ejpam-6089	102	5	2(ℑ2	2(ℑ2	NUM
ejpam-6089	103	1	−ℑ1)α	−ℑ1)α	ADP
ejpam-6089	103	2	∗	∗	NOUN
ejpam-6089	103	3	(	(	PUNCT
ejpam-6089	103	4	r−liα	r−liα	NOUN
ejpam-6089	103	5	∗	∗	NOUN
ejpam-6089	103	6	ℑ1+υ(ℑ2	ℑ1+υ(ℑ2	NOUN
ejpam-6089	103	7	)	)	PUNCT
ejpam-6089	103	8	+	+	NUM
ejpam-6089	103	9	r−liα	r−liα	NOUN
ejpam-6089	103	10	∗	∗	NOUN
ejpam-6089	103	11	ℑ2−υ(ℑ1	ℑ2−υ(ℑ1	NOUN
ejpam-6089	103	12	)	)	PUNCT
ejpam-6089	103	13	)	)	PUNCT
ejpam-6089	104	1	=	=	PUNCT
ejpam-6089	104	2	ℑ2	ℑ2	PROPN
ejpam-6089	104	3	−ℑ1	−ℑ1	NOUN
ejpam-6089	104	4	2	2	NUM
ejpam-6089	104	5	∫	∫	NOUN
ejpam-6089	104	6	1	1	NUM
ejpam-6089	104	7	0	0	NUM
ejpam-6089	104	8	(	(	PUNCT
ejpam-6089	104	9	(	(	PUNCT
ejpam-6089	104	10	1−	1−	NUM
ejpam-6089	104	11	t)α	t)α	NOUN
ejpam-6089	104	12	∗	∗	NOUN
ejpam-6089	104	13	−	−	PROPN
ejpam-6089	104	14	tα	tα	PROPN
ejpam-6089	104	15	∗	∗	NOUN
ejpam-6089	104	16	)	)	PUNCT
ejpam-6089	104	17	υ′(tℑ1	υ′(tℑ1	NOUN
ejpam-6089	104	18	+	+	CCONJ
ejpam-6089	104	19	(	(	PUNCT
ejpam-6089	104	20	1−	1−	NUM
ejpam-6089	104	21	t)ℑ2)dt	t)ℑ2)dt	PROPN
ejpam-6089	104	22	.	.	PUNCT
ejpam-6089	105	1	lemma	lemma	PROPN
ejpam-6089	105	2	2	2	NUM
ejpam-6089	105	3	.	.	X
ejpam-6089	106	1	for	for	ADP
ejpam-6089	106	2	υ	υ	NOUN
ejpam-6089	106	3	:	:	PUNCT
ejpam-6089	106	4	[	[	X
ejpam-6089	106	5	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	106	6	]	]	PUNCT
ejpam-6089	106	7	→	→	PUNCT
ejpam-6089	106	8	ℜ	ℜ	PROPN
ejpam-6089	106	9	in	in	ADP
ejpam-6089	106	10	l1	l1	PROPN
ejpam-6089	106	11	be	be	AUX
ejpam-6089	106	12	a	a	DET
ejpam-6089	106	13	differentiable	differentiable	ADJ
ejpam-6089	106	14	mapping	mapping	NOUN
ejpam-6089	106	15	on	on	ADP
ejpam-6089	106	16	(	(	PUNCT
ejpam-6089	106	17	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	106	18	)	)	PUNCT
ejpam-6089	106	19	with	with	ADP
ejpam-6089	106	20	ℑ1	ℑ1	NOUN
ejpam-6089	106	21	<	<	X
ejpam-6089	106	22	ℑ2	ℑ2	PROPN
ejpam-6089	106	23	and	and	CCONJ
ejpam-6089	106	24	if	if	SCONJ
ejpam-6089	106	25	υ′	υ′	DET
ejpam-6089	106	26	∈	∈	NOUN
ejpam-6089	106	27	l1[ℑ1,ℑ2	l1[ℑ1,ℑ2	NOUN
ejpam-6089	106	28	]	]	PUNCT
ejpam-6089	106	29	with	with	ADP
ejpam-6089	106	30	α	α	PROPN
ejpam-6089	106	31	∗	∗	NOUN
ejpam-6089	106	32	>	>	X
ejpam-6089	106	33	0	0	PUNCT
ejpam-6089	107	1	then	then	ADV
ejpam-6089	107	2	the	the	DET
ejpam-6089	107	3	following	follow	VERB
ejpam-6089	107	4	equality	equality	NOUN
ejpam-6089	107	5	holds	hold	VERB
ejpam-6089	107	6	2α	2α	NOUN
ejpam-6089	107	7	∗−1γ(α∗	∗−1γ(α∗	NOUN
ejpam-6089	108	1	+	+	CCONJ
ejpam-6089	108	2	1	1	X
ejpam-6089	108	3	)	)	PUNCT
ejpam-6089	108	4	(	(	PUNCT
ejpam-6089	108	5	ℑ2	ℑ2	PROPN
ejpam-6089	108	6	−ℑ1)α	−ℑ1)α	ADP
ejpam-6089	108	7	∗	∗	NOUN
ejpam-6089	108	8	(	(	PUNCT
ejpam-6089	108	9	r−liα	r−liα	NOUN
ejpam-6089	108	10	∗	∗	NOUN
ejpam-6089	108	11	(	(	PUNCT
ejpam-6089	108	12	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	108	13	2	2	NUM
ejpam-6089	108	14	)	)	PUNCT
ejpam-6089	108	15	+	+	CCONJ
ejpam-6089	108	16	υ(c	υ(c	X
ejpam-6089	108	17	)	)	PUNCT
ejpam-6089	109	1	+	+	CCONJ
ejpam-6089	109	2	r−liα	r−liα	NOUN
ejpam-6089	109	3	∗	∗	NOUN
ejpam-6089	109	4	(	(	PUNCT
ejpam-6089	109	5	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	109	6	2	2	NUM
ejpam-6089	109	7	)	)	PUNCT
ejpam-6089	109	8	−	−	PROPN
ejpam-6089	109	9	υ(y	υ(y	PROPN
ejpam-6089	109	10	)	)	PUNCT
ejpam-6089	109	11	)	)	PUNCT
ejpam-6089	109	12	−υ	−υ	NOUN
ejpam-6089	109	13	(	(	PUNCT
ejpam-6089	109	14	ℑ1	ℑ1	PROPN
ejpam-6089	109	15	+	+	CCONJ
ejpam-6089	109	16	ℑ2	ℑ2	PROPN
ejpam-6089	109	17	2	2	NUM
ejpam-6089	109	18	)	)	PUNCT
ejpam-6089	109	19	=	=	VERB
ejpam-6089	110	1	ℑ2	ℑ2	PROPN
ejpam-6089	110	2	−ℑ1	−ℑ1	NOUN
ejpam-6089	110	3	4	4	NUM
ejpam-6089	110	4	∫	∫	NOUN
ejpam-6089	110	5	1	1	NUM
ejpam-6089	110	6	0	0	NUM
ejpam-6089	110	7	tα	tα	PROPN
ejpam-6089	110	8	∗	∗	NOUN
ejpam-6089	110	9	(	(	PUNCT
ejpam-6089	110	10	υ′	υ′	X
ejpam-6089	110	11	(	(	PUNCT
ejpam-6089	110	12	t	t	PROPN
ejpam-6089	110	13	2	2	NUM
ejpam-6089	110	14	ℑ1	ℑ1	NOUN
ejpam-6089	110	15	+	+	CCONJ
ejpam-6089	110	16	2−	2−	NUM
ejpam-6089	110	17	t	t	NOUN
ejpam-6089	110	18	2	2	NUM
ejpam-6089	110	19	ℑ2	ℑ2	ADJ
ejpam-6089	110	20	)	)	PUNCT
ejpam-6089	110	21	−υ′	−υ′	NOUN
ejpam-6089	110	22	(	(	PUNCT
ejpam-6089	110	23	2−	2−	NUM
ejpam-6089	110	24	t	t	NOUN
ejpam-6089	110	25	2	2	NUM
ejpam-6089	110	26	ℑ1	ℑ1	NOUN
ejpam-6089	110	27	+	+	CCONJ
ejpam-6089	110	28	t	t	PROPN
ejpam-6089	110	29	2	2	NUM
ejpam-6089	110	30	ℑ2	ℑ2	PROPN
ejpam-6089	110	31	)	)	PUNCT
ejpam-6089	110	32	)	)	PUNCT
ejpam-6089	111	1	dt	dt	PROPN
ejpam-6089	111	2	.	.	PUNCT
ejpam-6089	112	1	s.	s.	PROPN
ejpam-6089	112	2	naheed	nahee	VERB
ejpam-6089	112	3	et	et	PROPN
ejpam-6089	112	4	al	al	PROPN
ejpam-6089	112	5	.	.	PUNCT
ejpam-6089	112	6	/	/	SYM
ejpam-6089	112	7	eur	eur	PROPN
ejpam-6089	112	8	.	.	PUNCT
ejpam-6089	113	1	j.	j.	PROPN
ejpam-6089	113	2	pure	pure	PROPN
ejpam-6089	113	3	appl	appl	PROPN
ejpam-6089	113	4	.	.	PROPN
ejpam-6089	113	5	math	math	PROPN
ejpam-6089	113	6	,	,	PUNCT
ejpam-6089	113	7	18	18	NUM
ejpam-6089	113	8	(	(	PUNCT
ejpam-6089	113	9	2	2	NUM
ejpam-6089	113	10	)	)	PUNCT
ejpam-6089	113	11	(	(	PUNCT
ejpam-6089	113	12	2025	2025	NUM
ejpam-6089	113	13	)	)	PUNCT
ejpam-6089	113	14	,	,	PUNCT
ejpam-6089	113	15	6089	6089	NUM
ejpam-6089	113	16	6	6	NUM
ejpam-6089	113	17	of	of	ADP
ejpam-6089	113	18	34	34	NUM
ejpam-6089	113	19	2	2	NUM
ejpam-6089	113	20	.	.	PUNCT
ejpam-6089	113	21	generalized	generalize	VERB
ejpam-6089	113	22	fractional	fractional	ADJ
ejpam-6089	113	23	integral	integral	ADJ
ejpam-6089	113	24	operators	operator	NOUN
ejpam-6089	113	25	and	and	CCONJ
ejpam-6089	113	26	hermite	hermite	PROPN
ejpam-6089	113	27	-	-	PUNCT
ejpam-6089	113	28	hadamard	hadamard	ADJ
ejpam-6089	113	29	inequality	inequality	NOUN
ejpam-6089	113	30	in	in	ADP
ejpam-6089	113	31	the	the	DET
ejpam-6089	113	32	fractional	fractional	ADJ
ejpam-6089	113	33	framework	framework	NOUN
ejpam-6089	113	34	in	in	ADP
ejpam-6089	113	35	this	this	DET
ejpam-6089	113	36	section	section	NOUN
ejpam-6089	113	37	,	,	PUNCT
ejpam-6089	113	38	we	we	PRON
ejpam-6089	113	39	examine	examine	VERB
ejpam-6089	113	40	inequalities	inequality	NOUN
ejpam-6089	113	41	involving	involve	VERB
ejpam-6089	113	42	fractional	fractional	ADJ
ejpam-6089	113	43	integral	integral	ADJ
ejpam-6089	113	44	of	of	ADP
ejpam-6089	113	45	the	the	DET
ejpam-6089	113	46	type	type	NOUN
ejpam-6089	113	47	(	(	PUNCT
ejpam-6089	113	48	ℑ1+,ℑ2−	ℑ1+,ℑ2−	PROPN
ejpam-6089	113	49	)	)	PUNCT
ejpam-6089	113	50	and	and	CCONJ
ejpam-6089	113	51	(	(	PUNCT
ejpam-6089	113	52	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	113	53	2	2	NUM
ejpam-6089	113	54	)	)	PUNCT
ejpam-6089	113	55	.	.	PUNCT
ejpam-6089	114	1	we	we	PRON
ejpam-6089	114	2	also	also	ADV
ejpam-6089	114	3	present	present	VERB
ejpam-6089	114	4	some	some	DET
ejpam-6089	114	5	examples	example	NOUN
ejpam-6089	114	6	and	and	CCONJ
ejpam-6089	114	7	their	their	PRON
ejpam-6089	114	8	graphical	graphical	ADJ
ejpam-6089	114	9	representations	representation	NOUN
ejpam-6089	114	10	to	to	PART
ejpam-6089	114	11	confirm	confirm	VERB
ejpam-6089	114	12	our	our	PRON
ejpam-6089	114	13	results	result	NOUN
ejpam-6089	114	14	.	.	PUNCT
ejpam-6089	115	1	2.1	2.1	NUM
ejpam-6089	115	2	.	.	PUNCT
ejpam-6089	115	3	inequalities	inequality	NOUN
ejpam-6089	115	4	involving	involve	VERB
ejpam-6089	115	5	fractional	fractional	ADJ
ejpam-6089	115	6	integral	integral	ADJ
ejpam-6089	115	7	of	of	ADP
ejpam-6089	115	8	the	the	DET
ejpam-6089	115	9	type	type	NOUN
ejpam-6089	115	10	(	(	PUNCT
ejpam-6089	115	11	ℑ1+,ℑ2−	ℑ1+,ℑ2−	PROPN
ejpam-6089	115	12	)	)	PUNCT
ejpam-6089	115	13	proposition	proposition	NOUN
ejpam-6089	115	14	1	1	NUM
ejpam-6089	115	15	.	.	PUNCT
ejpam-6089	116	1	if	if	SCONJ
ejpam-6089	116	2	♭	♭	PROPN
ejpam-6089	116	3	,	,	PUNCT
ejpam-6089	116	4	ℵ	ℵ	NOUN
ejpam-6089	116	5	,	,	PUNCT
ejpam-6089	116	6	℘	℘	PROPN
ejpam-6089	116	7	,	,	PUNCT
ejpam-6089	116	8	τ	τ	PROPN
ejpam-6089	116	9	,	,	PUNCT
ejpam-6089	116	10	δ	δ	PROPN
ejpam-6089	116	11	,	,	PUNCT
ejpam-6089	116	12	b	b	PROPN
ejpam-6089	116	13	∈	∈	PROPN
ejpam-6089	116	14	c	c	NOUN
ejpam-6089	116	15	with	with	ADP
ejpam-6089	116	16	ℜ(ℵ),ℜ(℘),ℜ(τ	ℜ(ℵ),ℜ(℘),ℜ(τ	PROPN
ejpam-6089	116	17	)	)	PUNCT
ejpam-6089	116	18	>	>	X
ejpam-6089	116	19	0	0	NUM
ejpam-6089	116	20	and	and	CCONJ
ejpam-6089	116	21	ℜ(b	ℜ(b	NOUN
ejpam-6089	116	22	)	)	PUNCT
ejpam-6089	116	23	>	>	X
ejpam-6089	117	1	ℜ(δ	ℜ(δ	X
ejpam-6089	117	2	)	)	PUNCT
ejpam-6089	117	3	>	>	X
ejpam-6089	117	4	0	0	PUNCT
ejpam-6089	118	1	and	and	CCONJ
ejpam-6089	118	2	let	let	VERB
ejpam-6089	118	3	g	g	PROPN
ejpam-6089	118	4	≥	≥	NOUN
ejpam-6089	118	5	0	0	NUM
ejpam-6089	118	6	,	,	PUNCT
ejpam-6089	118	7	l	l	NOUN
ejpam-6089	118	8	>	>	X
ejpam-6089	118	9	0	0	PUNCT
ejpam-6089	119	1	and	and	CCONJ
ejpam-6089	119	2	0	0	NUM
ejpam-6089	119	3	<	<	X
ejpam-6089	119	4	s	s	X
ejpam-6089	119	5	≤	≤	NUM
ejpam-6089	119	6	l+ℜ(ℵ	l+ℜ(ℵ	PROPN
ejpam-6089	119	7	)	)	PUNCT
ejpam-6089	119	8	.	.	PUNCT
ejpam-6089	120	1	for	for	ADP
ejpam-6089	120	2	a	a	DET
ejpam-6089	120	3	function	function	NOUN
ejpam-6089	120	4	υ	υ	X
ejpam-6089	120	5	∈	∈	PROPN
ejpam-6089	120	6	l1[ℑ1,ℑ2	l1[ℑ1,ℑ2	PROPN
ejpam-6089	120	7	]	]	PUNCT
ejpam-6089	120	8	and	and	CCONJ
ejpam-6089	120	9	c	c	NOUN
ejpam-6089	120	10	∈	∈	PROPN
ejpam-6089	120	11	[	[	X
ejpam-6089	120	12	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	120	13	]	]	PUNCT
ejpam-6089	120	14	,	,	PUNCT
ejpam-6089	120	15	then	then	ADV
ejpam-6089	120	16	the	the	DET
ejpam-6089	120	17	addition	addition	NOUN
ejpam-6089	120	18	of	of	ADP
ejpam-6089	120	19	left	left	ADJ
ejpam-6089	120	20	and	and	CCONJ
ejpam-6089	120	21	right	right	ADJ
ejpam-6089	120	22	sided	sided	ADJ
ejpam-6089	120	23	generalized	generalized	ADJ
ejpam-6089	120	24	fractional	fractional	ADJ
ejpam-6089	120	25	integral	integral	ADJ
ejpam-6089	120	26	operators	operator	NOUN
ejpam-6089	120	27	,	,	PUNCT
ejpam-6089	120	28	ε	ε	PROPN
ejpam-6089	120	29	♭	♭	PROPN
ejpam-6089	120	30	,δ	,δ	PUNCT
ejpam-6089	120	31	,	,	PUNCT
ejpam-6089	120	32	b	b	NOUN
ejpam-6089	120	33	,	,	PUNCT
ejpam-6089	120	34	s	s	NOUN
ejpam-6089	120	35	,	,	PUNCT
ejpam-6089	120	36	lℑ1+,ℵ,℘,τυ	lℑ1+,ℵ,℘,τυ	NOUN
ejpam-6089	120	37	,	,	PUNCT
ejpam-6089	120	38	ε	ε	PROPN
ejpam-6089	120	39	♭	♭	PROPN
ejpam-6089	120	40	,δ	,δ	PUNCT
ejpam-6089	120	41	,	,	PUNCT
ejpam-6089	120	42	b	b	NOUN
ejpam-6089	120	43	,	,	PUNCT
ejpam-6089	120	44	s	s	NOUN
ejpam-6089	120	45	,	,	PUNCT
ejpam-6089	120	46	lℑ2−,ℵ,℘,τυ	lℑ2−,ℵ,℘,τυ	NOUN
ejpam-6089	120	47	are	be	AUX
ejpam-6089	120	48	defined	define	VERB
ejpam-6089	120	49	by	by	ADP
ejpam-6089	120	50	ε	ε	PROPN
ejpam-6089	120	51	♭	♭	PROPN
ejpam-6089	120	52	,δ	,δ	PROPN
ejpam-6089	120	53	,	,	PUNCT
ejpam-6089	120	54	b	b	NOUN
ejpam-6089	120	55	,	,	PUNCT
ejpam-6089	120	56	s	s	NOUN
ejpam-6089	120	57	,	,	PUNCT
ejpam-6089	120	58	lℑ1+,ℵ,℘,τυ(ℑ2	lℑ1+,ℵ,℘,τυ(ℑ2	NOUN
ejpam-6089	120	59	;	;	PUNCT
ejpam-6089	120	60	g	g	NOUN
ejpam-6089	120	61	)	)	PUNCT
ejpam-6089	121	1	+	+	CCONJ
ejpam-6089	121	2	ε	ε	PROPN
ejpam-6089	121	3	♭	♭	PROPN
ejpam-6089	121	4	,δ	,δ	PUNCT
ejpam-6089	121	5	,	,	PUNCT
ejpam-6089	121	6	b	b	NOUN
ejpam-6089	121	7	,	,	PUNCT
ejpam-6089	121	8	s	s	PROPN
ejpam-6089	121	9	,	,	PUNCT
ejpam-6089	121	10	lℑ2−,ℵ,℘,τυ(ℑ1	lℑ2−,ℵ,℘,τυ(ℑ1	PROPN
ejpam-6089	121	11	;	;	PUNCT
ejpam-6089	121	12	g	g	NOUN
ejpam-6089	121	13	)	)	PUNCT
ejpam-6089	121	14	=	=	PUNCT
ejpam-6089	122	1	∞∑	∞∑	NUM
ejpam-6089	122	2	ð=0	ð=0	X
ejpam-6089	122	3	að	að	X
ejpam-6089	122	4	(	(	PUNCT
ejpam-6089	122	5	r−li	r−li	NOUN
ejpam-6089	122	6	(	(	PUNCT
ejpam-6089	122	7	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	122	8	)	)	PUNCT
ejpam-6089	122	9	ℑ1	ℑ1	NOUN
ejpam-6089	122	10	+	+	CCONJ
ejpam-6089	122	11	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	122	12	)	)	PUNCT
ejpam-6089	122	13	+	+	NUM
ejpam-6089	122	14	r−li	r−li	NOUN
ejpam-6089	122	15	(	(	PUNCT
ejpam-6089	122	16	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	122	17	)	)	PUNCT
ejpam-6089	122	18	ℑ2−	ℑ2−	NUM
ejpam-6089	122	19	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	122	20	)	)	PUNCT
ejpam-6089	122	21	)	)	PUNCT
ejpam-6089	122	22	,	,	PUNCT
ejpam-6089	122	23	where	where	SCONJ
ejpam-6089	122	24	að	að	PROPN
ejpam-6089	122	25	=	=	SYM
ejpam-6089	122	26	bg(δ+ðs	bg(δ+ðs	PROPN
ejpam-6089	122	27	,	,	PUNCT
ejpam-6089	122	28	b−δ	b−δ	NOUN
ejpam-6089	122	29	)	)	PUNCT
ejpam-6089	122	30	b(δ	b(δ	NOUN
ejpam-6089	122	31	,	,	PUNCT
ejpam-6089	122	32	b−δ	b−δ	NOUN
ejpam-6089	122	33	)	)	PUNCT
ejpam-6089	122	34	(	(	PUNCT
ejpam-6089	122	35	b)ðs	b)ðs	PROPN
ejpam-6089	122	36	♭	♭	PROPN
ejpam-6089	122	37	ð	ð	X
ejpam-6089	122	38	(	(	PUNCT
ejpam-6089	122	39	τ)ðl	τ)ðl	PROPN
ejpam-6089	122	40	.	.	PUNCT
ejpam-6089	123	1	proof	proof	NOUN
ejpam-6089	123	2	.	.	PUNCT
ejpam-6089	124	1	using	use	VERB
ejpam-6089	124	2	left	left	ADJ
ejpam-6089	124	3	sided	side	VERB
ejpam-6089	124	4	generalized	generalized	ADJ
ejpam-6089	124	5	fractional	fractional	ADJ
ejpam-6089	124	6	integral	integral	ADJ
ejpam-6089	124	7	operator	operator	NOUN
ejpam-6089	124	8	(	(	PUNCT
ejpam-6089	124	9	10	10	NUM
ejpam-6089	124	10	)	)	PUNCT
ejpam-6089	124	11	,	,	PUNCT
ejpam-6089	124	12	we	we	PRON
ejpam-6089	124	13	get	get	VERB
ejpam-6089	124	14	ε	ε	PROPN
ejpam-6089	124	15	♭	♭	PROPN
ejpam-6089	124	16	,δ	,δ	PUNCT
ejpam-6089	124	17	,	,	PUNCT
ejpam-6089	124	18	b	b	NOUN
ejpam-6089	124	19	,	,	PUNCT
ejpam-6089	124	20	s	s	X
ejpam-6089	124	21	,	,	PUNCT
ejpam-6089	124	22	lℑ1+,ℵ,℘,τυ(c	lℑ1+,ℵ,℘,τυ(c	PROPN
ejpam-6089	124	23	;	;	PUNCT
ejpam-6089	124	24	g	g	NOUN
ejpam-6089	124	25	)	)	PUNCT
ejpam-6089	124	26	=	=	SYM
ejpam-6089	124	27	∫	∫	PROPN
ejpam-6089	124	28	c	c	PROPN
ejpam-6089	124	29	ℑ1	ℑ1	PROPN
ejpam-6089	124	30	(	(	PUNCT
ejpam-6089	124	31	c−	c−	X
ejpam-6089	124	32	ψ)℘−1eδ	ψ)℘−1eδ	NOUN
ejpam-6089	124	33	,	,	PUNCT
ejpam-6089	124	34	b	b	NOUN
ejpam-6089	124	35	,	,	PUNCT
ejpam-6089	124	36	s	s	NOUN
ejpam-6089	124	37	,	,	PUNCT
ejpam-6089	124	38	lℵ,℘,τ	lℵ,℘,τ	NOUN
ejpam-6089	124	39	(	(	PUNCT
ejpam-6089	124	40	♭	♭	PROPN
ejpam-6089	124	41	(	(	PUNCT
ejpam-6089	124	42	c−	c−	NOUN
ejpam-6089	124	43	ψ)ℵ	ψ)ℵ	NOUN
ejpam-6089	124	44	;	;	PUNCT
ejpam-6089	124	45	g	g	NOUN
ejpam-6089	124	46	)	)	PUNCT
ejpam-6089	124	47	υ(ψ)dψ	υ(ψ)dψ	PROPN
ejpam-6089	124	48	,	,	PUNCT
ejpam-6089	124	49	using	use	VERB
ejpam-6089	124	50	extended	extended	ADJ
ejpam-6089	124	51	generalized	generalize	VERB
ejpam-6089	124	52	mittag	mittag	ADJ
ejpam-6089	124	53	-	-	PUNCT
ejpam-6089	124	54	leffler	leffler	NOUN
ejpam-6089	124	55	function	function	NOUN
ejpam-6089	124	56	(	(	PUNCT
ejpam-6089	124	57	9	9	NUM
ejpam-6089	124	58	)	)	PUNCT
ejpam-6089	124	59	in	in	ADP
ejpam-6089	124	60	the	the	DET
ejpam-6089	124	61	above	above	ADJ
ejpam-6089	124	62	expression	expression	NOUN
ejpam-6089	124	63	,	,	PUNCT
ejpam-6089	124	64	we	we	PRON
ejpam-6089	124	65	get	get	VERB
ejpam-6089	124	66	ε	ε	PROPN
ejpam-6089	124	67	♭	♭	PROPN
ejpam-6089	124	68	,δ	,δ	PUNCT
ejpam-6089	124	69	,	,	PUNCT
ejpam-6089	124	70	b	b	NOUN
ejpam-6089	124	71	,	,	PUNCT
ejpam-6089	124	72	s	s	X
ejpam-6089	124	73	,	,	PUNCT
ejpam-6089	124	74	lℑ1+,ℵ,℘,τυ(c	lℑ1+,ℵ,℘,τυ(c	PROPN
ejpam-6089	124	75	;	;	PUNCT
ejpam-6089	124	76	g	g	NOUN
ejpam-6089	124	77	)	)	PUNCT
ejpam-6089	124	78	=	=	SYM
ejpam-6089	124	79	∫	∫	PROPN
ejpam-6089	124	80	c	c	PROPN
ejpam-6089	124	81	ℑ1	ℑ1	PROPN
ejpam-6089	124	82	(	(	PUNCT
ejpam-6089	124	83	c−	c−	X
ejpam-6089	124	84	ψ)℘−1	ψ)℘−1	PRON
ejpam-6089	124	85	×	×	NOUN
ejpam-6089	124	86	∞∑	∞∑	NUM
ejpam-6089	124	87	ð=0	ð=0	X
ejpam-6089	124	88	(	(	PUNCT
ejpam-6089	124	89	bg(δ	bg(δ	X
ejpam-6089	124	90	+	+	CCONJ
ejpam-6089	124	91	ðs	ðs	CCONJ
ejpam-6089	124	92	,	,	PUNCT
ejpam-6089	124	93	b−	b−	PROPN
ejpam-6089	124	94	δ	δ	PROPN
ejpam-6089	124	95	)	)	PUNCT
ejpam-6089	124	96	b(δ	b(δ	PROPN
ejpam-6089	124	97	,	,	PUNCT
ejpam-6089	124	98	b−	b−	PROPN
ejpam-6089	124	99	δ	δ	PROPN
ejpam-6089	124	100	)	)	PUNCT
ejpam-6089	124	101	(	(	PUNCT
ejpam-6089	125	1	b)ðs	b)ðs	PROPN
ejpam-6089	125	2	γ(ℵð+	γ(ℵð+	VERB
ejpam-6089	125	3	℘	℘	PROPN
ejpam-6089	125	4	)	)	PUNCT
ejpam-6089	125	5	♭	♭	PROPN
ejpam-6089	125	6	ð(y	ð(y	PROPN
ejpam-6089	126	1	−	−	PUNCT
ejpam-6089	126	2	ψ)ℵð	ψ)ℵð	PROPN
ejpam-6089	126	3	(	(	PUNCT
ejpam-6089	126	4	τ)ðl	τ)ðl	PROPN
ejpam-6089	126	5	)	)	PUNCT
ejpam-6089	126	6	υ(ψ)dψ	υ(ψ)dψ	NOUN
ejpam-6089	126	7	,	,	PUNCT
ejpam-6089	126	8	after	after	ADP
ejpam-6089	126	9	rearranging	rearrange	VERB
ejpam-6089	126	10	,	,	PUNCT
ejpam-6089	126	11	the	the	DET
ejpam-6089	126	12	above	above	ADJ
ejpam-6089	126	13	equation	equation	NOUN
ejpam-6089	126	14	can	can	AUX
ejpam-6089	126	15	be	be	AUX
ejpam-6089	126	16	expressed	express	VERB
ejpam-6089	126	17	as	as	ADP
ejpam-6089	126	18	ε	ε	PROPN
ejpam-6089	126	19	♭	♭	PROPN
ejpam-6089	126	20	,δ	,δ	PUNCT
ejpam-6089	126	21	,	,	PUNCT
ejpam-6089	126	22	b	b	NOUN
ejpam-6089	126	23	,	,	PUNCT
ejpam-6089	126	24	s	s	X
ejpam-6089	126	25	,	,	PUNCT
ejpam-6089	126	26	lℑ1+,ℵ,℘,τυ(c	lℑ1+,ℵ,℘,τυ(c	PROPN
ejpam-6089	126	27	;	;	PUNCT
ejpam-6089	126	28	g	g	NOUN
ejpam-6089	126	29	)	)	PUNCT
ejpam-6089	126	30	=	=	PUNCT
ejpam-6089	127	1	∞∑	∞∑	NUM
ejpam-6089	127	2	ð=0	ð=0	X
ejpam-6089	127	3	(	(	PUNCT
ejpam-6089	127	4	bg(δ	bg(δ	X
ejpam-6089	127	5	+	+	CCONJ
ejpam-6089	127	6	ðs	ðs	CCONJ
ejpam-6089	127	7	,	,	PUNCT
ejpam-6089	127	8	b−	b−	PROPN
ejpam-6089	127	9	δ	δ	PROPN
ejpam-6089	127	10	)	)	PUNCT
ejpam-6089	127	11	b(δ	b(δ	PROPN
ejpam-6089	127	12	,	,	PUNCT
ejpam-6089	127	13	b−	b−	PROPN
ejpam-6089	127	14	δ	δ	PROPN
ejpam-6089	127	15	)	)	PUNCT
ejpam-6089	127	16	(	(	PUNCT
ejpam-6089	127	17	b)ðs	b)ðs	PROPN
ejpam-6089	127	18	♭	♭	PROPN
ejpam-6089	127	19	ð	ð	X
ejpam-6089	127	20	(	(	PUNCT
ejpam-6089	127	21	τ)ðl	τ)ðl	PROPN
ejpam-6089	127	22	)	)	PUNCT
ejpam-6089	127	23	×	×	NOUN
ejpam-6089	127	24	(	(	PUNCT
ejpam-6089	127	25	1	1	NUM
ejpam-6089	127	26	γ(ℵð+	γ(ℵð+	NOUN
ejpam-6089	127	27	℘	℘	PROPN
ejpam-6089	127	28	)	)	PUNCT
ejpam-6089	127	29	∫	∫	PROPN
ejpam-6089	127	30	c	c	PROPN
ejpam-6089	127	31	ℑ1	ℑ1	PROPN
ejpam-6089	127	32	(	(	PUNCT
ejpam-6089	127	33	c−	c−	PROPN
ejpam-6089	127	34	ψ)℘−1+ℵðυ(ψ)dψ	ψ)℘−1+ℵðυ(ψ)dψ	PROPN
ejpam-6089	127	35	)	)	PUNCT
ejpam-6089	127	36	,	,	PUNCT
ejpam-6089	127	37	using	use	VERB
ejpam-6089	127	38	left	left	ADJ
ejpam-6089	127	39	sided	sided	ADJ
ejpam-6089	127	40	reimann	reimann	NOUN
ejpam-6089	127	41	-	-	PUNCT
ejpam-6089	127	42	liouville	liouville	NOUN
ejpam-6089	127	43	integral	integral	ADJ
ejpam-6089	127	44	(	(	PUNCT
ejpam-6089	127	45	1	1	NUM
ejpam-6089	127	46	)	)	PUNCT
ejpam-6089	127	47	in	in	ADP
ejpam-6089	127	48	above	above	ADP
ejpam-6089	127	49	equation	equation	NOUN
ejpam-6089	127	50	,	,	PUNCT
ejpam-6089	127	51	we	we	PRON
ejpam-6089	127	52	acquire	acquire	VERB
ejpam-6089	127	53	ε	ε	PROPN
ejpam-6089	127	54	♭	♭	PROPN
ejpam-6089	127	55	,δ	,δ	PUNCT
ejpam-6089	127	56	,	,	PUNCT
ejpam-6089	127	57	b	b	NOUN
ejpam-6089	127	58	,	,	PUNCT
ejpam-6089	127	59	s	s	X
ejpam-6089	127	60	,	,	PUNCT
ejpam-6089	127	61	lℑ1+,ℵ,℘,τυ(c	lℑ1+,ℵ,℘,τυ(c	PROPN
ejpam-6089	127	62	;	;	PUNCT
ejpam-6089	127	63	g	g	NOUN
ejpam-6089	127	64	)	)	PUNCT
ejpam-6089	127	65	=	=	PUNCT
ejpam-6089	128	1	∞∑	∞∑	NUM
ejpam-6089	128	2	ð=0	ð=0	X
ejpam-6089	128	3	(	(	PUNCT
ejpam-6089	128	4	bg(δ	bg(δ	X
ejpam-6089	128	5	+	+	CCONJ
ejpam-6089	128	6	ðs	ðs	CCONJ
ejpam-6089	128	7	,	,	PUNCT
ejpam-6089	128	8	b−	b−	PROPN
ejpam-6089	128	9	δ	δ	PROPN
ejpam-6089	128	10	)	)	PUNCT
ejpam-6089	128	11	b(δ	b(δ	PROPN
ejpam-6089	128	12	,	,	PUNCT
ejpam-6089	128	13	b−	b−	PROPN
ejpam-6089	128	14	δ	δ	PROPN
ejpam-6089	128	15	)	)	PUNCT
ejpam-6089	128	16	(	(	PUNCT
ejpam-6089	128	17	b)ðs	b)ðs	PROPN
ejpam-6089	128	18	♭	♭	PROPN
ejpam-6089	128	19	ð	ð	X
ejpam-6089	128	20	(	(	PUNCT
ejpam-6089	128	21	τ)ðl	τ)ðl	PROPN
ejpam-6089	128	22	)	)	PUNCT
ejpam-6089	128	23	r−li	r−li	NOUN
ejpam-6089	128	24	(	(	PUNCT
ejpam-6089	128	25	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	128	26	)	)	PUNCT
ejpam-6089	128	27	ℑ1	ℑ1	NOUN
ejpam-6089	128	28	+	+	CCONJ
ejpam-6089	128	29	υ(c	υ(c	PROPN
ejpam-6089	128	30	)	)	PUNCT
ejpam-6089	128	31	.	.	PUNCT
ejpam-6089	129	1	(	(	PUNCT
ejpam-6089	129	2	12	12	NUM
ejpam-6089	129	3	)	)	PUNCT
ejpam-6089	129	4	s.	s.	PROPN
ejpam-6089	129	5	naheed	nahee	VERB
ejpam-6089	129	6	et	et	PROPN
ejpam-6089	129	7	al	al	PROPN
ejpam-6089	129	8	.	.	PUNCT
ejpam-6089	129	9	/	/	SYM
ejpam-6089	129	10	eur	eur	PROPN
ejpam-6089	129	11	.	.	PUNCT
ejpam-6089	130	1	j.	j.	PROPN
ejpam-6089	130	2	pure	pure	PROPN
ejpam-6089	130	3	appl	appl	PROPN
ejpam-6089	130	4	.	.	PROPN
ejpam-6089	130	5	math	math	PROPN
ejpam-6089	130	6	,	,	PUNCT
ejpam-6089	130	7	18	18	NUM
ejpam-6089	130	8	(	(	PUNCT
ejpam-6089	130	9	2	2	NUM
ejpam-6089	130	10	)	)	PUNCT
ejpam-6089	130	11	(	(	PUNCT
ejpam-6089	130	12	2025	2025	NUM
ejpam-6089	130	13	)	)	PUNCT
ejpam-6089	130	14	,	,	PUNCT
ejpam-6089	130	15	6089	6089	NUM
ejpam-6089	130	16	7	7	NUM
ejpam-6089	130	17	of	of	ADP
ejpam-6089	130	18	34	34	NUM
ejpam-6089	130	19	similarly	similarly	ADV
ejpam-6089	130	20	for	for	ADP
ejpam-6089	130	21	right	right	ADJ
ejpam-6089	130	22	sided	sided	ADJ
ejpam-6089	130	23	generalized	generalized	ADJ
ejpam-6089	130	24	fractional	fractional	ADJ
ejpam-6089	130	25	integral	integral	ADJ
ejpam-6089	130	26	operator	operator	NOUN
ejpam-6089	130	27	(	(	PUNCT
ejpam-6089	130	28	11	11	NUM
ejpam-6089	130	29	)	)	PUNCT
ejpam-6089	130	30	,	,	PUNCT
ejpam-6089	130	31	we	we	PRON
ejpam-6089	130	32	have	have	AUX
ejpam-6089	130	33	ε	ε	PROPN
ejpam-6089	130	34	♭	♭	PROPN
ejpam-6089	130	35	,δ	,δ	PUNCT
ejpam-6089	130	36	,	,	PUNCT
ejpam-6089	130	37	b	b	NOUN
ejpam-6089	130	38	,	,	PUNCT
ejpam-6089	130	39	s	s	PROPN
ejpam-6089	130	40	,	,	PUNCT
ejpam-6089	130	41	lℑ2−,ℵ,℘,τυ(ℑ1	lℑ2−,ℵ,℘,τυ(ℑ1	PROPN
ejpam-6089	130	42	;	;	PUNCT
ejpam-6089	130	43	g	g	NOUN
ejpam-6089	130	44	)	)	PUNCT
ejpam-6089	130	45	=	=	PUNCT
ejpam-6089	131	1	∞∑	∞∑	NUM
ejpam-6089	131	2	ð=0	ð=0	X
ejpam-6089	131	3	(	(	PUNCT
ejpam-6089	131	4	bg(δ	bg(δ	X
ejpam-6089	131	5	+	+	CCONJ
ejpam-6089	131	6	ðs	ðs	CCONJ
ejpam-6089	131	7	,	,	PUNCT
ejpam-6089	131	8	b−	b−	PROPN
ejpam-6089	131	9	δ	δ	PROPN
ejpam-6089	131	10	)	)	PUNCT
ejpam-6089	131	11	b(δ	b(δ	PROPN
ejpam-6089	131	12	,	,	PUNCT
ejpam-6089	131	13	b−	b−	PROPN
ejpam-6089	131	14	δ	δ	PROPN
ejpam-6089	131	15	)	)	PUNCT
ejpam-6089	131	16	(	(	PUNCT
ejpam-6089	131	17	b)ðs	b)ðs	PROPN
ejpam-6089	131	18	♭	♭	PROPN
ejpam-6089	131	19	ð	ð	X
ejpam-6089	131	20	(	(	PUNCT
ejpam-6089	131	21	τ)ðl	τ)ðl	PROPN
ejpam-6089	131	22	)	)	PUNCT
ejpam-6089	131	23	r−li	r−li	NOUN
ejpam-6089	131	24	(	(	PUNCT
ejpam-6089	131	25	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	131	26	)	)	PUNCT
ejpam-6089	131	27	ℑ2−	ℑ2−	NUM
ejpam-6089	131	28	υ(c	υ(c	PROPN
ejpam-6089	131	29	)	)	PUNCT
ejpam-6089	131	30	.	.	PUNCT
ejpam-6089	132	1	(	(	PUNCT
ejpam-6089	132	2	13	13	X
ejpam-6089	132	3	)	)	PUNCT
ejpam-6089	132	4	adding	add	VERB
ejpam-6089	132	5	(	(	PUNCT
ejpam-6089	132	6	12	12	NUM
ejpam-6089	132	7	)	)	PUNCT
ejpam-6089	132	8	and	and	CCONJ
ejpam-6089	132	9	(	(	PUNCT
ejpam-6089	132	10	13	13	NUM
ejpam-6089	132	11	)	)	PUNCT
ejpam-6089	132	12	ε	ε	PROPN
ejpam-6089	132	13	♭	♭	PROPN
ejpam-6089	132	14	,δ	,δ	PUNCT
ejpam-6089	132	15	,	,	PUNCT
ejpam-6089	132	16	b	b	NOUN
ejpam-6089	132	17	,	,	PUNCT
ejpam-6089	132	18	s	s	NOUN
ejpam-6089	132	19	,	,	PUNCT
ejpam-6089	132	20	lℑ1+,ℵ,℘,τυ(ℑ2	lℑ1+,ℵ,℘,τυ(ℑ2	NOUN
ejpam-6089	132	21	;	;	PUNCT
ejpam-6089	132	22	g	g	NOUN
ejpam-6089	132	23	)	)	PUNCT
ejpam-6089	133	1	+	+	CCONJ
ejpam-6089	133	2	ε	ε	PROPN
ejpam-6089	133	3	♭	♭	PROPN
ejpam-6089	133	4	,δ	,δ	PUNCT
ejpam-6089	133	5	,	,	PUNCT
ejpam-6089	133	6	b	b	NOUN
ejpam-6089	133	7	,	,	PUNCT
ejpam-6089	133	8	s	s	PROPN
ejpam-6089	133	9	,	,	PUNCT
ejpam-6089	133	10	lℑ2−,ℵ,℘,τυ(ℑ1	lℑ2−,ℵ,℘,τυ(ℑ1	PROPN
ejpam-6089	133	11	;	;	PUNCT
ejpam-6089	133	12	g	g	NOUN
ejpam-6089	133	13	)	)	PUNCT
ejpam-6089	133	14	=	=	PUNCT
ejpam-6089	134	1	∞∑	∞∑	NUM
ejpam-6089	134	2	ð=0	ð=0	X
ejpam-6089	134	3	(	(	PUNCT
ejpam-6089	134	4	bg(δ	bg(δ	X
ejpam-6089	134	5	+	+	CCONJ
ejpam-6089	134	6	ðs	ðs	CCONJ
ejpam-6089	134	7	,	,	PUNCT
ejpam-6089	134	8	b−	b−	PROPN
ejpam-6089	134	9	δ	δ	PROPN
ejpam-6089	134	10	)	)	PUNCT
ejpam-6089	134	11	b(δ	b(δ	PROPN
ejpam-6089	134	12	,	,	PUNCT
ejpam-6089	134	13	b−	b−	PROPN
ejpam-6089	134	14	δ	δ	PROPN
ejpam-6089	134	15	)	)	PUNCT
ejpam-6089	134	16	(	(	PUNCT
ejpam-6089	134	17	b)ðs	b)ðs	PROPN
ejpam-6089	134	18	♭	♭	PROPN
ejpam-6089	134	19	ð	ð	X
ejpam-6089	134	20	(	(	PUNCT
ejpam-6089	134	21	τ)ðl	τ)ðl	PROPN
ejpam-6089	134	22	)	)	PUNCT
ejpam-6089	134	23	(	(	PUNCT
ejpam-6089	134	24	r−li	r−li	NOUN
ejpam-6089	134	25	(	(	PUNCT
ejpam-6089	134	26	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	134	27	)	)	PUNCT
ejpam-6089	134	28	ℑ1	ℑ1	NOUN
ejpam-6089	134	29	+	+	CCONJ
ejpam-6089	134	30	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	134	31	)	)	PUNCT
ejpam-6089	134	32	+	+	NUM
ejpam-6089	134	33	r−li	r−li	NOUN
ejpam-6089	134	34	(	(	PUNCT
ejpam-6089	134	35	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	134	36	)	)	PUNCT
ejpam-6089	134	37	ℑ2−	ℑ2−	NUM
ejpam-6089	135	1	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	135	2	)	)	PUNCT
ejpam-6089	135	3	)	)	PUNCT
ejpam-6089	136	1	=	=	PUNCT
ejpam-6089	137	1	∞∑	∞∑	NUM
ejpam-6089	137	2	ð=0	ð=0	X
ejpam-6089	137	3	að	að	X
ejpam-6089	137	4	(	(	PUNCT
ejpam-6089	137	5	r−li	r−li	NOUN
ejpam-6089	137	6	(	(	PUNCT
ejpam-6089	137	7	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	137	8	)	)	PUNCT
ejpam-6089	137	9	ℑ1	ℑ1	NOUN
ejpam-6089	137	10	+	+	CCONJ
ejpam-6089	137	11	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	137	12	)	)	PUNCT
ejpam-6089	137	13	+	+	NUM
ejpam-6089	137	14	r−li	r−li	NOUN
ejpam-6089	137	15	(	(	PUNCT
ejpam-6089	137	16	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	137	17	)	)	PUNCT
ejpam-6089	137	18	ℑ2−	ℑ2−	NUM
ejpam-6089	137	19	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	137	20	)	)	PUNCT
ejpam-6089	137	21	)	)	PUNCT
ejpam-6089	137	22	.	.	PUNCT
ejpam-6089	138	1	here	here	ADV
ejpam-6089	138	2	,	,	PUNCT
ejpam-6089	138	3	the	the	DET
ejpam-6089	138	4	integral	integral	ADJ
ejpam-6089	138	5	transform	transform	NOUN
ejpam-6089	138	6	gives	give	VERB
ejpam-6089	138	7	(	(	PUNCT
ejpam-6089	138	8	ℵð+℘)th	ℵð+℘)th	ADP
ejpam-6089	138	9	order	order	NOUN
ejpam-6089	138	10	left	leave	VERB
ejpam-6089	138	11	and	and	CCONJ
ejpam-6089	138	12	right	right	ADJ
ejpam-6089	138	13	sided	sided	ADJ
ejpam-6089	138	14	reimann	reimann	NOUN
ejpam-6089	138	15	-	-	PUNCT
ejpam-6089	138	16	liouville	liouville	NOUN
ejpam-6089	138	17	fractional	fractional	ADJ
ejpam-6089	138	18	integrals	integral	NOUN
ejpam-6089	138	19	of	of	ADP
ejpam-6089	138	20	υ(c	υ(c	PROPN
ejpam-6089	138	21	)	)	PUNCT
ejpam-6089	138	22	,	,	PUNCT
ejpam-6089	138	23	provided	provide	VERB
ejpam-6089	138	24	that	that	SCONJ
ejpam-6089	138	25	ℜ(ℵð+	ℜ(ℵð+	PRON
ejpam-6089	138	26	℘	℘	NOUN
ejpam-6089	138	27	)	)	PUNCT
ejpam-6089	138	28	>	>	X
ejpam-6089	138	29	0	0	X
ejpam-6089	138	30	.	.	PUNCT
ejpam-6089	138	31	theorem	theorem	NOUN
ejpam-6089	138	32	5	5	NUM
ejpam-6089	138	33	.	.	PUNCT
ejpam-6089	139	1	let	let	VERB
ejpam-6089	139	2	υ	υ	NOUN
ejpam-6089	139	3	:	:	PUNCT
ejpam-6089	139	4	[	[	X
ejpam-6089	139	5	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	139	6	]	]	X
ejpam-6089	139	7	→	→	PUNCT
ejpam-6089	139	8	ℜ	ℜ	PROPN
ejpam-6089	139	9	be	be	AUX
ejpam-6089	139	10	a	a	DET
ejpam-6089	139	11	convex	convex	NOUN
ejpam-6089	139	12	function	function	NOUN
ejpam-6089	139	13	with	with	ADP
ejpam-6089	139	14	υ	υ	PRON
ejpam-6089	139	15	∈	∈	PROPN
ejpam-6089	139	16	l1[ℑ1,ℑ2	l1[ℑ1,ℑ2	PROPN
ejpam-6089	139	17	]	]	PUNCT
ejpam-6089	139	18	and	and	CCONJ
ejpam-6089	139	19	♭	♭	PROPN
ejpam-6089	139	20	,	,	PUNCT
ejpam-6089	139	21	ℵ	ℵ	NOUN
ejpam-6089	139	22	,	,	PUNCT
ejpam-6089	139	23	℘	℘	PROPN
ejpam-6089	139	24	,	,	PUNCT
ejpam-6089	139	25	τ	τ	PROPN
ejpam-6089	139	26	,	,	PUNCT
ejpam-6089	139	27	δ	δ	PROPN
ejpam-6089	139	28	,	,	PUNCT
ejpam-6089	139	29	b	b	PROPN
ejpam-6089	139	30	∈	∈	PROPN
ejpam-6089	139	31	c	c	NOUN
ejpam-6089	139	32	such	such	ADJ
ejpam-6089	139	33	that	that	SCONJ
ejpam-6089	139	34	ℜ(ℵ),ℜ(℘),ℜ(τ	ℜ(ℵ),ℜ(℘),ℜ(τ	PROPN
ejpam-6089	139	35	)	)	PUNCT
ejpam-6089	139	36	>	>	X
ejpam-6089	139	37	0	0	NUM
ejpam-6089	139	38	,	,	PUNCT
ejpam-6089	139	39	ℜ(b	ℜ(b	NOUN
ejpam-6089	139	40	)	)	PUNCT
ejpam-6089	139	41	>	>	X
ejpam-6089	140	1	ℜ(δ	ℜ(δ	X
ejpam-6089	140	2	)	)	PUNCT
ejpam-6089	140	3	>	>	X
ejpam-6089	140	4	0	0	X
ejpam-6089	140	5	.	.	PUNCT
ejpam-6089	141	1	let	let	VERB
ejpam-6089	141	2	g	g	PROPN
ejpam-6089	141	3	≥	≥	NOUN
ejpam-6089	141	4	0	0	NUM
ejpam-6089	141	5	,	,	PUNCT
ejpam-6089	141	6	l	l	NOUN
ejpam-6089	141	7	>	>	X
ejpam-6089	141	8	0	0	PUNCT
ejpam-6089	142	1	and	and	CCONJ
ejpam-6089	142	2	0	0	NUM
ejpam-6089	142	3	<	<	X
ejpam-6089	142	4	s	s	X
ejpam-6089	142	5	≤	≤	NUM
ejpam-6089	142	6	l	l	NOUN
ejpam-6089	142	7	+	+	CCONJ
ejpam-6089	142	8	ℜ(ℵ	ℜ(ℵ	NOUN
ejpam-6089	142	9	)	)	PUNCT
ejpam-6089	142	10	,	,	PUNCT
ejpam-6089	142	11	then	then	ADV
ejpam-6089	142	12	for	for	ADP
ejpam-6089	142	13	(	(	PUNCT
ejpam-6089	142	14	ℵð+	ℵð+	ADJ
ejpam-6089	142	15	℘	℘	PROPN
ejpam-6089	142	16	)	)	PUNCT
ejpam-6089	142	17	>	>	X
ejpam-6089	142	18	0	0	NUM
ejpam-6089	142	19	,	,	PUNCT
ejpam-6089	142	20	we	we	PRON
ejpam-6089	142	21	can	can	AUX
ejpam-6089	142	22	write	write	VERB
ejpam-6089	142	23	∞∑	∞∑	NUM
ejpam-6089	142	24	ð=0	ð=0	X
ejpam-6089	142	25	aðvðυ	aðvðυ	X
ejpam-6089	142	26	(	(	PUNCT
ejpam-6089	142	27	ℑ1	ℑ1	X
ejpam-6089	142	28	+	+	CCONJ
ejpam-6089	142	29	ℑ2	ℑ2	PROPN
ejpam-6089	142	30	2	2	NUM
ejpam-6089	142	31	)	)	PUNCT
ejpam-6089	142	32	≤	≤	PUNCT
ejpam-6089	142	33	ε	ε	PROPN
ejpam-6089	142	34	♭	♭	PROPN
ejpam-6089	142	35	,δ	,δ	PUNCT
ejpam-6089	142	36	,	,	PUNCT
ejpam-6089	142	37	b	b	NOUN
ejpam-6089	142	38	,	,	PUNCT
ejpam-6089	142	39	s	s	NOUN
ejpam-6089	142	40	,	,	PUNCT
ejpam-6089	142	41	lℑ1+,ℵ,℘,τυ(ℑ2	lℑ1+,ℵ,℘,τυ(ℑ2	NOUN
ejpam-6089	142	42	;	;	PUNCT
ejpam-6089	142	43	g	g	NOUN
ejpam-6089	142	44	)	)	PUNCT
ejpam-6089	143	1	+	+	CCONJ
ejpam-6089	143	2	ε	ε	PROPN
ejpam-6089	143	3	♭	♭	PROPN
ejpam-6089	143	4	,δ	,δ	PUNCT
ejpam-6089	143	5	,	,	PUNCT
ejpam-6089	143	6	b	b	NOUN
ejpam-6089	143	7	,	,	PUNCT
ejpam-6089	143	8	s	s	PROPN
ejpam-6089	143	9	,	,	PUNCT
ejpam-6089	143	10	lℑ2−,ℵ,℘,τυ(ℑ1	lℑ2−,ℵ,℘,τυ(ℑ1	PROPN
ejpam-6089	143	11	;	;	PUNCT
ejpam-6089	143	12	g	g	X
ejpam-6089	143	13	)	)	PUNCT
ejpam-6089	143	14	≤	≤	NOUN
ejpam-6089	144	1	∞∑	∞∑	NUM
ejpam-6089	144	2	ð=0	ð=0	X
ejpam-6089	144	3	aðvð	aðvð	NOUN
ejpam-6089	144	4	(	(	PUNCT
ejpam-6089	144	5	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	144	6	)	)	PUNCT
ejpam-6089	144	7	+	+	CCONJ
ejpam-6089	144	8	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	144	9	)	)	PUNCT
ejpam-6089	144	10	2	2	NUM
ejpam-6089	144	11	)	)	PUNCT
ejpam-6089	144	12	,	,	PUNCT
ejpam-6089	144	13	where	where	SCONJ
ejpam-6089	144	14	að	að	PROPN
ejpam-6089	144	15	=	=	SYM
ejpam-6089	144	16	bg(δ+ðs	bg(δ+ðs	PROPN
ejpam-6089	144	17	,	,	PUNCT
ejpam-6089	144	18	b−δ	b−δ	NOUN
ejpam-6089	144	19	)	)	PUNCT
ejpam-6089	144	20	b(δ	b(δ	NOUN
ejpam-6089	144	21	,	,	PUNCT
ejpam-6089	144	22	b−δ	b−δ	NOUN
ejpam-6089	144	23	)	)	PUNCT
ejpam-6089	144	24	(	(	PUNCT
ejpam-6089	144	25	b)ðs	b)ðs	PROPN
ejpam-6089	144	26	♭	♭	PROPN
ejpam-6089	144	27	ð	ð	X
ejpam-6089	144	28	(	(	PUNCT
ejpam-6089	144	29	τ)ðl	τ)ðl	PROPN
ejpam-6089	144	30	and	and	CCONJ
ejpam-6089	144	31	vð	vð	VERB
ejpam-6089	144	32	=	=	SYM
ejpam-6089	144	33	2(ℑ2−ℑ1)(ℵð+℘	2(ℑ2−ℑ1)(ℵð+℘	NUM
ejpam-6089	144	34	)	)	PUNCT
ejpam-6089	144	35	γ(ℵð+℘+1	γ(ℵð+℘+1	NOUN
ejpam-6089	144	36	)	)	PUNCT
ejpam-6089	144	37	.	.	PUNCT
ejpam-6089	145	1	proof	proof	NOUN
ejpam-6089	145	2	.	.	PUNCT
ejpam-6089	146	1	replacing	replace	VERB
ejpam-6089	146	2	α∗	α∗	NOUN
ejpam-6089	146	3	by	by	ADP
ejpam-6089	146	4	(	(	PUNCT
ejpam-6089	146	5	ℵð+	ℵð+	ADJ
ejpam-6089	146	6	℘	℘	PROPN
ejpam-6089	146	7	)	)	PUNCT
ejpam-6089	146	8	in	in	ADP
ejpam-6089	146	9	theorem	theorem	NOUN
ejpam-6089	146	10	2	2	NUM
ejpam-6089	146	11	,	,	PUNCT
ejpam-6089	146	12	we	we	PRON
ejpam-6089	146	13	get	get	VERB
ejpam-6089	146	14	υ	υ	PRON
ejpam-6089	146	15	(	(	PUNCT
ejpam-6089	146	16	ℑ1	ℑ1	PROPN
ejpam-6089	146	17	+	+	CCONJ
ejpam-6089	146	18	ℑ2	ℑ2	PROPN
ejpam-6089	146	19	2	2	NUM
ejpam-6089	146	20	)	)	PUNCT
ejpam-6089	146	21	≤	≤	NUM
ejpam-6089	146	22	γ(ℵð+	γ(ℵð+	NOUN
ejpam-6089	146	23	℘+	℘+	ADJ
ejpam-6089	146	24	1	1	NUM
ejpam-6089	146	25	)	)	PUNCT
ejpam-6089	146	26	2(ℑ2	2(ℑ2	NUM
ejpam-6089	146	27	−ℑ1)(ℵð+℘	−ℑ1)(ℵð+℘	NUM
ejpam-6089	146	28	)	)	PUNCT
ejpam-6089	146	29	(	(	PUNCT
ejpam-6089	146	30	r−li	r−li	NOUN
ejpam-6089	146	31	(	(	PUNCT
ejpam-6089	146	32	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	146	33	)	)	PUNCT
ejpam-6089	146	34	ℑ1	ℑ1	NOUN
ejpam-6089	146	35	+	+	CCONJ
ejpam-6089	146	36	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	146	37	)	)	PUNCT
ejpam-6089	147	1	+	+	NUM
ejpam-6089	147	2	r−li	r−li	NOUN
ejpam-6089	147	3	(	(	PUNCT
ejpam-6089	147	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	147	5	)	)	PUNCT
ejpam-6089	147	6	ℑ2−	ℑ2−	NUM
ejpam-6089	148	1	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	148	2	)	)	PUNCT
ejpam-6089	148	3	)	)	PUNCT
ejpam-6089	149	1	≤	≤	NOUN
ejpam-6089	149	2	(	(	PUNCT
ejpam-6089	149	3	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	149	4	)	)	PUNCT
ejpam-6089	149	5	+	+	CCONJ
ejpam-6089	149	6	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	149	7	)	)	PUNCT
ejpam-6089	149	8	2	2	NUM
ejpam-6089	149	9	)	)	PUNCT
ejpam-6089	149	10	.	.	PUNCT
ejpam-6089	150	1	multiplying	multiply	VERB
ejpam-6089	150	2	the	the	DET
ejpam-6089	150	3	above	above	ADJ
ejpam-6089	150	4	inequality	inequality	NOUN
ejpam-6089	150	5	with	with	ADP
ejpam-6089	150	6	2(ℑ2−ℑ1)(ℵð+℘	2(ℑ2−ℑ1)(ℵð+℘	NUM
ejpam-6089	150	7	)	)	PUNCT
ejpam-6089	150	8	γ(ℵ,weobtainð+℘+1	γ(ℵ,weobtainð+℘+1	NOUN
ejpam-6089	150	9	)	)	PUNCT
ejpam-6089	150	10	,	,	PUNCT
ejpam-6089	150	11	we	we	PRON
ejpam-6089	150	12	obtain	obtain	VERB
ejpam-6089	150	13	2(ℑ2	2(ℑ2	NUM
ejpam-6089	150	14	−ℑ1	−ℑ1	NOUN
ejpam-6089	150	15	)	)	PUNCT
ejpam-6089	150	16	(	(	PUNCT
ejpam-6089	150	17	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	150	18	)	)	PUNCT
ejpam-6089	150	19	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	150	20	℘	℘	PROPN
ejpam-6089	150	21	)	)	PUNCT
ejpam-6089	150	22	+	+	CCONJ
ejpam-6089	151	1	1	1	X
ejpam-6089	151	2	)	)	PUNCT
ejpam-6089	151	3	υ	υ	NOUN
ejpam-6089	151	4	(	(	PUNCT
ejpam-6089	151	5	ℑ1	ℑ1	PROPN
ejpam-6089	151	6	+	+	CCONJ
ejpam-6089	151	7	ℑ2	ℑ2	PROPN
ejpam-6089	151	8	2	2	NUM
ejpam-6089	151	9	)	)	PUNCT
ejpam-6089	151	10	s.	s.	PROPN
ejpam-6089	151	11	naheed	nahee	VERB
ejpam-6089	151	12	et	et	PROPN
ejpam-6089	151	13	al	al	PROPN
ejpam-6089	151	14	.	.	PUNCT
ejpam-6089	151	15	/	/	SYM
ejpam-6089	151	16	eur	eur	PROPN
ejpam-6089	151	17	.	.	PUNCT
ejpam-6089	152	1	j.	j.	PROPN
ejpam-6089	152	2	pure	pure	PROPN
ejpam-6089	152	3	appl	appl	PROPN
ejpam-6089	152	4	.	.	PROPN
ejpam-6089	152	5	math	math	PROPN
ejpam-6089	152	6	,	,	PUNCT
ejpam-6089	152	7	18	18	NUM
ejpam-6089	152	8	(	(	PUNCT
ejpam-6089	152	9	2	2	NUM
ejpam-6089	152	10	)	)	PUNCT
ejpam-6089	152	11	(	(	PUNCT
ejpam-6089	152	12	2025	2025	NUM
ejpam-6089	152	13	)	)	PUNCT
ejpam-6089	152	14	,	,	PUNCT
ejpam-6089	152	15	6089	6089	NUM
ejpam-6089	152	16	8	8	NUM
ejpam-6089	152	17	of	of	ADP
ejpam-6089	152	18	34	34	NUM
ejpam-6089	152	19	≤	≤	NOUN
ejpam-6089	152	20	(	(	PUNCT
ejpam-6089	152	21	r−li	r−li	NOUN
ejpam-6089	152	22	(	(	PUNCT
ejpam-6089	152	23	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	152	24	)	)	PUNCT
ejpam-6089	152	25	ℑ1	ℑ1	NOUN
ejpam-6089	152	26	+	+	CCONJ
ejpam-6089	152	27	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	152	28	)	)	PUNCT
ejpam-6089	153	1	+	+	NUM
ejpam-6089	153	2	r−li	r−li	NOUN
ejpam-6089	153	3	(	(	PUNCT
ejpam-6089	153	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	153	5	)	)	PUNCT
ejpam-6089	153	6	ℑ2−	ℑ2−	NUM
ejpam-6089	154	1	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	154	2	)	)	PUNCT
ejpam-6089	154	3	)	)	PUNCT
ejpam-6089	155	1	≤	≤	NOUN
ejpam-6089	155	2	2(ℑ2	2(ℑ2	NUM
ejpam-6089	155	3	−ℑ1	−ℑ1	NOUN
ejpam-6089	155	4	)	)	PUNCT
ejpam-6089	155	5	(	(	PUNCT
ejpam-6089	155	6	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	155	7	)	)	PUNCT
ejpam-6089	155	8	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	155	9	℘	℘	PROPN
ejpam-6089	155	10	)	)	PUNCT
ejpam-6089	155	11	+	+	CCONJ
ejpam-6089	155	12	1	1	X
ejpam-6089	155	13	)	)	PUNCT
ejpam-6089	155	14	(	(	PUNCT
ejpam-6089	155	15	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	155	16	)	)	PUNCT
ejpam-6089	156	1	+	+	CCONJ
ejpam-6089	156	2	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	156	3	)	)	PUNCT
ejpam-6089	156	4	2	2	NUM
ejpam-6089	156	5	)	)	PUNCT
ejpam-6089	156	6	.	.	PUNCT
ejpam-6089	157	1	again	again	ADV
ejpam-6089	157	2	the	the	DET
ejpam-6089	157	3	above	above	ADJ
ejpam-6089	157	4	inequality	inequality	NOUN
ejpam-6089	157	5	is	be	AUX
ejpam-6089	157	6	multiplied	multiply	VERB
ejpam-6089	157	7	with	with	ADP
ejpam-6089	157	8	að	að	PROPN
ejpam-6089	157	9	to	to	PART
ejpam-6089	157	10	obtain	obtain	VERB
ejpam-6089	157	11	að	að	PROPN
ejpam-6089	157	12	2(ℑ2	2(ℑ2	NUM
ejpam-6089	157	13	−ℑ1	−ℑ1	NOUN
ejpam-6089	157	14	)	)	PUNCT
ejpam-6089	157	15	(	(	PUNCT
ejpam-6089	157	16	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	157	17	)	)	PUNCT
ejpam-6089	157	18	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	157	19	℘	℘	PROPN
ejpam-6089	157	20	)	)	PUNCT
ejpam-6089	158	1	+	+	CCONJ
ejpam-6089	158	2	1	1	X
ejpam-6089	158	3	)	)	PUNCT
ejpam-6089	158	4	υ	υ	NOUN
ejpam-6089	158	5	(	(	PUNCT
ejpam-6089	158	6	ℑ1	ℑ1	PROPN
ejpam-6089	158	7	+	+	CCONJ
ejpam-6089	158	8	ℑ2	ℑ2	PROPN
ejpam-6089	158	9	2	2	NUM
ejpam-6089	158	10	)	)	PUNCT
ejpam-6089	158	11	≤	≤	NUM
ejpam-6089	159	1	að	að	PROPN
ejpam-6089	159	2	(	(	PUNCT
ejpam-6089	159	3	r−li	r−li	NOUN
ejpam-6089	159	4	(	(	PUNCT
ejpam-6089	159	5	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	159	6	)	)	PUNCT
ejpam-6089	159	7	ℑ1	ℑ1	NOUN
ejpam-6089	159	8	+	+	CCONJ
ejpam-6089	159	9	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	159	10	)	)	PUNCT
ejpam-6089	160	1	+	+	NUM
ejpam-6089	160	2	r−li	r−li	NOUN
ejpam-6089	160	3	(	(	PUNCT
ejpam-6089	160	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	160	5	)	)	PUNCT
ejpam-6089	160	6	ℑ2−	ℑ2−	NUM
ejpam-6089	161	1	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	161	2	)	)	PUNCT
ejpam-6089	161	3	)	)	PUNCT
ejpam-6089	162	1	≤	≤	PUNCT
ejpam-6089	162	2	að	að	X
ejpam-6089	162	3	2(ℑ2	2(ℑ2	NUM
ejpam-6089	162	4	−ℑ1	−ℑ1	PROPN
ejpam-6089	162	5	)	)	PUNCT
ejpam-6089	162	6	(	(	PUNCT
ejpam-6089	162	7	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	162	8	)	)	PUNCT
ejpam-6089	162	9	γ(ℵð+	γ(ℵð+	NOUN
ejpam-6089	162	10	℘+	℘+	ADP
ejpam-6089	162	11	1	1	NUM
ejpam-6089	162	12	)	)	PUNCT
ejpam-6089	162	13	(	(	PUNCT
ejpam-6089	162	14	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	162	15	)	)	PUNCT
ejpam-6089	162	16	+	+	CCONJ
ejpam-6089	162	17	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	162	18	)	)	PUNCT
ejpam-6089	162	19	2	2	NUM
ejpam-6089	162	20	)	)	PUNCT
ejpam-6089	162	21	.	.	PUNCT
ejpam-6089	163	1	summing	sum	VERB
ejpam-6089	163	2	over	over	ADP
ejpam-6089	163	3	all	all	PRON
ejpam-6089	163	4	ð	ð	NOUN
ejpam-6089	163	5	∞∑	∞∑	NUM
ejpam-6089	163	6	ð=0	ð=0	X
ejpam-6089	163	7	að	að	PROPN
ejpam-6089	163	8	2(ℑ2	2(ℑ2	NUM
ejpam-6089	163	9	−ℑ1	−ℑ1	NOUN
ejpam-6089	163	10	)	)	PUNCT
ejpam-6089	163	11	(	(	PUNCT
ejpam-6089	163	12	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	163	13	)	)	PUNCT
ejpam-6089	163	14	γ(ℵð+	γ(ℵð+	NOUN
ejpam-6089	163	15	℘+	℘+	ADJ
ejpam-6089	163	16	1	1	NUM
ejpam-6089	163	17	)	)	PUNCT
ejpam-6089	163	18	υ	υ	NOUN
ejpam-6089	163	19	(	(	PUNCT
ejpam-6089	163	20	ℑ1	ℑ1	PROPN
ejpam-6089	163	21	+	+	CCONJ
ejpam-6089	163	22	ℑ2	ℑ2	PROPN
ejpam-6089	163	23	2	2	NUM
ejpam-6089	163	24	)	)	PUNCT
ejpam-6089	163	25	≤	≤	NOUN
ejpam-6089	164	1	∞∑	∞∑	NUM
ejpam-6089	164	2	ð=0	ð=0	X
ejpam-6089	164	3	að	að	X
ejpam-6089	164	4	(	(	PUNCT
ejpam-6089	164	5	r−li	r−li	NOUN
ejpam-6089	164	6	(	(	PUNCT
ejpam-6089	164	7	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	164	8	)	)	PUNCT
ejpam-6089	164	9	ℑ1	ℑ1	NOUN
ejpam-6089	164	10	+	+	CCONJ
ejpam-6089	164	11	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	164	12	)	)	PUNCT
ejpam-6089	164	13	+	+	NUM
ejpam-6089	164	14	r−li	r−li	NOUN
ejpam-6089	164	15	(	(	PUNCT
ejpam-6089	164	16	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	164	17	)	)	PUNCT
ejpam-6089	164	18	ℑ2−	ℑ2−	NUM
ejpam-6089	164	19	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	164	20	)	)	PUNCT
ejpam-6089	164	21	)	)	PUNCT
ejpam-6089	164	22	≤	≤	NOUN
ejpam-6089	164	23	∞∑	∞∑	NUM
ejpam-6089	164	24	ð=0	ð=0	X
ejpam-6089	164	25	að	að	PROPN
ejpam-6089	164	26	2(ℑ2	2(ℑ2	NUM
ejpam-6089	164	27	−ℑ1	−ℑ1	NOUN
ejpam-6089	164	28	)	)	PUNCT
ejpam-6089	164	29	(	(	PUNCT
ejpam-6089	164	30	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	164	31	)	)	PUNCT
ejpam-6089	164	32	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	164	33	℘	℘	PROPN
ejpam-6089	164	34	)	)	PUNCT
ejpam-6089	164	35	+	+	CCONJ
ejpam-6089	164	36	1	1	X
ejpam-6089	164	37	)	)	PUNCT
ejpam-6089	164	38	(	(	PUNCT
ejpam-6089	164	39	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	164	40	)	)	PUNCT
ejpam-6089	164	41	+	+	CCONJ
ejpam-6089	164	42	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	164	43	)	)	PUNCT
ejpam-6089	164	44	2	2	NUM
ejpam-6089	164	45	)	)	PUNCT
ejpam-6089	164	46	.	.	PUNCT
ejpam-6089	165	1	using	use	VERB
ejpam-6089	165	2	proposition	proposition	NOUN
ejpam-6089	165	3	1	1	NUM
ejpam-6089	165	4	,	,	PUNCT
ejpam-6089	165	5	we	we	PRON
ejpam-6089	165	6	get	get	VERB
ejpam-6089	165	7	∞∑	∞∑	NUM
ejpam-6089	165	8	ð=0	ð=0	X
ejpam-6089	165	9	aðvðυ	aðvðυ	X
ejpam-6089	165	10	(	(	PUNCT
ejpam-6089	165	11	ℑ1	ℑ1	X
ejpam-6089	165	12	+	+	CCONJ
ejpam-6089	165	13	ℑ2	ℑ2	PROPN
ejpam-6089	165	14	2	2	NUM
ejpam-6089	165	15	)	)	PUNCT
ejpam-6089	165	16	≤	≤	PUNCT
ejpam-6089	165	17	ε	ε	PROPN
ejpam-6089	165	18	♭	♭	PROPN
ejpam-6089	165	19	,δ	,δ	PUNCT
ejpam-6089	165	20	,	,	PUNCT
ejpam-6089	165	21	b	b	NOUN
ejpam-6089	165	22	,	,	PUNCT
ejpam-6089	165	23	s	s	NOUN
ejpam-6089	165	24	,	,	PUNCT
ejpam-6089	165	25	lℑ1+,ℵ,℘,τυ(ℑ2	lℑ1+,ℵ,℘,τυ(ℑ2	NOUN
ejpam-6089	165	26	;	;	PUNCT
ejpam-6089	165	27	g	g	NOUN
ejpam-6089	165	28	)	)	PUNCT
ejpam-6089	166	1	+	+	CCONJ
ejpam-6089	166	2	ε	ε	PROPN
ejpam-6089	166	3	♭	♭	PROPN
ejpam-6089	166	4	,δ	,δ	PUNCT
ejpam-6089	166	5	,	,	PUNCT
ejpam-6089	166	6	b	b	NOUN
ejpam-6089	166	7	,	,	PUNCT
ejpam-6089	166	8	s	s	PROPN
ejpam-6089	166	9	,	,	PUNCT
ejpam-6089	166	10	lℑ2−,ℵ,℘,τυ(ℑ1	lℑ2−,ℵ,℘,τυ(ℑ1	PROPN
ejpam-6089	166	11	;	;	PUNCT
ejpam-6089	166	12	g	g	X
ejpam-6089	166	13	)	)	PUNCT
ejpam-6089	166	14	≤	≤	NOUN
ejpam-6089	167	1	∞∑	∞∑	NUM
ejpam-6089	167	2	ð=0	ð=0	X
ejpam-6089	167	3	aðvð	aðvð	NOUN
ejpam-6089	167	4	(	(	PUNCT
ejpam-6089	167	5	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	167	6	)	)	PUNCT
ejpam-6089	167	7	+	+	CCONJ
ejpam-6089	167	8	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	167	9	)	)	PUNCT
ejpam-6089	167	10	2	2	NUM
ejpam-6089	167	11	)	)	PUNCT
ejpam-6089	167	12	.	.	PUNCT
ejpam-6089	168	1	hence	hence	ADV
ejpam-6089	168	2	the	the	DET
ejpam-6089	168	3	result	result	NOUN
ejpam-6089	168	4	is	be	AUX
ejpam-6089	168	5	proved	prove	VERB
ejpam-6089	168	6	.	.	PUNCT
ejpam-6089	169	1	proposition	proposition	NOUN
ejpam-6089	169	2	2	2	NUM
ejpam-6089	169	3	.	.	PUNCT
ejpam-6089	170	1	if	if	SCONJ
ejpam-6089	170	2	υ	υ	PRON
ejpam-6089	170	3	:	:	PUNCT
ejpam-6089	170	4	[	[	X
ejpam-6089	170	5	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	170	6	]	]	PUNCT
ejpam-6089	170	7	→	→	SYM
ejpam-6089	170	8	ℜ	ℜ	PROPN
ejpam-6089	170	9	is	be	AUX
ejpam-6089	170	10	l1	l1	PROPN
ejpam-6089	170	11	(	(	PUNCT
ejpam-6089	170	12	convex	convex	PROPN
ejpam-6089	170	13	)	)	PUNCT
ejpam-6089	170	14	and	and	CCONJ
ejpam-6089	170	15	(	(	PUNCT
ejpam-6089	170	16	ℵð	ℵð	NOUN
ejpam-6089	170	17	+	+	CCONJ
ejpam-6089	170	18	℘	℘	PROPN
ejpam-6089	170	19	)	)	PUNCT
ejpam-6089	170	20	∈	∈	PROPN
ejpam-6089	170	21	(	(	PUNCT
ejpam-6089	170	22	0	0	NUM
ejpam-6089	170	23	,	,	PUNCT
ejpam-6089	170	24	1	1	NUM
ejpam-6089	170	25	)	)	PUNCT
ejpam-6089	170	26	,	,	PUNCT
ejpam-6089	170	27	we	we	PRON
ejpam-6089	170	28	have	have	VERB
ejpam-6089	170	29	(	(	PUNCT
ejpam-6089	170	30	h−h	h−h	NOUN
ejpam-6089	170	31	)	)	PUNCT
ejpam-6089	170	32	inequality	inequality	NOUN
ejpam-6089	170	33	for	for	ADP
ejpam-6089	170	34	atangana	atangana	PROPN
ejpam-6089	170	35	-	-	PUNCT
ejpam-6089	170	36	baleanu	baleanu	ADJ
ejpam-6089	170	37	fractional	fractional	ADJ
ejpam-6089	170	38	integrals	integral	NOUN
ejpam-6089	170	39	,	,	PUNCT
ejpam-6089	170	40	where	where	SCONJ
ejpam-6089	170	41	,	,	PUNCT
ejpam-6089	170	42	♭	♭	INTJ
ejpam-6089	170	43	,	,	PUNCT
ejpam-6089	170	44	ℵ	ℵ	NOUN
ejpam-6089	170	45	,	,	PUNCT
ejpam-6089	170	46	℘	℘	PROPN
ejpam-6089	170	47	,	,	PUNCT
ejpam-6089	170	48	τ	τ	PROPN
ejpam-6089	170	49	,	,	PUNCT
ejpam-6089	170	50	δ	δ	PROPN
ejpam-6089	170	51	,	,	PUNCT
ejpam-6089	170	52	b	b	PROPN
ejpam-6089	170	53	∈	∈	PROPN
ejpam-6089	170	54	c	c	NOUN
ejpam-6089	170	55	with	with	ADP
ejpam-6089	170	56	ℜ(ℵ),ℜ(℘),ℜ(τ	ℜ(ℵ),ℜ(℘),ℜ(τ	PROPN
ejpam-6089	170	57	)	)	PUNCT
ejpam-6089	170	58	>	>	X
ejpam-6089	170	59	0	0	NUM
ejpam-6089	170	60	and	and	CCONJ
ejpam-6089	170	61	ℜ(b	ℜ(b	NOUN
ejpam-6089	170	62	)	)	PUNCT
ejpam-6089	170	63	>	>	X
ejpam-6089	170	64	ℜ(δ	ℜ(δ	X
ejpam-6089	170	65	)	)	PUNCT
ejpam-6089	170	66	>	>	X
ejpam-6089	170	67	0	0	PUNCT
ejpam-6089	171	1	and	and	CCONJ
ejpam-6089	171	2	let	let	VERB
ejpam-6089	171	3	g	g	PROPN
ejpam-6089	171	4	≥	≥	NOUN
ejpam-6089	171	5	0	0	NUM
ejpam-6089	171	6	,	,	PUNCT
ejpam-6089	171	7	l	l	NOUN
ejpam-6089	171	8	>	>	X
ejpam-6089	171	9	0	0	PUNCT
ejpam-6089	172	1	and	and	CCONJ
ejpam-6089	172	2	0	0	NUM
ejpam-6089	172	3	<	<	X
ejpam-6089	172	4	s	s	X
ejpam-6089	172	5	≤	≤	NUM
ejpam-6089	172	6	l	l	NOUN
ejpam-6089	173	1	+	+	NOUN
ejpam-6089	173	2	ℜ(ℵ	ℜ(ℵ	NOUN
ejpam-6089	173	3	)	)	PUNCT
ejpam-6089	173	4	∞∑	∞∑	PROPN
ejpam-6089	173	5	ð=0	ð=0	X
ejpam-6089	173	6	aðuðυ	aðuðυ	NOUN
ejpam-6089	173	7	(	(	PUNCT
ejpam-6089	173	8	ℑ1	ℑ1	PROPN
ejpam-6089	173	9	+	+	CCONJ
ejpam-6089	173	10	ℑ2	ℑ2	PROPN
ejpam-6089	173	11	2	2	NUM
ejpam-6089	173	12	)	)	PUNCT
ejpam-6089	173	13	≤	≤	PUNCT
ejpam-6089	173	14	ε	ε	PROPN
ejpam-6089	173	15	♭	♭	PROPN
ejpam-6089	173	16	,δ	,δ	PUNCT
ejpam-6089	173	17	,	,	PUNCT
ejpam-6089	173	18	b	b	NOUN
ejpam-6089	173	19	,	,	PUNCT
ejpam-6089	173	20	s	s	NOUN
ejpam-6089	173	21	,	,	PUNCT
ejpam-6089	173	22	lℑ1+,ℵ,℘,τυ(ℑ2	lℑ1+,ℵ,℘,τυ(ℑ2	NOUN
ejpam-6089	173	23	;	;	PUNCT
ejpam-6089	173	24	g	g	NOUN
ejpam-6089	173	25	)	)	PUNCT
ejpam-6089	174	1	+	+	CCONJ
ejpam-6089	174	2	ε	ε	PROPN
ejpam-6089	174	3	♭	♭	PROPN
ejpam-6089	174	4	,δ	,δ	PUNCT
ejpam-6089	174	5	,	,	PUNCT
ejpam-6089	174	6	b	b	NOUN
ejpam-6089	174	7	,	,	PUNCT
ejpam-6089	174	8	s	s	PROPN
ejpam-6089	174	9	,	,	PUNCT
ejpam-6089	174	10	lℑ2−,ℵ,℘,τυ(ℑ1	lℑ2−,ℵ,℘,τυ(ℑ1	PROPN
ejpam-6089	174	11	;	;	PUNCT
ejpam-6089	174	12	g	g	X
ejpam-6089	174	13	)	)	PUNCT
ejpam-6089	174	14	≤	≤	NOUN
ejpam-6089	175	1	∞∑	∞∑	NUM
ejpam-6089	175	2	ð=0	ð=0	X
ejpam-6089	175	3	aðuð	aðuð	NOUN
ejpam-6089	175	4	(	(	PUNCT
ejpam-6089	175	5	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	175	6	)	)	PUNCT
ejpam-6089	175	7	+	+	CCONJ
ejpam-6089	175	8	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	175	9	)	)	PUNCT
ejpam-6089	175	10	2	2	NUM
ejpam-6089	175	11	)	)	PUNCT
ejpam-6089	176	1	,	,	PUNCT
ejpam-6089	176	2	s.	s.	PROPN
ejpam-6089	176	3	naheed	nahee	VERB
ejpam-6089	176	4	et	et	PROPN
ejpam-6089	176	5	al	al	PROPN
ejpam-6089	176	6	.	.	PUNCT
ejpam-6089	176	7	/	/	SYM
ejpam-6089	176	8	eur	eur	PROPN
ejpam-6089	176	9	.	.	PUNCT
ejpam-6089	177	1	j.	j.	PROPN
ejpam-6089	177	2	pure	pure	PROPN
ejpam-6089	177	3	appl	appl	PROPN
ejpam-6089	177	4	.	.	PROPN
ejpam-6089	177	5	math	math	PROPN
ejpam-6089	177	6	,	,	PUNCT
ejpam-6089	177	7	18	18	NUM
ejpam-6089	177	8	(	(	PUNCT
ejpam-6089	177	9	2	2	NUM
ejpam-6089	177	10	)	)	PUNCT
ejpam-6089	177	11	(	(	PUNCT
ejpam-6089	177	12	2025	2025	NUM
ejpam-6089	177	13	)	)	PUNCT
ejpam-6089	177	14	,	,	PUNCT
ejpam-6089	177	15	6089	6089	NUM
ejpam-6089	177	16	9	9	NUM
ejpam-6089	177	17	of	of	ADP
ejpam-6089	177	18	34	34	NUM
ejpam-6089	177	19	where	where	SCONJ
ejpam-6089	177	20	að	að	PROPN
ejpam-6089	177	21	=	=	SYM
ejpam-6089	177	22	bg(δ+ðs	bg(δ+ðs	PROPN
ejpam-6089	177	23	,	,	PUNCT
ejpam-6089	177	24	b−δ	b−δ	NOUN
ejpam-6089	177	25	)	)	PUNCT
ejpam-6089	177	26	b(δ	b(δ	NOUN
ejpam-6089	177	27	,	,	PUNCT
ejpam-6089	177	28	b−δ	b−δ	NOUN
ejpam-6089	177	29	)	)	PUNCT
ejpam-6089	177	30	(	(	PUNCT
ejpam-6089	178	1	b)ðs	b)ðs	PROPN
ejpam-6089	178	2	♭	♭	PROPN
ejpam-6089	178	3	ð	ð	X
ejpam-6089	178	4	(	(	PUNCT
ejpam-6089	178	5	τ)ðl	τ)ðl	ADJ
ejpam-6089	178	6	and	and	CCONJ
ejpam-6089	178	7	uð	uð	ADJ
ejpam-6089	178	8	=	=	NOUN
ejpam-6089	178	9	2((ℑ2−ℑ1)ℵð+℘+(1−ℵð−℘)γ(ℵð+℘	2((ℑ2−ℑ1)ℵð+℘+(1−ℵð−℘)γ(ℵð+℘	NUM
ejpam-6089	178	10	)	)	PUNCT
ejpam-6089	178	11	)	)	PUNCT
ejpam-6089	178	12	γ(ℵð+℘+1	γ(ℵð+℘+1	NOUN
ejpam-6089	178	13	)	)	PUNCT
ejpam-6089	178	14	−	−	PROPN
ejpam-6089	178	15	2(1−ℵð−℘	2(1−ℵð−℘	NUM
ejpam-6089	178	16	)	)	PUNCT
ejpam-6089	178	17	(	(	PUNCT
ejpam-6089	178	18	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	178	19	)	)	PUNCT
ejpam-6089	178	20	.	.	PUNCT
ejpam-6089	179	1	proof	proof	NOUN
ejpam-6089	179	2	.	.	PUNCT
ejpam-6089	180	1	replacing	replace	VERB
ejpam-6089	180	2	α∗	α∗	NOUN
ejpam-6089	180	3	by	by	ADP
ejpam-6089	180	4	(	(	PUNCT
ejpam-6089	180	5	ℵð+	ℵð+	ADJ
ejpam-6089	180	6	℘	℘	PROPN
ejpam-6089	180	7	)	)	PUNCT
ejpam-6089	180	8	in	in	ADP
ejpam-6089	180	9	theorem	theorem	NOUN
ejpam-6089	180	10	3	3	NUM
ejpam-6089	180	11	,	,	PUNCT
ejpam-6089	180	12	we	we	PRON
ejpam-6089	180	13	obtain	obtain	VERB
ejpam-6089	180	14	υ	υ	PRON
ejpam-6089	180	15	(	(	PUNCT
ejpam-6089	180	16	ℑ1	ℑ1	PROPN
ejpam-6089	180	17	+	+	CCONJ
ejpam-6089	180	18	ℑ2	ℑ2	PROPN
ejpam-6089	180	19	2	2	NUM
ejpam-6089	180	20	)	)	PUNCT
ejpam-6089	180	21	≤	≤	NUM
ejpam-6089	180	22	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	180	23	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	180	24	℘	℘	PROPN
ejpam-6089	180	25	)	)	PUNCT
ejpam-6089	180	26	2	2	NUM
ejpam-6089	180	27	(	(	PUNCT
ejpam-6089	180	28	(	(	PUNCT
ejpam-6089	180	29	ℑ2	ℑ2	PROPN
ejpam-6089	180	30	−ℑ1)(ℵð+℘	−ℑ1)(ℵð+℘	NUM
ejpam-6089	180	31	)	)	PUNCT
ejpam-6089	181	1	+	+	CCONJ
ejpam-6089	181	2	(	(	PUNCT
ejpam-6089	181	3	1−	1−	NUM
ejpam-6089	181	4	ℵð−	ℵð−	PROPN
ejpam-6089	181	5	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	181	6	℘	℘	PROPN
ejpam-6089	181	7	)	)	PUNCT
ejpam-6089	181	8	)	)	PUNCT
ejpam-6089	181	9	×	×	NOUN
ejpam-6089	181	10	(	(	PUNCT
ejpam-6089	181	11	a−bi	a−bi	PROPN
ejpam-6089	181	12	(	(	PUNCT
ejpam-6089	181	13	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	181	14	)	)	PUNCT
ejpam-6089	181	15	ℑ1	ℑ1	NOUN
ejpam-6089	181	16	+	+	CCONJ
ejpam-6089	181	17	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	181	18	)	)	PUNCT
ejpam-6089	182	1	+	+	CCONJ
ejpam-6089	182	2	a−bi	a−bi	PROPN
ejpam-6089	182	3	(	(	PUNCT
ejpam-6089	182	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	182	5	)	)	PUNCT
ejpam-6089	182	6	ℑ2−	ℑ2−	NUM
ejpam-6089	183	1	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	183	2	)	)	PUNCT
ejpam-6089	183	3	)	)	PUNCT
ejpam-6089	184	1	≤	≤	NOUN
ejpam-6089	184	2	(	(	PUNCT
ejpam-6089	184	3	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	184	4	)	)	PUNCT
ejpam-6089	184	5	+	+	CCONJ
ejpam-6089	184	6	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	184	7	)	)	PUNCT
ejpam-6089	184	8	2	2	NUM
ejpam-6089	184	9	)	)	PUNCT
ejpam-6089	184	10	.	.	PUNCT
ejpam-6089	185	1	multiplying	multiply	VERB
ejpam-6089	185	2	the	the	DET
ejpam-6089	185	3	above	above	ADJ
ejpam-6089	185	4	inequality	inequality	NOUN
ejpam-6089	185	5	with	with	ADP
ejpam-6089	185	6	2((ℑ2−ℑ1)(ℵð+℘)+(1−ℵð−℘),wehaveγ(ℵð+℘	2((ℑ2−ℑ1)(ℵð+℘)+(1−ℵð−℘),wehaveγ(ℵð+℘	NUM
ejpam-6089	185	7	)	)	PUNCT
ejpam-6089	185	8	)	)	PUNCT
ejpam-6089	185	9	b(ℵð+℘)γ(ℵð+℘	b(ℵð+℘)γ(ℵð+℘	NOUN
ejpam-6089	185	10	)	)	PUNCT
ejpam-6089	185	11	,	,	PUNCT
ejpam-6089	185	12	we	we	PRON
ejpam-6089	185	13	get	get	VERB
ejpam-6089	185	14	2	2	NUM
ejpam-6089	185	15	(	(	PUNCT
ejpam-6089	185	16	(	(	PUNCT
ejpam-6089	185	17	ℑ2	ℑ2	PROPN
ejpam-6089	185	18	−ℑ1	−ℑ1	PROPN
ejpam-6089	185	19	)	)	PUNCT
ejpam-6089	185	20	(	(	PUNCT
ejpam-6089	185	21	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	185	22	)	)	PUNCT
ejpam-6089	186	1	+	+	CCONJ
ejpam-6089	186	2	(	(	PUNCT
ejpam-6089	186	3	1−	1−	NUM
ejpam-6089	186	4	ℵð−	ℵð−	PROPN
ejpam-6089	186	5	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	186	6	℘	℘	PROPN
ejpam-6089	186	7	)	)	PUNCT
ejpam-6089	186	8	)	)	PUNCT
ejpam-6089	187	1	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	187	2	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	187	3	℘	℘	PROPN
ejpam-6089	187	4	)	)	PUNCT
ejpam-6089	187	5	υ	υ	NOUN
ejpam-6089	187	6	(	(	PUNCT
ejpam-6089	187	7	ℑ1	ℑ1	PROPN
ejpam-6089	187	8	+	+	CCONJ
ejpam-6089	187	9	ℑ2	ℑ2	PROPN
ejpam-6089	187	10	2	2	NUM
ejpam-6089	187	11	)	)	PUNCT
ejpam-6089	187	12	≤	≤	NOUN
ejpam-6089	187	13	(	(	PUNCT
ejpam-6089	187	14	a−bi	a−bi	PROPN
ejpam-6089	187	15	(	(	PUNCT
ejpam-6089	187	16	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	187	17	)	)	PUNCT
ejpam-6089	187	18	ℑ1	ℑ1	NOUN
ejpam-6089	187	19	+	+	CCONJ
ejpam-6089	187	20	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	187	21	)	)	PUNCT
ejpam-6089	187	22	+	+	CCONJ
ejpam-6089	187	23	a−bi	a−bi	PROPN
ejpam-6089	187	24	(	(	PUNCT
ejpam-6089	187	25	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	187	26	)	)	PUNCT
ejpam-6089	187	27	ℑ2−	ℑ2−	NUM
ejpam-6089	188	1	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	188	2	)	)	PUNCT
ejpam-6089	188	3	)	)	PUNCT
ejpam-6089	189	1	≤	≤	ADV
ejpam-6089	189	2	2	2	NUM
ejpam-6089	189	3	(	(	PUNCT
ejpam-6089	189	4	(	(	PUNCT
ejpam-6089	189	5	ℑ2	ℑ2	PROPN
ejpam-6089	189	6	−ℑ1	−ℑ1	PROPN
ejpam-6089	189	7	)	)	PUNCT
ejpam-6089	189	8	(	(	PUNCT
ejpam-6089	189	9	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	189	10	)	)	PUNCT
ejpam-6089	190	1	+	+	CCONJ
ejpam-6089	190	2	(	(	PUNCT
ejpam-6089	190	3	1−	1−	NUM
ejpam-6089	190	4	ℵð−	ℵð−	PROPN
ejpam-6089	190	5	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	190	6	℘	℘	PROPN
ejpam-6089	190	7	)	)	PUNCT
ejpam-6089	190	8	)	)	PUNCT
ejpam-6089	191	1	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	191	2	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	191	3	℘	℘	PROPN
ejpam-6089	191	4	)	)	PUNCT
ejpam-6089	191	5	(	(	PUNCT
ejpam-6089	191	6	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	191	7	)	)	PUNCT
ejpam-6089	192	1	+	+	CCONJ
ejpam-6089	192	2	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	192	3	)	)	PUNCT
ejpam-6089	192	4	2	2	NUM
ejpam-6089	192	5	)	)	PUNCT
ejpam-6089	192	6	.	.	PUNCT
ejpam-6089	193	1	(	(	PUNCT
ejpam-6089	193	2	14	14	X
ejpam-6089	193	3	)	)	PUNCT
ejpam-6089	193	4	adding	add	VERB
ejpam-6089	193	5	left	left	ADJ
ejpam-6089	193	6	and	and	CCONJ
ejpam-6089	193	7	right	right	ADV
ejpam-6089	193	8	sided	sided	ADJ
ejpam-6089	193	9	atangana	atangana	PROPN
ejpam-6089	193	10	-	-	PUNCT
ejpam-6089	193	11	baleanu	baleanu	PROPN
ejpam-6089	193	12	integrals	integral	NOUN
ejpam-6089	193	13	(	(	PUNCT
ejpam-6089	193	14	3	3	NUM
ejpam-6089	193	15	)	)	PUNCT
ejpam-6089	193	16	and	and	CCONJ
ejpam-6089	193	17	(	(	PUNCT
ejpam-6089	193	18	4	4	NUM
ejpam-6089	193	19	)	)	PUNCT
ejpam-6089	193	20	,	,	PUNCT
ejpam-6089	193	21	we	we	PRON
ejpam-6089	193	22	acquire	acquire	VERB
ejpam-6089	193	23	a−biα	a−biα	ADJ
ejpam-6089	193	24	∗	∗	NOUN
ejpam-6089	193	25	ℑ1+υ(ℑ2	ℑ1+υ(ℑ2	NOUN
ejpam-6089	193	26	)	)	PUNCT
ejpam-6089	193	27	+	+	NUM
ejpam-6089	193	28	a−biα	a−biα	ADJ
ejpam-6089	193	29	∗	∗	NOUN
ejpam-6089	193	30	ℑ2−υ(ℑ1	ℑ2−υ(ℑ1	NOUN
ejpam-6089	193	31	)	)	PUNCT
ejpam-6089	193	32	=	=	PUNCT
ejpam-6089	194	1	α∗	α∗	VERB
ejpam-6089	194	2	b(ℑ1	b(ℑ1	NOUN
ejpam-6089	194	3	)	)	PUNCT
ejpam-6089	195	1	(	(	PUNCT
ejpam-6089	195	2	r−liα	r−liα	VERB
ejpam-6089	195	3	∗	∗	NOUN
ejpam-6089	195	4	ℑ1+υ(ℑ2	ℑ1+υ(ℑ2	NOUN
ejpam-6089	195	5	)	)	PUNCT
ejpam-6089	195	6	+	+	NUM
ejpam-6089	195	7	r−liα	r−liα	NOUN
ejpam-6089	195	8	∗	∗	NOUN
ejpam-6089	195	9	ℑ2−υ(ℑ1	ℑ2−υ(ℑ1	NOUN
ejpam-6089	195	10	)	)	PUNCT
ejpam-6089	195	11	)	)	PUNCT
ejpam-6089	196	1	+	+	CCONJ
ejpam-6089	196	2	1−	1−	NUM
ejpam-6089	196	3	α∗	α∗	NOUN
ejpam-6089	196	4	b(ℑ1	b(ℑ1	NOUN
ejpam-6089	196	5	)	)	PUNCT
ejpam-6089	196	6	(	(	PUNCT
ejpam-6089	196	7	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	196	8	)	)	PUNCT
ejpam-6089	196	9	+	+	CCONJ
ejpam-6089	196	10	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	196	11	)	)	PUNCT
ejpam-6089	196	12	2	2	NUM
ejpam-6089	196	13	)	)	PUNCT
ejpam-6089	196	14	.	.	PUNCT
ejpam-6089	197	1	using	use	VERB
ejpam-6089	197	2	α∗	α∗	NOUN
ejpam-6089	197	3	=	=	SYM
ejpam-6089	197	4	(	(	PUNCT
ejpam-6089	197	5	ℵð+	ℵð+	ADJ
ejpam-6089	197	6	℘	℘	PROPN
ejpam-6089	197	7	)	)	PUNCT
ejpam-6089	197	8	in	in	ADP
ejpam-6089	197	9	the	the	DET
ejpam-6089	197	10	above	above	ADJ
ejpam-6089	197	11	expression	expression	NOUN
ejpam-6089	197	12	and	and	CCONJ
ejpam-6089	197	13	then	then	ADV
ejpam-6089	197	14	put	put	VERB
ejpam-6089	197	15	the	the	DET
ejpam-6089	197	16	results	result	NOUN
ejpam-6089	197	17	in	in	ADP
ejpam-6089	197	18	(	(	PUNCT
ejpam-6089	197	19	14	14	NUM
ejpam-6089	197	20	)	)	PUNCT
ejpam-6089	197	21	,	,	PUNCT
ejpam-6089	197	22	we	we	PRON
ejpam-6089	197	23	get	get	VERB
ejpam-6089	197	24	2	2	NUM
ejpam-6089	197	25	(	(	PUNCT
ejpam-6089	197	26	(	(	PUNCT
ejpam-6089	197	27	ℑ2	ℑ2	PROPN
ejpam-6089	197	28	−ℑ1	−ℑ1	PROPN
ejpam-6089	197	29	)	)	PUNCT
ejpam-6089	197	30	(	(	PUNCT
ejpam-6089	197	31	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	197	32	)	)	PUNCT
ejpam-6089	198	1	+	+	CCONJ
ejpam-6089	198	2	(	(	PUNCT
ejpam-6089	198	3	1−	1−	NUM
ejpam-6089	198	4	ℵð−	ℵð−	PROPN
ejpam-6089	198	5	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	198	6	℘	℘	PROPN
ejpam-6089	198	7	)	)	PUNCT
ejpam-6089	198	8	)	)	PUNCT
ejpam-6089	199	1	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	199	2	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	199	3	℘	℘	PROPN
ejpam-6089	199	4	)	)	PUNCT
ejpam-6089	199	5	υ	υ	NOUN
ejpam-6089	199	6	(	(	PUNCT
ejpam-6089	199	7	ℑ1	ℑ1	PROPN
ejpam-6089	199	8	+	+	CCONJ
ejpam-6089	199	9	ℑ2	ℑ2	PROPN
ejpam-6089	199	10	2	2	NUM
ejpam-6089	199	11	)	)	PUNCT
ejpam-6089	199	12	≤	≤	NOUN
ejpam-6089	199	13	(	(	PUNCT
ejpam-6089	199	14	ℵð+	ℵð+	ADJ
ejpam-6089	199	15	℘	℘	PROPN
ejpam-6089	199	16	)	)	PUNCT
ejpam-6089	199	17	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	199	18	℘	℘	PROPN
ejpam-6089	199	19	)	)	PUNCT
ejpam-6089	199	20	(	(	PUNCT
ejpam-6089	199	21	r−li	r−li	NOUN
ejpam-6089	199	22	(	(	PUNCT
ejpam-6089	199	23	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	199	24	)	)	PUNCT
ejpam-6089	199	25	ℑ1	ℑ1	NOUN
ejpam-6089	199	26	+	+	CCONJ
ejpam-6089	199	27	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	199	28	)	)	PUNCT
ejpam-6089	200	1	+	+	NUM
ejpam-6089	200	2	r−li	r−li	NOUN
ejpam-6089	200	3	(	(	PUNCT
ejpam-6089	200	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	200	5	)	)	PUNCT
ejpam-6089	200	6	ℑ2−	ℑ2−	NUM
ejpam-6089	201	1	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	201	2	)	)	PUNCT
ejpam-6089	201	3	)	)	PUNCT
ejpam-6089	202	1	+	+	CCONJ
ejpam-6089	202	2	(	(	PUNCT
ejpam-6089	202	3	1−	1−	NUM
ejpam-6089	202	4	ℵð−	ℵð−	NUM
ejpam-6089	202	5	℘	℘	PROPN
ejpam-6089	202	6	)	)	PUNCT
ejpam-6089	202	7	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	202	8	℘	℘	PROPN
ejpam-6089	202	9	)	)	PUNCT
ejpam-6089	202	10	(	(	PUNCT
ejpam-6089	202	11	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	202	12	)	)	PUNCT
ejpam-6089	202	13	+	+	CCONJ
ejpam-6089	202	14	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	202	15	)	)	PUNCT
ejpam-6089	202	16	)	)	PUNCT
ejpam-6089	202	17	≤	≤	ADV
ejpam-6089	202	18	2	2	NUM
ejpam-6089	202	19	(	(	PUNCT
ejpam-6089	202	20	(	(	PUNCT
ejpam-6089	202	21	ℑ2	ℑ2	PROPN
ejpam-6089	202	22	−ℑ1	−ℑ1	PROPN
ejpam-6089	202	23	)	)	PUNCT
ejpam-6089	202	24	(	(	PUNCT
ejpam-6089	202	25	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	202	26	)	)	PUNCT
ejpam-6089	203	1	+	+	CCONJ
ejpam-6089	203	2	(	(	PUNCT
ejpam-6089	203	3	1−	1−	NUM
ejpam-6089	203	4	ℵð−	ℵð−	PROPN
ejpam-6089	203	5	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	203	6	℘	℘	PROPN
ejpam-6089	203	7	)	)	PUNCT
ejpam-6089	203	8	)	)	PUNCT
ejpam-6089	204	1	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	204	2	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	204	3	℘	℘	PROPN
ejpam-6089	204	4	)	)	PUNCT
ejpam-6089	204	5	(	(	PUNCT
ejpam-6089	204	6	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	204	7	)	)	PUNCT
ejpam-6089	205	1	+	+	CCONJ
ejpam-6089	205	2	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	205	3	)	)	PUNCT
ejpam-6089	205	4	2	2	NUM
ejpam-6089	205	5	)	)	PUNCT
ejpam-6089	205	6	.	.	PUNCT
ejpam-6089	206	1	subtracting	subtract	VERB
ejpam-6089	206	2	1−ℵð−℘	1−ℵð−℘	NUM
ejpam-6089	206	3	b(ℵð+℘)(υ(ℑ1)+υ(ℑ2	b(ℵð+℘)(υ(ℑ1)+υ(ℑ2	NOUN
ejpam-6089	206	4	)	)	PUNCT
ejpam-6089	206	5	)	)	PUNCT
ejpam-6089	206	6	from	from	ADP
ejpam-6089	206	7	the	the	DET
ejpam-6089	206	8	above	above	ADJ
ejpam-6089	206	9	inequality	inequality	NOUN
ejpam-6089	206	10	and	and	CCONJ
ejpam-6089	206	11	then	then	ADV
ejpam-6089	206	12	multiplying	multiply	VERB
ejpam-6089	206	13	with	with	ADP
ejpam-6089	206	14	b(ℵð+℘	b(ℵð+℘	NOUN
ejpam-6089	206	15	)	)	PUNCT
ejpam-6089	206	16	(	(	PUNCT
ejpam-6089	206	17	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	206	18	)	)	PUNCT
ejpam-6089	206	19	,	,	PUNCT
ejpam-6089	206	20	we	we	PRON
ejpam-6089	206	21	obtain	obtain	VERB
ejpam-6089	206	22	2	2	NUM
ejpam-6089	206	23	(	(	PUNCT
ejpam-6089	206	24	(	(	PUNCT
ejpam-6089	206	25	ℑ2	ℑ2	PROPN
ejpam-6089	206	26	−ℑ1	−ℑ1	PROPN
ejpam-6089	206	27	)	)	PUNCT
ejpam-6089	206	28	(	(	PUNCT
ejpam-6089	206	29	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	206	30	)	)	PUNCT
ejpam-6089	207	1	+	+	CCONJ
ejpam-6089	207	2	(	(	PUNCT
ejpam-6089	207	3	1−	1−	NUM
ejpam-6089	207	4	ℵð−	ℵð−	PROPN
ejpam-6089	207	5	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	207	6	℘	℘	PROPN
ejpam-6089	207	7	)	)	PUNCT
ejpam-6089	207	8	)	)	PUNCT
ejpam-6089	208	1	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	208	2	℘	℘	PROPN
ejpam-6089	208	3	)	)	PUNCT
ejpam-6089	208	4	+	+	CCONJ
ejpam-6089	208	5	1	1	X
ejpam-6089	208	6	)	)	PUNCT
ejpam-6089	208	7	υ	υ	NOUN
ejpam-6089	208	8	(	(	PUNCT
ejpam-6089	208	9	ℑ1	ℑ1	PROPN
ejpam-6089	208	10	+	+	CCONJ
ejpam-6089	208	11	ℑ2	ℑ2	PROPN
ejpam-6089	208	12	2	2	NUM
ejpam-6089	208	13	)	)	PUNCT
ejpam-6089	208	14	s.	s.	PROPN
ejpam-6089	208	15	naheed	nahee	VERB
ejpam-6089	208	16	et	et	PROPN
ejpam-6089	208	17	al	al	PROPN
ejpam-6089	208	18	.	.	PUNCT
ejpam-6089	208	19	/	/	SYM
ejpam-6089	208	20	eur	eur	PROPN
ejpam-6089	208	21	.	.	PUNCT
ejpam-6089	209	1	j.	j.	PROPN
ejpam-6089	209	2	pure	pure	PROPN
ejpam-6089	209	3	appl	appl	PROPN
ejpam-6089	209	4	.	.	PROPN
ejpam-6089	209	5	math	math	PROPN
ejpam-6089	209	6	,	,	PUNCT
ejpam-6089	209	7	18	18	NUM
ejpam-6089	209	8	(	(	PUNCT
ejpam-6089	209	9	2	2	NUM
ejpam-6089	209	10	)	)	PUNCT
ejpam-6089	209	11	(	(	PUNCT
ejpam-6089	209	12	2025	2025	NUM
ejpam-6089	209	13	)	)	PUNCT
ejpam-6089	209	14	,	,	PUNCT
ejpam-6089	209	15	6089	6089	NUM
ejpam-6089	209	16	10	10	NUM
ejpam-6089	209	17	of	of	ADP
ejpam-6089	209	18	34	34	NUM
ejpam-6089	209	19	−	−	PROPN
ejpam-6089	209	20	1−	1−	NUM
ejpam-6089	209	21	ℵð−	ℵð−	PUNCT
ejpam-6089	209	22	℘	℘	PROPN
ejpam-6089	209	23	(	(	PUNCT
ejpam-6089	209	24	ℵð+	ℵð+	ADJ
ejpam-6089	209	25	℘	℘	PROPN
ejpam-6089	209	26	)	)	PUNCT
ejpam-6089	209	27	(	(	PUNCT
ejpam-6089	209	28	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	209	29	)	)	PUNCT
ejpam-6089	209	30	+	+	CCONJ
ejpam-6089	209	31	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	209	32	)	)	PUNCT
ejpam-6089	209	33	)	)	PUNCT
ejpam-6089	209	34	≤	≤	NOUN
ejpam-6089	209	35	(	(	PUNCT
ejpam-6089	209	36	r−li	r−li	NOUN
ejpam-6089	209	37	(	(	PUNCT
ejpam-6089	209	38	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	209	39	)	)	PUNCT
ejpam-6089	209	40	ℑ1	ℑ1	NOUN
ejpam-6089	209	41	+	+	CCONJ
ejpam-6089	209	42	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	209	43	)	)	PUNCT
ejpam-6089	210	1	+	+	NUM
ejpam-6089	210	2	r−li	r−li	NOUN
ejpam-6089	210	3	(	(	PUNCT
ejpam-6089	210	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	210	5	)	)	PUNCT
ejpam-6089	210	6	ℑ2−	ℑ2−	NUM
ejpam-6089	211	1	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	211	2	)	)	PUNCT
ejpam-6089	211	3	)	)	PUNCT
ejpam-6089	212	1	≤	≤	ADV
ejpam-6089	212	2	2	2	NUM
ejpam-6089	212	3	(	(	PUNCT
ejpam-6089	212	4	(	(	PUNCT
ejpam-6089	212	5	ℑ2	ℑ2	PROPN
ejpam-6089	212	6	−ℑ1	−ℑ1	PROPN
ejpam-6089	212	7	)	)	PUNCT
ejpam-6089	212	8	(	(	PUNCT
ejpam-6089	212	9	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	212	10	)	)	PUNCT
ejpam-6089	213	1	+	+	CCONJ
ejpam-6089	213	2	(	(	PUNCT
ejpam-6089	213	3	1−	1−	NUM
ejpam-6089	213	4	ℵð−	ℵð−	PROPN
ejpam-6089	213	5	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	213	6	℘	℘	PROPN
ejpam-6089	213	7	)	)	PUNCT
ejpam-6089	213	8	)	)	PUNCT
ejpam-6089	214	1	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	214	2	℘	℘	PROPN
ejpam-6089	214	3	)	)	PUNCT
ejpam-6089	214	4	+	+	CCONJ
ejpam-6089	214	5	1	1	X
ejpam-6089	214	6	)	)	PUNCT
ejpam-6089	214	7	(	(	PUNCT
ejpam-6089	214	8	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	214	9	)	)	PUNCT
ejpam-6089	215	1	+	+	CCONJ
ejpam-6089	215	2	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	215	3	)	)	PUNCT
ejpam-6089	215	4	2	2	NUM
ejpam-6089	215	5	)	)	PUNCT
ejpam-6089	215	6	−	−	PROPN
ejpam-6089	215	7	1−	1−	NUM
ejpam-6089	215	8	ℵð−	ℵð−	PUNCT
ejpam-6089	215	9	℘	℘	PROPN
ejpam-6089	215	10	(	(	PUNCT
ejpam-6089	215	11	ℵð+	ℵð+	ADJ
ejpam-6089	215	12	℘	℘	PROPN
ejpam-6089	215	13	)	)	PUNCT
ejpam-6089	215	14	(	(	PUNCT
ejpam-6089	215	15	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	215	16	)	)	PUNCT
ejpam-6089	215	17	+	+	CCONJ
ejpam-6089	215	18	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	215	19	)	)	PUNCT
ejpam-6089	215	20	)	)	PUNCT
ejpam-6089	215	21	.	.	PUNCT
ejpam-6089	216	1	again	again	ADV
ejpam-6089	216	2	we	we	PRON
ejpam-6089	216	3	multiply	multiply	VERB
ejpam-6089	216	4	the	the	DET
ejpam-6089	216	5	above	above	ADJ
ejpam-6089	216	6	inequality	inequality	NOUN
ejpam-6089	216	7	with	with	ADP
ejpam-6089	216	8	að	að	PROPN
ejpam-6089	216	9	to	to	PART
ejpam-6089	216	10	obtain	obtain	VERB
ejpam-6089	216	11	að	að	PROPN
ejpam-6089	216	12	(	(	PUNCT
ejpam-6089	216	13	2	2	NUM
ejpam-6089	216	14	(	(	PUNCT
ejpam-6089	216	15	(	(	PUNCT
ejpam-6089	216	16	ℑ2	ℑ2	PROPN
ejpam-6089	216	17	−ℑ1	−ℑ1	PROPN
ejpam-6089	216	18	)	)	PUNCT
ejpam-6089	216	19	(	(	PUNCT
ejpam-6089	216	20	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	216	21	)	)	PUNCT
ejpam-6089	217	1	+	+	CCONJ
ejpam-6089	217	2	(	(	PUNCT
ejpam-6089	217	3	1−	1−	NUM
ejpam-6089	217	4	ℵð−	ℵð−	PROPN
ejpam-6089	217	5	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	217	6	℘	℘	PROPN
ejpam-6089	217	7	)	)	PUNCT
ejpam-6089	217	8	)	)	PUNCT
ejpam-6089	218	1	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	218	2	℘	℘	PROPN
ejpam-6089	218	3	)	)	PUNCT
ejpam-6089	218	4	+	+	CCONJ
ejpam-6089	218	5	1	1	X
ejpam-6089	218	6	)	)	PUNCT
ejpam-6089	218	7	υ	υ	NOUN
ejpam-6089	218	8	(	(	PUNCT
ejpam-6089	218	9	ℑ1	ℑ1	PROPN
ejpam-6089	218	10	+	+	CCONJ
ejpam-6089	218	11	ℑ2	ℑ2	PROPN
ejpam-6089	218	12	2	2	NUM
ejpam-6089	218	13	)	)	PUNCT
ejpam-6089	218	14	)	)	PUNCT
ejpam-6089	218	15	−	−	PROPN
ejpam-6089	219	1	að	að	INTJ
ejpam-6089	219	2	(	(	PUNCT
ejpam-6089	219	3	1−	1−	NUM
ejpam-6089	219	4	ℵð−	ℵð−	PUNCT
ejpam-6089	219	5	℘	℘	PROPN
ejpam-6089	219	6	(	(	PUNCT
ejpam-6089	219	7	ℵð+	ℵð+	ADJ
ejpam-6089	219	8	℘	℘	PROPN
ejpam-6089	219	9	)	)	PUNCT
ejpam-6089	219	10	(	(	PUNCT
ejpam-6089	219	11	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	219	12	)	)	PUNCT
ejpam-6089	219	13	+	+	CCONJ
ejpam-6089	219	14	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	219	15	)	)	PUNCT
ejpam-6089	219	16	)	)	PUNCT
ejpam-6089	219	17	)	)	PUNCT
ejpam-6089	220	1	≤	≤	NUM
ejpam-6089	220	2	að	að	PROPN
ejpam-6089	220	3	(	(	PUNCT
ejpam-6089	220	4	r−li	r−li	NOUN
ejpam-6089	220	5	(	(	PUNCT
ejpam-6089	220	6	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	220	7	)	)	PUNCT
ejpam-6089	220	8	ℑ1	ℑ1	NOUN
ejpam-6089	220	9	+	+	CCONJ
ejpam-6089	220	10	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	220	11	)	)	PUNCT
ejpam-6089	220	12	+	+	NUM
ejpam-6089	220	13	r−li	r−li	NOUN
ejpam-6089	220	14	(	(	PUNCT
ejpam-6089	220	15	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	220	16	)	)	PUNCT
ejpam-6089	220	17	ℑ2−	ℑ2−	NUM
ejpam-6089	220	18	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	220	19	)	)	PUNCT
ejpam-6089	220	20	)	)	PUNCT
ejpam-6089	221	1	≤	≤	NUM
ejpam-6089	221	2	að	að	PROPN
ejpam-6089	221	3	(	(	PUNCT
ejpam-6089	221	4	2	2	NUM
ejpam-6089	221	5	(	(	PUNCT
ejpam-6089	221	6	(	(	PUNCT
ejpam-6089	221	7	ℑ2	ℑ2	PROPN
ejpam-6089	221	8	−ℑ1	−ℑ1	PROPN
ejpam-6089	221	9	)	)	PUNCT
ejpam-6089	221	10	(	(	PUNCT
ejpam-6089	221	11	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	221	12	)	)	PUNCT
ejpam-6089	221	13	+	+	CCONJ
ejpam-6089	221	14	(	(	PUNCT
ejpam-6089	221	15	1−	1−	NUM
ejpam-6089	221	16	ℵð−	ℵð−	PROPN
ejpam-6089	221	17	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	221	18	℘	℘	PROPN
ejpam-6089	221	19	)	)	PUNCT
ejpam-6089	221	20	)	)	PUNCT
ejpam-6089	221	21	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	221	22	℘	℘	PROPN
ejpam-6089	221	23	)	)	PUNCT
ejpam-6089	221	24	+	+	CCONJ
ejpam-6089	221	25	1	1	X
ejpam-6089	221	26	)	)	PUNCT
ejpam-6089	221	27	(	(	PUNCT
ejpam-6089	221	28	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	221	29	)	)	PUNCT
ejpam-6089	221	30	+	+	CCONJ
ejpam-6089	221	31	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	221	32	)	)	PUNCT
ejpam-6089	221	33	2	2	NUM
ejpam-6089	221	34	)	)	PUNCT
ejpam-6089	221	35	)	)	PUNCT
ejpam-6089	222	1	−	−	PROPN
ejpam-6089	222	2	að	að	INTJ
ejpam-6089	222	3	(	(	PUNCT
ejpam-6089	222	4	1−	1−	NUM
ejpam-6089	222	5	ℵð−	ℵð−	PUNCT
ejpam-6089	222	6	℘	℘	PROPN
ejpam-6089	222	7	(	(	PUNCT
ejpam-6089	222	8	ℵð+	ℵð+	ADJ
ejpam-6089	222	9	℘	℘	PROPN
ejpam-6089	222	10	)	)	PUNCT
ejpam-6089	222	11	(	(	PUNCT
ejpam-6089	222	12	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	222	13	)	)	PUNCT
ejpam-6089	222	14	+	+	CCONJ
ejpam-6089	222	15	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	222	16	)	)	PUNCT
ejpam-6089	222	17	)	)	PUNCT
ejpam-6089	222	18	)	)	PUNCT
ejpam-6089	222	19	.	.	PUNCT
ejpam-6089	223	1	by	by	ADP
ejpam-6089	223	2	convexity	convexity	NOUN
ejpam-6089	223	3	of	of	ADP
ejpam-6089	223	4	υ	υ	NOUN
ejpam-6089	223	5	we	we	PRON
ejpam-6089	223	6	have	have	VERB
ejpam-6089	223	7	,	,	PUNCT
ejpam-6089	223	8	υ	υ	PROPN
ejpam-6089	223	9	(	(	PUNCT
ejpam-6089	223	10	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	223	11	2	2	NUM
ejpam-6089	223	12	)	)	PUNCT
ejpam-6089	223	13	≤	≤	NOUN
ejpam-6089	223	14	(	(	PUNCT
ejpam-6089	223	15	υ(ℑ1)+υ(ℑ2	υ(ℑ1)+υ(ℑ2	PROPN
ejpam-6089	223	16	)	)	PUNCT
ejpam-6089	223	17	2	2	NUM
ejpam-6089	223	18	)	)	PUNCT
ejpam-6089	223	19	að	að	PROPN
ejpam-6089	223	20	(	(	PUNCT
ejpam-6089	223	21	2	2	NUM
ejpam-6089	223	22	(	(	PUNCT
ejpam-6089	223	23	(	(	PUNCT
ejpam-6089	223	24	ℑ2	ℑ2	PROPN
ejpam-6089	223	25	−ℑ1	−ℑ1	PROPN
ejpam-6089	223	26	)	)	PUNCT
ejpam-6089	223	27	(	(	PUNCT
ejpam-6089	223	28	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	223	29	)	)	PUNCT
ejpam-6089	223	30	+	+	CCONJ
ejpam-6089	223	31	(	(	PUNCT
ejpam-6089	223	32	1−	1−	NUM
ejpam-6089	223	33	ℵð−	ℵð−	PROPN
ejpam-6089	223	34	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	223	35	℘	℘	PROPN
ejpam-6089	223	36	)	)	PUNCT
ejpam-6089	223	37	)	)	PUNCT
ejpam-6089	223	38	γ(ℵð℘+	γ(ℵð℘+	ADJ
ejpam-6089	223	39	1	1	NUM
ejpam-6089	223	40	)	)	PUNCT
ejpam-6089	223	41	−	−	ADP
ejpam-6089	223	42	2(1−	2(1−	X
ejpam-6089	223	43	ℵð−	ℵð−	PUNCT
ejpam-6089	223	44	℘	℘	NUM
ejpam-6089	223	45	)	)	PUNCT
ejpam-6089	223	46	(	(	PUNCT
ejpam-6089	223	47	ℵð+	ℵð+	ADJ
ejpam-6089	223	48	℘	℘	PROPN
ejpam-6089	223	49	)	)	PUNCT
ejpam-6089	223	50	)	)	PUNCT
ejpam-6089	223	51	×υ	×υ	X
ejpam-6089	223	52	(	(	PUNCT
ejpam-6089	223	53	ℑ1	ℑ1	PROPN
ejpam-6089	223	54	+	+	CCONJ
ejpam-6089	223	55	ℑ2	ℑ2	PROPN
ejpam-6089	223	56	2	2	NUM
ejpam-6089	223	57	)	)	PUNCT
ejpam-6089	223	58	≤	≤	NUM
ejpam-6089	223	59	að	að	PROPN
ejpam-6089	223	60	(	(	PUNCT
ejpam-6089	223	61	r−li	r−li	NOUN
ejpam-6089	223	62	(	(	PUNCT
ejpam-6089	223	63	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	223	64	)	)	PUNCT
ejpam-6089	223	65	ℑ1	ℑ1	NOUN
ejpam-6089	223	66	+	+	CCONJ
ejpam-6089	223	67	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	223	68	)	)	PUNCT
ejpam-6089	224	1	+	+	NUM
ejpam-6089	224	2	r−li	r−li	NOUN
ejpam-6089	224	3	(	(	PUNCT
ejpam-6089	224	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	224	5	)	)	PUNCT
ejpam-6089	224	6	ℑ2−	ℑ2−	NUM
ejpam-6089	225	1	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	225	2	)	)	PUNCT
ejpam-6089	225	3	)	)	PUNCT
ejpam-6089	226	1	≤	≤	NUM
ejpam-6089	226	2	að	að	PROPN
ejpam-6089	226	3	(	(	PUNCT
ejpam-6089	226	4	2	2	NUM
ejpam-6089	226	5	(	(	PUNCT
ejpam-6089	226	6	(	(	PUNCT
ejpam-6089	226	7	ℑ2	ℑ2	PROPN
ejpam-6089	226	8	−ℑ1	−ℑ1	PROPN
ejpam-6089	226	9	)	)	PUNCT
ejpam-6089	226	10	(	(	PUNCT
ejpam-6089	226	11	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	226	12	)	)	PUNCT
ejpam-6089	226	13	+	+	CCONJ
ejpam-6089	226	14	(	(	PUNCT
ejpam-6089	226	15	1−	1−	NUM
ejpam-6089	226	16	ℵð−	ℵð−	PROPN
ejpam-6089	226	17	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	226	18	℘	℘	PROPN
ejpam-6089	226	19	)	)	PUNCT
ejpam-6089	226	20	)	)	PUNCT
ejpam-6089	226	21	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	226	22	℘	℘	PROPN
ejpam-6089	226	23	)	)	PUNCT
ejpam-6089	226	24	+	+	CCONJ
ejpam-6089	226	25	1	1	X
ejpam-6089	226	26	)	)	PUNCT
ejpam-6089	226	27	−	−	ADP
ejpam-6089	226	28	2(1−	2(1−	X
ejpam-6089	226	29	ℵð−	ℵð−	PUNCT
ejpam-6089	226	30	℘	℘	PROPN
ejpam-6089	226	31	)	)	PUNCT
ejpam-6089	226	32	ℵð℘	ℵð℘	PUNCT
ejpam-6089	226	33	)	)	PUNCT
ejpam-6089	226	34	×	×	NOUN
ejpam-6089	226	35	(	(	PUNCT
ejpam-6089	226	36	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	226	37	)	)	PUNCT
ejpam-6089	226	38	+	+	CCONJ
ejpam-6089	226	39	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	226	40	)	)	PUNCT
ejpam-6089	226	41	2	2	NUM
ejpam-6089	226	42	)	)	PUNCT
ejpam-6089	226	43	.	.	PUNCT
ejpam-6089	227	1	summing	sum	VERB
ejpam-6089	227	2	over	over	ADP
ejpam-6089	227	3	all	all	PRON
ejpam-6089	227	4	ð	ð	NOUN
ejpam-6089	227	5	∞∑	∞∑	NUM
ejpam-6089	227	6	ð=0	ð=0	X
ejpam-6089	227	7	að	að	X
ejpam-6089	227	8	(	(	PUNCT
ejpam-6089	227	9	2	2	NUM
ejpam-6089	227	10	(	(	PUNCT
ejpam-6089	227	11	(	(	PUNCT
ejpam-6089	227	12	ℑ2	ℑ2	PROPN
ejpam-6089	227	13	−ℑ1	−ℑ1	PROPN
ejpam-6089	227	14	)	)	PUNCT
ejpam-6089	227	15	(	(	PUNCT
ejpam-6089	227	16	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	227	17	)	)	PUNCT
ejpam-6089	228	1	+	+	CCONJ
ejpam-6089	228	2	(	(	PUNCT
ejpam-6089	228	3	1−	1−	NUM
ejpam-6089	228	4	ℵð−	ℵð−	PROPN
ejpam-6089	228	5	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	228	6	℘	℘	PROPN
ejpam-6089	228	7	)	)	PUNCT
ejpam-6089	228	8	)	)	PUNCT
ejpam-6089	229	1	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	229	2	℘	℘	PROPN
ejpam-6089	229	3	)	)	PUNCT
ejpam-6089	229	4	+	+	CCONJ
ejpam-6089	229	5	1	1	X
ejpam-6089	229	6	)	)	PUNCT
ejpam-6089	229	7	−	−	ADP
ejpam-6089	229	8	2(1−	2(1−	X
ejpam-6089	229	9	ℵð−	ℵð−	PUNCT
ejpam-6089	229	10	℘	℘	PROPN
ejpam-6089	229	11	)	)	PUNCT
ejpam-6089	229	12	ℵð℘	ℵð℘	PUNCT
ejpam-6089	229	13	)	)	PUNCT
ejpam-6089	229	14	×υ	×υ	X
ejpam-6089	229	15	(	(	PUNCT
ejpam-6089	229	16	ℑ1	ℑ1	PROPN
ejpam-6089	229	17	+	+	CCONJ
ejpam-6089	229	18	ℑ2	ℑ2	PROPN
ejpam-6089	229	19	2	2	NUM
ejpam-6089	229	20	)	)	PUNCT
ejpam-6089	229	21	≤	≤	NOUN
ejpam-6089	230	1	∞∑	∞∑	NUM
ejpam-6089	230	2	ð=0	ð=0	X
ejpam-6089	230	3	að	að	X
ejpam-6089	230	4	(	(	PUNCT
ejpam-6089	230	5	r−li	r−li	NOUN
ejpam-6089	230	6	(	(	PUNCT
ejpam-6089	230	7	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	230	8	)	)	PUNCT
ejpam-6089	230	9	ℑ1	ℑ1	NOUN
ejpam-6089	230	10	+	+	CCONJ
ejpam-6089	230	11	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	230	12	)	)	PUNCT
ejpam-6089	230	13	+	+	NUM
ejpam-6089	230	14	r−li	r−li	NOUN
ejpam-6089	230	15	(	(	PUNCT
ejpam-6089	230	16	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	230	17	)	)	PUNCT
ejpam-6089	230	18	ℑ2−	ℑ2−	NUM
ejpam-6089	230	19	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	230	20	)	)	PUNCT
ejpam-6089	230	21	)	)	PUNCT
ejpam-6089	230	22	≤	≤	NOUN
ejpam-6089	231	1	∞∑	∞∑	NUM
ejpam-6089	231	2	ð=0	ð=0	X
ejpam-6089	231	3	að	að	X
ejpam-6089	231	4	(	(	PUNCT
ejpam-6089	231	5	2	2	NUM
ejpam-6089	231	6	(	(	PUNCT
ejpam-6089	231	7	(	(	PUNCT
ejpam-6089	231	8	ℑ2	ℑ2	PROPN
ejpam-6089	231	9	−ℑ1	−ℑ1	PROPN
ejpam-6089	231	10	)	)	PUNCT
ejpam-6089	231	11	ℵð+℘	ℵð+℘	PROPN
ejpam-6089	232	1	+	+	CCONJ
ejpam-6089	232	2	(	(	PUNCT
ejpam-6089	232	3	1−	1−	NUM
ejpam-6089	232	4	ℵð−	ℵð−	PROPN
ejpam-6089	232	5	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	232	6	℘	℘	PROPN
ejpam-6089	232	7	)	)	PUNCT
ejpam-6089	232	8	)	)	PUNCT
ejpam-6089	232	9	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	232	10	℘	℘	PROPN
ejpam-6089	232	11	)	)	PUNCT
ejpam-6089	232	12	+	+	CCONJ
ejpam-6089	232	13	1	1	X
ejpam-6089	232	14	)	)	PUNCT
ejpam-6089	232	15	−	−	ADP
ejpam-6089	232	16	2(1−	2(1−	X
ejpam-6089	232	17	ℵð−	ℵð−	PUNCT
ejpam-6089	232	18	℘	℘	NUM
ejpam-6089	232	19	)	)	PUNCT
ejpam-6089	232	20	(	(	PUNCT
ejpam-6089	232	21	ℵð+	ℵð+	ADJ
ejpam-6089	232	22	℘	℘	PROPN
ejpam-6089	232	23	)	)	PUNCT
ejpam-6089	232	24	)	)	PUNCT
ejpam-6089	233	1	s.	s.	PROPN
ejpam-6089	233	2	naheed	nahee	VERB
ejpam-6089	233	3	et	et	PROPN
ejpam-6089	233	4	al	al	PROPN
ejpam-6089	233	5	.	.	PUNCT
ejpam-6089	233	6	/	/	SYM
ejpam-6089	233	7	eur	eur	PROPN
ejpam-6089	233	8	.	.	PUNCT
ejpam-6089	234	1	j.	j.	PROPN
ejpam-6089	234	2	pure	pure	PROPN
ejpam-6089	234	3	appl	appl	PROPN
ejpam-6089	234	4	.	.	PROPN
ejpam-6089	234	5	math	math	PROPN
ejpam-6089	234	6	,	,	PUNCT
ejpam-6089	234	7	18	18	NUM
ejpam-6089	234	8	(	(	PUNCT
ejpam-6089	234	9	2	2	NUM
ejpam-6089	234	10	)	)	PUNCT
ejpam-6089	234	11	(	(	PUNCT
ejpam-6089	234	12	2025	2025	NUM
ejpam-6089	234	13	)	)	PUNCT
ejpam-6089	234	14	,	,	PUNCT
ejpam-6089	234	15	6089	6089	NUM
ejpam-6089	234	16	11	11	NUM
ejpam-6089	234	17	of	of	ADP
ejpam-6089	234	18	34	34	NUM
ejpam-6089	234	19	×	×	NOUN
ejpam-6089	234	20	(	(	PUNCT
ejpam-6089	234	21	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	234	22	)	)	PUNCT
ejpam-6089	234	23	+	+	CCONJ
ejpam-6089	234	24	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	234	25	)	)	PUNCT
ejpam-6089	234	26	2	2	NUM
ejpam-6089	234	27	)	)	PUNCT
ejpam-6089	234	28	.	.	PUNCT
ejpam-6089	235	1	using	use	VERB
ejpam-6089	235	2	proposition	proposition	NOUN
ejpam-6089	235	3	1	1	NUM
ejpam-6089	235	4	,	,	PUNCT
ejpam-6089	235	5	we	we	PRON
ejpam-6089	235	6	get	get	VERB
ejpam-6089	235	7	∞∑	∞∑	NUM
ejpam-6089	235	8	ð=0	ð=0	X
ejpam-6089	235	9	aðuðυ	aðuðυ	NOUN
ejpam-6089	235	10	(	(	PUNCT
ejpam-6089	235	11	ℑ1	ℑ1	PROPN
ejpam-6089	235	12	+	+	CCONJ
ejpam-6089	235	13	ℑ2	ℑ2	PROPN
ejpam-6089	235	14	2	2	NUM
ejpam-6089	235	15	)	)	PUNCT
ejpam-6089	235	16	≤	≤	PUNCT
ejpam-6089	235	17	ε	ε	PROPN
ejpam-6089	235	18	♭	♭	PROPN
ejpam-6089	235	19	,δ	,δ	PUNCT
ejpam-6089	235	20	,	,	PUNCT
ejpam-6089	235	21	b	b	NOUN
ejpam-6089	235	22	,	,	PUNCT
ejpam-6089	235	23	s	s	NOUN
ejpam-6089	235	24	,	,	PUNCT
ejpam-6089	235	25	lℑ1+,ℵ,℘,τυ(ℑ2	lℑ1+,ℵ,℘,τυ(ℑ2	NOUN
ejpam-6089	235	26	;	;	PUNCT
ejpam-6089	235	27	g	g	NOUN
ejpam-6089	235	28	)	)	PUNCT
ejpam-6089	236	1	+	+	CCONJ
ejpam-6089	236	2	ε	ε	PROPN
ejpam-6089	236	3	♭	♭	PROPN
ejpam-6089	236	4	,δ	,δ	PUNCT
ejpam-6089	236	5	,	,	PUNCT
ejpam-6089	236	6	b	b	NOUN
ejpam-6089	236	7	,	,	PUNCT
ejpam-6089	236	8	s	s	PROPN
ejpam-6089	236	9	,	,	PUNCT
ejpam-6089	236	10	lℑ2−,ℵ,℘,τυ(ℑ1	lℑ2−,ℵ,℘,τυ(ℑ1	PROPN
ejpam-6089	236	11	;	;	PUNCT
ejpam-6089	236	12	g	g	X
ejpam-6089	236	13	)	)	PUNCT
ejpam-6089	236	14	≤	≤	NOUN
ejpam-6089	237	1	∞∑	∞∑	NUM
ejpam-6089	237	2	ð=0	ð=0	X
ejpam-6089	237	3	aðuð	aðuð	NOUN
ejpam-6089	237	4	(	(	PUNCT
ejpam-6089	237	5	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	237	6	)	)	PUNCT
ejpam-6089	237	7	+	+	CCONJ
ejpam-6089	237	8	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	237	9	)	)	PUNCT
ejpam-6089	237	10	2	2	NUM
ejpam-6089	237	11	)	)	PUNCT
ejpam-6089	237	12	.	.	PUNCT
ejpam-6089	238	1	it	it	PRON
ejpam-6089	238	2	is	be	AUX
ejpam-6089	238	3	our	our	PRON
ejpam-6089	238	4	required	required	ADJ
ejpam-6089	238	5	result	result	NOUN
ejpam-6089	238	6	.	.	PUNCT
ejpam-6089	239	1	proposition	proposition	NOUN
ejpam-6089	239	2	3	3	NUM
ejpam-6089	239	3	.	.	X
ejpam-6089	239	4	for	for	ADP
ejpam-6089	239	5	a	a	DET
ejpam-6089	239	6	function	function	NOUN
ejpam-6089	239	7	υ	υ	X
ejpam-6089	239	8	∈	∈	PROPN
ejpam-6089	239	9	l1[ℑ1,ℑ2	l1[ℑ1,ℑ2	PROPN
ejpam-6089	239	10	]	]	PUNCT
ejpam-6089	239	11	and	and	CCONJ
ejpam-6089	239	12	c	c	NOUN
ejpam-6089	239	13	∈	∈	PROPN
ejpam-6089	240	1	[	[	X
ejpam-6089	240	2	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	240	3	]	]	PUNCT
ejpam-6089	240	4	,	,	PUNCT
ejpam-6089	240	5	the	the	DET
ejpam-6089	240	6	addition	addition	NOUN
ejpam-6089	240	7	of	of	ADP
ejpam-6089	240	8	the	the	DET
ejpam-6089	240	9	left	left	ADJ
ejpam-6089	240	10	and	and	CCONJ
ejpam-6089	240	11	right	right	ADJ
ejpam-6089	240	12	sided	sided	ADJ
ejpam-6089	240	13	prabhakar	prabhakar	NOUN
ejpam-6089	240	14	and	and	CCONJ
ejpam-6089	240	15	the	the	DET
ejpam-6089	240	16	left	left	ADJ
ejpam-6089	240	17	and	and	CCONJ
ejpam-6089	240	18	right	right	ADJ
ejpam-6089	240	19	sided	sided	ADJ
ejpam-6089	240	20	generalized	generalized	ADJ
ejpam-6089	240	21	fractional	fractional	ADJ
ejpam-6089	240	22	integral	integral	ADJ
ejpam-6089	240	23	operators	operator	NOUN
ejpam-6089	240	24	applied	apply	VERB
ejpam-6089	240	25	to	to	ADP
ejpam-6089	240	26	υ(c	υ(c	PROPN
ejpam-6089	240	27	)	)	PUNCT
ejpam-6089	240	28	are	be	AUX
ejpam-6089	240	29	defined	define	VERB
ejpam-6089	240	30	by	by	ADP
ejpam-6089	240	31	the	the	DET
ejpam-6089	240	32	following	follow	VERB
ejpam-6089	240	33	integral	integral	ADJ
ejpam-6089	240	34	transforms	transform	NOUN
ejpam-6089	240	35	,	,	PUNCT
ejpam-6089	240	36	where	where	SCONJ
ejpam-6089	240	37	ℜ(ℵð	ℜ(ℵð	NOUN
ejpam-6089	240	38	+	+	CCONJ
ejpam-6089	240	39	℘	℘	NOUN
ejpam-6089	240	40	)	)	PUNCT
ejpam-6089	240	41	>	>	X
ejpam-6089	240	42	0	0	PUNCT
ejpam-6089	241	1	also	also	ADV
ejpam-6089	241	2	♭	♭	PROPN
ejpam-6089	241	3	,	,	PUNCT
ejpam-6089	241	4	γ,ℵ	γ,ℵ	PROPN
ejpam-6089	241	5	,	,	PUNCT
ejpam-6089	241	6	℘	℘	PROPN
ejpam-6089	241	7	,	,	PUNCT
ejpam-6089	241	8	τ	τ	PROPN
ejpam-6089	241	9	,	,	PUNCT
ejpam-6089	241	10	δ	δ	PROPN
ejpam-6089	241	11	,	,	PUNCT
ejpam-6089	241	12	b	b	PROPN
ejpam-6089	241	13	∈	∈	PROPN
ejpam-6089	241	14	c	c	PROPN
ejpam-6089	241	15	with	with	ADP
ejpam-6089	241	16	ℜ(	ℜ(	NOUN
ejpam-6089	241	17	♭	♭	PROPN
ejpam-6089	241	18	),ℜ(γ),ℜ(ℵ),ℜ(℘),ℜ(τ	),ℜ(γ),ℜ(ℵ),ℜ(℘),ℜ(τ	PUNCT
ejpam-6089	241	19	)	)	PUNCT
ejpam-6089	241	20	>	>	X
ejpam-6089	241	21	0	0	NUM
ejpam-6089	241	22	and	and	CCONJ
ejpam-6089	241	23	ℜ(b	ℜ(b	NOUN
ejpam-6089	241	24	)	)	PUNCT
ejpam-6089	241	25	>	>	X
ejpam-6089	241	26	ℜ(δ	ℜ(δ	X
ejpam-6089	241	27	)	)	PUNCT
ejpam-6089	241	28	>	>	X
ejpam-6089	241	29	0	0	PUNCT
ejpam-6089	242	1	and	and	CCONJ
ejpam-6089	242	2	let	let	VERB
ejpam-6089	242	3	g	g	PROPN
ejpam-6089	242	4	≥	≥	NOUN
ejpam-6089	242	5	0	0	NUM
ejpam-6089	242	6	,	,	PUNCT
ejpam-6089	242	7	l	l	NOUN
ejpam-6089	242	8	>	>	X
ejpam-6089	242	9	0	0	PUNCT
ejpam-6089	243	1	and	and	CCONJ
ejpam-6089	243	2	0	0	NUM
ejpam-6089	243	3	<	<	X
ejpam-6089	243	4	s	s	X
ejpam-6089	243	5	≤	≤	NUM
ejpam-6089	243	6	l	l	NOUN
ejpam-6089	243	7	+	+	CCONJ
ejpam-6089	243	8	ℜ(ℵ	ℜ(ℵ	NOUN
ejpam-6089	243	9	)	)	PUNCT
ejpam-6089	243	10	piℵ,℘,γ,	piℵ,℘,γ,	NOUN
ejpam-6089	243	11	♭	♭	NOUN
ejpam-6089	243	12	ℑ1	ℑ1	NOUN
ejpam-6089	243	13	+	+	CCONJ
ejpam-6089	243	14	υ(c	υ(c	PROPN
ejpam-6089	243	15	)	)	PUNCT
ejpam-6089	244	1	+	+	CCONJ
ejpam-6089	244	2	ε	ε	PROPN
ejpam-6089	244	3	♭	♭	PROPN
ejpam-6089	244	4	,δ	,δ	PUNCT
ejpam-6089	244	5	,	,	PUNCT
ejpam-6089	244	6	b	b	NOUN
ejpam-6089	244	7	,	,	PUNCT
ejpam-6089	244	8	s	s	X
ejpam-6089	244	9	,	,	PUNCT
ejpam-6089	244	10	lℑ1+,ℵ,℘,τυ(c	lℑ1+,ℵ,℘,τυ(c	PROPN
ejpam-6089	244	11	;	;	PUNCT
ejpam-6089	244	12	g	g	NOUN
ejpam-6089	244	13	)	)	PUNCT
ejpam-6089	245	1	+	+	NUM
ejpam-6089	245	2	piℵ,℘,γ,	piℵ,℘,γ,	VERB
ejpam-6089	245	3	♭	♭	PROPN
ejpam-6089	245	4	ℑ2−	ℑ2−	NUM
ejpam-6089	245	5	υ(c	υ(c	PROPN
ejpam-6089	245	6	)	)	PUNCT
ejpam-6089	246	1	+	+	CCONJ
ejpam-6089	246	2	ε	ε	PROPN
ejpam-6089	246	3	♭	♭	PROPN
ejpam-6089	246	4	,δ	,δ	PUNCT
ejpam-6089	246	5	,	,	PUNCT
ejpam-6089	246	6	b	b	NOUN
ejpam-6089	246	7	,	,	PUNCT
ejpam-6089	246	8	s	s	NOUN
ejpam-6089	246	9	,	,	PUNCT
ejpam-6089	246	10	lℑ2−,ℵ,℘,τυ(c	lℑ2−,ℵ,℘,τυ(c	NOUN
ejpam-6089	246	11	;	;	PUNCT
ejpam-6089	246	12	g	g	NOUN
ejpam-6089	246	13	)	)	PUNCT
ejpam-6089	246	14	=	=	PUNCT
ejpam-6089	247	1	∞∑	∞∑	NUM
ejpam-6089	247	2	ð=0	ð=0	PUNCT
ejpam-6089	247	3	hð	hð	PUNCT
ejpam-6089	247	4	(	(	PUNCT
ejpam-6089	247	5	r−li	r−li	NOUN
ejpam-6089	247	6	(	(	PUNCT
ejpam-6089	247	7	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	247	8	)	)	PUNCT
ejpam-6089	247	9	ℑ1	ℑ1	NOUN
ejpam-6089	247	10	+	+	SYM
ejpam-6089	247	11	υ(c	υ(c	PROPN
ejpam-6089	247	12	)	)	PUNCT
ejpam-6089	247	13	+	+	CCONJ
ejpam-6089	247	14	r−li	r−li	NOUN
ejpam-6089	247	15	(	(	PUNCT
ejpam-6089	247	16	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	247	17	)	)	PUNCT
ejpam-6089	247	18	ℑ2−	ℑ2−	NUM
ejpam-6089	247	19	υ(c	υ(c	PROPN
ejpam-6089	247	20	)	)	PUNCT
ejpam-6089	247	21	)	)	PUNCT
ejpam-6089	247	22	,	,	PUNCT
ejpam-6089	247	23	where	where	SCONJ
ejpam-6089	247	24	hð	hð	X
ejpam-6089	247	25	=	=	SYM
ejpam-6089	247	26	bg(δ+ðs	bg(δ+ð	NOUN
ejpam-6089	247	27	,	,	PUNCT
ejpam-6089	247	28	b−δ	b−δ	NOUN
ejpam-6089	247	29	)	)	PUNCT
ejpam-6089	247	30	b(δ	b(δ	NOUN
ejpam-6089	247	31	,	,	PUNCT
ejpam-6089	247	32	b−δ	b−δ	NOUN
ejpam-6089	247	33	)	)	PUNCT
ejpam-6089	247	34	(	(	PUNCT
ejpam-6089	247	35	b)ðs	b)ðs	PROPN
ejpam-6089	247	36	♭	♭	PROPN
ejpam-6089	247	37	ð	ð	X
ejpam-6089	247	38	(	(	PUNCT
ejpam-6089	247	39	τ)ðl	τ)ðl	ADJ
ejpam-6089	247	40	+	+	NUM
ejpam-6089	247	41	γ(γ+ð)	γ(γ+ð)	PROPN
ejpam-6089	247	42	♭	♭	PROPN
ejpam-6089	247	43	ð	ð	X
ejpam-6089	247	44	γ(γ)ð	γ(γ)ð	NOUN
ejpam-6089	247	45	!	!	PUNCT
ejpam-6089	247	46	.	.	PUNCT
ejpam-6089	248	1	proof	proof	NOUN
ejpam-6089	248	2	.	.	PUNCT
ejpam-6089	249	1	adding	add	VERB
ejpam-6089	249	2	infinite	infinite	ADJ
ejpam-6089	249	3	series	series	NOUN
ejpam-6089	249	4	formula	formula	NOUN
ejpam-6089	249	5	for	for	ADP
ejpam-6089	249	6	left	left	ADJ
ejpam-6089	249	7	prabhakar	prabhakar	NOUN
ejpam-6089	249	8	integral	integral	ADJ
ejpam-6089	249	9	(	(	PUNCT
ejpam-6089	249	10	7	7	NUM
ejpam-6089	249	11	)	)	PUNCT
ejpam-6089	249	12	and	and	CCONJ
ejpam-6089	249	13	left	leave	VERB
ejpam-6089	249	14	sided	side	VERB
ejpam-6089	249	15	generalized	generalized	ADJ
ejpam-6089	249	16	fractional	fractional	ADJ
ejpam-6089	249	17	integral	integral	ADJ
ejpam-6089	249	18	operator	operator	NOUN
ejpam-6089	249	19	(	(	PUNCT
ejpam-6089	249	20	10	10	NUM
ejpam-6089	249	21	)	)	PUNCT
ejpam-6089	249	22	,	,	PUNCT
ejpam-6089	249	23	we	we	PRON
ejpam-6089	249	24	get	get	VERB
ejpam-6089	249	25	piℵ,℘,γ,	piℵ,℘,γ,	NOUN
ejpam-6089	249	26	♭	♭	NOUN
ejpam-6089	249	27	ℑ1	ℑ1	NOUN
ejpam-6089	249	28	+	+	CCONJ
ejpam-6089	249	29	υ(c	υ(c	PROPN
ejpam-6089	249	30	)	)	PUNCT
ejpam-6089	250	1	+	+	CCONJ
ejpam-6089	250	2	ε	ε	PROPN
ejpam-6089	250	3	♭	♭	PROPN
ejpam-6089	250	4	,δ	,δ	PUNCT
ejpam-6089	250	5	,	,	PUNCT
ejpam-6089	250	6	b	b	NOUN
ejpam-6089	250	7	,	,	PUNCT
ejpam-6089	250	8	s	s	X
ejpam-6089	250	9	,	,	PUNCT
ejpam-6089	250	10	lℑ1+,ℵ,℘,τυ(c	lℑ1+,ℵ,℘,τυ(c	PROPN
ejpam-6089	250	11	;	;	PUNCT
ejpam-6089	250	12	g	g	NOUN
ejpam-6089	250	13	)	)	PUNCT
ejpam-6089	250	14	=	=	PUNCT
ejpam-6089	251	1	∞∑	∞∑	NUM
ejpam-6089	251	2	ð=0	ð=0	X
ejpam-6089	251	3	(	(	PUNCT
ejpam-6089	251	4	bg(δ	bg(δ	X
ejpam-6089	251	5	+	+	CCONJ
ejpam-6089	251	6	ðs	ðs	CCONJ
ejpam-6089	251	7	,	,	PUNCT
ejpam-6089	251	8	b−	b−	PROPN
ejpam-6089	251	9	δ	δ	PROPN
ejpam-6089	251	10	)	)	PUNCT
ejpam-6089	251	11	b(δ	b(δ	PROPN
ejpam-6089	251	12	,	,	PUNCT
ejpam-6089	251	13	b−	b−	PROPN
ejpam-6089	251	14	δ	δ	PROPN
ejpam-6089	251	15	)	)	PUNCT
ejpam-6089	251	16	(	(	PUNCT
ejpam-6089	251	17	b)ðs	b)ðs	PROPN
ejpam-6089	251	18	♭	♭	PROPN
ejpam-6089	251	19	ð	ð	X
ejpam-6089	251	20	(	(	PUNCT
ejpam-6089	251	21	τ)ðl	τ)ðl	PUNCT
ejpam-6089	251	22	+	+	NUM
ejpam-6089	251	23	∞∑	∞∑	NUM
ejpam-6089	251	24	ð=0	ð=0	PUNCT
ejpam-6089	251	25	γ(γ	γ(γ	PROPN
ejpam-6089	251	26	+	+	CCONJ
ejpam-6089	251	27	ð)	ð)	PUNCT
ejpam-6089	251	28	♭	♭	PROPN
ejpam-6089	251	29	ð	ð	X
ejpam-6089	251	30	γ(γ)ð	γ(γ)ð	PROPN
ejpam-6089	251	31	!	!	PUNCT
ejpam-6089	251	32	)	)	PUNCT
ejpam-6089	251	33	r−li	r−li	NOUN
ejpam-6089	251	34	(	(	PUNCT
ejpam-6089	251	35	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	251	36	)	)	PUNCT
ejpam-6089	251	37	ℑ1	ℑ1	NOUN
ejpam-6089	251	38	+	+	CCONJ
ejpam-6089	251	39	υ(c	υ(c	PROPN
ejpam-6089	251	40	)	)	PUNCT
ejpam-6089	251	41	.	.	PUNCT
ejpam-6089	252	1	(	(	PUNCT
ejpam-6089	252	2	15	15	NUM
ejpam-6089	252	3	)	)	PUNCT
ejpam-6089	252	4	similarly	similarly	ADV
ejpam-6089	252	5	adding	add	VERB
ejpam-6089	252	6	infinite	infinite	ADJ
ejpam-6089	252	7	series	series	NOUN
ejpam-6089	252	8	formula	formula	NOUN
ejpam-6089	252	9	for	for	ADP
ejpam-6089	252	10	right	right	ADJ
ejpam-6089	252	11	prabhakar	prabhakar	NOUN
ejpam-6089	252	12	integral	integral	ADJ
ejpam-6089	252	13	(	(	PUNCT
ejpam-6089	252	14	8)	8)	NUM
ejpam-6089	252	15	and	and	CCONJ
ejpam-6089	252	16	right	right	NOUN
ejpam-6089	252	17	sided	side	VERB
ejpam-6089	252	18	generalized	generalized	ADJ
ejpam-6089	252	19	fractional	fractional	ADJ
ejpam-6089	252	20	integral	integral	ADJ
ejpam-6089	252	21	operator	operator	NOUN
ejpam-6089	252	22	(	(	PUNCT
ejpam-6089	252	23	11	11	NUM
ejpam-6089	252	24	)	)	PUNCT
ejpam-6089	252	25	,	,	PUNCT
ejpam-6089	252	26	we	we	PRON
ejpam-6089	252	27	have	have	AUX
ejpam-6089	252	28	piℵ,℘,γ,	piℵ,℘,γ,	VERB
ejpam-6089	252	29	♭	♭	PROPN
ejpam-6089	252	30	ℑ2−	ℑ2−	NUM
ejpam-6089	252	31	υ(c	υ(c	PROPN
ejpam-6089	252	32	)	)	PUNCT
ejpam-6089	253	1	+	+	CCONJ
ejpam-6089	253	2	ε	ε	PROPN
ejpam-6089	253	3	♭	♭	PROPN
ejpam-6089	253	4	,δ	,δ	PUNCT
ejpam-6089	253	5	,	,	PUNCT
ejpam-6089	253	6	b	b	NOUN
ejpam-6089	253	7	,	,	PUNCT
ejpam-6089	253	8	s	s	NOUN
ejpam-6089	253	9	,	,	PUNCT
ejpam-6089	253	10	lℑ2−,ℵ,℘,τυ(c	lℑ2−,ℵ,℘,τυ(c	NOUN
ejpam-6089	253	11	;	;	PUNCT
ejpam-6089	253	12	g	g	NOUN
ejpam-6089	253	13	)	)	PUNCT
ejpam-6089	253	14	=	=	PUNCT
ejpam-6089	254	1	∞∑	∞∑	NUM
ejpam-6089	254	2	ð=0	ð=0	X
ejpam-6089	254	3	(	(	PUNCT
ejpam-6089	254	4	bg(δ	bg(δ	X
ejpam-6089	254	5	+	+	CCONJ
ejpam-6089	254	6	ðs	ðs	CCONJ
ejpam-6089	254	7	,	,	PUNCT
ejpam-6089	254	8	b−	b−	PROPN
ejpam-6089	254	9	δ	δ	PROPN
ejpam-6089	254	10	)	)	PUNCT
ejpam-6089	254	11	b(δ	b(δ	PROPN
ejpam-6089	254	12	,	,	PUNCT
ejpam-6089	254	13	b−	b−	PROPN
ejpam-6089	254	14	δ	δ	PROPN
ejpam-6089	254	15	)	)	PUNCT
ejpam-6089	254	16	(	(	PUNCT
ejpam-6089	254	17	b)ðs	b)ðs	PROPN
ejpam-6089	254	18	♭	♭	PROPN
ejpam-6089	254	19	ð	ð	X
ejpam-6089	254	20	(	(	PUNCT
ejpam-6089	254	21	τ)ðl	τ)ðl	PUNCT
ejpam-6089	254	22	+	+	NUM
ejpam-6089	254	23	∞∑	∞∑	NUM
ejpam-6089	254	24	ð=0	ð=0	PUNCT
ejpam-6089	254	25	γ(γ	γ(γ	PROPN
ejpam-6089	254	26	+	+	CCONJ
ejpam-6089	254	27	ð)	ð)	PUNCT
ejpam-6089	254	28	♭	♭	PROPN
ejpam-6089	254	29	ð	ð	X
ejpam-6089	254	30	γ(γ)ð	γ(γ)ð	PROPN
ejpam-6089	254	31	!	!	PUNCT
ejpam-6089	254	32	)	)	PUNCT
ejpam-6089	254	33	r−li	r−li	NOUN
ejpam-6089	254	34	(	(	PUNCT
ejpam-6089	254	35	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	254	36	)	)	PUNCT
ejpam-6089	254	37	ℑ2−	ℑ2−	NUM
ejpam-6089	254	38	υ(c	υ(c	PROPN
ejpam-6089	254	39	)	)	PUNCT
ejpam-6089	254	40	.	.	PUNCT
ejpam-6089	255	1	(	(	PUNCT
ejpam-6089	255	2	16	16	NUM
ejpam-6089	255	3	)	)	PUNCT
ejpam-6089	255	4	finally	finally	ADV
ejpam-6089	255	5	,	,	PUNCT
ejpam-6089	255	6	we	we	PRON
ejpam-6089	255	7	add	add	VERB
ejpam-6089	255	8	(	(	PUNCT
ejpam-6089	255	9	15	15	NUM
ejpam-6089	255	10	)	)	PUNCT
ejpam-6089	255	11	and	and	CCONJ
ejpam-6089	255	12	(	(	PUNCT
ejpam-6089	255	13	16	16	NUM
ejpam-6089	255	14	)	)	PUNCT
ejpam-6089	255	15	to	to	PART
ejpam-6089	255	16	get	get	VERB
ejpam-6089	255	17	following	follow	VERB
ejpam-6089	255	18	required	require	VERB
ejpam-6089	255	19	result	result	NOUN
ejpam-6089	255	20	piℵ,℘,γ,	piℵ,℘,γ,	NOUN
ejpam-6089	255	21	♭	♭	NOUN
ejpam-6089	255	22	ℑ1	ℑ1	NOUN
ejpam-6089	255	23	+	+	CCONJ
ejpam-6089	255	24	υ(c	υ(c	PROPN
ejpam-6089	255	25	)	)	PUNCT
ejpam-6089	256	1	+	+	CCONJ
ejpam-6089	256	2	ε	ε	PROPN
ejpam-6089	256	3	♭	♭	PROPN
ejpam-6089	256	4	,δ	,δ	PUNCT
ejpam-6089	256	5	,	,	PUNCT
ejpam-6089	256	6	b	b	NOUN
ejpam-6089	256	7	,	,	PUNCT
ejpam-6089	256	8	s	s	X
ejpam-6089	256	9	,	,	PUNCT
ejpam-6089	256	10	lℑ1+,ℵ,℘,τυ(c	lℑ1+,ℵ,℘,τυ(c	PROPN
ejpam-6089	256	11	;	;	PUNCT
ejpam-6089	256	12	g	g	NOUN
ejpam-6089	256	13	)	)	PUNCT
ejpam-6089	257	1	+	+	NUM
ejpam-6089	257	2	piℵ,℘,γ,	piℵ,℘,γ,	VERB
ejpam-6089	257	3	♭	♭	PROPN
ejpam-6089	257	4	ℑ2−	ℑ2−	NUM
ejpam-6089	257	5	υ(c	υ(c	PROPN
ejpam-6089	257	6	)	)	PUNCT
ejpam-6089	258	1	+	+	CCONJ
ejpam-6089	258	2	ε	ε	PROPN
ejpam-6089	258	3	♭	♭	PROPN
ejpam-6089	258	4	,δ	,δ	PUNCT
ejpam-6089	258	5	,	,	PUNCT
ejpam-6089	258	6	b	b	NOUN
ejpam-6089	258	7	,	,	PUNCT
ejpam-6089	258	8	s	s	NOUN
ejpam-6089	258	9	,	,	PUNCT
ejpam-6089	258	10	lℑ2−,ℵ,℘,τυ(c	lℑ2−,ℵ,℘,τυ(c	NOUN
ejpam-6089	258	11	;	;	PUNCT
ejpam-6089	258	12	g	g	X
ejpam-6089	258	13	)	)	PUNCT
ejpam-6089	258	14	s.	s.	PROPN
ejpam-6089	258	15	naheed	nahee	VERB
ejpam-6089	258	16	et	et	PROPN
ejpam-6089	258	17	al	al	PROPN
ejpam-6089	258	18	.	.	PUNCT
ejpam-6089	258	19	/	/	SYM
ejpam-6089	258	20	eur	eur	PROPN
ejpam-6089	258	21	.	.	PUNCT
ejpam-6089	259	1	j.	j.	PROPN
ejpam-6089	259	2	pure	pure	PROPN
ejpam-6089	259	3	appl	appl	PROPN
ejpam-6089	259	4	.	.	PROPN
ejpam-6089	259	5	math	math	PROPN
ejpam-6089	259	6	,	,	PUNCT
ejpam-6089	259	7	18	18	NUM
ejpam-6089	259	8	(	(	PUNCT
ejpam-6089	259	9	2	2	NUM
ejpam-6089	259	10	)	)	PUNCT
ejpam-6089	259	11	(	(	PUNCT
ejpam-6089	259	12	2025	2025	NUM
ejpam-6089	259	13	)	)	PUNCT
ejpam-6089	259	14	,	,	PUNCT
ejpam-6089	259	15	6089	6089	NUM
ejpam-6089	259	16	12	12	NUM
ejpam-6089	259	17	of	of	ADP
ejpam-6089	259	18	34	34	NUM
ejpam-6089	259	19	=	=	SYM
ejpam-6089	259	20	(	(	PUNCT
ejpam-6089	259	21	∞∑	∞∑	NUM
ejpam-6089	259	22	ð=0	ð=0	X
ejpam-6089	259	23	bg(δ	bg(δ	NOUN
ejpam-6089	259	24	+	+	CCONJ
ejpam-6089	259	25	ðs	ðs	CCONJ
ejpam-6089	259	26	,	,	PUNCT
ejpam-6089	259	27	b−	b−	PROPN
ejpam-6089	259	28	δ	δ	PROPN
ejpam-6089	259	29	)	)	PUNCT
ejpam-6089	259	30	b(δ	b(δ	PROPN
ejpam-6089	259	31	,	,	PUNCT
ejpam-6089	259	32	b−	b−	PROPN
ejpam-6089	259	33	δ	δ	PROPN
ejpam-6089	259	34	)	)	PUNCT
ejpam-6089	259	35	(	(	PUNCT
ejpam-6089	259	36	b)ðs	b)ðs	PROPN
ejpam-6089	259	37	♭	♭	PROPN
ejpam-6089	259	38	ð	ð	X
ejpam-6089	259	39	(	(	PUNCT
ejpam-6089	260	1	τ)ðl	τ)ðl	PUNCT
ejpam-6089	260	2	+	+	NUM
ejpam-6089	260	3	∞∑	∞∑	NUM
ejpam-6089	260	4	ð=0	ð=0	PUNCT
ejpam-6089	260	5	γ(γ	γ(γ	PROPN
ejpam-6089	260	6	+	+	CCONJ
ejpam-6089	260	7	ð)	ð)	PUNCT
ejpam-6089	260	8	♭	♭	PROPN
ejpam-6089	260	9	ð	ð	X
ejpam-6089	260	10	γ(γ)ð	γ(γ)ð	PROPN
ejpam-6089	260	11	!	!	PUNCT
ejpam-6089	260	12	)	)	PUNCT
ejpam-6089	261	1	×	×	NOUN
ejpam-6089	261	2	(	(	PUNCT
ejpam-6089	261	3	r−li	r−li	NOUN
ejpam-6089	261	4	(	(	PUNCT
ejpam-6089	261	5	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	261	6	)	)	PUNCT
ejpam-6089	261	7	ℑ1	ℑ1	NOUN
ejpam-6089	261	8	+	+	SYM
ejpam-6089	261	9	υ(c	υ(c	PROPN
ejpam-6089	261	10	)	)	PUNCT
ejpam-6089	262	1	+	+	CCONJ
ejpam-6089	262	2	r−li	r−li	NOUN
ejpam-6089	262	3	(	(	PUNCT
ejpam-6089	262	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	262	5	)	)	PUNCT
ejpam-6089	262	6	ℑ2−	ℑ2−	NUM
ejpam-6089	262	7	υ(c	υ(c	PROPN
ejpam-6089	262	8	)	)	PUNCT
ejpam-6089	262	9	)	)	PUNCT
ejpam-6089	263	1	=	=	PUNCT
ejpam-6089	264	1	∞∑	∞∑	NUM
ejpam-6089	264	2	ð=0	ð=0	PUNCT
ejpam-6089	264	3	hð	hð	PUNCT
ejpam-6089	264	4	(	(	PUNCT
ejpam-6089	264	5	r−li	r−li	NOUN
ejpam-6089	264	6	(	(	PUNCT
ejpam-6089	264	7	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	264	8	)	)	PUNCT
ejpam-6089	264	9	ℑ1	ℑ1	NOUN
ejpam-6089	264	10	+	+	SYM
ejpam-6089	264	11	υ(c	υ(c	PROPN
ejpam-6089	264	12	)	)	PUNCT
ejpam-6089	264	13	+	+	CCONJ
ejpam-6089	264	14	r−li	r−li	NOUN
ejpam-6089	264	15	(	(	PUNCT
ejpam-6089	264	16	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	264	17	)	)	PUNCT
ejpam-6089	264	18	ℑ2−	ℑ2−	NUM
ejpam-6089	264	19	υ(c	υ(c	PROPN
ejpam-6089	264	20	)	)	PUNCT
ejpam-6089	264	21	)	)	PUNCT
ejpam-6089	264	22	.	.	PUNCT
ejpam-6089	265	1	theorem	theorem	VERB
ejpam-6089	265	2	6	6	NUM
ejpam-6089	265	3	.	.	PUNCT
ejpam-6089	266	1	if	if	SCONJ
ejpam-6089	266	2	υ	υ	PRON
ejpam-6089	266	3	:	:	PUNCT
ejpam-6089	266	4	[	[	X
ejpam-6089	266	5	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	266	6	]	]	PUNCT
ejpam-6089	266	7	→	→	SYM
ejpam-6089	266	8	ℜ	ℜ	PROPN
ejpam-6089	266	9	is	be	AUX
ejpam-6089	266	10	l1	l1	PROPN
ejpam-6089	266	11	and	and	CCONJ
ejpam-6089	266	12	convex	convex	PROPN
ejpam-6089	266	13	and	and	CCONJ
ejpam-6089	266	14	the	the	DET
ejpam-6089	266	15	parameters	parameter	NOUN
ejpam-6089	266	16	,	,	PUNCT
ejpam-6089	266	17	ℜ(ℵð	ℜ(ℵð	NOUN
ejpam-6089	266	18	+	+	CCONJ
ejpam-6089	266	19	℘	℘	NOUN
ejpam-6089	266	20	)	)	PUNCT
ejpam-6089	266	21	>	>	X
ejpam-6089	266	22	0	0	NUM
ejpam-6089	266	23	also	also	ADV
ejpam-6089	266	24	ℜ(	ℜ(	VERB
ejpam-6089	266	25	♭	♭	NOUN
ejpam-6089	266	26	),ℜ(γ),ℜ(ℵ),ℜ(℘),ℜ(τ	),ℜ(γ),ℜ(ℵ),ℜ(℘),ℜ(τ	PUNCT
ejpam-6089	266	27	)	)	PUNCT
ejpam-6089	266	28	>	>	X
ejpam-6089	266	29	0	0	NUM
ejpam-6089	266	30	and	and	CCONJ
ejpam-6089	266	31	ℜ(b	ℜ(b	NOUN
ejpam-6089	266	32	)	)	PUNCT
ejpam-6089	266	33	>	>	X
ejpam-6089	267	1	ℜ(δ	ℜ(δ	X
ejpam-6089	267	2	)	)	PUNCT
ejpam-6089	267	3	>	>	X
ejpam-6089	267	4	0	0	PUNCT
ejpam-6089	268	1	and	and	CCONJ
ejpam-6089	268	2	let	let	VERB
ejpam-6089	268	3	g	g	PROPN
ejpam-6089	268	4	≥	≥	NOUN
ejpam-6089	268	5	0	0	NUM
ejpam-6089	268	6	,	,	PUNCT
ejpam-6089	268	7	l	l	NOUN
ejpam-6089	268	8	>	>	X
ejpam-6089	268	9	0	0	PUNCT
ejpam-6089	269	1	and	and	CCONJ
ejpam-6089	269	2	0	0	NUM
ejpam-6089	269	3	<	<	X
ejpam-6089	269	4	s	s	X
ejpam-6089	269	5	≤	≤	NUM
ejpam-6089	269	6	l	l	NOUN
ejpam-6089	269	7	+	+	CCONJ
ejpam-6089	269	8	ℜ(ℵ	ℜ(ℵ	NOUN
ejpam-6089	269	9	)	)	PUNCT
ejpam-6089	269	10	,	,	PUNCT
ejpam-6089	269	11	then	then	ADV
ejpam-6089	269	12	we	we	PRON
ejpam-6089	269	13	have	have	VERB
ejpam-6089	269	14	the	the	DET
ejpam-6089	269	15	following	follow	VERB
ejpam-6089	269	16	(	(	PUNCT
ejpam-6089	269	17	h−h	h−h	NOUN
ejpam-6089	269	18	)	)	PUNCT
ejpam-6089	269	19	inequality	inequality	NOUN
ejpam-6089	269	20	for	for	ADP
ejpam-6089	269	21	prabhakar	prabhakar	NOUN
ejpam-6089	269	22	fractional	fractional	ADJ
ejpam-6089	269	23	integrals	integral	NOUN
ejpam-6089	269	24	and	and	CCONJ
ejpam-6089	269	25	generalized	generalize	VERB
ejpam-6089	269	26	fractional	fractional	ADJ
ejpam-6089	269	27	integral	integral	ADJ
ejpam-6089	269	28	operators	operator	NOUN
ejpam-6089	269	29	∞∑	∞∑	PRON
ejpam-6089	269	30	ð=0	ð=0	X
ejpam-6089	269	31	hðvðυ	hðvðυ	NOUN
ejpam-6089	269	32	(	(	PUNCT
ejpam-6089	269	33	ℑ1	ℑ1	X
ejpam-6089	269	34	+	+	CCONJ
ejpam-6089	269	35	ℑ2	ℑ2	PROPN
ejpam-6089	269	36	2	2	NUM
ejpam-6089	269	37	)	)	PUNCT
ejpam-6089	269	38	≤	≤	NUM
ejpam-6089	269	39	piℵ,℘,γ,	piℵ,℘,γ,	NOUN
ejpam-6089	269	40	♭	♭	X
ejpam-6089	269	41	ℑ1	ℑ1	NOUN
ejpam-6089	269	42	+	+	CCONJ
ejpam-6089	269	43	υ(c	υ(c	PROPN
ejpam-6089	269	44	)	)	PUNCT
ejpam-6089	269	45	+	+	CCONJ
ejpam-6089	269	46	ε	ε	PROPN
ejpam-6089	269	47	♭	♭	PROPN
ejpam-6089	269	48	,δ	,δ	PUNCT
ejpam-6089	269	49	,	,	PUNCT
ejpam-6089	269	50	b	b	NOUN
ejpam-6089	269	51	,	,	PUNCT
ejpam-6089	269	52	s	s	X
ejpam-6089	269	53	,	,	PUNCT
ejpam-6089	269	54	lℑ1+,ℵ,℘,τυ(c	lℑ1+,ℵ,℘,τυ(c	PROPN
ejpam-6089	269	55	;	;	PUNCT
ejpam-6089	269	56	g	g	NOUN
ejpam-6089	269	57	)	)	PUNCT
ejpam-6089	269	58	+	+	NUM
ejpam-6089	269	59	piℵ,℘,γ,	piℵ,℘,γ,	VERB
ejpam-6089	269	60	♭	♭	PROPN
ejpam-6089	269	61	ℑ2−	ℑ2−	NUM
ejpam-6089	269	62	υ(c	υ(c	PROPN
ejpam-6089	269	63	)	)	PUNCT
ejpam-6089	270	1	+	+	CCONJ
ejpam-6089	270	2	ε	ε	PROPN
ejpam-6089	270	3	♭	♭	PROPN
ejpam-6089	270	4	,δ	,δ	PUNCT
ejpam-6089	270	5	,	,	PUNCT
ejpam-6089	270	6	b	b	NOUN
ejpam-6089	270	7	,	,	PUNCT
ejpam-6089	270	8	s	s	NOUN
ejpam-6089	270	9	,	,	PUNCT
ejpam-6089	270	10	lℑ2−,ℵ,℘,τυ(c	lℑ2−,ℵ,℘,τυ(c	NOUN
ejpam-6089	270	11	;	;	PUNCT
ejpam-6089	270	12	g	g	X
ejpam-6089	270	13	)	)	PUNCT
ejpam-6089	270	14	≤	≤	NOUN
ejpam-6089	271	1	∞∑	∞∑	NUM
ejpam-6089	271	2	ð=0	ð=0	X
ejpam-6089	271	3	hðvð	hðvð	ADJ
ejpam-6089	271	4	(	(	PUNCT
ejpam-6089	271	5	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	271	6	)	)	PUNCT
ejpam-6089	271	7	+	+	CCONJ
ejpam-6089	271	8	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	271	9	)	)	PUNCT
ejpam-6089	271	10	2	2	NUM
ejpam-6089	271	11	)	)	PUNCT
ejpam-6089	271	12	,	,	PUNCT
ejpam-6089	271	13	(	(	PUNCT
ejpam-6089	271	14	17	17	NUM
ejpam-6089	271	15	)	)	PUNCT
ejpam-6089	271	16	where	where	SCONJ
ejpam-6089	271	17	hð	hð	VERB
ejpam-6089	271	18	=	=	SYM
ejpam-6089	271	19	bg(δ+ðs	bg(δ+ð	NOUN
ejpam-6089	271	20	,	,	PUNCT
ejpam-6089	271	21	b−δ	b−δ	NOUN
ejpam-6089	271	22	)	)	PUNCT
ejpam-6089	271	23	b(δ	b(δ	NOUN
ejpam-6089	271	24	,	,	PUNCT
ejpam-6089	271	25	b−δ	b−δ	NOUN
ejpam-6089	271	26	)	)	PUNCT
ejpam-6089	271	27	(	(	PUNCT
ejpam-6089	271	28	b)ðs	b)ðs	PROPN
ejpam-6089	271	29	♭	♭	PROPN
ejpam-6089	271	30	ð	ð	X
ejpam-6089	271	31	(	(	PUNCT
ejpam-6089	271	32	τ)ðl	τ)ðl	ADJ
ejpam-6089	271	33	+	+	NUM
ejpam-6089	271	34	γ(γ+ð)	γ(γ+ð)	PROPN
ejpam-6089	271	35	♭	♭	PROPN
ejpam-6089	271	36	ð	ð	X
ejpam-6089	271	37	γ(γ)ð	γ(γ)ð	PROPN
ejpam-6089	271	38	!	!	PUNCT
ejpam-6089	272	1	and	and	CCONJ
ejpam-6089	272	2	vð	vð	VERB
ejpam-6089	272	3	=	=	SYM
ejpam-6089	272	4	2(ℑ2−ℑ1)(ℵð+℘	2(ℑ2−ℑ1)(ℵð+℘	NUM
ejpam-6089	272	5	)	)	PUNCT
ejpam-6089	272	6	γ((ℵð+℘)+1	γ((ℵð+℘)+1	NOUN
ejpam-6089	272	7	)	)	PUNCT
ejpam-6089	272	8	.	.	PUNCT
ejpam-6089	273	1	proof	proof	NOUN
ejpam-6089	273	2	.	.	PUNCT
ejpam-6089	274	1	replacing	replace	VERB
ejpam-6089	274	2	α∗	α∗	NOUN
ejpam-6089	274	3	by	by	ADP
ejpam-6089	274	4	(	(	PUNCT
ejpam-6089	274	5	ℵð+	ℵð+	ADJ
ejpam-6089	274	6	℘	℘	PROPN
ejpam-6089	274	7	)	)	PUNCT
ejpam-6089	274	8	in	in	ADP
ejpam-6089	274	9	theorem	theorem	NOUN
ejpam-6089	274	10	2	2	NUM
ejpam-6089	274	11	,	,	PUNCT
ejpam-6089	274	12	we	we	PRON
ejpam-6089	274	13	obtain	obtain	VERB
ejpam-6089	274	14	υ	υ	PRON
ejpam-6089	274	15	(	(	PUNCT
ejpam-6089	274	16	ℑ1	ℑ1	PROPN
ejpam-6089	274	17	+	+	CCONJ
ejpam-6089	274	18	ℑ2	ℑ2	PROPN
ejpam-6089	274	19	2	2	NUM
ejpam-6089	274	20	)	)	PUNCT
ejpam-6089	274	21	≤	≤	NOUN
ejpam-6089	274	22	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	274	23	℘	℘	PROPN
ejpam-6089	274	24	)	)	PUNCT
ejpam-6089	274	25	+	+	CCONJ
ejpam-6089	274	26	1	1	NUM
ejpam-6089	274	27	)	)	PUNCT
ejpam-6089	274	28	2(ℑ2	2(ℑ2	NUM
ejpam-6089	274	29	−ℑ1)(ℵð+℘	−ℑ1)(ℵð+℘	NUM
ejpam-6089	274	30	)	)	PUNCT
ejpam-6089	274	31	(	(	PUNCT
ejpam-6089	274	32	r−li	r−li	NOUN
ejpam-6089	274	33	(	(	PUNCT
ejpam-6089	274	34	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	274	35	)	)	PUNCT
ejpam-6089	274	36	ℑ1	ℑ1	NOUN
ejpam-6089	274	37	+	+	CCONJ
ejpam-6089	274	38	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	274	39	)	)	PUNCT
ejpam-6089	275	1	+	+	NUM
ejpam-6089	275	2	r−li	r−li	NOUN
ejpam-6089	275	3	(	(	PUNCT
ejpam-6089	275	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	275	5	)	)	PUNCT
ejpam-6089	275	6	ℑ2−	ℑ2−	NUM
ejpam-6089	276	1	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	276	2	)	)	PUNCT
ejpam-6089	276	3	)	)	PUNCT
ejpam-6089	277	1	≤	≤	PUNCT
ejpam-6089	278	1	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	278	2	)	)	PUNCT
ejpam-6089	278	3	+	+	PUNCT
ejpam-6089	278	4	υ(ℑ1	υ(ℑ1	NOUN
ejpam-6089	278	5	)	)	PUNCT
ejpam-6089	278	6	2	2	NUM
ejpam-6089	278	7	.	.	PUNCT
ejpam-6089	279	1	multiplying	multiply	VERB
ejpam-6089	279	2	the	the	DET
ejpam-6089	279	3	above	above	ADJ
ejpam-6089	279	4	inequality	inequality	NOUN
ejpam-6089	279	5	with	with	ADP
ejpam-6089	279	6	2(ℑ2−ℑ1)(ℵð+℘	2(ℑ2−ℑ1)(ℵð+℘	NUM
ejpam-6089	279	7	)	)	PUNCT
ejpam-6089	279	8	γ((ℵð+℘)+1	γ((ℵð+℘)+1	NOUN
ejpam-6089	279	9	)	)	PUNCT
ejpam-6089	279	10	,	,	PUNCT
ejpam-6089	279	11	we	we	PRON
ejpam-6089	279	12	get	get	VERB
ejpam-6089	279	13	2(ℑ2	2(ℑ2	NUM
ejpam-6089	279	14	−ℑ1	−ℑ1	NOUN
ejpam-6089	279	15	)	)	PUNCT
ejpam-6089	279	16	(	(	PUNCT
ejpam-6089	279	17	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	279	18	)	)	PUNCT
ejpam-6089	279	19	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	279	20	℘	℘	PROPN
ejpam-6089	279	21	)	)	PUNCT
ejpam-6089	280	1	+	+	CCONJ
ejpam-6089	280	2	1	1	X
ejpam-6089	280	3	)	)	PUNCT
ejpam-6089	280	4	υ	υ	NOUN
ejpam-6089	280	5	(	(	PUNCT
ejpam-6089	280	6	ℑ1	ℑ1	PROPN
ejpam-6089	280	7	+	+	CCONJ
ejpam-6089	280	8	ℑ2	ℑ2	PROPN
ejpam-6089	280	9	2	2	NUM
ejpam-6089	280	10	)	)	PUNCT
ejpam-6089	280	11	≤	≤	NOUN
ejpam-6089	280	12	(	(	PUNCT
ejpam-6089	280	13	r−li	r−li	NOUN
ejpam-6089	280	14	(	(	PUNCT
ejpam-6089	280	15	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	280	16	)	)	PUNCT
ejpam-6089	280	17	ℑ1	ℑ1	NOUN
ejpam-6089	280	18	+	+	CCONJ
ejpam-6089	280	19	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	280	20	)	)	PUNCT
ejpam-6089	281	1	+	+	NUM
ejpam-6089	281	2	r−li	r−li	NOUN
ejpam-6089	281	3	(	(	PUNCT
ejpam-6089	281	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	281	5	)	)	PUNCT
ejpam-6089	281	6	ℑ2−	ℑ2−	NUM
ejpam-6089	282	1	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	282	2	)	)	PUNCT
ejpam-6089	282	3	)	)	PUNCT
ejpam-6089	283	1	≤	≤	NOUN
ejpam-6089	283	2	2(ℑ2	2(ℑ2	NUM
ejpam-6089	283	3	−ℑ1	−ℑ1	NOUN
ejpam-6089	283	4	)	)	PUNCT
ejpam-6089	283	5	(	(	PUNCT
ejpam-6089	283	6	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	283	7	)	)	PUNCT
ejpam-6089	283	8	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	283	9	℘	℘	PROPN
ejpam-6089	283	10	)	)	PUNCT
ejpam-6089	283	11	+	+	CCONJ
ejpam-6089	283	12	1	1	X
ejpam-6089	283	13	)	)	PUNCT
ejpam-6089	283	14	(	(	PUNCT
ejpam-6089	283	15	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	283	16	)	)	PUNCT
ejpam-6089	284	1	+	+	CCONJ
ejpam-6089	284	2	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	284	3	)	)	PUNCT
ejpam-6089	284	4	2	2	NUM
ejpam-6089	284	5	)	)	PUNCT
ejpam-6089	284	6	.	.	PUNCT
ejpam-6089	285	1	again	again	ADV
ejpam-6089	285	2	we	we	PRON
ejpam-6089	285	3	multiply	multiply	VERB
ejpam-6089	285	4	the	the	DET
ejpam-6089	285	5	above	above	ADJ
ejpam-6089	285	6	inequality	inequality	NOUN
ejpam-6089	285	7	with	with	ADP
ejpam-6089	285	8	hð	hð	ADP
ejpam-6089	285	9	to	to	PART
ejpam-6089	285	10	obtain	obtain	VERB
ejpam-6089	285	11	hð	hð	NOUN
ejpam-6089	285	12	2(ℑ2	2(ℑ2	NUM
ejpam-6089	285	13	−ℑ1	−ℑ1	NOUN
ejpam-6089	285	14	)	)	PUNCT
ejpam-6089	285	15	(	(	PUNCT
ejpam-6089	285	16	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	285	17	)	)	PUNCT
ejpam-6089	285	18	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	285	19	℘	℘	PROPN
ejpam-6089	285	20	)	)	PUNCT
ejpam-6089	285	21	+	+	CCONJ
ejpam-6089	285	22	1	1	X
ejpam-6089	285	23	)	)	PUNCT
ejpam-6089	285	24	υ	υ	NOUN
ejpam-6089	285	25	(	(	PUNCT
ejpam-6089	285	26	ℑ1	ℑ1	PROPN
ejpam-6089	285	27	+	+	CCONJ
ejpam-6089	285	28	ℑ2	ℑ2	PROPN
ejpam-6089	285	29	2	2	NUM
ejpam-6089	285	30	)	)	PUNCT
ejpam-6089	285	31	s.	s.	PROPN
ejpam-6089	285	32	naheed	nahee	VERB
ejpam-6089	285	33	et	et	PROPN
ejpam-6089	285	34	al	al	PROPN
ejpam-6089	285	35	.	.	PUNCT
ejpam-6089	285	36	/	/	SYM
ejpam-6089	285	37	eur	eur	PROPN
ejpam-6089	285	38	.	.	PUNCT
ejpam-6089	286	1	j.	j.	PROPN
ejpam-6089	286	2	pure	pure	PROPN
ejpam-6089	286	3	appl	appl	PROPN
ejpam-6089	286	4	.	.	PROPN
ejpam-6089	286	5	math	math	PROPN
ejpam-6089	286	6	,	,	PUNCT
ejpam-6089	286	7	18	18	NUM
ejpam-6089	286	8	(	(	PUNCT
ejpam-6089	286	9	2	2	NUM
ejpam-6089	286	10	)	)	PUNCT
ejpam-6089	286	11	(	(	PUNCT
ejpam-6089	286	12	2025	2025	NUM
ejpam-6089	286	13	)	)	PUNCT
ejpam-6089	286	14	,	,	PUNCT
ejpam-6089	286	15	6089	6089	NUM
ejpam-6089	286	16	13	13	NUM
ejpam-6089	286	17	of	of	ADP
ejpam-6089	286	18	34	34	NUM
ejpam-6089	286	19	≤	≤	NUM
ejpam-6089	286	20	hð	hð	PUNCT
ejpam-6089	286	21	(	(	PUNCT
ejpam-6089	286	22	r−li	r−li	NOUN
ejpam-6089	286	23	(	(	PUNCT
ejpam-6089	286	24	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	286	25	)	)	PUNCT
ejpam-6089	286	26	ℑ1	ℑ1	NOUN
ejpam-6089	286	27	+	+	CCONJ
ejpam-6089	286	28	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	286	29	)	)	PUNCT
ejpam-6089	287	1	+	+	NUM
ejpam-6089	287	2	r−li	r−li	NOUN
ejpam-6089	287	3	(	(	PUNCT
ejpam-6089	287	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	287	5	)	)	PUNCT
ejpam-6089	287	6	ℑ2−	ℑ2−	NUM
ejpam-6089	288	1	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	288	2	)	)	PUNCT
ejpam-6089	288	3	)	)	PUNCT
ejpam-6089	289	1	≤	≤	NUM
ejpam-6089	289	2	hð	hð	VERB
ejpam-6089	289	3	2(ℑ2	2(ℑ2	NUM
ejpam-6089	289	4	−ℑ1	−ℑ1	NOUN
ejpam-6089	289	5	)	)	PUNCT
ejpam-6089	289	6	(	(	PUNCT
ejpam-6089	289	7	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	289	8	)	)	PUNCT
ejpam-6089	289	9	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	289	10	℘	℘	PROPN
ejpam-6089	289	11	)	)	PUNCT
ejpam-6089	289	12	+	+	CCONJ
ejpam-6089	289	13	1	1	X
ejpam-6089	289	14	)	)	PUNCT
ejpam-6089	289	15	(	(	PUNCT
ejpam-6089	289	16	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	289	17	)	)	PUNCT
ejpam-6089	289	18	+	+	CCONJ
ejpam-6089	289	19	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	289	20	)	)	PUNCT
ejpam-6089	289	21	2	2	NUM
ejpam-6089	289	22	)	)	PUNCT
ejpam-6089	289	23	.	.	PUNCT
ejpam-6089	290	1	summing	sum	VERB
ejpam-6089	290	2	over	over	ADP
ejpam-6089	290	3	all	all	PRON
ejpam-6089	290	4	ð	ð	NOUN
ejpam-6089	290	5	∞∑	∞∑	NUM
ejpam-6089	290	6	ð=0	ð=0	PUNCT
ejpam-6089	290	7	hð	hð	VERB
ejpam-6089	290	8	2(ℑ2	2(ℑ2	NUM
ejpam-6089	290	9	−ℑ1	−ℑ1	NOUN
ejpam-6089	290	10	)	)	PUNCT
ejpam-6089	290	11	(	(	PUNCT
ejpam-6089	290	12	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	290	13	)	)	PUNCT
ejpam-6089	290	14	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	290	15	℘	℘	PROPN
ejpam-6089	290	16	)	)	PUNCT
ejpam-6089	290	17	+	+	CCONJ
ejpam-6089	290	18	1	1	X
ejpam-6089	290	19	)	)	PUNCT
ejpam-6089	290	20	υ	υ	NOUN
ejpam-6089	290	21	(	(	PUNCT
ejpam-6089	290	22	ℑ1	ℑ1	PROPN
ejpam-6089	290	23	+	+	CCONJ
ejpam-6089	290	24	ℑ2	ℑ2	PROPN
ejpam-6089	290	25	2	2	NUM
ejpam-6089	290	26	)	)	PUNCT
ejpam-6089	290	27	≤	≤	NOUN
ejpam-6089	290	28	∞∑	∞∑	NUM
ejpam-6089	290	29	ð=0	ð=0	PUNCT
ejpam-6089	290	30	hð	hð	PUNCT
ejpam-6089	290	31	(	(	PUNCT
ejpam-6089	290	32	r−li	r−li	NOUN
ejpam-6089	290	33	(	(	PUNCT
ejpam-6089	290	34	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	290	35	)	)	PUNCT
ejpam-6089	290	36	ℑ1	ℑ1	NOUN
ejpam-6089	290	37	+	+	CCONJ
ejpam-6089	290	38	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	290	39	)	)	PUNCT
ejpam-6089	290	40	+	+	NUM
ejpam-6089	290	41	r−li	r−li	NOUN
ejpam-6089	290	42	(	(	PUNCT
ejpam-6089	290	43	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	290	44	)	)	PUNCT
ejpam-6089	290	45	ℑ2−	ℑ2−	NUM
ejpam-6089	291	1	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	291	2	)	)	PUNCT
ejpam-6089	291	3	)	)	PUNCT
ejpam-6089	292	1	≤	≤	NOUN
ejpam-6089	293	1	∞∑	∞∑	NUM
ejpam-6089	293	2	ð=0	ð=0	PUNCT
ejpam-6089	293	3	hð	hð	VERB
ejpam-6089	293	4	2(ℑ2	2(ℑ2	NUM
ejpam-6089	293	5	−ℑ1	−ℑ1	NOUN
ejpam-6089	293	6	)	)	PUNCT
ejpam-6089	293	7	(	(	PUNCT
ejpam-6089	293	8	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	293	9	)	)	PUNCT
ejpam-6089	293	10	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	293	11	℘	℘	PROPN
ejpam-6089	293	12	)	)	PUNCT
ejpam-6089	293	13	+	+	CCONJ
ejpam-6089	293	14	1	1	X
ejpam-6089	293	15	)	)	PUNCT
ejpam-6089	293	16	(	(	PUNCT
ejpam-6089	293	17	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	293	18	)	)	PUNCT
ejpam-6089	293	19	+	+	CCONJ
ejpam-6089	293	20	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	293	21	)	)	PUNCT
ejpam-6089	293	22	2	2	NUM
ejpam-6089	293	23	)	)	PUNCT
ejpam-6089	293	24	.	.	PUNCT
ejpam-6089	294	1	using	use	VERB
ejpam-6089	294	2	proposition	proposition	NOUN
ejpam-6089	294	3	3	3	NUM
ejpam-6089	294	4	in	in	ADP
ejpam-6089	294	5	the	the	DET
ejpam-6089	294	6	above	above	ADJ
ejpam-6089	294	7	expression	expression	NOUN
ejpam-6089	294	8	,	,	PUNCT
ejpam-6089	294	9	we	we	PRON
ejpam-6089	294	10	get	get	VERB
ejpam-6089	294	11	∞∑	∞∑	NUM
ejpam-6089	294	12	ð=0	ð=0	X
ejpam-6089	294	13	hðvðυ	hðvðυ	NOUN
ejpam-6089	294	14	(	(	PUNCT
ejpam-6089	294	15	ℑ1	ℑ1	X
ejpam-6089	294	16	+	+	CCONJ
ejpam-6089	294	17	ℑ2	ℑ2	PROPN
ejpam-6089	294	18	2	2	NUM
ejpam-6089	294	19	)	)	PUNCT
ejpam-6089	294	20	≤	≤	NUM
ejpam-6089	294	21	piℵ,℘,γ,	piℵ,℘,γ,	NOUN
ejpam-6089	294	22	♭	♭	X
ejpam-6089	294	23	ℑ1	ℑ1	NOUN
ejpam-6089	294	24	+	+	CCONJ
ejpam-6089	294	25	υ(c	υ(c	PROPN
ejpam-6089	294	26	)	)	PUNCT
ejpam-6089	294	27	+	+	CCONJ
ejpam-6089	294	28	ε	ε	PROPN
ejpam-6089	294	29	♭	♭	PROPN
ejpam-6089	294	30	,δ	,δ	PUNCT
ejpam-6089	294	31	,	,	PUNCT
ejpam-6089	294	32	b	b	NOUN
ejpam-6089	294	33	,	,	PUNCT
ejpam-6089	294	34	s	s	X
ejpam-6089	294	35	,	,	PUNCT
ejpam-6089	294	36	lℑ1+,ℵ,℘,τυ(c	lℑ1+,ℵ,℘,τυ(c	PROPN
ejpam-6089	294	37	;	;	PUNCT
ejpam-6089	294	38	g	g	NOUN
ejpam-6089	294	39	)	)	PUNCT
ejpam-6089	294	40	+	+	NUM
ejpam-6089	294	41	piℵ,℘,γ,	piℵ,℘,γ,	VERB
ejpam-6089	294	42	♭	♭	PROPN
ejpam-6089	294	43	ℑ2−	ℑ2−	NUM
ejpam-6089	294	44	υ(c	υ(c	PROPN
ejpam-6089	294	45	)	)	PUNCT
ejpam-6089	295	1	+	+	CCONJ
ejpam-6089	295	2	ε	ε	PROPN
ejpam-6089	295	3	♭	♭	PROPN
ejpam-6089	295	4	,δ	,δ	PUNCT
ejpam-6089	295	5	,	,	PUNCT
ejpam-6089	295	6	b	b	NOUN
ejpam-6089	295	7	,	,	PUNCT
ejpam-6089	295	8	s	s	NOUN
ejpam-6089	295	9	,	,	PUNCT
ejpam-6089	295	10	lℑ2−,ℵ,℘,τυ(c	lℑ2−,ℵ,℘,τυ(c	NOUN
ejpam-6089	295	11	;	;	PUNCT
ejpam-6089	295	12	g	g	X
ejpam-6089	295	13	)	)	PUNCT
ejpam-6089	295	14	≤	≤	NOUN
ejpam-6089	296	1	∞∑	∞∑	NUM
ejpam-6089	296	2	ð=0	ð=0	X
ejpam-6089	296	3	hðvð	hðvð	ADJ
ejpam-6089	296	4	(	(	PUNCT
ejpam-6089	296	5	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	296	6	)	)	PUNCT
ejpam-6089	296	7	+	+	CCONJ
ejpam-6089	296	8	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	296	9	)	)	PUNCT
ejpam-6089	296	10	2	2	NUM
ejpam-6089	296	11	)	)	PUNCT
ejpam-6089	296	12	.	.	PUNCT
ejpam-6089	297	1	hence	hence	ADV
ejpam-6089	297	2	the	the	DET
ejpam-6089	297	3	required	require	VERB
ejpam-6089	297	4	result	result	NOUN
ejpam-6089	297	5	is	be	AUX
ejpam-6089	297	6	proved	prove	VERB
ejpam-6089	297	7	.	.	PUNCT
ejpam-6089	298	1	example	example	NOUN
ejpam-6089	299	1	1	1	NUM
ejpam-6089	299	2	.	.	X
ejpam-6089	299	3	we	we	PRON
ejpam-6089	299	4	verify	verify	VERB
ejpam-6089	299	5	the	the	DET
ejpam-6089	299	6	result	result	NOUN
ejpam-6089	299	7	of	of	ADP
ejpam-6089	299	8	theorem	theorem	NOUN
ejpam-6089	299	9	6	6	NUM
ejpam-6089	299	10	for	for	ADP
ejpam-6089	299	11	convex	convex	PROPN
ejpam-6089	299	12	function	function	PROPN
ejpam-6089	299	13	υ(c	υ(c	PROPN
ejpam-6089	299	14	)	)	PUNCT
ejpam-6089	300	1	=	=	SYM
ejpam-6089	300	2	c2	c2	PROPN
ejpam-6089	300	3	on	on	ADP
ejpam-6089	300	4	the	the	DET
ejpam-6089	300	5	interval	interval	NOUN
ejpam-6089	300	6	[	[	X
ejpam-6089	300	7	0	0	NUM
ejpam-6089	300	8	,	,	PUNCT
ejpam-6089	300	9	1	1	NUM
ejpam-6089	300	10	]	]	PUNCT
ejpam-6089	300	11	.	.	PUNCT
ejpam-6089	301	1	using	use	VERB
ejpam-6089	301	2	substitution	substitution	NOUN
ejpam-6089	301	3	t	t	NOUN
ejpam-6089	301	4	=	=	PUNCT
ejpam-6089	301	5	ψ	ψ	X
ejpam-6089	301	6	c	c	NOUN
ejpam-6089	301	7	in	in	ADP
ejpam-6089	301	8	left	left	ADJ
ejpam-6089	301	9	and	and	CCONJ
ejpam-6089	301	10	right	right	ADJ
ejpam-6089	301	11	sided	sided	ADJ
ejpam-6089	301	12	reimann	reimann	NOUN
ejpam-6089	301	13	-	-	PUNCT
ejpam-6089	301	14	liouville	liouville	NOUN
ejpam-6089	301	15	integrals	integral	NOUN
ejpam-6089	301	16	(	(	PUNCT
ejpam-6089	301	17	1	1	NUM
ejpam-6089	301	18	)	)	PUNCT
ejpam-6089	301	19	and	and	CCONJ
ejpam-6089	301	20	(	(	PUNCT
ejpam-6089	301	21	2	2	NUM
ejpam-6089	301	22	)	)	PUNCT
ejpam-6089	301	23	,	,	PUNCT
ejpam-6089	301	24	we	we	PRON
ejpam-6089	301	25	get	get	VERB
ejpam-6089	301	26	r−li	r−li	NOUN
ejpam-6089	301	27	(	(	PUNCT
ejpam-6089	301	28	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	301	29	)	)	PUNCT
ejpam-6089	301	30	ℑ1	ℑ1	NOUN
ejpam-6089	301	31	+	+	CCONJ
ejpam-6089	301	32	ℑ2	ℑ2	ADJ
ejpam-6089	301	33	2	2	NUM
ejpam-6089	301	34	=	=	SYM
ejpam-6089	301	35	γ(3	γ(3	PROPN
ejpam-6089	301	36	)	)	PUNCT
ejpam-6089	301	37	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	301	38	℘	℘	PROPN
ejpam-6089	301	39	)	)	PUNCT
ejpam-6089	301	40	+	+	CCONJ
ejpam-6089	302	1	3	3	NUM
ejpam-6089	302	2	)	)	PUNCT
ejpam-6089	302	3	,	,	PUNCT
ejpam-6089	302	4	(	(	PUNCT
ejpam-6089	302	5	18	18	NUM
ejpam-6089	302	6	)	)	PUNCT
ejpam-6089	302	7	r−li	r−li	NOUN
ejpam-6089	302	8	(	(	PUNCT
ejpam-6089	302	9	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	302	10	)	)	PUNCT
ejpam-6089	302	11	ℑ2−	ℑ2−	NUM
ejpam-6089	302	12	ℑ1	ℑ1	NOUN
ejpam-6089	302	13	2	2	NUM
ejpam-6089	302	14	=	=	SYM
ejpam-6089	302	15	0	0	NUM
ejpam-6089	302	16	.	.	PUNCT
ejpam-6089	303	1	(	(	PUNCT
ejpam-6089	303	2	19	19	NUM
ejpam-6089	303	3	)	)	PUNCT
ejpam-6089	303	4	using	use	VERB
ejpam-6089	303	5	(	(	PUNCT
ejpam-6089	303	6	18	18	NUM
ejpam-6089	303	7	)	)	PUNCT
ejpam-6089	303	8	in	in	ADP
ejpam-6089	303	9	infinite	infinite	ADJ
ejpam-6089	303	10	series	series	NOUN
ejpam-6089	303	11	formula	formula	NOUN
ejpam-6089	303	12	for	for	ADP
ejpam-6089	303	13	left	left	ADJ
ejpam-6089	303	14	prabhakar	prabhakar	NOUN
ejpam-6089	303	15	integrals	integral	NOUN
ejpam-6089	303	16	(	(	PUNCT
ejpam-6089	303	17	7	7	NUM
ejpam-6089	303	18	)	)	PUNCT
ejpam-6089	303	19	and	and	CCONJ
ejpam-6089	303	20	(	(	PUNCT
ejpam-6089	303	21	19	19	NUM
ejpam-6089	303	22	)	)	PUNCT
ejpam-6089	303	23	in	in	ADP
ejpam-6089	303	24	infinite	infinite	ADJ
ejpam-6089	303	25	series	series	NOUN
ejpam-6089	303	26	formula	formula	NOUN
ejpam-6089	303	27	for	for	ADP
ejpam-6089	303	28	right	right	ADJ
ejpam-6089	303	29	prabhakar	prabhakar	NOUN
ejpam-6089	303	30	integrals	integral	NOUN
ejpam-6089	303	31	(	(	PUNCT
ejpam-6089	303	32	8)	8)	NUM
ejpam-6089	303	33	,	,	PUNCT
ejpam-6089	303	34	we	we	PRON
ejpam-6089	303	35	have	have	AUX
ejpam-6089	303	36	piℵ,℘,γ,	piℵ,℘,γ,	VERB
ejpam-6089	303	37	♭	♭	NOUN
ejpam-6089	303	38	ℑ1	ℑ1	NOUN
ejpam-6089	303	39	+	+	X
ejpam-6089	303	40	ℑ2	ℑ2	ADJ
ejpam-6089	303	41	2	2	NUM
ejpam-6089	303	42	=	=	SYM
ejpam-6089	303	43	∞∑	∞∑	NUM
ejpam-6089	303	44	ð=0	ð=0	PUNCT
ejpam-6089	304	1	γ(γ	γ(γ	PROPN
ejpam-6089	304	2	+	+	CCONJ
ejpam-6089	304	3	ð)	ð)	PUNCT
ejpam-6089	304	4	♭	♭	PROPN
ejpam-6089	304	5	ð	ð	X
ejpam-6089	304	6	γ(γ)ð	γ(γ)ð	PROPN
ejpam-6089	304	7	!	!	PUNCT
ejpam-6089	304	8	×	×	PROPN
ejpam-6089	304	9	γ(3	γ(3	PROPN
ejpam-6089	304	10	)	)	PUNCT
ejpam-6089	304	11	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	304	12	℘	℘	PROPN
ejpam-6089	304	13	)	)	PUNCT
ejpam-6089	304	14	+	+	CCONJ
ejpam-6089	304	15	3	3	NUM
ejpam-6089	304	16	)	)	PUNCT
ejpam-6089	304	17	,	,	PUNCT
ejpam-6089	304	18	(	(	PUNCT
ejpam-6089	304	19	20	20	X
ejpam-6089	304	20	)	)	PUNCT
ejpam-6089	304	21	piℵ,℘,γ,	piℵ,℘,γ,	NOUN
ejpam-6089	305	1	♭	♭	NOUN
ejpam-6089	305	2	ℑ2−	ℑ2−	NUM
ejpam-6089	305	3	ℑ1	ℑ1	NOUN
ejpam-6089	305	4	2	2	NUM
ejpam-6089	305	5	=	=	SYM
ejpam-6089	305	6	∞∑	∞∑	NUM
ejpam-6089	305	7	ð=0	ð=0	PUNCT
ejpam-6089	305	8	γ(γ	γ(γ	PROPN
ejpam-6089	306	1	+	+	CCONJ
ejpam-6089	306	2	ð)	ð)	PUNCT
ejpam-6089	306	3	♭	♭	PROPN
ejpam-6089	306	4	ð	ð	X
ejpam-6089	306	5	γ(γ)ð	γ(γ)ð	PROPN
ejpam-6089	306	6	!	!	PUNCT
ejpam-6089	306	7	×	×	NOUN
ejpam-6089	306	8	(	(	PUNCT
ejpam-6089	306	9	0	0	NUM
ejpam-6089	306	10	)	)	PUNCT
ejpam-6089	306	11	.	.	PUNCT
ejpam-6089	307	1	(	(	PUNCT
ejpam-6089	307	2	21	21	NUM
ejpam-6089	307	3	)	)	PUNCT
ejpam-6089	307	4	s.	s.	PROPN
ejpam-6089	307	5	naheed	nahee	VERB
ejpam-6089	307	6	et	et	PROPN
ejpam-6089	307	7	al	al	PROPN
ejpam-6089	307	8	.	.	PUNCT
ejpam-6089	307	9	/	/	SYM
ejpam-6089	307	10	eur	eur	PROPN
ejpam-6089	307	11	.	.	PUNCT
ejpam-6089	308	1	j.	j.	PROPN
ejpam-6089	308	2	pure	pure	PROPN
ejpam-6089	308	3	appl	appl	PROPN
ejpam-6089	308	4	.	.	PROPN
ejpam-6089	308	5	math	math	PROPN
ejpam-6089	308	6	,	,	PUNCT
ejpam-6089	308	7	18	18	NUM
ejpam-6089	308	8	(	(	PUNCT
ejpam-6089	308	9	2	2	NUM
ejpam-6089	308	10	)	)	PUNCT
ejpam-6089	308	11	(	(	PUNCT
ejpam-6089	308	12	2025	2025	NUM
ejpam-6089	308	13	)	)	PUNCT
ejpam-6089	308	14	,	,	PUNCT
ejpam-6089	308	15	6089	6089	NUM
ejpam-6089	308	16	14	14	NUM
ejpam-6089	308	17	of	of	ADP
ejpam-6089	308	18	34	34	NUM
ejpam-6089	308	19	also	also	ADV
ejpam-6089	308	20	substitute	substitute	NOUN
ejpam-6089	308	21	(	(	PUNCT
ejpam-6089	308	22	18	18	NUM
ejpam-6089	308	23	)	)	PUNCT
ejpam-6089	308	24	in	in	ADP
ejpam-6089	308	25	left	left	ADJ
ejpam-6089	308	26	sided	side	VERB
ejpam-6089	308	27	generalized	generalized	ADJ
ejpam-6089	308	28	fractional	fractional	ADJ
ejpam-6089	308	29	integral	integral	ADJ
ejpam-6089	308	30	operator	operator	NOUN
ejpam-6089	308	31	(	(	PUNCT
ejpam-6089	308	32	10	10	NUM
ejpam-6089	308	33	)	)	PUNCT
ejpam-6089	308	34	and	and	CCONJ
ejpam-6089	308	35	(	(	PUNCT
ejpam-6089	308	36	19	19	NUM
ejpam-6089	308	37	)	)	PUNCT
ejpam-6089	308	38	in	in	ADP
ejpam-6089	308	39	right	right	ADJ
ejpam-6089	308	40	sided	sided	ADJ
ejpam-6089	308	41	generalized	generalized	ADJ
ejpam-6089	308	42	fractional	fractional	ADJ
ejpam-6089	308	43	integral	integral	ADJ
ejpam-6089	308	44	operator	operator	NOUN
ejpam-6089	308	45	(	(	PUNCT
ejpam-6089	308	46	11	11	NUM
ejpam-6089	308	47	)	)	PUNCT
ejpam-6089	308	48	,	,	PUNCT
ejpam-6089	308	49	we	we	PRON
ejpam-6089	308	50	acquire	acquire	VERB
ejpam-6089	308	51	ε	ε	PROPN
ejpam-6089	308	52	♭	♭	PROPN
ejpam-6089	308	53	,δ	,δ	PUNCT
ejpam-6089	308	54	,	,	PUNCT
ejpam-6089	308	55	b	b	NOUN
ejpam-6089	308	56	,	,	PUNCT
ejpam-6089	308	57	s	s	NOUN
ejpam-6089	308	58	,	,	PUNCT
ejpam-6089	308	59	lℑ1+,ℵ,℘,τυ	lℑ1+,ℵ,℘,τυ	PROPN
ejpam-6089	308	60	(	(	PUNCT
ejpam-6089	308	61	ℑ2	ℑ2	PROPN
ejpam-6089	308	62	2	2	NUM
ejpam-6089	308	63	;	;	PUNCT
ejpam-6089	308	64	g	g	NOUN
ejpam-6089	308	65	)	)	PUNCT
ejpam-6089	308	66	=	=	PUNCT
ejpam-6089	309	1	∞∑	∞∑	NUM
ejpam-6089	309	2	ð=0	ð=0	X
ejpam-6089	309	3	að	að	PROPN
ejpam-6089	309	4	×	×	PROPN
ejpam-6089	309	5	γ(3	γ(3	PROPN
ejpam-6089	309	6	)	)	PUNCT
ejpam-6089	309	7	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	309	8	℘	℘	PROPN
ejpam-6089	309	9	)	)	PUNCT
ejpam-6089	309	10	+	+	CCONJ
ejpam-6089	309	11	3	3	NUM
ejpam-6089	309	12	)	)	PUNCT
ejpam-6089	309	13	,	,	PUNCT
ejpam-6089	309	14	(	(	PUNCT
ejpam-6089	309	15	22	22	NUM
ejpam-6089	309	16	)	)	PUNCT
ejpam-6089	309	17	ε	ε	PROPN
ejpam-6089	309	18	♭	♭	PROPN
ejpam-6089	309	19	,δ	,δ	PUNCT
ejpam-6089	309	20	,	,	PUNCT
ejpam-6089	309	21	b	b	NOUN
ejpam-6089	309	22	,	,	PUNCT
ejpam-6089	309	23	s	s	PROPN
ejpam-6089	309	24	,	,	PUNCT
ejpam-6089	309	25	lℑ2−,ℵ,℘,τυ	lℑ2−,ℵ,℘,τυ	NOUN
ejpam-6089	309	26	(	(	PUNCT
ejpam-6089	309	27	ℑ1	ℑ1	PROPN
ejpam-6089	309	28	2	2	NUM
ejpam-6089	309	29	;	;	PUNCT
ejpam-6089	309	30	g	g	NOUN
ejpam-6089	309	31	)	)	PUNCT
ejpam-6089	309	32	=	=	PUNCT
ejpam-6089	310	1	∞∑	∞∑	NUM
ejpam-6089	310	2	ð=0	ð=0	X
ejpam-6089	310	3	að	að	X
ejpam-6089	310	4	×	×	NOUN
ejpam-6089	310	5	(	(	PUNCT
ejpam-6089	310	6	0	0	NUM
ejpam-6089	310	7	)	)	PUNCT
ejpam-6089	310	8	.	.	PUNCT
ejpam-6089	311	1	(	(	PUNCT
ejpam-6089	311	2	23	23	X
ejpam-6089	311	3	)	)	PUNCT
ejpam-6089	311	4	substituting	substitute	VERB
ejpam-6089	311	5	these	these	DET
ejpam-6089	311	6	expressions	expression	NOUN
ejpam-6089	311	7	(	(	PUNCT
ejpam-6089	311	8	20	20	NUM
ejpam-6089	311	9	)	)	PUNCT
ejpam-6089	311	10	,	,	PUNCT
ejpam-6089	311	11	(	(	PUNCT
ejpam-6089	311	12	21	21	NUM
ejpam-6089	311	13	)	)	PUNCT
ejpam-6089	311	14	,	,	PUNCT
ejpam-6089	311	15	(	(	PUNCT
ejpam-6089	311	16	22	22	NUM
ejpam-6089	311	17	)	)	PUNCT
ejpam-6089	311	18	and	and	CCONJ
ejpam-6089	311	19	(	(	PUNCT
ejpam-6089	311	20	23	23	NUM
ejpam-6089	311	21	)	)	PUNCT
ejpam-6089	311	22	in	in	ADP
ejpam-6089	311	23	the	the	DET
ejpam-6089	311	24	inequality	inequality	NOUN
ejpam-6089	311	25	(	(	PUNCT
ejpam-6089	311	26	17	17	NUM
ejpam-6089	311	27	)	)	PUNCT
ejpam-6089	311	28	and	and	CCONJ
ejpam-6089	311	29	after	after	ADP
ejpam-6089	311	30	some	some	DET
ejpam-6089	311	31	simplification	simplification	NOUN
ejpam-6089	311	32	,	,	PUNCT
ejpam-6089	311	33	we	we	PRON
ejpam-6089	311	34	get	get	VERB
ejpam-6089	311	35	∞∑	∞∑	NUM
ejpam-6089	311	36	ð=0	ð=0	PUNCT
ejpam-6089	311	37	hð	hð	VERB
ejpam-6089	311	38	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	311	39	℘	℘	PROPN
ejpam-6089	311	40	)	)	PUNCT
ejpam-6089	312	1	+	+	CCONJ
ejpam-6089	312	2	1	1	X
ejpam-6089	312	3	)	)	SYM
ejpam-6089	312	4	2	2	NUM
ejpam-6089	312	5	≤	≤	NOUN
ejpam-6089	312	6	∞∑	∞∑	NUM
ejpam-6089	312	7	ð=0	ð=0	X
ejpam-6089	312	8	(	(	PUNCT
ejpam-6089	312	9	γ(γ	γ(γ	PROPN
ejpam-6089	312	10	+	+	CCONJ
ejpam-6089	312	11	ð)	ð)	PUNCT
ejpam-6089	312	12	♭	♭	PROPN
ejpam-6089	312	13	ð	ð	X
ejpam-6089	312	14	γ(γ)ð	γ(γ)ð	PROPN
ejpam-6089	312	15	!	!	PUNCT
ejpam-6089	312	16	×	×	PROPN
ejpam-6089	312	17	γ(3	γ(3	PROPN
ejpam-6089	312	18	)	)	PUNCT
ejpam-6089	312	19	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	312	20	℘	℘	PROPN
ejpam-6089	312	21	)	)	PUNCT
ejpam-6089	312	22	+	+	CCONJ
ejpam-6089	312	23	3	3	NUM
ejpam-6089	312	24	)	)	PUNCT
ejpam-6089	312	25	)	)	PUNCT
ejpam-6089	313	1	+	+	CCONJ
ejpam-6089	314	1	∞∑	∞∑	NUM
ejpam-6089	314	2	ð=0	ð=0	X
ejpam-6089	314	3	(	(	PUNCT
ejpam-6089	314	4	að	að	X
ejpam-6089	314	5	×	×	PROPN
ejpam-6089	314	6	γ(3	γ(3	PROPN
ejpam-6089	314	7	)	)	PUNCT
ejpam-6089	314	8	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	314	9	℘	℘	PROPN
ejpam-6089	314	10	)	)	PUNCT
ejpam-6089	314	11	+	+	CCONJ
ejpam-6089	314	12	3	3	NUM
ejpam-6089	314	13	)	)	PUNCT
ejpam-6089	314	14	)	)	PUNCT
ejpam-6089	314	15	≤	≤	NOUN
ejpam-6089	315	1	∞∑	∞∑	NUM
ejpam-6089	315	2	ð=0	ð=0	PUNCT
ejpam-6089	315	3	hð	hð	VERB
ejpam-6089	315	4	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	315	5	℘	℘	PROPN
ejpam-6089	315	6	)	)	PUNCT
ejpam-6089	315	7	+	+	CCONJ
ejpam-6089	315	8	1	1	NUM
ejpam-6089	315	9	)	)	PUNCT
ejpam-6089	315	10	.	.	PUNCT
ejpam-6089	316	1	figure	figure	VERB
ejpam-6089	316	2	1	1	NUM
ejpam-6089	316	3	:	:	PUNCT
ejpam-6089	316	4	the	the	DET
ejpam-6089	316	5	2d	2d	NOUN
ejpam-6089	316	6	graph	graph	NOUN
ejpam-6089	316	7	exhibiting	exhibit	VERB
ejpam-6089	316	8	the	the	DET
ejpam-6089	316	9	inequality	inequality	NOUN
ejpam-6089	316	10	(	(	PUNCT
ejpam-6089	316	11	17	17	NUM
ejpam-6089	316	12	)	)	PUNCT
ejpam-6089	316	13	for	for	ADP
ejpam-6089	316	14	ð	ð	PROPN
ejpam-6089	316	15	=	=	SYM
ejpam-6089	316	16	1	1	NUM
ejpam-6089	316	17	.	.	X
ejpam-6089	316	18	2.2	2.2	NUM
ejpam-6089	316	19	.	.	PUNCT
ejpam-6089	317	1	inequalities	inequality	NOUN
ejpam-6089	317	2	involving	involve	VERB
ejpam-6089	317	3	fractional	fractional	ADJ
ejpam-6089	317	4	integral	integral	ADJ
ejpam-6089	317	5	of	of	ADP
ejpam-6089	317	6	the	the	DET
ejpam-6089	317	7	type	type	NOUN
ejpam-6089	317	8	(	(	PUNCT
ejpam-6089	317	9	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	317	10	2	2	NUM
ejpam-6089	317	11	)	)	PUNCT
ejpam-6089	317	12	theorem	theorem	VERB
ejpam-6089	317	13	7	7	NUM
ejpam-6089	317	14	.	.	PUNCT
ejpam-6089	318	1	if	if	SCONJ
ejpam-6089	318	2	υ	υ	PRON
ejpam-6089	318	3	:	:	PUNCT
ejpam-6089	318	4	[	[	X
ejpam-6089	318	5	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	318	6	]	]	PUNCT
ejpam-6089	318	7	→	→	SYM
ejpam-6089	318	8	ℜ	ℜ	PROPN
ejpam-6089	318	9	is	be	AUX
ejpam-6089	318	10	l1	l1	PROPN
ejpam-6089	318	11	and	and	CCONJ
ejpam-6089	318	12	convex	convex	PROPN
ejpam-6089	318	13	and	and	CCONJ
ejpam-6089	318	14	the	the	DET
ejpam-6089	318	15	parameters	parameter	NOUN
ejpam-6089	318	16	,	,	PUNCT
ejpam-6089	318	17	ℜ(ℵð	ℜ(ℵð	NOUN
ejpam-6089	318	18	+	+	CCONJ
ejpam-6089	318	19	℘	℘	NOUN
ejpam-6089	318	20	)	)	PUNCT
ejpam-6089	318	21	>	>	X
ejpam-6089	318	22	0	0	NUM
ejpam-6089	318	23	also	also	ADV
ejpam-6089	318	24	ℜ(	ℜ(	VERB
ejpam-6089	318	25	♭	♭	NOUN
ejpam-6089	318	26	),ℜ(γ),ℜ(ℵ),ℜ(℘),ℜ(τ	),ℜ(γ),ℜ(ℵ),ℜ(℘),ℜ(τ	PUNCT
ejpam-6089	318	27	)	)	PUNCT
ejpam-6089	318	28	>	>	X
ejpam-6089	318	29	0	0	NUM
ejpam-6089	318	30	and	and	CCONJ
ejpam-6089	318	31	ℜ(b	ℜ(b	NOUN
ejpam-6089	318	32	)	)	PUNCT
ejpam-6089	318	33	>	>	X
ejpam-6089	319	1	ℜ(δ	ℜ(δ	X
ejpam-6089	319	2	)	)	PUNCT
ejpam-6089	319	3	>	>	X
ejpam-6089	319	4	0	0	PUNCT
ejpam-6089	320	1	and	and	CCONJ
ejpam-6089	320	2	let	let	VERB
ejpam-6089	320	3	g	g	PROPN
ejpam-6089	320	4	≥	≥	NOUN
ejpam-6089	320	5	0	0	NUM
ejpam-6089	320	6	,	,	PUNCT
ejpam-6089	320	7	l	l	NOUN
ejpam-6089	320	8	>	>	X
ejpam-6089	320	9	0	0	PUNCT
ejpam-6089	320	10	and	and	CCONJ
ejpam-6089	320	11	s.	s.	PROPN
ejpam-6089	320	12	naheed	nahee	VERB
ejpam-6089	320	13	et	et	PROPN
ejpam-6089	320	14	al	al	PROPN
ejpam-6089	320	15	.	.	PUNCT
ejpam-6089	320	16	/	/	SYM
ejpam-6089	320	17	eur	eur	PROPN
ejpam-6089	320	18	.	.	PUNCT
ejpam-6089	321	1	j.	j.	PROPN
ejpam-6089	321	2	pure	pure	PROPN
ejpam-6089	321	3	appl	appl	PROPN
ejpam-6089	321	4	.	.	PROPN
ejpam-6089	321	5	math	math	PROPN
ejpam-6089	321	6	,	,	PUNCT
ejpam-6089	321	7	18	18	NUM
ejpam-6089	321	8	(	(	PUNCT
ejpam-6089	321	9	2	2	NUM
ejpam-6089	321	10	)	)	PUNCT
ejpam-6089	321	11	(	(	PUNCT
ejpam-6089	321	12	2025	2025	NUM
ejpam-6089	321	13	)	)	PUNCT
ejpam-6089	321	14	,	,	PUNCT
ejpam-6089	321	15	6089	6089	NUM
ejpam-6089	321	16	15	15	NUM
ejpam-6089	321	17	of	of	ADP
ejpam-6089	321	18	34	34	NUM
ejpam-6089	321	19	figure	figure	NOUN
ejpam-6089	321	20	2	2	NUM
ejpam-6089	321	21	:	:	PUNCT
ejpam-6089	321	22	the	the	DET
ejpam-6089	321	23	3d	3d	NOUN
ejpam-6089	321	24	graph	graph	NOUN
ejpam-6089	321	25	exhibiting	exhibit	VERB
ejpam-6089	321	26	the	the	DET
ejpam-6089	321	27	inequality	inequality	NOUN
ejpam-6089	321	28	(	(	PUNCT
ejpam-6089	321	29	17	17	NUM
ejpam-6089	321	30	)	)	PUNCT
ejpam-6089	321	31	for	for	ADP
ejpam-6089	321	32	convex	convex	PROPN
ejpam-6089	321	33	function	function	PROPN
ejpam-6089	321	34	υ(c	υ(c	PROPN
ejpam-6089	321	35	)	)	PUNCT
ejpam-6089	321	36	=	=	SYM
ejpam-6089	321	37	c2	c2	PROPN
ejpam-6089	321	38	on	on	ADP
ejpam-6089	321	39	the	the	DET
ejpam-6089	321	40	interval	interval	NOUN
ejpam-6089	322	1	[	[	X
ejpam-6089	322	2	0	0	NUM
ejpam-6089	322	3	,	,	PUNCT
ejpam-6089	322	4	1	1	NUM
ejpam-6089	322	5	]	]	PUNCT
ejpam-6089	322	6	and	and	CCONJ
ejpam-6089	322	7	for	for	ADP
ejpam-6089	322	8	ð	ð	PROPN
ejpam-6089	322	9	=	=	SYM
ejpam-6089	322	10	1	1	NUM
ejpam-6089	322	11	.	.	NOUN
ejpam-6089	322	12	0	0	PUNCT
ejpam-6089	323	1	<	<	X
ejpam-6089	323	2	s	s	X
ejpam-6089	323	3	≤	≤	NUM
ejpam-6089	323	4	l+ℜ(ℵ	l+ℜ(ℵ	PROPN
ejpam-6089	323	5	)	)	PUNCT
ejpam-6089	323	6	,	,	PUNCT
ejpam-6089	323	7	then	then	ADV
ejpam-6089	323	8	we	we	PRON
ejpam-6089	323	9	have	have	VERB
ejpam-6089	323	10	a	a	DET
ejpam-6089	323	11	distinct	distinct	ADJ
ejpam-6089	323	12	fractional	fractional	ADJ
ejpam-6089	323	13	development	development	NOUN
ejpam-6089	323	14	of	of	ADP
ejpam-6089	323	15	the	the	DET
ejpam-6089	323	16	(	(	PUNCT
ejpam-6089	323	17	h−h	h−h	NOUN
ejpam-6089	323	18	)	)	PUNCT
ejpam-6089	323	19	inequality	inequality	NOUN
ejpam-6089	323	20	∞∑	∞∑	NUM
ejpam-6089	323	21	ð=0	ð=0	X
ejpam-6089	323	22	aðoðυ	aðoðυ	NOUN
ejpam-6089	323	23	(	(	PUNCT
ejpam-6089	323	24	ℑ1	ℑ1	PROPN
ejpam-6089	323	25	+	+	CCONJ
ejpam-6089	323	26	ℑ2	ℑ2	PROPN
ejpam-6089	323	27	2	2	NUM
ejpam-6089	323	28	)	)	PUNCT
ejpam-6089	323	29	≤	≤	PUNCT
ejpam-6089	324	1	ε	ε	PROPN
ejpam-6089	324	2	♭	♭	PROPN
ejpam-6089	324	3	,δ	,δ	PUNCT
ejpam-6089	324	4	,	,	PUNCT
ejpam-6089	324	5	b	b	NOUN
ejpam-6089	324	6	,	,	PUNCT
ejpam-6089	324	7	s	s	X
ejpam-6089	324	8	,	,	PUNCT
ejpam-6089	324	9	l	l	NOUN
ejpam-6089	324	10	(	(	PUNCT
ejpam-6089	324	11	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	324	12	2	2	NUM
ejpam-6089	324	13	)	)	PUNCT
ejpam-6089	324	14	+	+	ADV
ejpam-6089	324	15	,	,	PUNCT
ejpam-6089	324	16	ℵ,℘,τ	ℵ,℘,τ	PROPN
ejpam-6089	324	17	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	324	18	;	;	PUNCT
ejpam-6089	324	19	g	g	NOUN
ejpam-6089	324	20	)	)	PUNCT
ejpam-6089	325	1	+	+	CCONJ
ejpam-6089	325	2	ε	ε	PROPN
ejpam-6089	325	3	♭	♭	PROPN
ejpam-6089	325	4	,δ	,δ	PUNCT
ejpam-6089	325	5	,	,	PUNCT
ejpam-6089	325	6	b	b	NOUN
ejpam-6089	325	7	,	,	PUNCT
ejpam-6089	325	8	s	s	X
ejpam-6089	325	9	,	,	PUNCT
ejpam-6089	325	10	l	l	NOUN
ejpam-6089	325	11	(	(	PUNCT
ejpam-6089	325	12	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	325	13	2	2	NUM
ejpam-6089	325	14	)	)	PUNCT
ejpam-6089	325	15	−,ℵ,℘,τ	−,ℵ,℘,τ	NOUN
ejpam-6089	325	16	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	325	17	;	;	PUNCT
ejpam-6089	325	18	g	g	X
ejpam-6089	325	19	)	)	PUNCT
ejpam-6089	325	20	≤	≤	NOUN
ejpam-6089	326	1	∞∑	∞∑	NUM
ejpam-6089	326	2	ð=0	ð=0	X
ejpam-6089	326	3	aðoð	aðoð	ADJ
ejpam-6089	326	4	(	(	PUNCT
ejpam-6089	326	5	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	326	6	)	)	PUNCT
ejpam-6089	326	7	+	+	CCONJ
ejpam-6089	326	8	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	326	9	)	)	PUNCT
ejpam-6089	326	10	2	2	NUM
ejpam-6089	326	11	)	)	PUNCT
ejpam-6089	326	12	,	,	PUNCT
ejpam-6089	326	13	where	where	SCONJ
ejpam-6089	326	14	að	að	PROPN
ejpam-6089	326	15	=	=	SYM
ejpam-6089	326	16	bg(δ+ðs	bg(δ+ðs	PROPN
ejpam-6089	326	17	,	,	PUNCT
ejpam-6089	326	18	b−δ	b−δ	NOUN
ejpam-6089	326	19	)	)	PUNCT
ejpam-6089	326	20	b(δ	b(δ	NOUN
ejpam-6089	326	21	,	,	PUNCT
ejpam-6089	326	22	b−δ	b−δ	NOUN
ejpam-6089	326	23	)	)	PUNCT
ejpam-6089	326	24	(	(	PUNCT
ejpam-6089	326	25	b)ðs	b)ðs	PROPN
ejpam-6089	326	26	♭	♭	PROPN
ejpam-6089	326	27	ð	ð	X
ejpam-6089	326	28	(	(	PUNCT
ejpam-6089	326	29	τ)ðl	τ)ðl	PROPN
ejpam-6089	326	30	and	and	CCONJ
ejpam-6089	326	31	oð	oð	X
ejpam-6089	326	32	=	=	SYM
ejpam-6089	326	33	(	(	PUNCT
ejpam-6089	326	34	ℑ2−ℑ1)(ℵð+℘	ℑ2−ℑ1)(ℵð+℘	PROPN
ejpam-6089	326	35	)	)	PUNCT
ejpam-6089	326	36	2(ℵð+℘)−1γ((ℵð+℘)+1	2(ℵð+℘)−1γ((ℵð+℘)+1	NUM
ejpam-6089	326	37	)	)	PUNCT
ejpam-6089	326	38	.	.	PUNCT
ejpam-6089	327	1	proof	proof	NOUN
ejpam-6089	327	2	.	.	PUNCT
ejpam-6089	328	1	replacing	replace	VERB
ejpam-6089	328	2	α∗	α∗	NOUN
ejpam-6089	328	3	by	by	ADP
ejpam-6089	328	4	(	(	PUNCT
ejpam-6089	328	5	ℵð+	ℵð+	ADJ
ejpam-6089	328	6	℘	℘	PROPN
ejpam-6089	328	7	)	)	PUNCT
ejpam-6089	328	8	in	in	ADP
ejpam-6089	328	9	theorem	theorem	NOUN
ejpam-6089	328	10	4	4	NUM
ejpam-6089	328	11	,	,	PUNCT
ejpam-6089	328	12	we	we	PRON
ejpam-6089	328	13	get	get	VERB
ejpam-6089	328	14	υ	υ	PRON
ejpam-6089	328	15	(	(	PUNCT
ejpam-6089	328	16	ℑ1	ℑ1	PROPN
ejpam-6089	328	17	+	+	CCONJ
ejpam-6089	328	18	ℑ2	ℑ2	PROPN
ejpam-6089	328	19	2	2	NUM
ejpam-6089	328	20	)	)	PUNCT
ejpam-6089	328	21	≤	≤	NOUN
ejpam-6089	328	22	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	328	23	℘	℘	NOUN
ejpam-6089	328	24	)	)	PUNCT
ejpam-6089	328	25	+	+	NUM
ejpam-6089	328	26	1	1	X
ejpam-6089	328	27	)	)	PUNCT
ejpam-6089	328	28	(	(	PUNCT
ejpam-6089	328	29	ℑ2	ℑ2	ADP
ejpam-6089	328	30	−ℑ1)(ℵð+℘	−ℑ1)(ℵð+℘	NUM
ejpam-6089	328	31	)	)	PUNCT
ejpam-6089	328	32	(	(	PUNCT
ejpam-6089	328	33	r−li	r−li	NOUN
ejpam-6089	328	34	(	(	PUNCT
ejpam-6089	328	35	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	328	36	)	)	PUNCT
ejpam-6089	328	37	(	(	PUNCT
ejpam-6089	328	38	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	328	39	2	2	NUM
ejpam-6089	328	40	)	)	PUNCT
ejpam-6089	328	41	+	+	CCONJ
ejpam-6089	329	1	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	329	2	)	)	PUNCT
ejpam-6089	329	3	+	+	NUM
ejpam-6089	329	4	r−li	r−li	NOUN
ejpam-6089	329	5	(	(	PUNCT
ejpam-6089	329	6	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	329	7	)	)	PUNCT
ejpam-6089	329	8	(	(	PUNCT
ejpam-6089	329	9	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	329	10	2	2	NUM
ejpam-6089	329	11	)	)	PUNCT
ejpam-6089	329	12	−	−	PROPN
ejpam-6089	329	13	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	329	14	)	)	PUNCT
ejpam-6089	329	15	)	)	PUNCT
ejpam-6089	329	16	≤	≤	NOUN
ejpam-6089	329	17	(	(	PUNCT
ejpam-6089	329	18	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	329	19	)	)	PUNCT
ejpam-6089	329	20	+	+	CCONJ
ejpam-6089	329	21	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	329	22	)	)	PUNCT
ejpam-6089	329	23	2	2	NUM
ejpam-6089	329	24	)	)	PUNCT
ejpam-6089	329	25	.	.	PUNCT
ejpam-6089	330	1	multiply	multiply	VERB
ejpam-6089	330	2	the	the	DET
ejpam-6089	330	3	above	above	ADJ
ejpam-6089	330	4	expression	expression	NOUN
ejpam-6089	330	5	with	with	ADP
ejpam-6089	330	6	(	(	PUNCT
ejpam-6089	330	7	ℑ2−ℑ1)(ℵð+℘	ℑ2−ℑ1)(ℵð+℘	NOUN
ejpam-6089	330	8	)	)	PUNCT
ejpam-6089	330	9	2(ℵð+℘)−1γ((ℵð+℘)+1	2(ℵð+℘)−1γ((ℵð+℘)+1	NUM
ejpam-6089	330	10	)	)	PUNCT
ejpam-6089	330	11	to	to	PART
ejpam-6089	330	12	get	get	VERB
ejpam-6089	330	13	(	(	PUNCT
ejpam-6089	330	14	ℑ2	ℑ2	PROPN
ejpam-6089	330	15	−ℑ1	−ℑ1	PROPN
ejpam-6089	330	16	)	)	PUNCT
ejpam-6089	330	17	(	(	PUNCT
ejpam-6089	330	18	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	330	19	)	)	PUNCT
ejpam-6089	330	20	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	330	21	℘	℘	NOUN
ejpam-6089	330	22	)	)	PUNCT
ejpam-6089	330	23	+	+	NUM
ejpam-6089	330	24	1	1	X
ejpam-6089	330	25	)	)	PUNCT
ejpam-6089	330	26	υ	υ	NOUN
ejpam-6089	330	27	(	(	PUNCT
ejpam-6089	330	28	ℑ1	ℑ1	PROPN
ejpam-6089	330	29	+	+	CCONJ
ejpam-6089	330	30	ℑ2	ℑ2	PROPN
ejpam-6089	330	31	2	2	NUM
ejpam-6089	330	32	)	)	PUNCT
ejpam-6089	330	33	≤	≤	NOUN
ejpam-6089	330	34	(	(	PUNCT
ejpam-6089	330	35	r−li	r−li	NOUN
ejpam-6089	330	36	(	(	PUNCT
ejpam-6089	330	37	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	330	38	)	)	PUNCT
ejpam-6089	330	39	(	(	PUNCT
ejpam-6089	330	40	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	330	41	2	2	NUM
ejpam-6089	330	42	)	)	PUNCT
ejpam-6089	330	43	+	+	CCONJ
ejpam-6089	331	1	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	331	2	)	)	PUNCT
ejpam-6089	331	3	+	+	NUM
ejpam-6089	331	4	r−li	r−li	NOUN
ejpam-6089	331	5	(	(	PUNCT
ejpam-6089	331	6	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	331	7	)	)	PUNCT
ejpam-6089	331	8	(	(	PUNCT
ejpam-6089	331	9	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	331	10	2	2	NUM
ejpam-6089	331	11	)	)	PUNCT
ejpam-6089	331	12	−	−	PROPN
ejpam-6089	331	13	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	331	14	)	)	PUNCT
ejpam-6089	331	15	)	)	PUNCT
ejpam-6089	331	16	≤	≤	NOUN
ejpam-6089	331	17	(	(	PUNCT
ejpam-6089	331	18	ℑ2	ℑ2	PROPN
ejpam-6089	331	19	−ℑ1	−ℑ1	PROPN
ejpam-6089	331	20	)	)	PUNCT
ejpam-6089	331	21	(	(	PUNCT
ejpam-6089	331	22	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	331	23	)	)	PUNCT
ejpam-6089	331	24	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	331	25	℘	℘	NOUN
ejpam-6089	331	26	)	)	PUNCT
ejpam-6089	331	27	+	+	NUM
ejpam-6089	331	28	1	1	X
ejpam-6089	331	29	)	)	PUNCT
ejpam-6089	331	30	(	(	PUNCT
ejpam-6089	331	31	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	331	32	)	)	PUNCT
ejpam-6089	331	33	+	+	CCONJ
ejpam-6089	331	34	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	331	35	)	)	PUNCT
ejpam-6089	331	36	2	2	NUM
ejpam-6089	331	37	)	)	PUNCT
ejpam-6089	331	38	.	.	PUNCT
ejpam-6089	332	1	s.	s.	PROPN
ejpam-6089	332	2	naheed	nahee	VERB
ejpam-6089	332	3	et	et	PROPN
ejpam-6089	332	4	al	al	PROPN
ejpam-6089	332	5	.	.	PUNCT
ejpam-6089	332	6	/	/	SYM
ejpam-6089	332	7	eur	eur	PROPN
ejpam-6089	332	8	.	.	PUNCT
ejpam-6089	333	1	j.	j.	PROPN
ejpam-6089	333	2	pure	pure	PROPN
ejpam-6089	333	3	appl	appl	PROPN
ejpam-6089	333	4	.	.	PROPN
ejpam-6089	333	5	math	math	PROPN
ejpam-6089	333	6	,	,	PUNCT
ejpam-6089	333	7	18	18	NUM
ejpam-6089	333	8	(	(	PUNCT
ejpam-6089	333	9	2	2	NUM
ejpam-6089	333	10	)	)	PUNCT
ejpam-6089	333	11	(	(	PUNCT
ejpam-6089	333	12	2025	2025	NUM
ejpam-6089	333	13	)	)	PUNCT
ejpam-6089	333	14	,	,	PUNCT
ejpam-6089	333	15	6089	6089	NUM
ejpam-6089	333	16	16	16	NUM
ejpam-6089	333	17	of	of	ADP
ejpam-6089	333	18	34	34	NUM
ejpam-6089	333	19	again	again	ADV
ejpam-6089	333	20	the	the	DET
ejpam-6089	333	21	above	above	ADJ
ejpam-6089	333	22	inequality	inequality	NOUN
ejpam-6089	333	23	is	be	AUX
ejpam-6089	333	24	multiplied	multiply	VERB
ejpam-6089	333	25	with	with	ADP
ejpam-6089	333	26	að	að	X
ejpam-6089	333	27	and	and	CCONJ
ejpam-6089	333	28	then	then	ADV
ejpam-6089	333	29	summing	sum	VERB
ejpam-6089	333	30	over	over	ADP
ejpam-6089	333	31	all	all	PRON
ejpam-6089	333	32	ð	ð	NOUN
ejpam-6089	333	33	∞∑	∞∑	NUM
ejpam-6089	333	34	ð=0	ð=0	X
ejpam-6089	333	35	að	að	X
ejpam-6089	333	36	(	(	PUNCT
ejpam-6089	333	37	ℑ2	ℑ2	PROPN
ejpam-6089	333	38	−ℑ1	−ℑ1	PROPN
ejpam-6089	333	39	)	)	PUNCT
ejpam-6089	333	40	(	(	PUNCT
ejpam-6089	333	41	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	333	42	)	)	PUNCT
ejpam-6089	333	43	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	333	44	℘	℘	NOUN
ejpam-6089	333	45	)	)	PUNCT
ejpam-6089	334	1	+	+	NUM
ejpam-6089	334	2	1	1	X
ejpam-6089	334	3	)	)	PUNCT
ejpam-6089	334	4	υ	υ	NOUN
ejpam-6089	334	5	(	(	PUNCT
ejpam-6089	334	6	ℑ1	ℑ1	PROPN
ejpam-6089	334	7	+	+	CCONJ
ejpam-6089	334	8	ℑ2	ℑ2	PROPN
ejpam-6089	334	9	2	2	NUM
ejpam-6089	334	10	)	)	PUNCT
ejpam-6089	334	11	≤	≤	NOUN
ejpam-6089	335	1	∞∑	∞∑	NUM
ejpam-6089	335	2	ð=0	ð=0	X
ejpam-6089	335	3	að	að	X
ejpam-6089	335	4	(	(	PUNCT
ejpam-6089	335	5	r−li	r−li	NOUN
ejpam-6089	335	6	(	(	PUNCT
ejpam-6089	335	7	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	335	8	)	)	PUNCT
ejpam-6089	335	9	(	(	PUNCT
ejpam-6089	335	10	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	335	11	2	2	NUM
ejpam-6089	335	12	)	)	PUNCT
ejpam-6089	335	13	+	+	CCONJ
ejpam-6089	335	14	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	335	15	)	)	PUNCT
ejpam-6089	335	16	+	+	NUM
ejpam-6089	335	17	r−li	r−li	NOUN
ejpam-6089	335	18	(	(	PUNCT
ejpam-6089	335	19	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	335	20	)	)	PUNCT
ejpam-6089	335	21	(	(	PUNCT
ejpam-6089	335	22	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	335	23	2	2	NUM
ejpam-6089	335	24	)	)	PUNCT
ejpam-6089	335	25	−	−	PROPN
ejpam-6089	335	26	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	335	27	)	)	PUNCT
ejpam-6089	335	28	)	)	PUNCT
ejpam-6089	335	29	≤	≤	NOUN
ejpam-6089	336	1	∞∑	∞∑	NUM
ejpam-6089	336	2	ð=0	ð=0	X
ejpam-6089	336	3	að	að	X
ejpam-6089	336	4	(	(	PUNCT
ejpam-6089	336	5	ℑ2	ℑ2	PROPN
ejpam-6089	336	6	−ℑ1	−ℑ1	PROPN
ejpam-6089	336	7	)	)	PUNCT
ejpam-6089	336	8	(	(	PUNCT
ejpam-6089	336	9	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	336	10	)	)	PUNCT
ejpam-6089	336	11	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	336	12	℘	℘	NOUN
ejpam-6089	336	13	)	)	PUNCT
ejpam-6089	336	14	+	+	NUM
ejpam-6089	336	15	1	1	X
ejpam-6089	336	16	)	)	PUNCT
ejpam-6089	336	17	(	(	PUNCT
ejpam-6089	336	18	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	336	19	)	)	PUNCT
ejpam-6089	336	20	+	+	CCONJ
ejpam-6089	336	21	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	336	22	)	)	PUNCT
ejpam-6089	336	23	2	2	NUM
ejpam-6089	336	24	)	)	PUNCT
ejpam-6089	336	25	.	.	PUNCT
ejpam-6089	337	1	using	use	VERB
ejpam-6089	337	2	proposition	proposition	NOUN
ejpam-6089	337	3	1	1	NUM
ejpam-6089	337	4	from	from	ADP
ejpam-6089	337	5	the	the	DET
ejpam-6089	337	6	middle	middle	NOUN
ejpam-6089	337	7	of	of	ADP
ejpam-6089	337	8	interval	interval	NOUN
ejpam-6089	337	9	[	[	X
ejpam-6089	337	10	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	337	11	]	]	X
ejpam-6089	337	12	∞∑	∞∑	NUM
ejpam-6089	337	13	ð=0	ð=0	X
ejpam-6089	337	14	aðoðυ	aðoðυ	NOUN
ejpam-6089	337	15	(	(	PUNCT
ejpam-6089	337	16	ℑ1	ℑ1	PROPN
ejpam-6089	337	17	+	+	CCONJ
ejpam-6089	337	18	ℑ2	ℑ2	PROPN
ejpam-6089	337	19	2	2	NUM
ejpam-6089	337	20	)	)	PUNCT
ejpam-6089	337	21	≤	≤	PUNCT
ejpam-6089	337	22	ε	ε	PROPN
ejpam-6089	337	23	♭	♭	PROPN
ejpam-6089	337	24	,δ	,δ	PUNCT
ejpam-6089	337	25	,	,	PUNCT
ejpam-6089	337	26	b	b	NOUN
ejpam-6089	337	27	,	,	PUNCT
ejpam-6089	337	28	s	s	X
ejpam-6089	337	29	,	,	PUNCT
ejpam-6089	337	30	l	l	NOUN
ejpam-6089	337	31	(	(	PUNCT
ejpam-6089	337	32	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	337	33	2	2	NUM
ejpam-6089	337	34	)	)	PUNCT
ejpam-6089	338	1	+	+	ADV
ejpam-6089	338	2	,	,	PUNCT
ejpam-6089	338	3	ℵ,℘,τ	ℵ,℘,τ	PROPN
ejpam-6089	338	4	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	338	5	;	;	PUNCT
ejpam-6089	338	6	g	g	NOUN
ejpam-6089	338	7	)	)	PUNCT
ejpam-6089	339	1	+	+	CCONJ
ejpam-6089	339	2	ε	ε	PROPN
ejpam-6089	339	3	♭	♭	PROPN
ejpam-6089	339	4	,δ	,δ	PUNCT
ejpam-6089	339	5	,	,	PUNCT
ejpam-6089	339	6	b	b	NOUN
ejpam-6089	339	7	,	,	PUNCT
ejpam-6089	339	8	s	s	X
ejpam-6089	339	9	,	,	PUNCT
ejpam-6089	339	10	l	l	NOUN
ejpam-6089	339	11	(	(	PUNCT
ejpam-6089	339	12	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	339	13	2	2	NUM
ejpam-6089	339	14	)	)	PUNCT
ejpam-6089	339	15	−,ℵ,℘,τ	−,ℵ,℘,τ	NOUN
ejpam-6089	339	16	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	339	17	;	;	PUNCT
ejpam-6089	339	18	g	g	X
ejpam-6089	339	19	)	)	PUNCT
ejpam-6089	339	20	≤	≤	NOUN
ejpam-6089	340	1	∞∑	∞∑	NUM
ejpam-6089	340	2	ð=0	ð=0	X
ejpam-6089	340	3	aðoð	aðoð	ADJ
ejpam-6089	340	4	(	(	PUNCT
ejpam-6089	340	5	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	340	6	)	)	PUNCT
ejpam-6089	340	7	+	+	CCONJ
ejpam-6089	340	8	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	340	9	)	)	PUNCT
ejpam-6089	340	10	2	2	NUM
ejpam-6089	340	11	)	)	PUNCT
ejpam-6089	340	12	.	.	PUNCT
ejpam-6089	341	1	this	this	PRON
ejpam-6089	341	2	proves	prove	VERB
ejpam-6089	341	3	the	the	DET
ejpam-6089	341	4	desired	desire	VERB
ejpam-6089	341	5	result	result	NOUN
ejpam-6089	341	6	.	.	PUNCT
ejpam-6089	342	1	proposition	proposition	NOUN
ejpam-6089	342	2	4	4	NUM
ejpam-6089	342	3	.	.	PUNCT
ejpam-6089	343	1	if	if	SCONJ
ejpam-6089	343	2	υ	υ	PRON
ejpam-6089	343	3	:	:	PUNCT
ejpam-6089	343	4	[	[	X
ejpam-6089	343	5	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	343	6	]	]	PUNCT
ejpam-6089	343	7	→	→	SYM
ejpam-6089	343	8	ℜ	ℜ	PROPN
ejpam-6089	343	9	is	be	AUX
ejpam-6089	343	10	l1	l1	PROPN
ejpam-6089	343	11	and	and	CCONJ
ejpam-6089	343	12	convex	convex	PROPN
ejpam-6089	343	13	and	and	CCONJ
ejpam-6089	343	14	the	the	DET
ejpam-6089	343	15	parameters	parameter	NOUN
ejpam-6089	343	16	,	,	PUNCT
ejpam-6089	343	17	ℜ(ℵð+℘	ℜ(ℵð+℘	NOUN
ejpam-6089	343	18	)	)	PUNCT
ejpam-6089	343	19	>	>	X
ejpam-6089	343	20	0	0	PUNCT
ejpam-6089	343	21	also	also	ADV
ejpam-6089	343	22	ℜ(	ℜ(	VERB
ejpam-6089	343	23	♭	♭	NOUN
ejpam-6089	343	24	),ℜ(γ),ℜ(ℵ),ℜ(℘),ℜ(τ	),ℜ(γ),ℜ(ℵ),ℜ(℘),ℜ(τ	PUNCT
ejpam-6089	343	25	)	)	PUNCT
ejpam-6089	343	26	>	>	X
ejpam-6089	343	27	0	0	NUM
ejpam-6089	343	28	and	and	CCONJ
ejpam-6089	343	29	ℜ(b	ℜ(b	NOUN
ejpam-6089	343	30	)	)	PUNCT
ejpam-6089	343	31	>	>	X
ejpam-6089	344	1	ℜ(δ	ℜ(δ	X
ejpam-6089	344	2	)	)	PUNCT
ejpam-6089	344	3	>	>	X
ejpam-6089	344	4	0	0	PUNCT
ejpam-6089	345	1	and	and	CCONJ
ejpam-6089	345	2	let	let	VERB
ejpam-6089	345	3	g	g	PROPN
ejpam-6089	345	4	≥	≥	NOUN
ejpam-6089	345	5	0	0	NUM
ejpam-6089	345	6	,	,	PUNCT
ejpam-6089	345	7	l	l	NOUN
ejpam-6089	345	8	>	>	X
ejpam-6089	345	9	0	0	PUNCT
ejpam-6089	346	1	and	and	CCONJ
ejpam-6089	346	2	0	0	NUM
ejpam-6089	346	3	<	<	X
ejpam-6089	346	4	s	s	X
ejpam-6089	346	5	≤	≤	NUM
ejpam-6089	346	6	l	l	NOUN
ejpam-6089	346	7	+	+	CCONJ
ejpam-6089	346	8	ℜ(ℵ	ℜ(ℵ	NOUN
ejpam-6089	346	9	)	)	PUNCT
ejpam-6089	346	10	,	,	PUNCT
ejpam-6089	346	11	then	then	ADV
ejpam-6089	346	12	the	the	DET
ejpam-6089	346	13	(	(	PUNCT
ejpam-6089	346	14	h−h	h−h	NOUN
ejpam-6089	346	15	)	)	PUNCT
ejpam-6089	346	16	inequality	inequality	NOUN
ejpam-6089	346	17	for	for	ADP
ejpam-6089	346	18	atangana	atangana	PROPN
ejpam-6089	346	19	-	-	PUNCT
ejpam-6089	346	20	baleanu	baleanu	ADJ
ejpam-6089	346	21	fractional	fractional	ADJ
ejpam-6089	346	22	integrals	integral	NOUN
ejpam-6089	346	23	becomes	become	VERB
ejpam-6089	346	24	∞∑	∞∑	NUM
ejpam-6089	346	25	ð=0	ð=0	X
ejpam-6089	346	26	aðsðυ	aðsðυ	X
ejpam-6089	346	27	(	(	PUNCT
ejpam-6089	346	28	ℑ1	ℑ1	PROPN
ejpam-6089	346	29	+	+	CCONJ
ejpam-6089	346	30	ℑ2	ℑ2	PROPN
ejpam-6089	346	31	2	2	NUM
ejpam-6089	346	32	)	)	PUNCT
ejpam-6089	346	33	≤	≤	PUNCT
ejpam-6089	346	34	ε	ε	PROPN
ejpam-6089	346	35	♭	♭	PROPN
ejpam-6089	346	36	,δ	,δ	PUNCT
ejpam-6089	346	37	,	,	PUNCT
ejpam-6089	346	38	b	b	NOUN
ejpam-6089	346	39	,	,	PUNCT
ejpam-6089	346	40	s	s	X
ejpam-6089	346	41	,	,	PUNCT
ejpam-6089	346	42	l	l	NOUN
ejpam-6089	346	43	(	(	PUNCT
ejpam-6089	346	44	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	346	45	2	2	NUM
ejpam-6089	346	46	)	)	PUNCT
ejpam-6089	347	1	+	+	ADV
ejpam-6089	347	2	,	,	PUNCT
ejpam-6089	347	3	ℵ,℘,τ	ℵ,℘,τ	PROPN
ejpam-6089	347	4	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	347	5	;	;	PUNCT
ejpam-6089	347	6	g	g	NOUN
ejpam-6089	347	7	)	)	PUNCT
ejpam-6089	348	1	+	+	CCONJ
ejpam-6089	348	2	ε	ε	PROPN
ejpam-6089	348	3	♭	♭	PROPN
ejpam-6089	348	4	,δ	,δ	PUNCT
ejpam-6089	348	5	,	,	PUNCT
ejpam-6089	348	6	b	b	NOUN
ejpam-6089	348	7	,	,	PUNCT
ejpam-6089	348	8	s	s	X
ejpam-6089	348	9	,	,	PUNCT
ejpam-6089	348	10	l	l	NOUN
ejpam-6089	348	11	(	(	PUNCT
ejpam-6089	348	12	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	348	13	2	2	NUM
ejpam-6089	348	14	)	)	PUNCT
ejpam-6089	348	15	−,ℵ,℘,τ	−,ℵ,℘,τ	NOUN
ejpam-6089	348	16	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	348	17	;	;	PUNCT
ejpam-6089	348	18	g	g	X
ejpam-6089	348	19	)	)	PUNCT
ejpam-6089	348	20	≤	≤	NOUN
ejpam-6089	349	1	∞∑	∞∑	NUM
ejpam-6089	349	2	ð=0	ð=0	SYM
ejpam-6089	349	3	aðsð	aðsð	PROPN
ejpam-6089	349	4	(	(	PUNCT
ejpam-6089	349	5	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	349	6	)	)	PUNCT
ejpam-6089	349	7	+	+	CCONJ
ejpam-6089	349	8	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	349	9	)	)	PUNCT
ejpam-6089	349	10	2	2	NUM
ejpam-6089	349	11	)	)	PUNCT
ejpam-6089	349	12	,	,	PUNCT
ejpam-6089	349	13	where	where	SCONJ
ejpam-6089	349	14	að	að	PROPN
ejpam-6089	349	15	=	=	SYM
ejpam-6089	349	16	bg(δ+ðs	bg(δ+ðs	PROPN
ejpam-6089	349	17	,	,	PUNCT
ejpam-6089	349	18	b−δ	b−δ	NOUN
ejpam-6089	349	19	)	)	PUNCT
ejpam-6089	349	20	b(δ	b(δ	NOUN
ejpam-6089	349	21	,	,	PUNCT
ejpam-6089	349	22	b−δ	b−δ	NOUN
ejpam-6089	349	23	)	)	PUNCT
ejpam-6089	349	24	(	(	PUNCT
ejpam-6089	349	25	b)ðs	b)ðs	PROPN
ejpam-6089	349	26	♭	♭	PROPN
ejpam-6089	349	27	ð	ð	X
ejpam-6089	349	28	(	(	PUNCT
ejpam-6089	349	29	τ)ðl	τ)ðl	PROPN
ejpam-6089	349	30	and	and	CCONJ
ejpam-6089	349	31	sð	sð	X
ejpam-6089	349	32	=	=	SYM
ejpam-6089	349	33	(	(	PUNCT
ejpam-6089	349	34	(	(	PUNCT
ejpam-6089	349	35	ℑ2−ℑ1)(ℵð+℘)+2(ℵð+℘)(1−ℵð−℘)γ(ℵð+℘	ℑ2−ℑ1)(ℵð+℘)+2(ℵð+℘)(1−ℵð−℘)γ(ℵð+℘	NOUN
ejpam-6089	349	36	)	)	PUNCT
ejpam-6089	349	37	)	)	PUNCT
ejpam-6089	350	1	2(ℵð+℘)−1γ((ℵð+℘)+1	2(ℵð+℘)−1γ((ℵð+℘)+1	NUM
ejpam-6089	350	2	)	)	PUNCT
ejpam-6089	351	1	−	−	PROPN
ejpam-6089	351	2	2(1−ℵð−℘	2(1−ℵð−℘	NUM
ejpam-6089	351	3	)	)	PUNCT
ejpam-6089	351	4	(	(	PUNCT
ejpam-6089	351	5	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	351	6	)	)	PUNCT
ejpam-6089	351	7	.	.	PUNCT
ejpam-6089	352	1	proof	proof	NOUN
ejpam-6089	352	2	.	.	PUNCT
ejpam-6089	353	1	replacing	replace	VERB
ejpam-6089	353	2	α∗	α∗	NOUN
ejpam-6089	353	3	by	by	ADP
ejpam-6089	353	4	(	(	PUNCT
ejpam-6089	353	5	ℵð+	ℵð+	ADJ
ejpam-6089	353	6	℘	℘	PROPN
ejpam-6089	353	7	)	)	PUNCT
ejpam-6089	353	8	in	in	ADP
ejpam-6089	353	9	theorem	theorem	NOUN
ejpam-6089	353	10	3	3	NUM
ejpam-6089	353	11	,	,	PUNCT
ejpam-6089	353	12	we	we	PRON
ejpam-6089	353	13	have	have	VERB
ejpam-6089	353	14	υ	υ	NOUN
ejpam-6089	353	15	(	(	PUNCT
ejpam-6089	353	16	ℑ1	ℑ1	PROPN
ejpam-6089	353	17	+	+	CCONJ
ejpam-6089	353	18	ℑ2	ℑ2	PROPN
ejpam-6089	353	19	2	2	NUM
ejpam-6089	353	20	)	)	PUNCT
ejpam-6089	353	21	≤	≤	NOUN
ejpam-6089	353	22	2(ℵð+℘)−1b(ℵð+	2(ℵð+℘)−1b(ℵð+	NUM
ejpam-6089	353	23	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	353	24	℘	℘	NOUN
ejpam-6089	353	25	)	)	PUNCT
ejpam-6089	353	26	(	(	PUNCT
ejpam-6089	353	27	(	(	PUNCT
ejpam-6089	353	28	ℑ2	ℑ2	PROPN
ejpam-6089	353	29	−ℑ1)(ℵð+℘	−ℑ1)(ℵð+℘	NUM
ejpam-6089	353	30	)	)	PUNCT
ejpam-6089	354	1	+	+	CCONJ
ejpam-6089	354	2	2(ℵð+℘)(1−	2(ℵð+℘)(1−	X
ejpam-6089	354	3	ℵð−	ℵð−	PROPN
ejpam-6089	354	4	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	354	5	℘	℘	PROPN
ejpam-6089	354	6	)	)	PUNCT
ejpam-6089	354	7	)	)	PUNCT
ejpam-6089	355	1	s.	s.	PROPN
ejpam-6089	355	2	naheed	nahee	VERB
ejpam-6089	355	3	et	et	PROPN
ejpam-6089	355	4	al	al	PROPN
ejpam-6089	355	5	.	.	PUNCT
ejpam-6089	355	6	/	/	SYM
ejpam-6089	355	7	eur	eur	PROPN
ejpam-6089	355	8	.	.	PUNCT
ejpam-6089	356	1	j.	j.	PROPN
ejpam-6089	356	2	pure	pure	PROPN
ejpam-6089	356	3	appl	appl	PROPN
ejpam-6089	356	4	.	.	PROPN
ejpam-6089	356	5	math	math	PROPN
ejpam-6089	356	6	,	,	PUNCT
ejpam-6089	356	7	18	18	NUM
ejpam-6089	356	8	(	(	PUNCT
ejpam-6089	356	9	2	2	NUM
ejpam-6089	356	10	)	)	PUNCT
ejpam-6089	356	11	(	(	PUNCT
ejpam-6089	356	12	2025	2025	NUM
ejpam-6089	356	13	)	)	PUNCT
ejpam-6089	356	14	,	,	PUNCT
ejpam-6089	356	15	6089	6089	NUM
ejpam-6089	356	16	17	17	NUM
ejpam-6089	356	17	of	of	ADP
ejpam-6089	356	18	34	34	NUM
ejpam-6089	356	19	×	×	NOUN
ejpam-6089	356	20	(	(	PUNCT
ejpam-6089	356	21	a−bi	a−bi	PROPN
ejpam-6089	356	22	(	(	PUNCT
ejpam-6089	356	23	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	356	24	)	)	PUNCT
ejpam-6089	356	25	(	(	PUNCT
ejpam-6089	356	26	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	356	27	2	2	NUM
ejpam-6089	356	28	)	)	PUNCT
ejpam-6089	356	29	+	+	CCONJ
ejpam-6089	356	30	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	356	31	)	)	PUNCT
ejpam-6089	357	1	+	+	CCONJ
ejpam-6089	357	2	a−bi	a−bi	PROPN
ejpam-6089	357	3	(	(	PUNCT
ejpam-6089	357	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	357	5	)	)	PUNCT
ejpam-6089	357	6	(	(	PUNCT
ejpam-6089	357	7	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	357	8	2	2	NUM
ejpam-6089	357	9	)	)	PUNCT
ejpam-6089	357	10	−	−	PROPN
ejpam-6089	357	11	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	357	12	)	)	PUNCT
ejpam-6089	357	13	)	)	PUNCT
ejpam-6089	358	1	≤	≤	NOUN
ejpam-6089	358	2	(	(	PUNCT
ejpam-6089	358	3	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	358	4	)	)	PUNCT
ejpam-6089	358	5	+	+	CCONJ
ejpam-6089	358	6	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	358	7	)	)	PUNCT
ejpam-6089	358	8	2	2	NUM
ejpam-6089	358	9	)	)	PUNCT
ejpam-6089	358	10	.	.	PUNCT
ejpam-6089	359	1	multiplying	multiply	VERB
ejpam-6089	359	2	the	the	DET
ejpam-6089	359	3	above	above	ADJ
ejpam-6089	359	4	inequality	inequality	NOUN
ejpam-6089	359	5	with	with	ADP
ejpam-6089	359	6	(	(	PUNCT
ejpam-6089	359	7	(	(	PUNCT
ejpam-6089	359	8	ℑ2−ℑ1)(ℵð+℘)+2(ℵð+℘)(1−ℵð−℘)γ(ℵð+℘	ℑ2−ℑ1)(ℵð+℘)+2(ℵð+℘)(1−ℵð−℘)γ(ℵð+℘	NOUN
ejpam-6089	359	9	)	)	PUNCT
ejpam-6089	359	10	)	)	PUNCT
ejpam-6089	359	11	2(ℵð+℘)−1b(ℵð+℘)γ(ℵð+℘	2(ℵð+℘)−1b(ℵð+℘)γ(ℵð+℘	NOUN
ejpam-6089	359	12	)	)	PUNCT
ejpam-6089	359	13	,	,	PUNCT
ejpam-6089	359	14	we	we	PRON
ejpam-6089	359	15	get	get	VERB
ejpam-6089	359	16	(	(	PUNCT
ejpam-6089	359	17	(	(	PUNCT
ejpam-6089	359	18	ℑ2	ℑ2	PROPN
ejpam-6089	359	19	−ℑ1	−ℑ1	PROPN
ejpam-6089	359	20	)	)	PUNCT
ejpam-6089	359	21	(	(	PUNCT
ejpam-6089	359	22	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	359	23	)	)	PUNCT
ejpam-6089	359	24	+	+	CCONJ
ejpam-6089	360	1	2(ℵð+℘)(1−	2(ℵð+℘)(1−	X
ejpam-6089	360	2	ℵð−	ℵð−	PROPN
ejpam-6089	360	3	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	360	4	℘	℘	PROPN
ejpam-6089	360	5	)	)	PUNCT
ejpam-6089	360	6	)	)	PUNCT
ejpam-6089	361	1	2(ℵð+℘)−1b(ℵð+	2(ℵð+℘)−1b(ℵð+	NUM
ejpam-6089	361	2	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	361	3	℘	℘	PROPN
ejpam-6089	361	4	)	)	PUNCT
ejpam-6089	361	5	υ	υ	NOUN
ejpam-6089	361	6	(	(	PUNCT
ejpam-6089	361	7	ℑ1	ℑ1	PROPN
ejpam-6089	361	8	+	+	CCONJ
ejpam-6089	361	9	ℑ2	ℑ2	PROPN
ejpam-6089	361	10	2	2	NUM
ejpam-6089	361	11	)	)	PUNCT
ejpam-6089	361	12	≤	≤	NOUN
ejpam-6089	361	13	(	(	PUNCT
ejpam-6089	361	14	a−bi	a−bi	PROPN
ejpam-6089	361	15	(	(	PUNCT
ejpam-6089	361	16	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	361	17	)	)	PUNCT
ejpam-6089	361	18	(	(	PUNCT
ejpam-6089	361	19	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	361	20	2	2	NUM
ejpam-6089	361	21	)	)	PUNCT
ejpam-6089	361	22	+	+	CCONJ
ejpam-6089	361	23	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	361	24	)	)	PUNCT
ejpam-6089	362	1	+	+	CCONJ
ejpam-6089	362	2	a−bi	a−bi	PROPN
ejpam-6089	362	3	(	(	PUNCT
ejpam-6089	362	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	362	5	)	)	PUNCT
ejpam-6089	362	6	(	(	PUNCT
ejpam-6089	362	7	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	362	8	2	2	NUM
ejpam-6089	362	9	)	)	PUNCT
ejpam-6089	362	10	−	−	PROPN
ejpam-6089	362	11	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	362	12	)	)	PUNCT
ejpam-6089	362	13	)	)	PUNCT
ejpam-6089	362	14	≤	≤	NOUN
ejpam-6089	362	15	(	(	PUNCT
ejpam-6089	362	16	(	(	PUNCT
ejpam-6089	362	17	ℑ2	ℑ2	PROPN
ejpam-6089	362	18	−ℑ1	−ℑ1	PROPN
ejpam-6089	362	19	)	)	PUNCT
ejpam-6089	362	20	(	(	PUNCT
ejpam-6089	362	21	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	362	22	)	)	PUNCT
ejpam-6089	362	23	+	+	CCONJ
ejpam-6089	363	1	2(ℵð+℘)(1−	2(ℵð+℘)(1−	X
ejpam-6089	363	2	ℵð−	ℵð−	PROPN
ejpam-6089	363	3	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	363	4	℘	℘	PROPN
ejpam-6089	363	5	)	)	PUNCT
ejpam-6089	363	6	)	)	PUNCT
ejpam-6089	364	1	2(ℵð+℘)−1b(ℵð+	2(ℵð+℘)−1b(ℵð+	NUM
ejpam-6089	364	2	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	364	3	℘	℘	PROPN
ejpam-6089	364	4	)	)	PUNCT
ejpam-6089	364	5	×	×	NOUN
ejpam-6089	364	6	(	(	PUNCT
ejpam-6089	364	7	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	364	8	)	)	PUNCT
ejpam-6089	364	9	+	+	CCONJ
ejpam-6089	364	10	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	364	11	)	)	PUNCT
ejpam-6089	364	12	2	2	NUM
ejpam-6089	364	13	)	)	PUNCT
ejpam-6089	364	14	.	.	PUNCT
ejpam-6089	365	1	(	(	PUNCT
ejpam-6089	365	2	24	24	NUM
ejpam-6089	365	3	)	)	PUNCT
ejpam-6089	365	4	adding	add	VERB
ejpam-6089	365	5	left	left	ADJ
ejpam-6089	365	6	and	and	CCONJ
ejpam-6089	365	7	right	right	ADV
ejpam-6089	365	8	sided	sided	ADJ
ejpam-6089	365	9	atangana	atangana	PROPN
ejpam-6089	365	10	-	-	PUNCT
ejpam-6089	365	11	baleanu	baleanu	PROPN
ejpam-6089	365	12	integrals	integral	NOUN
ejpam-6089	365	13	(	(	PUNCT
ejpam-6089	365	14	3	3	NUM
ejpam-6089	365	15	)	)	PUNCT
ejpam-6089	365	16	and	and	CCONJ
ejpam-6089	365	17	(	(	PUNCT
ejpam-6089	365	18	4	4	NUM
ejpam-6089	365	19	)	)	PUNCT
ejpam-6089	365	20	from	from	ADP
ejpam-6089	365	21	the	the	DET
ejpam-6089	365	22	middle	middle	NOUN
ejpam-6089	365	23	of	of	ADP
ejpam-6089	365	24	interval	interval	NOUN
ejpam-6089	365	25	[	[	X
ejpam-6089	365	26	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	365	27	]	]	PUNCT
ejpam-6089	365	28	,	,	PUNCT
ejpam-6089	365	29	we	we	PRON
ejpam-6089	365	30	have	have	VERB
ejpam-6089	365	31	(	(	PUNCT
ejpam-6089	365	32	a−biα	a−biα	ADJ
ejpam-6089	365	33	∗	∗	NOUN
ejpam-6089	365	34	(	(	PUNCT
ejpam-6089	365	35	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	365	36	2	2	NUM
ejpam-6089	365	37	)	)	PUNCT
ejpam-6089	365	38	+	+	CCONJ
ejpam-6089	366	1	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	366	2	)	)	PUNCT
ejpam-6089	366	3	+	+	NUM
ejpam-6089	366	4	a−biα	a−biα	ADJ
ejpam-6089	366	5	∗	∗	NOUN
ejpam-6089	366	6	(	(	PUNCT
ejpam-6089	366	7	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	366	8	2	2	NUM
ejpam-6089	366	9	)	)	PUNCT
ejpam-6089	366	10	−	−	PROPN
ejpam-6089	366	11	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	366	12	)	)	PUNCT
ejpam-6089	366	13	)	)	PUNCT
ejpam-6089	367	1	=	=	PUNCT
ejpam-6089	367	2	α∗	α∗	NOUN
ejpam-6089	367	3	b(α∗	b(α∗	NOUN
ejpam-6089	367	4	)	)	PUNCT
ejpam-6089	367	5	(	(	PUNCT
ejpam-6089	367	6	r−liα	r−liα	NOUN
ejpam-6089	367	7	∗	∗	NOUN
ejpam-6089	367	8	(	(	PUNCT
ejpam-6089	367	9	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	367	10	2	2	NUM
ejpam-6089	367	11	)	)	PUNCT
ejpam-6089	367	12	+	+	CCONJ
ejpam-6089	368	1	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	368	2	)	)	PUNCT
ejpam-6089	368	3	+	+	NUM
ejpam-6089	368	4	r−liα	r−liα	NOUN
ejpam-6089	368	5	∗	∗	NOUN
ejpam-6089	368	6	(	(	PUNCT
ejpam-6089	368	7	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	368	8	2	2	NUM
ejpam-6089	368	9	)	)	PUNCT
ejpam-6089	368	10	−	−	PROPN
ejpam-6089	368	11	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	368	12	)	)	PUNCT
ejpam-6089	368	13	)	)	PUNCT
ejpam-6089	369	1	+	+	CCONJ
ejpam-6089	369	2	1−	1−	NUM
ejpam-6089	369	3	α∗	α∗	NOUN
ejpam-6089	369	4	b(α∗	b(α∗	NOUN
ejpam-6089	369	5	)	)	PUNCT
ejpam-6089	369	6	(	(	PUNCT
ejpam-6089	369	7	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	369	8	)	)	PUNCT
ejpam-6089	369	9	+	+	CCONJ
ejpam-6089	369	10	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	369	11	)	)	PUNCT
ejpam-6089	369	12	)	)	PUNCT
ejpam-6089	369	13	.	.	PUNCT
ejpam-6089	370	1	using	use	VERB
ejpam-6089	370	2	α∗	α∗	NOUN
ejpam-6089	370	3	=	=	SYM
ejpam-6089	370	4	(	(	PUNCT
ejpam-6089	370	5	ℵð+	ℵð+	ADJ
ejpam-6089	370	6	℘	℘	PROPN
ejpam-6089	370	7	)	)	PUNCT
ejpam-6089	370	8	in	in	ADP
ejpam-6089	370	9	the	the	DET
ejpam-6089	370	10	above	above	ADJ
ejpam-6089	370	11	equation	equation	NOUN
ejpam-6089	370	12	and	and	CCONJ
ejpam-6089	370	13	then	then	ADV
ejpam-6089	370	14	put	put	VERB
ejpam-6089	370	15	the	the	DET
ejpam-6089	370	16	results	result	NOUN
ejpam-6089	370	17	in	in	ADP
ejpam-6089	370	18	(	(	PUNCT
ejpam-6089	370	19	24	24	NUM
ejpam-6089	370	20	)	)	PUNCT
ejpam-6089	370	21	,	,	PUNCT
ejpam-6089	370	22	we	we	PRON
ejpam-6089	370	23	get	get	VERB
ejpam-6089	370	24	(	(	PUNCT
ejpam-6089	370	25	(	(	PUNCT
ejpam-6089	370	26	ℑ2	ℑ2	PROPN
ejpam-6089	370	27	−ℑ1	−ℑ1	PROPN
ejpam-6089	370	28	)	)	PUNCT
ejpam-6089	370	29	(	(	PUNCT
ejpam-6089	370	30	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	370	31	)	)	PUNCT
ejpam-6089	371	1	+	+	CCONJ
ejpam-6089	371	2	2(ℵð+℘)(1−	2(ℵð+℘)(1−	X
ejpam-6089	371	3	ℵð−	ℵð−	PROPN
ejpam-6089	371	4	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	371	5	℘	℘	PROPN
ejpam-6089	371	6	)	)	PUNCT
ejpam-6089	371	7	)	)	PUNCT
ejpam-6089	372	1	2(ℵð+℘)−1b(ℵð+	2(ℵð+℘)−1b(ℵð+	NUM
ejpam-6089	372	2	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	372	3	℘	℘	PROPN
ejpam-6089	372	4	)	)	PUNCT
ejpam-6089	372	5	υ	υ	NOUN
ejpam-6089	372	6	(	(	PUNCT
ejpam-6089	372	7	ℑ1	ℑ1	PROPN
ejpam-6089	372	8	+	+	CCONJ
ejpam-6089	372	9	ℑ2	ℑ2	PROPN
ejpam-6089	372	10	2	2	NUM
ejpam-6089	372	11	)	)	PUNCT
ejpam-6089	372	12	≤	≤	NOUN
ejpam-6089	372	13	(	(	PUNCT
ejpam-6089	372	14	ℵð+	ℵð+	ADJ
ejpam-6089	372	15	℘	℘	PROPN
ejpam-6089	372	16	)	)	PUNCT
ejpam-6089	372	17	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	372	18	℘	℘	PROPN
ejpam-6089	372	19	)	)	PUNCT
ejpam-6089	372	20	(	(	PUNCT
ejpam-6089	372	21	r−li	r−li	NOUN
ejpam-6089	372	22	(	(	PUNCT
ejpam-6089	372	23	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	372	24	)	)	PUNCT
ejpam-6089	372	25	(	(	PUNCT
ejpam-6089	372	26	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	372	27	2	2	NUM
ejpam-6089	372	28	)	)	PUNCT
ejpam-6089	372	29	+	+	CCONJ
ejpam-6089	372	30	(	(	PUNCT
ejpam-6089	372	31	ℑ2	ℑ2	PROPN
ejpam-6089	372	32	)	)	PUNCT
ejpam-6089	372	33	+	+	NUM
ejpam-6089	372	34	r−li	r−li	NOUN
ejpam-6089	372	35	(	(	PUNCT
ejpam-6089	372	36	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	372	37	)	)	PUNCT
ejpam-6089	372	38	(	(	PUNCT
ejpam-6089	372	39	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	372	40	2	2	NUM
ejpam-6089	372	41	)	)	PUNCT
ejpam-6089	372	42	−	−	PROPN
ejpam-6089	372	43	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	372	44	)	)	PUNCT
ejpam-6089	372	45	)	)	PUNCT
ejpam-6089	373	1	+	+	CCONJ
ejpam-6089	373	2	1−	1−	NUM
ejpam-6089	373	3	ℵð−	ℵð−	PUNCT
ejpam-6089	373	4	℘	℘	PROPN
ejpam-6089	373	5	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	373	6	℘	℘	PROPN
ejpam-6089	373	7	)	)	PUNCT
ejpam-6089	373	8	(	(	PUNCT
ejpam-6089	373	9	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	373	10	)	)	PUNCT
ejpam-6089	374	1	+	+	CCONJ
ejpam-6089	374	2	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	374	3	)	)	PUNCT
ejpam-6089	374	4	)	)	PUNCT
ejpam-6089	374	5	≤	≤	NOUN
ejpam-6089	374	6	(	(	PUNCT
ejpam-6089	374	7	(	(	PUNCT
ejpam-6089	374	8	ℑ2	ℑ2	PROPN
ejpam-6089	374	9	−ℑ1	−ℑ1	PROPN
ejpam-6089	374	10	)	)	PUNCT
ejpam-6089	374	11	(	(	PUNCT
ejpam-6089	374	12	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	374	13	)	)	PUNCT
ejpam-6089	375	1	+	+	CCONJ
ejpam-6089	375	2	2(ℵð+℘)(1−	2(ℵð+℘)(1−	X
ejpam-6089	375	3	ℵð−	ℵð−	PROPN
ejpam-6089	375	4	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	375	5	℘	℘	PROPN
ejpam-6089	375	6	)	)	PUNCT
ejpam-6089	375	7	)	)	PUNCT
ejpam-6089	376	1	2(ℵð+℘)−1b(ℵð+	2(ℵð+℘)−1b(ℵð+	NUM
ejpam-6089	376	2	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	376	3	℘	℘	PROPN
ejpam-6089	376	4	)	)	PUNCT
ejpam-6089	376	5	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	376	6	)	)	PUNCT
ejpam-6089	377	1	+	+	CCONJ
ejpam-6089	377	2	(	(	PUNCT
ejpam-6089	377	3	ℑ2	ℑ2	PROPN
ejpam-6089	377	4	)	)	PUNCT
ejpam-6089	377	5	2	2	NUM
ejpam-6089	377	6	.	.	PUNCT
ejpam-6089	377	7	subtracting	subtract	VERB
ejpam-6089	377	8	1−ℵð−℘	1−ℵð−℘	NUM
ejpam-6089	377	9	b(ℵð+℘	b(ℵð+℘	NOUN
ejpam-6089	377	10	)	)	PUNCT
ejpam-6089	377	11	[	[	X
ejpam-6089	377	12	υ(ℑ1)+υ(ℑ2	υ(ℑ1)+υ(ℑ2	PROPN
ejpam-6089	377	13	)	)	PUNCT
ejpam-6089	377	14	]	]	PUNCT
ejpam-6089	377	15	from	from	ADP
ejpam-6089	377	16	the	the	DET
ejpam-6089	377	17	above	above	ADJ
ejpam-6089	377	18	expression	expression	NOUN
ejpam-6089	377	19	and	and	CCONJ
ejpam-6089	377	20	then	then	ADV
ejpam-6089	377	21	multiplying	multiply	VERB
ejpam-6089	377	22	with	with	ADP
ejpam-6089	377	23	b(ℵð+℘	b(ℵð+℘	NOUN
ejpam-6089	377	24	)	)	PUNCT
ejpam-6089	377	25	(	(	PUNCT
ejpam-6089	377	26	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	377	27	)	)	PUNCT
ejpam-6089	377	28	,	,	PUNCT
ejpam-6089	377	29	we	we	PRON
ejpam-6089	377	30	obtain	obtain	VERB
ejpam-6089	377	31	(	(	PUNCT
ejpam-6089	377	32	(	(	PUNCT
ejpam-6089	377	33	ℑ2	ℑ2	PROPN
ejpam-6089	377	34	−ℑ1	−ℑ1	PROPN
ejpam-6089	377	35	)	)	PUNCT
ejpam-6089	377	36	(	(	PUNCT
ejpam-6089	377	37	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	377	38	)	)	PUNCT
ejpam-6089	377	39	+	+	CCONJ
ejpam-6089	378	1	2(ℵð+℘)(1−	2(ℵð+℘)(1−	X
ejpam-6089	378	2	ℵð−	ℵð−	PROPN
ejpam-6089	378	3	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	378	4	℘	℘	PROPN
ejpam-6089	378	5	)	)	PUNCT
ejpam-6089	378	6	)	)	PUNCT
ejpam-6089	379	1	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	379	2	℘	℘	NOUN
ejpam-6089	379	3	)	)	PUNCT
ejpam-6089	379	4	+	+	NUM
ejpam-6089	379	5	1	1	X
ejpam-6089	379	6	)	)	PUNCT
ejpam-6089	379	7	υ	υ	NOUN
ejpam-6089	379	8	(	(	PUNCT
ejpam-6089	379	9	ℑ1	ℑ1	PROPN
ejpam-6089	379	10	+	+	CCONJ
ejpam-6089	379	11	ℑ2	ℑ2	PROPN
ejpam-6089	379	12	2	2	NUM
ejpam-6089	379	13	)	)	PUNCT
ejpam-6089	379	14	s.	s.	PROPN
ejpam-6089	379	15	naheed	nahee	VERB
ejpam-6089	379	16	et	et	PROPN
ejpam-6089	379	17	al	al	PROPN
ejpam-6089	379	18	.	.	PUNCT
ejpam-6089	379	19	/	/	SYM
ejpam-6089	379	20	eur	eur	PROPN
ejpam-6089	379	21	.	.	PUNCT
ejpam-6089	380	1	j.	j.	PROPN
ejpam-6089	380	2	pure	pure	PROPN
ejpam-6089	380	3	appl	appl	PROPN
ejpam-6089	380	4	.	.	PROPN
ejpam-6089	380	5	math	math	PROPN
ejpam-6089	380	6	,	,	PUNCT
ejpam-6089	380	7	18	18	NUM
ejpam-6089	380	8	(	(	PUNCT
ejpam-6089	380	9	2	2	NUM
ejpam-6089	380	10	)	)	PUNCT
ejpam-6089	380	11	(	(	PUNCT
ejpam-6089	380	12	2025	2025	NUM
ejpam-6089	380	13	)	)	PUNCT
ejpam-6089	380	14	,	,	PUNCT
ejpam-6089	380	15	6089	6089	NUM
ejpam-6089	380	16	18	18	NUM
ejpam-6089	380	17	of	of	ADP
ejpam-6089	380	18	34	34	NUM
ejpam-6089	380	19	−	−	PROPN
ejpam-6089	380	20	1−	1−	NUM
ejpam-6089	380	21	ℵð−	ℵð−	PUNCT
ejpam-6089	380	22	℘	℘	PROPN
ejpam-6089	380	23	(	(	PUNCT
ejpam-6089	380	24	ℵð+	ℵð+	ADJ
ejpam-6089	380	25	℘	℘	PROPN
ejpam-6089	380	26	)	)	PUNCT
ejpam-6089	380	27	(	(	PUNCT
ejpam-6089	380	28	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	380	29	)	)	PUNCT
ejpam-6089	380	30	+	+	CCONJ
ejpam-6089	380	31	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	380	32	)	)	PUNCT
ejpam-6089	380	33	)	)	PUNCT
ejpam-6089	380	34	≤	≤	NOUN
ejpam-6089	380	35	(	(	PUNCT
ejpam-6089	380	36	r−li	r−li	NOUN
ejpam-6089	380	37	(	(	PUNCT
ejpam-6089	380	38	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	380	39	)	)	PUNCT
ejpam-6089	380	40	(	(	PUNCT
ejpam-6089	380	41	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	380	42	2	2	NUM
ejpam-6089	380	43	)	)	PUNCT
ejpam-6089	380	44	+	+	CCONJ
ejpam-6089	380	45	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	380	46	)	)	PUNCT
ejpam-6089	381	1	+	+	X
ejpam-6089	381	2	r−liℵð+℘	r−liℵð+℘	ADJ
ejpam-6089	381	3	(	(	PUNCT
ejpam-6089	381	4	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	381	5	2	2	NUM
ejpam-6089	381	6	)	)	PUNCT
ejpam-6089	381	7	−	−	PROPN
ejpam-6089	381	8	(	(	PUNCT
ejpam-6089	381	9	ℑ1	ℑ1	NOUN
ejpam-6089	381	10	)	)	PUNCT
ejpam-6089	381	11	)	)	PUNCT
ejpam-6089	382	1	≤	≤	NOUN
ejpam-6089	382	2	(	(	PUNCT
ejpam-6089	382	3	(	(	PUNCT
ejpam-6089	382	4	ℑ2	ℑ2	PROPN
ejpam-6089	382	5	−ℑ1	−ℑ1	PROPN
ejpam-6089	382	6	)	)	PUNCT
ejpam-6089	382	7	(	(	PUNCT
ejpam-6089	382	8	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	382	9	)	)	PUNCT
ejpam-6089	383	1	+	+	CCONJ
ejpam-6089	383	2	2(ℵð+℘)(1−	2(ℵð+℘)(1−	X
ejpam-6089	383	3	ℵð−	ℵð−	PROPN
ejpam-6089	383	4	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	383	5	℘	℘	PROPN
ejpam-6089	383	6	)	)	PUNCT
ejpam-6089	383	7	)	)	PUNCT
ejpam-6089	384	1	2ℵ̂ð+℘−1γ((ℵð+	2ℵ̂ð+℘−1γ((ℵð+	NUM
ejpam-6089	384	2	℘	℘	PROPN
ejpam-6089	384	3	)	)	PUNCT
ejpam-6089	384	4	+	+	CCONJ
ejpam-6089	384	5	1	1	X
ejpam-6089	384	6	)	)	PUNCT
ejpam-6089	384	7	(	(	PUNCT
ejpam-6089	384	8	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	384	9	)	)	PUNCT
ejpam-6089	384	10	+	+	CCONJ
ejpam-6089	384	11	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	384	12	)	)	PUNCT
ejpam-6089	384	13	2	2	NUM
ejpam-6089	384	14	)	)	PUNCT
ejpam-6089	384	15	−	−	PROPN
ejpam-6089	384	16	1−	1−	NUM
ejpam-6089	384	17	ℵð−	ℵð−	PUNCT
ejpam-6089	384	18	℘	℘	PROPN
ejpam-6089	384	19	(	(	PUNCT
ejpam-6089	384	20	ℵð+	ℵð+	ADJ
ejpam-6089	384	21	℘	℘	PROPN
ejpam-6089	384	22	)	)	PUNCT
ejpam-6089	384	23	(	(	PUNCT
ejpam-6089	384	24	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	384	25	)	)	PUNCT
ejpam-6089	384	26	+	+	CCONJ
ejpam-6089	384	27	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	384	28	)	)	PUNCT
ejpam-6089	384	29	)	)	PUNCT
ejpam-6089	384	30	.	.	PUNCT
ejpam-6089	385	1	again	again	ADV
ejpam-6089	385	2	multiplying	multiply	VERB
ejpam-6089	385	3	the	the	DET
ejpam-6089	385	4	above	above	ADJ
ejpam-6089	385	5	inequality	inequality	NOUN
ejpam-6089	385	6	with	with	ADP
ejpam-6089	385	7	að	að	PROPN
ejpam-6089	385	8	að	að	PROPN
ejpam-6089	385	9	(	(	PUNCT
ejpam-6089	385	10	(	(	PUNCT
ejpam-6089	385	11	(	(	PUNCT
ejpam-6089	385	12	ℑ2	ℑ2	PROPN
ejpam-6089	385	13	−ℑ1	−ℑ1	PROPN
ejpam-6089	385	14	)	)	PUNCT
ejpam-6089	385	15	(	(	PUNCT
ejpam-6089	385	16	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	385	17	)	)	PUNCT
ejpam-6089	385	18	+	+	CCONJ
ejpam-6089	386	1	2(ℵð+℘)(1−	2(ℵð+℘)(1−	X
ejpam-6089	386	2	ℵð−	ℵð−	PROPN
ejpam-6089	386	3	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	386	4	℘	℘	PROPN
ejpam-6089	386	5	)	)	PUNCT
ejpam-6089	386	6	)	)	PUNCT
ejpam-6089	387	1	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	387	2	℘	℘	NOUN
ejpam-6089	387	3	)	)	PUNCT
ejpam-6089	387	4	+	+	NUM
ejpam-6089	387	5	1	1	X
ejpam-6089	387	6	)	)	PUNCT
ejpam-6089	387	7	υ	υ	NOUN
ejpam-6089	387	8	(	(	PUNCT
ejpam-6089	387	9	ℑ1	ℑ1	PROPN
ejpam-6089	387	10	+	+	CCONJ
ejpam-6089	387	11	ℑ2	ℑ2	PROPN
ejpam-6089	387	12	2	2	NUM
ejpam-6089	387	13	)	)	PUNCT
ejpam-6089	387	14	)	)	PUNCT
ejpam-6089	388	1	−	−	PROPN
ejpam-6089	388	2	að	að	INTJ
ejpam-6089	388	3	(	(	PUNCT
ejpam-6089	388	4	2(1−	2(1−	NUM
ejpam-6089	388	5	ℵð−	ℵð−	NUM
ejpam-6089	388	6	℘	℘	NUM
ejpam-6089	388	7	)	)	PUNCT
ejpam-6089	388	8	(	(	PUNCT
ejpam-6089	388	9	ℵð+	ℵð+	ADJ
ejpam-6089	388	10	℘	℘	PROPN
ejpam-6089	388	11	)	)	PUNCT
ejpam-6089	388	12	(	(	PUNCT
ejpam-6089	388	13	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	388	14	)	)	PUNCT
ejpam-6089	388	15	+	+	CCONJ
ejpam-6089	388	16	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	388	17	)	)	PUNCT
ejpam-6089	388	18	2	2	NUM
ejpam-6089	388	19	)	)	PUNCT
ejpam-6089	388	20	)	)	PUNCT
ejpam-6089	388	21	≤	≤	NUM
ejpam-6089	388	22	að	að	PROPN
ejpam-6089	388	23	(	(	PUNCT
ejpam-6089	388	24	r−li	r−li	NOUN
ejpam-6089	388	25	(	(	PUNCT
ejpam-6089	388	26	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	388	27	)	)	PUNCT
ejpam-6089	388	28	(	(	PUNCT
ejpam-6089	388	29	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	388	30	2	2	NUM
ejpam-6089	388	31	)	)	PUNCT
ejpam-6089	388	32	+	+	CCONJ
ejpam-6089	388	33	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	388	34	)	)	PUNCT
ejpam-6089	388	35	+	+	NUM
ejpam-6089	388	36	r−li	r−li	NOUN
ejpam-6089	388	37	(	(	PUNCT
ejpam-6089	388	38	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	388	39	)	)	PUNCT
ejpam-6089	388	40	(	(	PUNCT
ejpam-6089	388	41	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	388	42	2	2	NUM
ejpam-6089	388	43	)	)	PUNCT
ejpam-6089	388	44	−	−	PROPN
ejpam-6089	388	45	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	388	46	)	)	PUNCT
ejpam-6089	388	47	)	)	PUNCT
ejpam-6089	388	48	≤	≤	NUM
ejpam-6089	388	49	að	að	INTJ
ejpam-6089	388	50	(	(	PUNCT
ejpam-6089	388	51	(	(	PUNCT
ejpam-6089	388	52	(	(	PUNCT
ejpam-6089	388	53	ℑ2	ℑ2	PROPN
ejpam-6089	388	54	−ℑ1	−ℑ1	PROPN
ejpam-6089	388	55	)	)	PUNCT
ejpam-6089	388	56	(	(	PUNCT
ejpam-6089	388	57	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	388	58	)	)	PUNCT
ejpam-6089	388	59	+	+	CCONJ
ejpam-6089	388	60	2(ℵð+℘)(1−	2(ℵð+℘)(1−	X
ejpam-6089	388	61	ℵð−	ℵð−	PROPN
ejpam-6089	388	62	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	388	63	℘	℘	PROPN
ejpam-6089	388	64	)	)	PUNCT
ejpam-6089	388	65	)	)	PUNCT
ejpam-6089	388	66	2(ℵð+℘)−1γ(ℵð+	2(ℵð+℘)−1γ(ℵð+	NUM
ejpam-6089	388	67	℘+	℘+	NOUN
ejpam-6089	388	68	1	1	NUM
ejpam-6089	388	69	)	)	PUNCT
ejpam-6089	388	70	(	(	PUNCT
ejpam-6089	388	71	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	388	72	)	)	PUNCT
ejpam-6089	388	73	+	+	CCONJ
ejpam-6089	388	74	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	388	75	)	)	PUNCT
ejpam-6089	388	76	2	2	NUM
ejpam-6089	388	77	)	)	PUNCT
ejpam-6089	388	78	)	)	PUNCT
ejpam-6089	388	79	−	−	PROPN
ejpam-6089	388	80	(	(	PUNCT
ejpam-6089	388	81	2(1−	2(1−	X
ejpam-6089	388	82	ℵð−	ℵð−	NUM
ejpam-6089	388	83	℘	℘	NUM
ejpam-6089	388	84	)	)	PUNCT
ejpam-6089	388	85	(	(	PUNCT
ejpam-6089	388	86	ℵð+	ℵð+	ADJ
ejpam-6089	388	87	℘	℘	PROPN
ejpam-6089	388	88	)	)	PUNCT
ejpam-6089	388	89	(	(	PUNCT
ejpam-6089	388	90	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	388	91	)	)	PUNCT
ejpam-6089	388	92	+	+	CCONJ
ejpam-6089	388	93	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	388	94	)	)	PUNCT
ejpam-6089	388	95	2	2	NUM
ejpam-6089	388	96	)	)	PUNCT
ejpam-6089	388	97	)	)	PUNCT
ejpam-6089	388	98	.	.	PUNCT
ejpam-6089	389	1	by	by	ADP
ejpam-6089	389	2	convexity	convexity	NOUN
ejpam-6089	389	3	of	of	ADP
ejpam-6089	389	4	υ	υ	NOUN
ejpam-6089	389	5	we	we	PRON
ejpam-6089	389	6	have	have	VERB
ejpam-6089	389	7	,	,	PUNCT
ejpam-6089	389	8	υ	υ	PROPN
ejpam-6089	389	9	(	(	PUNCT
ejpam-6089	389	10	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	389	11	2	2	NUM
ejpam-6089	389	12	)	)	PUNCT
ejpam-6089	389	13	≤	≤	NOUN
ejpam-6089	389	14	(	(	PUNCT
ejpam-6089	389	15	υ(ℑ1)+υ(ℑ2	υ(ℑ1)+υ(ℑ2	PROPN
ejpam-6089	389	16	)	)	PUNCT
ejpam-6089	389	17	2	2	NUM
ejpam-6089	389	18	)	)	PUNCT
ejpam-6089	389	19	að	að	PROPN
ejpam-6089	389	20	(	(	PUNCT
ejpam-6089	389	21	(	(	PUNCT
ejpam-6089	389	22	(	(	PUNCT
ejpam-6089	389	23	ℑ2	ℑ2	PROPN
ejpam-6089	389	24	−ℑ1	−ℑ1	PROPN
ejpam-6089	389	25	)	)	PUNCT
ejpam-6089	389	26	(	(	PUNCT
ejpam-6089	389	27	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	389	28	)	)	PUNCT
ejpam-6089	389	29	+	+	CCONJ
ejpam-6089	389	30	2(ℵð+℘)(1−	2(ℵð+℘)(1−	X
ejpam-6089	389	31	ℵð−	ℵð−	PROPN
ejpam-6089	389	32	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	389	33	℘	℘	PROPN
ejpam-6089	389	34	)	)	PUNCT
ejpam-6089	389	35	)	)	PUNCT
ejpam-6089	389	36	2ℵð+℘−1γ((ℵð+	2ℵð+℘−1γ((ℵð+	NUM
ejpam-6089	389	37	℘	℘	NOUN
ejpam-6089	389	38	)	)	PUNCT
ejpam-6089	389	39	+	+	CCONJ
ejpam-6089	389	40	1	1	X
ejpam-6089	389	41	)	)	PUNCT
ejpam-6089	389	42	−	−	ADP
ejpam-6089	389	43	2(1−	2(1−	X
ejpam-6089	389	44	ℵð−	ℵð−	PUNCT
ejpam-6089	389	45	℘	℘	NUM
ejpam-6089	389	46	)	)	PUNCT
ejpam-6089	389	47	(	(	PUNCT
ejpam-6089	389	48	ℵð+	ℵð+	ADJ
ejpam-6089	389	49	℘	℘	PROPN
ejpam-6089	389	50	)	)	PUNCT
ejpam-6089	389	51	)	)	PUNCT
ejpam-6089	389	52	×υ	×υ	X
ejpam-6089	389	53	(	(	PUNCT
ejpam-6089	389	54	ℑ1	ℑ1	PROPN
ejpam-6089	389	55	+	+	CCONJ
ejpam-6089	389	56	ℑ2	ℑ2	PROPN
ejpam-6089	389	57	2	2	NUM
ejpam-6089	389	58	)	)	PUNCT
ejpam-6089	389	59	≤	≤	NUM
ejpam-6089	390	1	að	að	PROPN
ejpam-6089	390	2	(	(	PUNCT
ejpam-6089	390	3	r−li	r−li	NOUN
ejpam-6089	390	4	(	(	PUNCT
ejpam-6089	390	5	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	390	6	)	)	PUNCT
ejpam-6089	390	7	(	(	PUNCT
ejpam-6089	390	8	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	390	9	2	2	NUM
ejpam-6089	390	10	)	)	PUNCT
ejpam-6089	390	11	+	+	CCONJ
ejpam-6089	390	12	+	+	PUNCT
ejpam-6089	390	13	r−liℵð+℘	r−liℵð+℘	ADJ
ejpam-6089	390	14	(	(	PUNCT
ejpam-6089	390	15	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	390	16	2	2	NUM
ejpam-6089	390	17	)	)	PUNCT
ejpam-6089	390	18	−	−	PROPN
ejpam-6089	390	19	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	390	20	)	)	PUNCT
ejpam-6089	390	21	)	)	PUNCT
ejpam-6089	391	1	≤	≤	NUM
ejpam-6089	391	2	að	að	INTJ
ejpam-6089	391	3	(	(	PUNCT
ejpam-6089	391	4	(	(	PUNCT
ejpam-6089	391	5	(	(	PUNCT
ejpam-6089	391	6	ℑ2	ℑ2	PROPN
ejpam-6089	391	7	−ℑ1	−ℑ1	PROPN
ejpam-6089	391	8	)	)	PUNCT
ejpam-6089	391	9	(	(	PUNCT
ejpam-6089	391	10	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	391	11	)	)	PUNCT
ejpam-6089	391	12	+	+	CCONJ
ejpam-6089	391	13	2(ℵð+℘)(1−	2(ℵð+℘)(1−	X
ejpam-6089	391	14	ℵð−	ℵð−	PROPN
ejpam-6089	391	15	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	391	16	℘	℘	PROPN
ejpam-6089	391	17	)	)	PUNCT
ejpam-6089	391	18	)	)	PUNCT
ejpam-6089	391	19	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	391	20	℘	℘	NOUN
ejpam-6089	391	21	)	)	PUNCT
ejpam-6089	391	22	+	+	CCONJ
ejpam-6089	391	23	1	1	X
ejpam-6089	391	24	)	)	PUNCT
ejpam-6089	391	25	−	−	ADP
ejpam-6089	391	26	2(1−	2(1−	X
ejpam-6089	391	27	ℵð−	ℵð−	PUNCT
ejpam-6089	391	28	℘	℘	NUM
ejpam-6089	391	29	)	)	PUNCT
ejpam-6089	391	30	(	(	PUNCT
ejpam-6089	391	31	ℵð+	ℵð+	ADJ
ejpam-6089	391	32	℘	℘	PROPN
ejpam-6089	391	33	)	)	PUNCT
ejpam-6089	391	34	)	)	PUNCT
ejpam-6089	391	35	×	×	NOUN
ejpam-6089	391	36	(	(	PUNCT
ejpam-6089	391	37	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	391	38	)	)	PUNCT
ejpam-6089	391	39	+	+	CCONJ
ejpam-6089	391	40	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	391	41	)	)	PUNCT
ejpam-6089	391	42	2	2	NUM
ejpam-6089	391	43	)	)	PUNCT
ejpam-6089	391	44	.	.	PUNCT
ejpam-6089	392	1	summing	sum	VERB
ejpam-6089	392	2	over	over	ADP
ejpam-6089	392	3	all	all	PRON
ejpam-6089	392	4	ð	ð	NOUN
ejpam-6089	393	1	∞∑	∞∑	NUM
ejpam-6089	393	2	ð=0	ð=0	X
ejpam-6089	393	3	að	að	X
ejpam-6089	393	4	(	(	PUNCT
ejpam-6089	393	5	(	(	PUNCT
ejpam-6089	393	6	(	(	PUNCT
ejpam-6089	393	7	ℑ2	ℑ2	PROPN
ejpam-6089	393	8	−ℑ1	−ℑ1	PROPN
ejpam-6089	393	9	)	)	PUNCT
ejpam-6089	393	10	(	(	PUNCT
ejpam-6089	393	11	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	393	12	)	)	PUNCT
ejpam-6089	393	13	+	+	CCONJ
ejpam-6089	393	14	2(ℵð+℘)(1−	2(ℵð+℘)(1−	X
ejpam-6089	393	15	ℵð−	ℵð−	PROPN
ejpam-6089	393	16	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	393	17	℘	℘	PROPN
ejpam-6089	393	18	)	)	PUNCT
ejpam-6089	393	19	)	)	PUNCT
ejpam-6089	393	20	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	393	21	℘	℘	NOUN
ejpam-6089	393	22	)	)	PUNCT
ejpam-6089	393	23	+	+	CCONJ
ejpam-6089	393	24	1	1	X
ejpam-6089	393	25	)	)	PUNCT
ejpam-6089	393	26	−	−	ADP
ejpam-6089	393	27	2(1−	2(1−	X
ejpam-6089	393	28	ℵð−	ℵð−	PUNCT
ejpam-6089	393	29	℘	℘	NUM
ejpam-6089	393	30	)	)	PUNCT
ejpam-6089	393	31	(	(	PUNCT
ejpam-6089	393	32	ℵð+	ℵð+	ADJ
ejpam-6089	393	33	℘	℘	PROPN
ejpam-6089	393	34	)	)	PUNCT
ejpam-6089	393	35	)	)	PUNCT
ejpam-6089	393	36	×υ	×υ	X
ejpam-6089	393	37	(	(	PUNCT
ejpam-6089	393	38	ℑ1	ℑ1	PROPN
ejpam-6089	393	39	+	+	CCONJ
ejpam-6089	393	40	ℑ2	ℑ2	PROPN
ejpam-6089	393	41	2	2	NUM
ejpam-6089	393	42	)	)	PUNCT
ejpam-6089	393	43	≤	≤	NOUN
ejpam-6089	393	44	∞∑	∞∑	NUM
ejpam-6089	393	45	ð=0	ð=0	X
ejpam-6089	393	46	að	að	X
ejpam-6089	393	47	(	(	PUNCT
ejpam-6089	393	48	r−li	r−li	NOUN
ejpam-6089	393	49	(	(	PUNCT
ejpam-6089	393	50	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	393	51	)	)	PUNCT
ejpam-6089	393	52	(	(	PUNCT
ejpam-6089	393	53	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	393	54	2	2	NUM
ejpam-6089	393	55	)	)	PUNCT
ejpam-6089	394	1	+	+	CCONJ
ejpam-6089	395	1	+	+	CCONJ
ejpam-6089	395	2	r−li	r−li	NOUN
ejpam-6089	395	3	(	(	PUNCT
ejpam-6089	395	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	395	5	)	)	PUNCT
ejpam-6089	395	6	(	(	PUNCT
ejpam-6089	395	7	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	395	8	2	2	NUM
ejpam-6089	395	9	)	)	PUNCT
ejpam-6089	395	10	−	−	PROPN
ejpam-6089	395	11	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	395	12	)	)	PUNCT
ejpam-6089	395	13	)	)	PUNCT
ejpam-6089	396	1	s.	s.	PROPN
ejpam-6089	396	2	naheed	nahee	VERB
ejpam-6089	396	3	et	et	PROPN
ejpam-6089	396	4	al	al	PROPN
ejpam-6089	396	5	.	.	PUNCT
ejpam-6089	396	6	/	/	SYM
ejpam-6089	396	7	eur	eur	PROPN
ejpam-6089	396	8	.	.	PUNCT
ejpam-6089	397	1	j.	j.	PROPN
ejpam-6089	397	2	pure	pure	PROPN
ejpam-6089	397	3	appl	appl	PROPN
ejpam-6089	397	4	.	.	PROPN
ejpam-6089	397	5	math	math	PROPN
ejpam-6089	397	6	,	,	PUNCT
ejpam-6089	397	7	18	18	NUM
ejpam-6089	397	8	(	(	PUNCT
ejpam-6089	397	9	2	2	NUM
ejpam-6089	397	10	)	)	PUNCT
ejpam-6089	397	11	(	(	PUNCT
ejpam-6089	397	12	2025	2025	NUM
ejpam-6089	397	13	)	)	PUNCT
ejpam-6089	397	14	,	,	PUNCT
ejpam-6089	397	15	6089	6089	NUM
ejpam-6089	397	16	19	19	NUM
ejpam-6089	397	17	of	of	ADP
ejpam-6089	397	18	34	34	NUM
ejpam-6089	397	19	≤	≤	NOUN
ejpam-6089	397	20	∞∑	∞∑	NUM
ejpam-6089	397	21	ð=0	ð=0	X
ejpam-6089	397	22	að	að	X
ejpam-6089	397	23	(	(	PUNCT
ejpam-6089	397	24	(	(	PUNCT
ejpam-6089	397	25	(	(	PUNCT
ejpam-6089	397	26	ℑ2	ℑ2	PROPN
ejpam-6089	397	27	−ℑ1	−ℑ1	PROPN
ejpam-6089	397	28	)	)	PUNCT
ejpam-6089	397	29	(	(	PUNCT
ejpam-6089	397	30	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	397	31	)	)	PUNCT
ejpam-6089	397	32	+	+	CCONJ
ejpam-6089	398	1	2(ℵð+℘)(1−	2(ℵð+℘)(1−	X
ejpam-6089	398	2	ℵð−	ℵð−	PROPN
ejpam-6089	398	3	℘)γ(ℵð+	℘)γ(ℵð+	NOUN
ejpam-6089	398	4	℘	℘	PROPN
ejpam-6089	398	5	)	)	PUNCT
ejpam-6089	398	6	)	)	PUNCT
ejpam-6089	399	1	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	399	2	℘	℘	NOUN
ejpam-6089	399	3	)	)	PUNCT
ejpam-6089	399	4	+	+	CCONJ
ejpam-6089	399	5	1	1	X
ejpam-6089	399	6	)	)	PUNCT
ejpam-6089	399	7	−	−	ADP
ejpam-6089	399	8	2(1−	2(1−	X
ejpam-6089	399	9	ℵð−	ℵð−	PUNCT
ejpam-6089	399	10	℘	℘	NUM
ejpam-6089	399	11	)	)	PUNCT
ejpam-6089	399	12	(	(	PUNCT
ejpam-6089	399	13	ℵð+	ℵð+	ADJ
ejpam-6089	399	14	℘	℘	PROPN
ejpam-6089	399	15	)	)	PUNCT
ejpam-6089	399	16	)	)	PUNCT
ejpam-6089	399	17	×	×	NOUN
ejpam-6089	399	18	(	(	PUNCT
ejpam-6089	399	19	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	399	20	)	)	PUNCT
ejpam-6089	399	21	+	+	CCONJ
ejpam-6089	399	22	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	399	23	)	)	PUNCT
ejpam-6089	399	24	2	2	NUM
ejpam-6089	399	25	)	)	PUNCT
ejpam-6089	399	26	,	,	PUNCT
ejpam-6089	399	27	using	use	VERB
ejpam-6089	399	28	proposition	proposition	NOUN
ejpam-6089	399	29	1	1	NUM
ejpam-6089	399	30	from	from	ADP
ejpam-6089	399	31	the	the	DET
ejpam-6089	399	32	middle	middle	NOUN
ejpam-6089	399	33	of	of	ADP
ejpam-6089	399	34	interval	interval	NOUN
ejpam-6089	399	35	[	[	X
ejpam-6089	399	36	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	399	37	]	]	PUNCT
ejpam-6089	399	38	,	,	PUNCT
ejpam-6089	399	39	we	we	PRON
ejpam-6089	399	40	acquire	acquire	VERB
ejpam-6089	399	41	∞∑	∞∑	PRON
ejpam-6089	399	42	ð=0	ð=0	X
ejpam-6089	399	43	aðsðυ	aðsðυ	X
ejpam-6089	399	44	(	(	PUNCT
ejpam-6089	399	45	ℑ1	ℑ1	PROPN
ejpam-6089	399	46	+	+	CCONJ
ejpam-6089	399	47	ℑ2	ℑ2	PROPN
ejpam-6089	399	48	2	2	NUM
ejpam-6089	399	49	)	)	PUNCT
ejpam-6089	399	50	≤	≤	PUNCT
ejpam-6089	399	51	ε	ε	PROPN
ejpam-6089	399	52	♭	♭	PROPN
ejpam-6089	399	53	,δ	,δ	PUNCT
ejpam-6089	399	54	,	,	PUNCT
ejpam-6089	399	55	b	b	NOUN
ejpam-6089	399	56	,	,	PUNCT
ejpam-6089	399	57	s	s	X
ejpam-6089	399	58	,	,	PUNCT
ejpam-6089	399	59	l	l	NOUN
ejpam-6089	399	60	(	(	PUNCT
ejpam-6089	399	61	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	399	62	2	2	NUM
ejpam-6089	399	63	)	)	PUNCT
ejpam-6089	400	1	+	+	ADV
ejpam-6089	400	2	,	,	PUNCT
ejpam-6089	400	3	ℵ,℘,τ	ℵ,℘,τ	PROPN
ejpam-6089	400	4	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	400	5	;	;	PUNCT
ejpam-6089	400	6	g	g	NOUN
ejpam-6089	400	7	)	)	PUNCT
ejpam-6089	401	1	+	+	CCONJ
ejpam-6089	401	2	ε	ε	PROPN
ejpam-6089	401	3	♭	♭	PROPN
ejpam-6089	401	4	,δ	,δ	PUNCT
ejpam-6089	401	5	,	,	PUNCT
ejpam-6089	401	6	b	b	NOUN
ejpam-6089	401	7	,	,	PUNCT
ejpam-6089	401	8	s	s	X
ejpam-6089	401	9	,	,	PUNCT
ejpam-6089	401	10	l	l	NOUN
ejpam-6089	401	11	(	(	PUNCT
ejpam-6089	401	12	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	401	13	2	2	NUM
ejpam-6089	401	14	)	)	PUNCT
ejpam-6089	401	15	−,ℵ,℘,τ	−,ℵ,℘,τ	NOUN
ejpam-6089	401	16	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	401	17	;	;	PUNCT
ejpam-6089	401	18	g	g	X
ejpam-6089	401	19	)	)	PUNCT
ejpam-6089	401	20	≤	≤	NOUN
ejpam-6089	402	1	∞∑	∞∑	NUM
ejpam-6089	402	2	ð=0	ð=0	SYM
ejpam-6089	402	3	aðsð	aðsð	PROPN
ejpam-6089	402	4	(	(	PUNCT
ejpam-6089	402	5	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	402	6	)	)	PUNCT
ejpam-6089	402	7	+	+	CCONJ
ejpam-6089	402	8	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	402	9	)	)	PUNCT
ejpam-6089	402	10	2	2	NUM
ejpam-6089	402	11	)	)	PUNCT
ejpam-6089	402	12	.	.	PUNCT
ejpam-6089	403	1	hence	hence	ADV
ejpam-6089	403	2	the	the	DET
ejpam-6089	403	3	result	result	NOUN
ejpam-6089	403	4	is	be	AUX
ejpam-6089	403	5	established	establish	VERB
ejpam-6089	403	6	.	.	PUNCT
ejpam-6089	404	1	theorem	theorem	VERB
ejpam-6089	404	2	8	8	NUM
ejpam-6089	404	3	.	.	PUNCT
ejpam-6089	405	1	if	if	SCONJ
ejpam-6089	405	2	υ	υ	PRON
ejpam-6089	405	3	:	:	PUNCT
ejpam-6089	405	4	[	[	X
ejpam-6089	405	5	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	405	6	]	]	PUNCT
ejpam-6089	405	7	→	→	SYM
ejpam-6089	405	8	ℜ	ℜ	PROPN
ejpam-6089	405	9	is	be	AUX
ejpam-6089	405	10	l1	l1	PROPN
ejpam-6089	405	11	convex	convex	PROPN
ejpam-6089	405	12	and	and	CCONJ
ejpam-6089	405	13	the	the	DET
ejpam-6089	405	14	parameters	parameter	NOUN
ejpam-6089	405	15	,	,	PUNCT
ejpam-6089	405	16	ℜ(ℵð	ℜ(ℵð	NOUN
ejpam-6089	405	17	+	+	CCONJ
ejpam-6089	405	18	℘	℘	NOUN
ejpam-6089	405	19	)	)	PUNCT
ejpam-6089	405	20	>	>	X
ejpam-6089	405	21	0	0	NUM
ejpam-6089	405	22	also	also	ADV
ejpam-6089	405	23	ℜ(	ℜ(	VERB
ejpam-6089	405	24	♭	♭	NOUN
ejpam-6089	405	25	),ℜ(γ),ℜ(ℵ),ℜ(℘),ℜ(τ	),ℜ(γ),ℜ(ℵ),ℜ(℘),ℜ(τ	PUNCT
ejpam-6089	405	26	)	)	PUNCT
ejpam-6089	405	27	>	>	X
ejpam-6089	405	28	0	0	NUM
ejpam-6089	405	29	and	and	CCONJ
ejpam-6089	405	30	ℜ(b	ℜ(b	NOUN
ejpam-6089	405	31	)	)	PUNCT
ejpam-6089	405	32	>	>	X
ejpam-6089	406	1	ℜ(δ	ℜ(δ	X
ejpam-6089	406	2	)	)	PUNCT
ejpam-6089	406	3	>	>	X
ejpam-6089	406	4	0	0	PUNCT
ejpam-6089	407	1	and	and	CCONJ
ejpam-6089	407	2	let	let	VERB
ejpam-6089	407	3	g	g	PROPN
ejpam-6089	407	4	≥	≥	NOUN
ejpam-6089	407	5	0	0	NUM
ejpam-6089	407	6	,	,	PUNCT
ejpam-6089	407	7	l	l	NOUN
ejpam-6089	407	8	>	>	X
ejpam-6089	407	9	0	0	PUNCT
ejpam-6089	408	1	and	and	CCONJ
ejpam-6089	408	2	0	0	NUM
ejpam-6089	408	3	<	<	X
ejpam-6089	408	4	s	s	X
ejpam-6089	408	5	≤	≤	NUM
ejpam-6089	408	6	l	l	NOUN
ejpam-6089	408	7	+	+	CCONJ
ejpam-6089	408	8	ℜ(ℵ	ℜ(ℵ	NOUN
ejpam-6089	408	9	)	)	PUNCT
ejpam-6089	408	10	,	,	PUNCT
ejpam-6089	408	11	then	then	ADV
ejpam-6089	408	12	we	we	PRON
ejpam-6089	408	13	have	have	VERB
ejpam-6089	408	14	the	the	DET
ejpam-6089	408	15	following	follow	VERB
ejpam-6089	408	16	(	(	PUNCT
ejpam-6089	408	17	h−h	h−h	NOUN
ejpam-6089	408	18	)	)	PUNCT
ejpam-6089	408	19	inequality	inequality	NOUN
ejpam-6089	408	20	for	for	ADP
ejpam-6089	408	21	prabhakar	prabhakar	NOUN
ejpam-6089	408	22	fractional	fractional	ADJ
ejpam-6089	408	23	integrals	integral	NOUN
ejpam-6089	408	24	and	and	CCONJ
ejpam-6089	408	25	generalized	generalize	VERB
ejpam-6089	408	26	fractional	fractional	ADJ
ejpam-6089	408	27	integral	integral	ADJ
ejpam-6089	408	28	operators	operator	NOUN
ejpam-6089	409	1	∞∑	∞∑	NUM
ejpam-6089	409	2	ð=0	ð=0	X
ejpam-6089	409	3	hðoðf	hðoðf	NOUN
ejpam-6089	409	4	(	(	PUNCT
ejpam-6089	409	5	ℑ1	ℑ1	PROPN
ejpam-6089	409	6	+	+	CCONJ
ejpam-6089	409	7	ℑ2	ℑ2	PROPN
ejpam-6089	409	8	2	2	NUM
ejpam-6089	409	9	)	)	PUNCT
ejpam-6089	409	10	≤	≤	NOUN
ejpam-6089	409	11	piℵ,℘,γ	piℵ,℘,γ	NOUN
ejpam-6089	409	12	,	,	PUNCT
ejpam-6089	409	13	♭	♭	PROPN
ejpam-6089	409	14	(	(	PUNCT
ejpam-6089	409	15	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	409	16	2	2	NUM
ejpam-6089	409	17	)	)	PUNCT
ejpam-6089	409	18	+	+	CCONJ
ejpam-6089	409	19	υ(c	υ(c	X
ejpam-6089	409	20	)	)	PUNCT
ejpam-6089	410	1	+	+	CCONJ
ejpam-6089	410	2	ε	ε	PROPN
ejpam-6089	410	3	♭	♭	PROPN
ejpam-6089	410	4	,δ	,δ	PUNCT
ejpam-6089	410	5	,	,	PUNCT
ejpam-6089	410	6	b	b	NOUN
ejpam-6089	410	7	,	,	PUNCT
ejpam-6089	410	8	s	s	X
ejpam-6089	410	9	,	,	PUNCT
ejpam-6089	410	10	l	l	NOUN
ejpam-6089	410	11	(	(	PUNCT
ejpam-6089	410	12	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	410	13	2	2	NUM
ejpam-6089	410	14	)	)	PUNCT
ejpam-6089	410	15	+	+	ADV
ejpam-6089	410	16	,	,	PUNCT
ejpam-6089	410	17	ℵ,℘,τ	ℵ,℘,τ	PROPN
ejpam-6089	410	18	υ(c	υ(c	PROPN
ejpam-6089	410	19	;	;	PUNCT
ejpam-6089	410	20	g	g	NOUN
ejpam-6089	410	21	)	)	PUNCT
ejpam-6089	411	1	+	+	CCONJ
ejpam-6089	411	2	piℵ,℘,γ	piℵ,℘,γ	NUM
ejpam-6089	411	3	,	,	PUNCT
ejpam-6089	411	4	♭	♭	PROPN
ejpam-6089	411	5	(	(	PUNCT
ejpam-6089	411	6	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	411	7	2	2	NUM
ejpam-6089	411	8	)	)	PUNCT
ejpam-6089	411	9	−	−	ADP
ejpam-6089	411	10	υ(c	υ(c	PROPN
ejpam-6089	411	11	)	)	PUNCT
ejpam-6089	412	1	+	+	CCONJ
ejpam-6089	412	2	ε	ε	PROPN
ejpam-6089	412	3	♭	♭	PROPN
ejpam-6089	412	4	,δ	,δ	PUNCT
ejpam-6089	412	5	,	,	PUNCT
ejpam-6089	412	6	b	b	NOUN
ejpam-6089	412	7	,	,	PUNCT
ejpam-6089	412	8	s	s	X
ejpam-6089	412	9	,	,	PUNCT
ejpam-6089	412	10	l	l	NOUN
ejpam-6089	412	11	(	(	PUNCT
ejpam-6089	412	12	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	412	13	2	2	NUM
ejpam-6089	412	14	)	)	PUNCT
ejpam-6089	412	15	−,ℵ,℘,τ	−,ℵ,℘,τ	NOUN
ejpam-6089	412	16	υ(c	υ(c	PROPN
ejpam-6089	412	17	;	;	PUNCT
ejpam-6089	412	18	g	g	NOUN
ejpam-6089	412	19	)	)	PUNCT
ejpam-6089	412	20	≤	≤	NOUN
ejpam-6089	413	1	∞∑	∞∑	NUM
ejpam-6089	413	2	ð=0	ð=0	X
ejpam-6089	413	3	hðoð	hðoð	NOUN
ejpam-6089	413	4	(	(	PUNCT
ejpam-6089	413	5	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	413	6	)	)	PUNCT
ejpam-6089	413	7	+	+	CCONJ
ejpam-6089	413	8	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	413	9	)	)	PUNCT
ejpam-6089	413	10	2	2	NUM
ejpam-6089	413	11	)	)	PUNCT
ejpam-6089	413	12	,	,	PUNCT
ejpam-6089	413	13	(	(	PUNCT
ejpam-6089	413	14	25	25	NUM
ejpam-6089	413	15	)	)	PUNCT
ejpam-6089	413	16	where	where	SCONJ
ejpam-6089	413	17	hð	hð	VERB
ejpam-6089	413	18	=	=	SYM
ejpam-6089	413	19	bg(δ+ðs	bg(δ+ð	NOUN
ejpam-6089	413	20	,	,	PUNCT
ejpam-6089	413	21	b−δ	b−δ	NOUN
ejpam-6089	413	22	)	)	PUNCT
ejpam-6089	413	23	b(δ	b(δ	NOUN
ejpam-6089	413	24	,	,	PUNCT
ejpam-6089	413	25	b−δ	b−δ	NOUN
ejpam-6089	413	26	)	)	PUNCT
ejpam-6089	413	27	(	(	PUNCT
ejpam-6089	414	1	b)ðs	b)ðs	PROPN
ejpam-6089	414	2	♭	♭	PROPN
ejpam-6089	414	3	ð	ð	X
ejpam-6089	414	4	(	(	PUNCT
ejpam-6089	414	5	τ)ðl	τ)ðl	ADJ
ejpam-6089	414	6	+	+	NUM
ejpam-6089	414	7	γ(γ+ð)	γ(γ+ð)	PROPN
ejpam-6089	414	8	♭	♭	PROPN
ejpam-6089	414	9	ð	ð	X
ejpam-6089	414	10	γ(γ)ð	γ(γ)ð	PROPN
ejpam-6089	414	11	!	!	PUNCT
ejpam-6089	415	1	and	and	CCONJ
ejpam-6089	415	2	oð	oð	X
ejpam-6089	415	3	=	=	SYM
ejpam-6089	415	4	(	(	PUNCT
ejpam-6089	415	5	ℑ2−ℑ1)(ℵð+℘	ℑ2−ℑ1)(ℵð+℘	PROPN
ejpam-6089	415	6	)	)	PUNCT
ejpam-6089	415	7	2(ℵð+℘)−1γ((ℵð+℘)+1	2(ℵð+℘)−1γ((ℵð+℘)+1	NUM
ejpam-6089	415	8	)	)	PUNCT
ejpam-6089	415	9	.	.	PUNCT
ejpam-6089	416	1	proof	proof	NOUN
ejpam-6089	416	2	.	.	PUNCT
ejpam-6089	417	1	replacing	replace	VERB
ejpam-6089	417	2	α∗	α∗	NOUN
ejpam-6089	417	3	by	by	ADP
ejpam-6089	417	4	(	(	PUNCT
ejpam-6089	417	5	ℵð+	ℵð+	ADJ
ejpam-6089	417	6	℘	℘	PROPN
ejpam-6089	417	7	)	)	PUNCT
ejpam-6089	417	8	in	in	ADP
ejpam-6089	417	9	theorem	theorem	NOUN
ejpam-6089	417	10	4	4	NUM
ejpam-6089	417	11	,	,	PUNCT
ejpam-6089	417	12	we	we	PRON
ejpam-6089	417	13	obtain	obtain	VERB
ejpam-6089	417	14	υ	υ	PRON
ejpam-6089	417	15	(	(	PUNCT
ejpam-6089	417	16	ℑ1	ℑ1	PROPN
ejpam-6089	417	17	+	+	CCONJ
ejpam-6089	417	18	ℑ2	ℑ2	PROPN
ejpam-6089	417	19	2	2	NUM
ejpam-6089	417	20	)	)	PUNCT
ejpam-6089	417	21	≤	≤	NOUN
ejpam-6089	417	22	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	417	23	℘	℘	NOUN
ejpam-6089	417	24	)	)	PUNCT
ejpam-6089	417	25	+	+	NUM
ejpam-6089	417	26	1	1	X
ejpam-6089	417	27	)	)	PUNCT
ejpam-6089	417	28	(	(	PUNCT
ejpam-6089	417	29	ℑ2	ℑ2	PROPN
ejpam-6089	417	30	−ℑ1)(ℵð+℘	−ℑ1)(ℵð+℘	NUM
ejpam-6089	417	31	)	)	PUNCT
ejpam-6089	417	32	×	×	NOUN
ejpam-6089	417	33	(	(	PUNCT
ejpam-6089	417	34	r−li	r−li	NOUN
ejpam-6089	417	35	(	(	PUNCT
ejpam-6089	417	36	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	417	37	)	)	PUNCT
ejpam-6089	417	38	(	(	PUNCT
ejpam-6089	417	39	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	417	40	2	2	NUM
ejpam-6089	417	41	)	)	PUNCT
ejpam-6089	417	42	+	+	CCONJ
ejpam-6089	417	43	υ(c	υ(c	X
ejpam-6089	417	44	)	)	PUNCT
ejpam-6089	418	1	+	+	CCONJ
ejpam-6089	418	2	r−li	r−li	NOUN
ejpam-6089	418	3	(	(	PUNCT
ejpam-6089	418	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	418	5	)	)	PUNCT
ejpam-6089	418	6	(	(	PUNCT
ejpam-6089	418	7	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	418	8	2	2	NUM
ejpam-6089	418	9	)	)	PUNCT
ejpam-6089	418	10	−	−	ADP
ejpam-6089	418	11	υ(c	υ(c	PROPN
ejpam-6089	418	12	)	)	PUNCT
ejpam-6089	418	13	)	)	PUNCT
ejpam-6089	418	14	≤	≤	NOUN
ejpam-6089	418	15	(	(	PUNCT
ejpam-6089	418	16	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	418	17	)	)	PUNCT
ejpam-6089	418	18	+	+	CCONJ
ejpam-6089	418	19	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	418	20	)	)	PUNCT
ejpam-6089	418	21	2	2	NUM
ejpam-6089	418	22	)	)	PUNCT
ejpam-6089	418	23	.	.	PUNCT
ejpam-6089	419	1	multiplying	multiply	VERB
ejpam-6089	419	2	the	the	DET
ejpam-6089	419	3	above	above	ADJ
ejpam-6089	419	4	inequality	inequality	NOUN
ejpam-6089	419	5	with	with	ADP
ejpam-6089	419	6	(	(	PUNCT
ejpam-6089	419	7	ℑ2−ℑ1)(ℵð+℘	ℑ2−ℑ1)(ℵð+℘	NOUN
ejpam-6089	419	8	)	)	PUNCT
ejpam-6089	419	9	2(ℵð+℘)−1γ((ℵð+℘)+1	2(ℵð+℘)−1γ((ℵð+℘)+1	NUM
ejpam-6089	419	10	)	)	PUNCT
ejpam-6089	419	11	,	,	PUNCT
ejpam-6089	419	12	we	we	PRON
ejpam-6089	419	13	obtain	obtain	VERB
ejpam-6089	419	14	(	(	PUNCT
ejpam-6089	419	15	ℑ2	ℑ2	PROPN
ejpam-6089	419	16	−ℑ1	−ℑ1	PROPN
ejpam-6089	419	17	)	)	PUNCT
ejpam-6089	419	18	(	(	PUNCT
ejpam-6089	419	19	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	419	20	)	)	PUNCT
ejpam-6089	419	21	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	419	22	℘	℘	NOUN
ejpam-6089	419	23	)	)	PUNCT
ejpam-6089	419	24	+	+	NUM
ejpam-6089	419	25	1	1	X
ejpam-6089	419	26	)	)	PUNCT
ejpam-6089	419	27	υ	υ	NOUN
ejpam-6089	419	28	(	(	PUNCT
ejpam-6089	419	29	ℑ1	ℑ1	PROPN
ejpam-6089	419	30	+	+	CCONJ
ejpam-6089	419	31	ℑ2	ℑ2	PROPN
ejpam-6089	419	32	2	2	NUM
ejpam-6089	419	33	)	)	PUNCT
ejpam-6089	420	1	s.	s.	PROPN
ejpam-6089	420	2	naheed	nahee	VERB
ejpam-6089	420	3	et	et	PROPN
ejpam-6089	420	4	al	al	PROPN
ejpam-6089	420	5	.	.	PUNCT
ejpam-6089	420	6	/	/	SYM
ejpam-6089	420	7	eur	eur	PROPN
ejpam-6089	420	8	.	.	PUNCT
ejpam-6089	421	1	j.	j.	PROPN
ejpam-6089	421	2	pure	pure	PROPN
ejpam-6089	421	3	appl	appl	PROPN
ejpam-6089	421	4	.	.	PROPN
ejpam-6089	421	5	math	math	PROPN
ejpam-6089	421	6	,	,	PUNCT
ejpam-6089	421	7	18	18	NUM
ejpam-6089	421	8	(	(	PUNCT
ejpam-6089	421	9	2	2	NUM
ejpam-6089	421	10	)	)	PUNCT
ejpam-6089	421	11	(	(	PUNCT
ejpam-6089	421	12	2025	2025	NUM
ejpam-6089	421	13	)	)	PUNCT
ejpam-6089	421	14	,	,	PUNCT
ejpam-6089	421	15	6089	6089	NUM
ejpam-6089	421	16	20	20	NUM
ejpam-6089	421	17	of	of	ADP
ejpam-6089	421	18	34	34	NUM
ejpam-6089	421	19	≤	≤	NOUN
ejpam-6089	421	20	(	(	PUNCT
ejpam-6089	421	21	r−li	r−li	NOUN
ejpam-6089	421	22	(	(	PUNCT
ejpam-6089	421	23	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	421	24	)	)	PUNCT
ejpam-6089	421	25	(	(	PUNCT
ejpam-6089	421	26	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	421	27	2	2	NUM
ejpam-6089	421	28	)	)	PUNCT
ejpam-6089	421	29	+	+	CCONJ
ejpam-6089	421	30	υ(c	υ(c	X
ejpam-6089	421	31	)	)	PUNCT
ejpam-6089	422	1	+	+	CCONJ
ejpam-6089	422	2	r−li	r−li	NOUN
ejpam-6089	422	3	(	(	PUNCT
ejpam-6089	422	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	422	5	)	)	PUNCT
ejpam-6089	422	6	(	(	PUNCT
ejpam-6089	422	7	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	422	8	2	2	NUM
ejpam-6089	422	9	)	)	PUNCT
ejpam-6089	422	10	−	−	ADP
ejpam-6089	422	11	υ(c	υ(c	PROPN
ejpam-6089	422	12	)	)	PUNCT
ejpam-6089	422	13	)	)	PUNCT
ejpam-6089	422	14	≤	≤	NOUN
ejpam-6089	422	15	(	(	PUNCT
ejpam-6089	422	16	ℑ2	ℑ2	PROPN
ejpam-6089	422	17	−ℑ1	−ℑ1	PROPN
ejpam-6089	422	18	)	)	PUNCT
ejpam-6089	422	19	(	(	PUNCT
ejpam-6089	422	20	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	422	21	)	)	PUNCT
ejpam-6089	422	22	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	422	23	℘	℘	NOUN
ejpam-6089	422	24	)	)	PUNCT
ejpam-6089	422	25	+	+	NUM
ejpam-6089	422	26	1	1	X
ejpam-6089	422	27	)	)	PUNCT
ejpam-6089	422	28	(	(	PUNCT
ejpam-6089	422	29	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	422	30	)	)	PUNCT
ejpam-6089	422	31	+	+	CCONJ
ejpam-6089	422	32	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	422	33	)	)	PUNCT
ejpam-6089	422	34	2	2	NUM
ejpam-6089	422	35	)	)	PUNCT
ejpam-6089	422	36	.	.	PUNCT
ejpam-6089	423	1	again	again	ADV
ejpam-6089	423	2	we	we	PRON
ejpam-6089	423	3	multiply	multiply	VERB
ejpam-6089	423	4	the	the	DET
ejpam-6089	423	5	above	above	ADJ
ejpam-6089	423	6	expression	expression	NOUN
ejpam-6089	423	7	with	with	ADP
ejpam-6089	423	8	hð	hð	X
ejpam-6089	423	9	,	,	PUNCT
ejpam-6089	423	10	then	then	ADV
ejpam-6089	423	11	it	it	PRON
ejpam-6089	423	12	becomes	become	VERB
ejpam-6089	423	13	hð	hð	PUNCT
ejpam-6089	423	14	(	(	PUNCT
ejpam-6089	423	15	ℑ2	ℑ2	PROPN
ejpam-6089	423	16	−ℑ1	−ℑ1	PROPN
ejpam-6089	423	17	)	)	PUNCT
ejpam-6089	423	18	(	(	PUNCT
ejpam-6089	423	19	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	423	20	)	)	PUNCT
ejpam-6089	423	21	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	423	22	℘	℘	NOUN
ejpam-6089	423	23	)	)	PUNCT
ejpam-6089	424	1	+	+	NUM
ejpam-6089	424	2	1	1	X
ejpam-6089	424	3	)	)	PUNCT
ejpam-6089	424	4	υ	υ	NOUN
ejpam-6089	424	5	(	(	PUNCT
ejpam-6089	424	6	ℑ1	ℑ1	PROPN
ejpam-6089	424	7	+	+	CCONJ
ejpam-6089	424	8	ℑ2	ℑ2	PROPN
ejpam-6089	424	9	2	2	NUM
ejpam-6089	424	10	)	)	PUNCT
ejpam-6089	424	11	≤	≤	NUM
ejpam-6089	424	12	hð	hð	PUNCT
ejpam-6089	424	13	(	(	PUNCT
ejpam-6089	424	14	r−li	r−li	NOUN
ejpam-6089	424	15	(	(	PUNCT
ejpam-6089	424	16	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	424	17	)	)	PUNCT
ejpam-6089	424	18	(	(	PUNCT
ejpam-6089	424	19	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	424	20	2	2	NUM
ejpam-6089	424	21	)	)	PUNCT
ejpam-6089	424	22	+	+	CCONJ
ejpam-6089	424	23	υ(c	υ(c	X
ejpam-6089	424	24	)	)	PUNCT
ejpam-6089	425	1	+	+	SYM
ejpam-6089	425	2	r−liℵi+℘	r−liℵi+℘	PROPN
ejpam-6089	425	3	(	(	PUNCT
ejpam-6089	425	4	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	425	5	2	2	NUM
ejpam-6089	425	6	)	)	PUNCT
ejpam-6089	425	7	−	−	ADP
ejpam-6089	425	8	υ(c	υ(c	PROPN
ejpam-6089	425	9	)	)	PUNCT
ejpam-6089	425	10	)	)	PUNCT
ejpam-6089	426	1	≤	≤	NUM
ejpam-6089	426	2	hð	hð	VERB
ejpam-6089	426	3	(	(	PUNCT
ejpam-6089	426	4	ℑ2	ℑ2	PROPN
ejpam-6089	426	5	−ℑ1	−ℑ1	PROPN
ejpam-6089	426	6	)	)	PUNCT
ejpam-6089	426	7	(	(	PUNCT
ejpam-6089	426	8	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	426	9	)	)	PUNCT
ejpam-6089	426	10	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	426	11	℘	℘	NOUN
ejpam-6089	426	12	)	)	PUNCT
ejpam-6089	426	13	+	+	NUM
ejpam-6089	426	14	1	1	X
ejpam-6089	426	15	)	)	PUNCT
ejpam-6089	426	16	(	(	PUNCT
ejpam-6089	426	17	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	426	18	)	)	PUNCT
ejpam-6089	426	19	+	+	CCONJ
ejpam-6089	426	20	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	426	21	)	)	PUNCT
ejpam-6089	426	22	2	2	NUM
ejpam-6089	426	23	)	)	PUNCT
ejpam-6089	426	24	.	.	PUNCT
ejpam-6089	427	1	summing	sum	VERB
ejpam-6089	427	2	over	over	ADP
ejpam-6089	427	3	all	all	PRON
ejpam-6089	427	4	ð	ð	NOUN
ejpam-6089	427	5	∞∑	∞∑	NUM
ejpam-6089	427	6	ð=0	ð=0	PUNCT
ejpam-6089	427	7	hð	hð	X
ejpam-6089	427	8	(	(	PUNCT
ejpam-6089	427	9	ℑ2	ℑ2	PROPN
ejpam-6089	427	10	−ℑ1	−ℑ1	PROPN
ejpam-6089	427	11	)	)	PUNCT
ejpam-6089	427	12	(	(	PUNCT
ejpam-6089	427	13	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	427	14	)	)	PUNCT
ejpam-6089	427	15	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	427	16	℘	℘	NOUN
ejpam-6089	427	17	)	)	PUNCT
ejpam-6089	427	18	+	+	NUM
ejpam-6089	427	19	1	1	X
ejpam-6089	427	20	)	)	PUNCT
ejpam-6089	427	21	υ	υ	NOUN
ejpam-6089	427	22	(	(	PUNCT
ejpam-6089	427	23	ℑ1	ℑ1	PROPN
ejpam-6089	427	24	+	+	CCONJ
ejpam-6089	427	25	ℑ2	ℑ2	PROPN
ejpam-6089	427	26	2	2	NUM
ejpam-6089	427	27	)	)	PUNCT
ejpam-6089	427	28	≤	≤	NOUN
ejpam-6089	427	29	∞∑	∞∑	NUM
ejpam-6089	427	30	ð=0	ð=0	PUNCT
ejpam-6089	427	31	hð	hð	PUNCT
ejpam-6089	427	32	(	(	PUNCT
ejpam-6089	427	33	r−li	r−li	NOUN
ejpam-6089	427	34	(	(	PUNCT
ejpam-6089	427	35	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	427	36	)	)	PUNCT
ejpam-6089	427	37	(	(	PUNCT
ejpam-6089	427	38	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	427	39	2	2	NUM
ejpam-6089	427	40	)	)	PUNCT
ejpam-6089	427	41	+	+	CCONJ
ejpam-6089	427	42	υ(c	υ(c	X
ejpam-6089	427	43	)	)	PUNCT
ejpam-6089	428	1	+	+	CCONJ
ejpam-6089	428	2	r−li	r−li	NOUN
ejpam-6089	428	3	(	(	PUNCT
ejpam-6089	428	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	428	5	)	)	PUNCT
ejpam-6089	428	6	(	(	PUNCT
ejpam-6089	428	7	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	428	8	2	2	NUM
ejpam-6089	428	9	)	)	PUNCT
ejpam-6089	428	10	−	−	ADP
ejpam-6089	428	11	υ(c	υ(c	PROPN
ejpam-6089	428	12	)	)	PUNCT
ejpam-6089	428	13	)	)	PUNCT
ejpam-6089	429	1	≤	≤	NOUN
ejpam-6089	430	1	∞∑	∞∑	NUM
ejpam-6089	430	2	ð=0	ð=0	PUNCT
ejpam-6089	430	3	hð	hð	X
ejpam-6089	430	4	(	(	PUNCT
ejpam-6089	430	5	ℑ2	ℑ2	PROPN
ejpam-6089	430	6	−ℑ1	−ℑ1	PROPN
ejpam-6089	430	7	)	)	PUNCT
ejpam-6089	430	8	(	(	PUNCT
ejpam-6089	430	9	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	430	10	)	)	PUNCT
ejpam-6089	430	11	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	430	12	℘	℘	NOUN
ejpam-6089	430	13	)	)	PUNCT
ejpam-6089	430	14	+	+	NUM
ejpam-6089	430	15	1	1	X
ejpam-6089	430	16	)	)	PUNCT
ejpam-6089	430	17	(	(	PUNCT
ejpam-6089	430	18	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	430	19	)	)	PUNCT
ejpam-6089	430	20	+	+	CCONJ
ejpam-6089	430	21	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	430	22	)	)	PUNCT
ejpam-6089	430	23	2	2	NUM
ejpam-6089	430	24	)	)	PUNCT
ejpam-6089	430	25	.	.	PUNCT
ejpam-6089	431	1	(	(	PUNCT
ejpam-6089	431	2	26	26	NUM
ejpam-6089	431	3	)	)	PUNCT
ejpam-6089	431	4	from	from	ADP
ejpam-6089	431	5	the	the	DET
ejpam-6089	431	6	middle	middle	NOUN
ejpam-6089	431	7	of	of	ADP
ejpam-6089	431	8	interval	interval	NOUN
ejpam-6089	431	9	[	[	X
ejpam-6089	431	10	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	431	11	]	]	PUNCT
ejpam-6089	431	12	,	,	PUNCT
ejpam-6089	431	13	proposition	proposition	NOUN
ejpam-6089	431	14	3	3	NUM
ejpam-6089	431	15	becomes	become	VERB
ejpam-6089	431	16	piℵ,℘,γ	piℵ,℘,γ	NOUN
ejpam-6089	431	17	,	,	PUNCT
ejpam-6089	431	18	♭	♭	PROPN
ejpam-6089	431	19	(	(	PUNCT
ejpam-6089	431	20	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	431	21	2	2	NUM
ejpam-6089	431	22	)	)	PUNCT
ejpam-6089	431	23	+	+	CCONJ
ejpam-6089	431	24	υ(c	υ(c	X
ejpam-6089	431	25	)	)	PUNCT
ejpam-6089	432	1	+	+	CCONJ
ejpam-6089	432	2	ε	ε	PROPN
ejpam-6089	432	3	♭	♭	PROPN
ejpam-6089	432	4	,δ	,δ	PUNCT
ejpam-6089	432	5	,	,	PUNCT
ejpam-6089	432	6	b	b	NOUN
ejpam-6089	432	7	,	,	PUNCT
ejpam-6089	432	8	s	s	X
ejpam-6089	432	9	,	,	PUNCT
ejpam-6089	432	10	l	l	NOUN
ejpam-6089	432	11	(	(	PUNCT
ejpam-6089	432	12	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	432	13	2	2	NUM
ejpam-6089	432	14	)	)	PUNCT
ejpam-6089	432	15	+	+	ADV
ejpam-6089	432	16	,	,	PUNCT
ejpam-6089	432	17	ℵ,℘,τ	ℵ,℘,τ	PROPN
ejpam-6089	432	18	υ(c	υ(c	PROPN
ejpam-6089	432	19	;	;	PUNCT
ejpam-6089	432	20	g	g	NOUN
ejpam-6089	432	21	)	)	PUNCT
ejpam-6089	433	1	+	+	CCONJ
ejpam-6089	433	2	piℵ,℘,γ	piℵ,℘,γ	NUM
ejpam-6089	433	3	,	,	PUNCT
ejpam-6089	433	4	♭	♭	PROPN
ejpam-6089	433	5	(	(	PUNCT
ejpam-6089	433	6	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	433	7	2	2	NUM
ejpam-6089	433	8	)	)	PUNCT
ejpam-6089	433	9	−	−	ADP
ejpam-6089	433	10	υ(c	υ(c	PROPN
ejpam-6089	433	11	)	)	PUNCT
ejpam-6089	434	1	+	+	CCONJ
ejpam-6089	434	2	ε	ε	PROPN
ejpam-6089	434	3	♭	♭	PROPN
ejpam-6089	434	4	,δ	,δ	PUNCT
ejpam-6089	434	5	,	,	PUNCT
ejpam-6089	434	6	b	b	NOUN
ejpam-6089	434	7	,	,	PUNCT
ejpam-6089	434	8	s	s	X
ejpam-6089	434	9	,	,	PUNCT
ejpam-6089	434	10	l	l	NOUN
ejpam-6089	434	11	(	(	PUNCT
ejpam-6089	434	12	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	434	13	2	2	NUM
ejpam-6089	434	14	)	)	PUNCT
ejpam-6089	434	15	−,ℵ,℘,τ	−,ℵ,℘,τ	NOUN
ejpam-6089	434	16	υ(c	υ(c	PROPN
ejpam-6089	434	17	;	;	PUNCT
ejpam-6089	434	18	g	g	NOUN
ejpam-6089	434	19	)	)	PUNCT
ejpam-6089	434	20	=	=	PUNCT
ejpam-6089	435	1	∞∑	∞∑	NUM
ejpam-6089	435	2	ð=0	ð=0	PUNCT
ejpam-6089	435	3	hð	hð	PUNCT
ejpam-6089	435	4	(	(	PUNCT
ejpam-6089	435	5	r−li	r−li	NOUN
ejpam-6089	435	6	(	(	PUNCT
ejpam-6089	435	7	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	435	8	)	)	PUNCT
ejpam-6089	435	9	(	(	PUNCT
ejpam-6089	435	10	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	435	11	2	2	NUM
ejpam-6089	435	12	)	)	PUNCT
ejpam-6089	435	13	+	+	CCONJ
ejpam-6089	435	14	υ(c	υ(c	X
ejpam-6089	435	15	)	)	PUNCT
ejpam-6089	436	1	+	+	CCONJ
ejpam-6089	436	2	r−li	r−li	NOUN
ejpam-6089	436	3	(	(	PUNCT
ejpam-6089	436	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	436	5	)	)	PUNCT
ejpam-6089	436	6	(	(	PUNCT
ejpam-6089	436	7	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	436	8	2	2	NUM
ejpam-6089	436	9	)	)	PUNCT
ejpam-6089	436	10	−	−	ADP
ejpam-6089	436	11	υ(c	υ(c	PROPN
ejpam-6089	436	12	)	)	PUNCT
ejpam-6089	436	13	)	)	PUNCT
ejpam-6089	436	14	.	.	PUNCT
ejpam-6089	437	1	(	(	PUNCT
ejpam-6089	437	2	27	27	NUM
ejpam-6089	437	3	)	)	PUNCT
ejpam-6089	437	4	using	use	VERB
ejpam-6089	437	5	(	(	PUNCT
ejpam-6089	437	6	27	27	NUM
ejpam-6089	437	7	)	)	PUNCT
ejpam-6089	437	8	in	in	ADP
ejpam-6089	437	9	(	(	PUNCT
ejpam-6089	437	10	26	26	NUM
ejpam-6089	437	11	)	)	PUNCT
ejpam-6089	437	12	,	,	PUNCT
ejpam-6089	437	13	we	we	PRON
ejpam-6089	437	14	obtain	obtain	VERB
ejpam-6089	437	15	∞∑	∞∑	NUM
ejpam-6089	437	16	ð=0	ð=0	X
ejpam-6089	437	17	hðoðυ	hðoðυ	NOUN
ejpam-6089	437	18	(	(	PUNCT
ejpam-6089	437	19	ℑ1	ℑ1	PROPN
ejpam-6089	437	20	+	+	CCONJ
ejpam-6089	437	21	ℑ2	ℑ2	PROPN
ejpam-6089	437	22	2	2	NUM
ejpam-6089	437	23	)	)	PUNCT
ejpam-6089	437	24	≤	≤	NOUN
ejpam-6089	437	25	piℵ,℘,γ	piℵ,℘,γ	NOUN
ejpam-6089	437	26	,	,	PUNCT
ejpam-6089	437	27	♭	♭	PROPN
ejpam-6089	437	28	(	(	PUNCT
ejpam-6089	437	29	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	437	30	2	2	NUM
ejpam-6089	437	31	)	)	PUNCT
ejpam-6089	437	32	+	+	CCONJ
ejpam-6089	437	33	υ(c	υ(c	X
ejpam-6089	437	34	)	)	PUNCT
ejpam-6089	438	1	+	+	CCONJ
ejpam-6089	438	2	ε	ε	PROPN
ejpam-6089	438	3	♭	♭	PROPN
ejpam-6089	438	4	,δ	,δ	PUNCT
ejpam-6089	438	5	,	,	PUNCT
ejpam-6089	438	6	b	b	NOUN
ejpam-6089	438	7	,	,	PUNCT
ejpam-6089	438	8	s	s	X
ejpam-6089	438	9	,	,	PUNCT
ejpam-6089	438	10	l	l	NOUN
ejpam-6089	438	11	(	(	PUNCT
ejpam-6089	438	12	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	438	13	2	2	NUM
ejpam-6089	438	14	)	)	PUNCT
ejpam-6089	438	15	+	+	ADV
ejpam-6089	438	16	,	,	PUNCT
ejpam-6089	438	17	ℵ,℘,τ	ℵ,℘,τ	PROPN
ejpam-6089	438	18	υ(c	υ(c	PROPN
ejpam-6089	438	19	;	;	PUNCT
ejpam-6089	438	20	g	g	NOUN
ejpam-6089	438	21	)	)	PUNCT
ejpam-6089	439	1	+	+	CCONJ
ejpam-6089	439	2	piℵ,℘,γ	piℵ,℘,γ	NUM
ejpam-6089	439	3	,	,	PUNCT
ejpam-6089	439	4	♭	♭	PROPN
ejpam-6089	439	5	(	(	PUNCT
ejpam-6089	439	6	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	439	7	2	2	NUM
ejpam-6089	439	8	)	)	PUNCT
ejpam-6089	439	9	−	−	ADP
ejpam-6089	439	10	υ(c	υ(c	PROPN
ejpam-6089	439	11	)	)	PUNCT
ejpam-6089	440	1	+	+	CCONJ
ejpam-6089	440	2	ε	ε	PROPN
ejpam-6089	440	3	♭	♭	PROPN
ejpam-6089	440	4	,δ	,δ	PUNCT
ejpam-6089	440	5	,	,	PUNCT
ejpam-6089	440	6	b	b	NOUN
ejpam-6089	440	7	,	,	PUNCT
ejpam-6089	440	8	s	s	X
ejpam-6089	440	9	,	,	PUNCT
ejpam-6089	440	10	l	l	NOUN
ejpam-6089	440	11	(	(	PUNCT
ejpam-6089	440	12	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	440	13	2	2	NUM
ejpam-6089	440	14	)	)	PUNCT
ejpam-6089	440	15	−,ℵ,℘,τ	−,ℵ,℘,τ	NOUN
ejpam-6089	440	16	υ(c	υ(c	PROPN
ejpam-6089	440	17	;	;	PUNCT
ejpam-6089	440	18	g	g	NOUN
ejpam-6089	440	19	)	)	PUNCT
ejpam-6089	440	20	≤	≤	NOUN
ejpam-6089	441	1	∞∑	∞∑	NUM
ejpam-6089	441	2	ð=0	ð=0	X
ejpam-6089	441	3	hðoð	hðoð	NOUN
ejpam-6089	441	4	(	(	PUNCT
ejpam-6089	441	5	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	441	6	)	)	PUNCT
ejpam-6089	441	7	+	+	CCONJ
ejpam-6089	441	8	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	441	9	)	)	PUNCT
ejpam-6089	441	10	2	2	NUM
ejpam-6089	441	11	)	)	PUNCT
ejpam-6089	441	12	.	.	PUNCT
ejpam-6089	442	1	that	that	PRON
ejpam-6089	442	2	is	be	AUX
ejpam-6089	442	3	our	our	PRON
ejpam-6089	442	4	required	required	ADJ
ejpam-6089	442	5	result	result	NOUN
ejpam-6089	442	6	.	.	PUNCT
ejpam-6089	443	1	s.	s.	PROPN
ejpam-6089	443	2	naheed	nahee	VERB
ejpam-6089	443	3	et	et	PROPN
ejpam-6089	443	4	al	al	PROPN
ejpam-6089	443	5	.	.	PUNCT
ejpam-6089	443	6	/	/	SYM
ejpam-6089	443	7	eur	eur	PROPN
ejpam-6089	443	8	.	.	PUNCT
ejpam-6089	444	1	j.	j.	PROPN
ejpam-6089	444	2	pure	pure	PROPN
ejpam-6089	444	3	appl	appl	PROPN
ejpam-6089	444	4	.	.	PROPN
ejpam-6089	444	5	math	math	PROPN
ejpam-6089	444	6	,	,	PUNCT
ejpam-6089	444	7	18	18	NUM
ejpam-6089	444	8	(	(	PUNCT
ejpam-6089	444	9	2	2	NUM
ejpam-6089	444	10	)	)	PUNCT
ejpam-6089	444	11	(	(	PUNCT
ejpam-6089	444	12	2025	2025	NUM
ejpam-6089	444	13	)	)	PUNCT
ejpam-6089	444	14	,	,	PUNCT
ejpam-6089	444	15	6089	6089	NUM
ejpam-6089	444	16	21	21	NUM
ejpam-6089	444	17	of	of	ADP
ejpam-6089	444	18	34	34	NUM
ejpam-6089	444	19	example	example	NOUN
ejpam-6089	444	20	2	2	NUM
ejpam-6089	444	21	.	.	X
ejpam-6089	445	1	we	we	PRON
ejpam-6089	445	2	verify	verify	VERB
ejpam-6089	445	3	the	the	DET
ejpam-6089	445	4	result	result	NOUN
ejpam-6089	445	5	of	of	ADP
ejpam-6089	445	6	theorem	theorem	ADJ
ejpam-6089	445	7	8	8	NUM
ejpam-6089	445	8	for	for	ADP
ejpam-6089	445	9	convex	convex	PROPN
ejpam-6089	445	10	function	function	PROPN
ejpam-6089	445	11	υ(c	υ(c	PROPN
ejpam-6089	445	12	)	)	PUNCT
ejpam-6089	445	13	=	=	SYM
ejpam-6089	445	14	c4n	c4n	PROPN
ejpam-6089	445	15	,	,	PUNCT
ejpam-6089	445	16	n	n	PROPN
ejpam-6089	445	17	∈	∈	PROPN
ejpam-6089	445	18	n	n	NOUN
ejpam-6089	445	19	on	on	ADP
ejpam-6089	445	20	the	the	DET
ejpam-6089	445	21	interval	interval	NOUN
ejpam-6089	445	22	[	[	X
ejpam-6089	445	23	−1	−1	NOUN
ejpam-6089	445	24	,	,	PUNCT
ejpam-6089	445	25	1	1	NUM
ejpam-6089	445	26	]	]	PUNCT
ejpam-6089	445	27	.	.	PUNCT
ejpam-6089	446	1	using	use	VERB
ejpam-6089	446	2	substitution	substitution	NOUN
ejpam-6089	446	3	t	t	NOUN
ejpam-6089	446	4	=	=	PUNCT
ejpam-6089	446	5	ψ	ψ	X
ejpam-6089	446	6	c	c	NOUN
ejpam-6089	446	7	in	in	ADP
ejpam-6089	446	8	left	left	ADJ
ejpam-6089	446	9	and	and	CCONJ
ejpam-6089	446	10	right	right	ADJ
ejpam-6089	446	11	sided	sided	ADJ
ejpam-6089	446	12	reimann	reimann	NOUN
ejpam-6089	446	13	-	-	PUNCT
ejpam-6089	446	14	liouville	liouville	NOUN
ejpam-6089	446	15	integrals	integral	NOUN
ejpam-6089	446	16	(	(	PUNCT
ejpam-6089	446	17	1	1	NUM
ejpam-6089	446	18	)	)	PUNCT
ejpam-6089	446	19	and	and	CCONJ
ejpam-6089	446	20	(	(	PUNCT
ejpam-6089	446	21	2	2	NUM
ejpam-6089	446	22	)	)	PUNCT
ejpam-6089	446	23	,	,	PUNCT
ejpam-6089	446	24	we	we	PRON
ejpam-6089	446	25	get	get	VERB
ejpam-6089	446	26	r−li	r−li	NOUN
ejpam-6089	446	27	(	(	PUNCT
ejpam-6089	446	28	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	446	29	)	)	PUNCT
ejpam-6089	446	30	0	0	NUM
ejpam-6089	447	1	+	+	CCONJ
ejpam-6089	447	2	(	(	PUNCT
ejpam-6089	447	3	1)4n	1)4n	NUM
ejpam-6089	447	4	=	=	SYM
ejpam-6089	447	5	(	(	PUNCT
ejpam-6089	447	6	4n	4n	NOUN
ejpam-6089	447	7	)	)	PUNCT
ejpam-6089	447	8	!	!	PUNCT
ejpam-6089	448	1	γ(ℵð+	γ(ℵð+	PROPN
ejpam-6089	448	2	℘+	℘+	ADP
ejpam-6089	448	3	4n+	4n+	NUM
ejpam-6089	448	4	1	1	NUM
ejpam-6089	448	5	)	)	PUNCT
ejpam-6089	448	6	,	,	PUNCT
ejpam-6089	448	7	(	(	PUNCT
ejpam-6089	448	8	28	28	X
ejpam-6089	448	9	)	)	PUNCT
ejpam-6089	448	10	r−li	r−li	NOUN
ejpam-6089	448	11	(	(	PUNCT
ejpam-6089	448	12	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	448	13	)	)	PUNCT
ejpam-6089	448	14	0	0	NUM
ejpam-6089	449	1	+	+	CCONJ
ejpam-6089	449	2	(	(	PUNCT
ejpam-6089	449	3	−1)4n	−1)4n	NOUN
ejpam-6089	449	4	=	=	SYM
ejpam-6089	449	5	(	(	PUNCT
ejpam-6089	449	6	4n	4n	NOUN
ejpam-6089	449	7	)	)	PUNCT
ejpam-6089	449	8	!	!	PUNCT
ejpam-6089	450	1	γ(ℵð+	γ(ℵð+	PROPN
ejpam-6089	450	2	℘+	℘+	ADP
ejpam-6089	450	3	4n+	4n+	NUM
ejpam-6089	450	4	1	1	NUM
ejpam-6089	450	5	)	)	PUNCT
ejpam-6089	450	6	.	.	PUNCT
ejpam-6089	451	1	(	(	PUNCT
ejpam-6089	451	2	29	29	NUM
ejpam-6089	451	3	)	)	PUNCT
ejpam-6089	451	4	use	use	NOUN
ejpam-6089	451	5	(	(	PUNCT
ejpam-6089	451	6	28	28	NUM
ejpam-6089	451	7	)	)	PUNCT
ejpam-6089	451	8	in	in	ADP
ejpam-6089	451	9	infinite	infinite	ADJ
ejpam-6089	451	10	series	series	NOUN
ejpam-6089	451	11	formula	formula	NOUN
ejpam-6089	451	12	for	for	ADP
ejpam-6089	451	13	left	left	ADJ
ejpam-6089	451	14	prabhakar	prabhakar	NOUN
ejpam-6089	451	15	integral	integral	ADJ
ejpam-6089	451	16	(	(	PUNCT
ejpam-6089	451	17	7	7	NUM
ejpam-6089	451	18	)	)	PUNCT
ejpam-6089	451	19	and	and	CCONJ
ejpam-6089	451	20	(	(	PUNCT
ejpam-6089	451	21	29	29	NUM
ejpam-6089	451	22	)	)	PUNCT
ejpam-6089	451	23	in	in	ADP
ejpam-6089	451	24	infinite	infinite	ADJ
ejpam-6089	451	25	series	series	NOUN
ejpam-6089	451	26	formula	formula	NOUN
ejpam-6089	451	27	for	for	ADP
ejpam-6089	451	28	right	right	ADJ
ejpam-6089	451	29	prabhakar	prabhakar	NOUN
ejpam-6089	451	30	integral	integral	ADJ
ejpam-6089	451	31	(	(	PUNCT
ejpam-6089	451	32	8)	8)	NUM
ejpam-6089	451	33	,	,	PUNCT
ejpam-6089	451	34	we	we	PRON
ejpam-6089	451	35	have	have	AUX
ejpam-6089	451	36	piℵ,℘,γ,	piℵ,℘,γ,	VERB
ejpam-6089	451	37	♭	♭	PRON
ejpam-6089	451	38	0	0	NUM
ejpam-6089	452	1	+	+	CCONJ
ejpam-6089	452	2	(	(	PUNCT
ejpam-6089	452	3	1)4n	1)4n	NOUN
ejpam-6089	452	4	=	=	SYM
ejpam-6089	452	5	∞∑	∞∑	NUM
ejpam-6089	452	6	ð=0	ð=0	PUNCT
ejpam-6089	452	7	γ(γ	γ(γ	PROPN
ejpam-6089	452	8	+	+	CCONJ
ejpam-6089	452	9	ð)	ð)	PUNCT
ejpam-6089	452	10	♭	♭	PROPN
ejpam-6089	452	11	ð	ð	X
ejpam-6089	452	12	γ(γ)ð	γ(γ)ð	PROPN
ejpam-6089	452	13	!	!	PUNCT
ejpam-6089	453	1	(	(	PUNCT
ejpam-6089	453	2	4n	4n	NOUN
ejpam-6089	453	3	)	)	PUNCT
ejpam-6089	453	4	!	!	PUNCT
ejpam-6089	454	1	γ(ℵð+	γ(ℵð+	PROPN
ejpam-6089	454	2	℘+	℘+	ADP
ejpam-6089	454	3	4n+	4n+	NUM
ejpam-6089	454	4	1	1	NUM
ejpam-6089	454	5	)	)	PUNCT
ejpam-6089	454	6	,	,	PUNCT
ejpam-6089	454	7	(	(	PUNCT
ejpam-6089	454	8	30	30	X
ejpam-6089	454	9	)	)	PUNCT
ejpam-6089	454	10	piℵ,℘,γ,	piℵ,℘,γ,	NOUN
ejpam-6089	455	1	♭	♭	NOUN
ejpam-6089	455	2	0−	0−	NUM
ejpam-6089	455	3	(	(	PUNCT
ejpam-6089	455	4	−1)4n	−1)4n	NOUN
ejpam-6089	455	5	=	=	SYM
ejpam-6089	455	6	∞∑	∞∑	NUM
ejpam-6089	455	7	ð=0	ð=0	PUNCT
ejpam-6089	455	8	γ(γ	γ(γ	PROPN
ejpam-6089	455	9	+	+	CCONJ
ejpam-6089	455	10	ð)	ð)	PUNCT
ejpam-6089	455	11	♭	♭	PROPN
ejpam-6089	455	12	ð	ð	X
ejpam-6089	455	13	γ(γ)ð	γ(γ)ð	PROPN
ejpam-6089	455	14	!	!	PUNCT
ejpam-6089	456	1	(	(	PUNCT
ejpam-6089	456	2	4n	4n	X
ejpam-6089	456	3	!	!	PUNCT
ejpam-6089	457	1	γ(ℵð+	γ(ℵð+	PROPN
ejpam-6089	457	2	℘+	℘+	ADP
ejpam-6089	457	3	4n+	4n+	NUM
ejpam-6089	457	4	1	1	NUM
ejpam-6089	457	5	)	)	PUNCT
ejpam-6089	457	6	.	.	PUNCT
ejpam-6089	458	1	(	(	PUNCT
ejpam-6089	458	2	31	31	NUM
ejpam-6089	458	3	)	)	PUNCT
ejpam-6089	458	4	also	also	ADV
ejpam-6089	458	5	substitute	substitute	VERB
ejpam-6089	458	6	(	(	PUNCT
ejpam-6089	458	7	28	28	NUM
ejpam-6089	458	8	)	)	PUNCT
ejpam-6089	458	9	in	in	ADP
ejpam-6089	458	10	left	left	ADJ
ejpam-6089	458	11	sided	side	VERB
ejpam-6089	458	12	generalized	generalized	ADJ
ejpam-6089	458	13	fractional	fractional	ADJ
ejpam-6089	458	14	integral	integral	ADJ
ejpam-6089	458	15	operator	operator	NOUN
ejpam-6089	458	16	(	(	PUNCT
ejpam-6089	458	17	10	10	NUM
ejpam-6089	458	18	)	)	PUNCT
ejpam-6089	458	19	and	and	CCONJ
ejpam-6089	458	20	(	(	PUNCT
ejpam-6089	458	21	29	29	NUM
ejpam-6089	458	22	)	)	PUNCT
ejpam-6089	458	23	in	in	ADP
ejpam-6089	458	24	right	right	ADJ
ejpam-6089	458	25	sided	sided	ADJ
ejpam-6089	458	26	generalized	generalized	ADJ
ejpam-6089	458	27	fractional	fractional	ADJ
ejpam-6089	458	28	integral	integral	ADJ
ejpam-6089	458	29	operator	operator	NOUN
ejpam-6089	458	30	(	(	PUNCT
ejpam-6089	458	31	11	11	NUM
ejpam-6089	458	32	)	)	PUNCT
ejpam-6089	458	33	,	,	PUNCT
ejpam-6089	458	34	we	we	PRON
ejpam-6089	458	35	acquire	acquire	VERB
ejpam-6089	458	36	ε	ε	PROPN
ejpam-6089	458	37	♭	♭	PROPN
ejpam-6089	458	38	,δ	,δ	PUNCT
ejpam-6089	458	39	,	,	PUNCT
ejpam-6089	458	40	b	b	NOUN
ejpam-6089	458	41	,	,	PUNCT
ejpam-6089	458	42	s	s	NOUN
ejpam-6089	458	43	,	,	PUNCT
ejpam-6089	458	44	l	l	NOUN
ejpam-6089	458	45	0+,ℵ,℘,τυ	0+,ℵ,℘,τυ	NUM
ejpam-6089	459	1	(	(	PUNCT
ejpam-6089	459	2	(	(	PUNCT
ejpam-6089	459	3	1)4n	1)4n	NOUN
ejpam-6089	459	4	;	;	PUNCT
ejpam-6089	459	5	g	g	NOUN
ejpam-6089	459	6	)	)	PUNCT
ejpam-6089	459	7	=	=	PUNCT
ejpam-6089	460	1	∞∑	∞∑	NUM
ejpam-6089	460	2	ð=0	ð=0	X
ejpam-6089	460	3	að	að	X
ejpam-6089	460	4	(	(	PUNCT
ejpam-6089	460	5	4n	4n	NOUN
ejpam-6089	460	6	)	)	PUNCT
ejpam-6089	460	7	!	!	PUNCT
ejpam-6089	461	1	γ(ℵð+	γ(ℵð+	PROPN
ejpam-6089	461	2	℘+	℘+	ADP
ejpam-6089	461	3	4n+	4n+	NUM
ejpam-6089	461	4	1	1	NUM
ejpam-6089	461	5	)	)	PUNCT
ejpam-6089	461	6	,	,	PUNCT
ejpam-6089	461	7	(	(	PUNCT
ejpam-6089	461	8	32	32	NUM
ejpam-6089	461	9	)	)	PUNCT
ejpam-6089	461	10	ε	ε	PROPN
ejpam-6089	461	11	♭	♭	PROPN
ejpam-6089	461	12	,δ	,δ	PUNCT
ejpam-6089	461	13	,	,	PUNCT
ejpam-6089	461	14	b	b	NOUN
ejpam-6089	461	15	,	,	PUNCT
ejpam-6089	461	16	s	s	PROPN
ejpam-6089	461	17	,	,	PUNCT
ejpam-6089	461	18	l	l	NOUN
ejpam-6089	461	19	0−,ℵ,℘,τυ	0−,ℵ,℘,τυ	PUNCT
ejpam-6089	462	1	(	(	PUNCT
ejpam-6089	462	2	(	(	PUNCT
ejpam-6089	462	3	−1)4n	−1)4n	NOUN
ejpam-6089	462	4	;	;	PUNCT
ejpam-6089	462	5	g	g	NOUN
ejpam-6089	462	6	)	)	PUNCT
ejpam-6089	462	7	=	=	PUNCT
ejpam-6089	463	1	∞∑	∞∑	NUM
ejpam-6089	463	2	ð=0	ð=0	X
ejpam-6089	463	3	að	að	X
ejpam-6089	463	4	(	(	PUNCT
ejpam-6089	463	5	4n	4n	NOUN
ejpam-6089	463	6	)	)	PUNCT
ejpam-6089	463	7	!	!	PUNCT
ejpam-6089	464	1	γ(ℵð+	γ(ℵð+	PROPN
ejpam-6089	464	2	℘+	℘+	ADP
ejpam-6089	464	3	4n+	4n+	NUM
ejpam-6089	464	4	1	1	NUM
ejpam-6089	464	5	)	)	PUNCT
ejpam-6089	464	6	.	.	PUNCT
ejpam-6089	465	1	(	(	PUNCT
ejpam-6089	465	2	33	33	NUM
ejpam-6089	465	3	)	)	PUNCT
ejpam-6089	465	4	substituting	substitute	VERB
ejpam-6089	465	5	these	these	DET
ejpam-6089	465	6	expressions	expression	NOUN
ejpam-6089	465	7	(	(	PUNCT
ejpam-6089	465	8	30	30	NUM
ejpam-6089	465	9	)	)	PUNCT
ejpam-6089	465	10	,	,	PUNCT
ejpam-6089	465	11	(	(	PUNCT
ejpam-6089	465	12	31	31	NUM
ejpam-6089	465	13	)	)	PUNCT
ejpam-6089	465	14	,	,	PUNCT
ejpam-6089	465	15	(	(	PUNCT
ejpam-6089	465	16	32	32	NUM
ejpam-6089	465	17	)	)	PUNCT
ejpam-6089	465	18	and	and	CCONJ
ejpam-6089	465	19	(	(	PUNCT
ejpam-6089	465	20	33	33	NUM
ejpam-6089	465	21	)	)	PUNCT
ejpam-6089	465	22	in	in	ADP
ejpam-6089	465	23	the	the	DET
ejpam-6089	465	24	inequality	inequality	NOUN
ejpam-6089	465	25	(	(	PUNCT
ejpam-6089	465	26	25	25	NUM
ejpam-6089	465	27	)	)	PUNCT
ejpam-6089	465	28	and	and	CCONJ
ejpam-6089	465	29	after	after	ADP
ejpam-6089	465	30	some	some	DET
ejpam-6089	465	31	simplification	simplification	NOUN
ejpam-6089	465	32	,	,	PUNCT
ejpam-6089	465	33	we	we	PRON
ejpam-6089	465	34	get	get	VERB
ejpam-6089	465	35	04ð	04ð	NOUN
ejpam-6089	465	36	≤	≤	VERB
ejpam-6089	465	37	∞∑	∞∑	NUM
ejpam-6089	465	38	ð=0	ð=0	X
ejpam-6089	465	39	(	(	PUNCT
ejpam-6089	465	40	γ(γ	γ(γ	PROPN
ejpam-6089	465	41	+	+	CCONJ
ejpam-6089	465	42	ð)	ð)	PUNCT
ejpam-6089	465	43	♭	♭	PROPN
ejpam-6089	465	44	ð	ð	X
ejpam-6089	465	45	γ(γ)ð	γ(γ)ð	PROPN
ejpam-6089	465	46	!	!	PUNCT
ejpam-6089	466	1	+	+	CCONJ
ejpam-6089	466	2	að	að	X
ejpam-6089	466	3	)	)	PUNCT
ejpam-6089	466	4	(	(	PUNCT
ejpam-6089	466	5	4n	4n	NOUN
ejpam-6089	466	6	)	)	PUNCT
ejpam-6089	466	7	!	!	PUNCT
ejpam-6089	467	1	γ(ℵð+	γ(ℵð+	PROPN
ejpam-6089	467	2	℘+	℘+	ADP
ejpam-6089	467	3	4n+	4n+	NUM
ejpam-6089	467	4	1	1	NUM
ejpam-6089	467	5	)	)	PUNCT
ejpam-6089	467	6	≤	≤	NOUN
ejpam-6089	468	1	∞∑	∞∑	NUM
ejpam-6089	468	2	ð=0	ð=0	NOUN
ejpam-6089	468	3	hð	hð	VERB
ejpam-6089	468	4	γ(ℵð+	γ(ℵð+	NOUN
ejpam-6089	468	5	℘+	℘+	ADJ
ejpam-6089	468	6	1	1	NUM
ejpam-6089	468	7	)	)	PUNCT
ejpam-6089	468	8	.	.	PUNCT
ejpam-6089	469	1	3	3	X
ejpam-6089	469	2	.	.	X
ejpam-6089	469	3	applications	application	NOUN
ejpam-6089	469	4	of	of	ADP
ejpam-6089	469	5	key	key	ADJ
ejpam-6089	469	6	results	result	NOUN
ejpam-6089	469	7	in	in	ADP
ejpam-6089	469	8	terms	term	NOUN
ejpam-6089	469	9	of	of	ADP
ejpam-6089	469	10	means	mean	NOUN
ejpam-6089	469	11	(	(	PUNCT
ejpam-6089	469	12	h−h	h−h	NOUN
ejpam-6089	469	13	)	)	PUNCT
ejpam-6089	469	14	inequality	inequality	NOUN
ejpam-6089	469	15	are	be	AUX
ejpam-6089	469	16	often	often	ADV
ejpam-6089	469	17	connected	connect	VERB
ejpam-6089	469	18	to	to	ADP
ejpam-6089	469	19	additional	additional	ADJ
ejpam-6089	469	20	integral	integral	ADJ
ejpam-6089	469	21	inequalities	inequality	NOUN
ejpam-6089	469	22	,	,	PUNCT
ejpam-6089	469	23	such	such	ADJ
ejpam-6089	469	24	as	as	ADP
ejpam-6089	469	25	trapezoid	trapezoid	NOUN
ejpam-6089	469	26	-	-	PUNCT
ejpam-6089	469	27	type	type	NOUN
ejpam-6089	469	28	(	(	PUNCT
ejpam-6089	469	29	utilizing	utilize	VERB
ejpam-6089	469	30	the	the	DET
ejpam-6089	469	31	interval	interval	NOUN
ejpam-6089	469	32	’s	’s	PART
ejpam-6089	469	33	endpoints	endpoint	NOUN
ejpam-6089	469	34	ℑ1	ℑ1	PROPN
ejpam-6089	469	35	and	and	CCONJ
ejpam-6089	469	36	ℑ2	ℑ2	VERB
ejpam-6089	469	37	)	)	PUNCT
ejpam-6089	469	38	and	and	CCONJ
ejpam-6089	469	39	midpoint	midpoint	NOUN
ejpam-6089	469	40	-	-	PUNCT
ejpam-6089	469	41	type	type	NOUN
ejpam-6089	469	42	(	(	PUNCT
ejpam-6089	469	43	utilizing	utilize	VERB
ejpam-6089	469	44	the	the	DET
ejpam-6089	469	45	midpoint	midpoint	NOUN
ejpam-6089	469	46	(	(	PUNCT
ejpam-6089	469	47	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	469	48	2	2	NUM
ejpam-6089	469	49	)	)	PUNCT
ejpam-6089	469	50	of	of	ADP
ejpam-6089	469	51	the	the	DET
ejpam-6089	469	52	interval	interval	NOUN
ejpam-6089	469	53	)	)	PUNCT
ejpam-6089	469	54	.	.	PUNCT
ejpam-6089	470	1	many	many	ADJ
ejpam-6089	470	2	researchers	researcher	NOUN
ejpam-6089	470	3	have	have	AUX
ejpam-6089	470	4	contributed	contribute	VERB
ejpam-6089	470	5	to	to	ADP
ejpam-6089	470	6	establishing	establish	VERB
ejpam-6089	470	7	these	these	DET
ejpam-6089	470	8	inequalities	inequality	NOUN
ejpam-6089	470	9	[	[	X
ejpam-6089	470	10	15	15	NUM
ejpam-6089	470	11	,	,	PUNCT
ejpam-6089	470	12	38	38	NUM
ejpam-6089	470	13	]	]	PUNCT
ejpam-6089	470	14	.	.	PUNCT
ejpam-6089	471	1	in	in	ADP
ejpam-6089	471	2	this	this	DET
ejpam-6089	471	3	section	section	NOUN
ejpam-6089	471	4	,	,	PUNCT
ejpam-6089	471	5	we	we	PRON
ejpam-6089	471	6	employed	employ	VERB
ejpam-6089	471	7	an	an	DET
ejpam-6089	471	8	equality	equality	NOUN
ejpam-6089	471	9	of	of	ADP
ejpam-6089	471	10	trapezoid	trapezoid	ADJ
ejpam-6089	471	11	type	type	NOUN
ejpam-6089	471	12	and	and	CCONJ
ejpam-6089	471	13	an	an	DET
ejpam-6089	471	14	inequality	inequality	NOUN
ejpam-6089	471	15	of	of	ADP
ejpam-6089	471	16	midpoint	midpoint	NOUN
ejpam-6089	471	17	type	type	NOUN
ejpam-6089	471	18	for	for	ADP
ejpam-6089	471	19	the	the	DET
ejpam-6089	471	20	(	(	PUNCT
ejpam-6089	471	21	h−h	h−h	NOUN
ejpam-6089	471	22	)	)	PUNCT
ejpam-6089	471	23	integrals	integral	NOUN
ejpam-6089	471	24	.	.	PUNCT
ejpam-6089	472	1	s.	s.	PROPN
ejpam-6089	472	2	naheed	nahee	VERB
ejpam-6089	472	3	et	et	PROPN
ejpam-6089	472	4	al	al	PROPN
ejpam-6089	472	5	.	.	PUNCT
ejpam-6089	472	6	/	/	SYM
ejpam-6089	472	7	eur	eur	PROPN
ejpam-6089	472	8	.	.	PUNCT
ejpam-6089	473	1	j.	j.	PROPN
ejpam-6089	473	2	pure	pure	PROPN
ejpam-6089	473	3	appl	appl	PROPN
ejpam-6089	473	4	.	.	PROPN
ejpam-6089	473	5	math	math	PROPN
ejpam-6089	473	6	,	,	PUNCT
ejpam-6089	473	7	18	18	NUM
ejpam-6089	473	8	(	(	PUNCT
ejpam-6089	473	9	2	2	NUM
ejpam-6089	473	10	)	)	PUNCT
ejpam-6089	473	11	(	(	PUNCT
ejpam-6089	473	12	2025	2025	NUM
ejpam-6089	473	13	)	)	PUNCT
ejpam-6089	473	14	,	,	PUNCT
ejpam-6089	473	15	6089	6089	NUM
ejpam-6089	473	16	22	22	NUM
ejpam-6089	473	17	of	of	ADP
ejpam-6089	473	18	34	34	NUM
ejpam-6089	473	19	figure	figure	NOUN
ejpam-6089	473	20	3	3	NUM
ejpam-6089	473	21	:	:	PUNCT
ejpam-6089	473	22	the	the	DET
ejpam-6089	473	23	2d	2d	NOUN
ejpam-6089	473	24	graph	graph	NOUN
ejpam-6089	473	25	exhibiting	exhibit	VERB
ejpam-6089	473	26	the	the	DET
ejpam-6089	473	27	inequality	inequality	NOUN
ejpam-6089	473	28	(	(	PUNCT
ejpam-6089	473	29	25	25	NUM
ejpam-6089	473	30	)	)	PUNCT
ejpam-6089	473	31	for	for	ADP
ejpam-6089	473	32	ð	ð	PROPN
ejpam-6089	473	33	=	=	SYM
ejpam-6089	473	34	1	1	X
ejpam-6089	473	35	.	.	X
ejpam-6089	473	36	figure	figure	VERB
ejpam-6089	473	37	4	4	NUM
ejpam-6089	473	38	:	:	PUNCT
ejpam-6089	473	39	the	the	DET
ejpam-6089	473	40	3d	3d	NOUN
ejpam-6089	473	41	graph	graph	NOUN
ejpam-6089	473	42	exhibiting	exhibit	VERB
ejpam-6089	473	43	the	the	DET
ejpam-6089	473	44	inequality	inequality	NOUN
ejpam-6089	473	45	(	(	PUNCT
ejpam-6089	473	46	25	25	NUM
ejpam-6089	473	47	)	)	PUNCT
ejpam-6089	473	48	for	for	ADP
ejpam-6089	473	49	convex	convex	PROPN
ejpam-6089	473	50	function	function	PROPN
ejpam-6089	473	51	υ(c	υ(c	PROPN
ejpam-6089	473	52	)	)	PUNCT
ejpam-6089	473	53	=	=	PRON
ejpam-6089	473	54	(	(	PUNCT
ejpam-6089	473	55	c)4ð	c)4ð	PROPN
ejpam-6089	473	56	on	on	ADP
ejpam-6089	473	57	the	the	DET
ejpam-6089	473	58	interval	interval	NOUN
ejpam-6089	473	59	[	[	X
ejpam-6089	473	60	−1	−1	NOUN
ejpam-6089	473	61	,	,	PUNCT
ejpam-6089	473	62	1	1	NUM
ejpam-6089	473	63	]	]	PUNCT
ejpam-6089	473	64	and	and	CCONJ
ejpam-6089	473	65	for	for	ADP
ejpam-6089	473	66	ð	ð	PROPN
ejpam-6089	473	67	=	=	SYM
ejpam-6089	473	68	1	1	NUM
ejpam-6089	473	69	.	.	NUM
ejpam-6089	473	70	3.1	3.1	NUM
ejpam-6089	473	71	.	.	PUNCT
ejpam-6089	474	1	an	an	DET
ejpam-6089	474	2	equality	equality	NOUN
ejpam-6089	474	3	of	of	ADP
ejpam-6089	474	4	trapezoid	trapezoid	ADJ
ejpam-6089	474	5	type	type	NOUN
ejpam-6089	474	6	for	for	ADP
ejpam-6089	474	7	the	the	DET
ejpam-6089	474	8	hermite	hermite	PROPN
ejpam-6089	474	9	-	-	PUNCT
ejpam-6089	474	10	hadamard	hadamard	ADJ
ejpam-6089	474	11	integrals	integral	NOUN
ejpam-6089	474	12	lemma	lemma	PROPN
ejpam-6089	474	13	3	3	X
ejpam-6089	474	14	.	.	PUNCT
ejpam-6089	475	1	let	let	VERB
ejpam-6089	475	2	υ	υ	NOUN
ejpam-6089	475	3	:	:	PUNCT
ejpam-6089	475	4	[	[	X
ejpam-6089	475	5	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	475	6	]	]	PUNCT
ejpam-6089	475	7	→	→	SYM
ejpam-6089	475	8	ℜ	ℜ	PROPN
ejpam-6089	475	9	is	be	AUX
ejpam-6089	475	10	an	an	DET
ejpam-6089	475	11	l1	l1	PROPN
ejpam-6089	475	12	function	function	NOUN
ejpam-6089	475	13	and	and	CCONJ
ejpam-6089	475	14	(	(	PUNCT
ejpam-6089	475	15	ℵð+	ℵð+	ADJ
ejpam-6089	475	16	℘	℘	PROPN
ejpam-6089	475	17	)	)	PUNCT
ejpam-6089	475	18	∈	∈	PROPN
ejpam-6089	475	19	(	(	PUNCT
ejpam-6089	475	20	0	0	NUM
ejpam-6089	475	21	,	,	PUNCT
ejpam-6089	475	22	1	1	NUM
ejpam-6089	475	23	)	)	PUNCT
ejpam-6089	475	24	also	also	ADV
ejpam-6089	475	25	a	a	DET
ejpam-6089	475	26	differentiable	differentiable	ADJ
ejpam-6089	475	27	function	function	NOUN
ejpam-6089	475	28	on	on	ADP
ejpam-6089	475	29	(	(	PUNCT
ejpam-6089	475	30	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	475	31	)	)	PUNCT
ejpam-6089	475	32	with	with	ADP
ejpam-6089	475	33	ℑ1	ℑ1	NOUN
ejpam-6089	475	34	<	<	X
ejpam-6089	475	35	ℑ2	ℑ2	PROPN
ejpam-6089	475	36	,	,	PUNCT
ejpam-6089	475	37	and	and	CCONJ
ejpam-6089	475	38	assume	assume	VERB
ejpam-6089	475	39	υ′	υ′	NOUN
ejpam-6089	475	40	∈	∈	NOUN
ejpam-6089	475	41	l1[ℑ1,ℑ2	l1[ℑ1,ℑ2	PROPN
ejpam-6089	475	42	]	]	PUNCT
ejpam-6089	475	43	.	.	PUNCT
ejpam-6089	476	1	consider	consider	VERB
ejpam-6089	476	2	♭	♭	PRON
ejpam-6089	476	3	,	,	PUNCT
ejpam-6089	476	4	ℵ	ℵ	NOUN
ejpam-6089	476	5	,	,	PUNCT
ejpam-6089	476	6	℘	℘	PROPN
ejpam-6089	476	7	,	,	PUNCT
ejpam-6089	476	8	τ	τ	PROPN
ejpam-6089	476	9	,	,	PUNCT
ejpam-6089	476	10	δ	δ	PROPN
ejpam-6089	476	11	,	,	PUNCT
ejpam-6089	476	12	b	b	PROPN
ejpam-6089	476	13	∈	∈	PROPN
ejpam-6089	476	14	c	c	NOUN
ejpam-6089	476	15	with	with	ADP
ejpam-6089	476	16	ℜ(ℵ),ℜ(℘),ℜ(τ	ℜ(ℵ),ℜ(℘),ℜ(τ	PROPN
ejpam-6089	476	17	)	)	PUNCT
ejpam-6089	476	18	>	>	X
ejpam-6089	476	19	0	0	NUM
ejpam-6089	476	20	and	and	CCONJ
ejpam-6089	476	21	ℜ(b	ℜ(b	NOUN
ejpam-6089	476	22	)	)	PUNCT
ejpam-6089	476	23	>	>	X
ejpam-6089	477	1	ℜ(δ	ℜ(δ	X
ejpam-6089	477	2	)	)	PUNCT
ejpam-6089	477	3	>	>	X
ejpam-6089	477	4	0	0	X
ejpam-6089	477	5	.	.	PUNCT
ejpam-6089	478	1	moreover	moreover	ADV
ejpam-6089	478	2	,	,	PUNCT
ejpam-6089	478	3	let	let	VERB
ejpam-6089	478	4	g	g	PROPN
ejpam-6089	478	5	≥	≥	NOUN
ejpam-6089	478	6	0	0	NUM
ejpam-6089	478	7	,	,	PUNCT
ejpam-6089	478	8	l	l	NOUN
ejpam-6089	478	9	>	>	X
ejpam-6089	478	10	0	0	PUNCT
ejpam-6089	478	11	and	and	CCONJ
ejpam-6089	478	12	0	0	NUM
ejpam-6089	478	13	<	<	X
ejpam-6089	478	14	s	s	X
ejpam-6089	478	15	≤	≤	NUM
ejpam-6089	478	16	l	l	NOUN
ejpam-6089	478	17	+	+	CCONJ
ejpam-6089	478	18	ℜ(ℵ	ℜ(ℵ	NOUN
ejpam-6089	478	19	)	)	PUNCT
ejpam-6089	478	20	with	with	ADP
ejpam-6089	478	21	(	(	PUNCT
ejpam-6089	478	22	ℵð+	ℵð+	ADJ
ejpam-6089	478	23	℘	℘	PROPN
ejpam-6089	478	24	)	)	PUNCT
ejpam-6089	478	25	>	>	X
ejpam-6089	478	26	0	0	NUM
ejpam-6089	478	27	,	,	PUNCT
ejpam-6089	478	28	then	then	ADV
ejpam-6089	478	29	we	we	PRON
ejpam-6089	478	30	have	have	VERB
ejpam-6089	478	31	ε	ε	PROPN
ejpam-6089	478	32	♭	♭	PROPN
ejpam-6089	478	33	,δ	,δ	PUNCT
ejpam-6089	478	34	,	,	PUNCT
ejpam-6089	478	35	b	b	NOUN
ejpam-6089	478	36	,	,	PUNCT
ejpam-6089	478	37	s	s	NOUN
ejpam-6089	478	38	,	,	PUNCT
ejpam-6089	478	39	lℑ1+,ℵ,℘,τυ(ℑ2	lℑ1+,ℵ,℘,τυ(ℑ2	NOUN
ejpam-6089	478	40	;	;	PUNCT
ejpam-6089	478	41	g	g	NOUN
ejpam-6089	478	42	)	)	PUNCT
ejpam-6089	479	1	+	+	CCONJ
ejpam-6089	479	2	ε	ε	PROPN
ejpam-6089	479	3	♭	♭	PROPN
ejpam-6089	479	4	,δ	,δ	PUNCT
ejpam-6089	479	5	,	,	PUNCT
ejpam-6089	479	6	b	b	NOUN
ejpam-6089	479	7	,	,	PUNCT
ejpam-6089	479	8	s	s	PROPN
ejpam-6089	479	9	,	,	PUNCT
ejpam-6089	479	10	lℑ2−,ℵ,℘,τυ(ℑ1	lℑ2−,ℵ,℘,τυ(ℑ1	PROPN
ejpam-6089	479	11	;	;	PUNCT
ejpam-6089	479	12	g	g	NOUN
ejpam-6089	479	13	)	)	PUNCT
ejpam-6089	479	14	=	=	PUNCT
ejpam-6089	480	1	∞∑	∞∑	NUM
ejpam-6089	480	2	ð=0	ð=0	X
ejpam-6089	480	3	aðvð	aðvð	NOUN
ejpam-6089	480	4	(	(	PUNCT
ejpam-6089	480	5	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	480	6	)	)	PUNCT
ejpam-6089	480	7	+	+	CCONJ
ejpam-6089	480	8	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	480	9	)	)	PUNCT
ejpam-6089	480	10	2	2	NUM
ejpam-6089	480	11	)	)	PUNCT
ejpam-6089	480	12	−	−	PROPN
ejpam-6089	481	1	∞∑	∞∑	NUM
ejpam-6089	481	2	ð=0	ð=0	SYM
ejpam-6089	481	3	aðvð	aðvð	NOUN
ejpam-6089	481	4	×	×	NOUN
ejpam-6089	481	5	(	(	PUNCT
ejpam-6089	481	6	ℑ2	ℑ2	PROPN
ejpam-6089	481	7	−ℑ1	−ℑ1	PROPN
ejpam-6089	481	8	2	2	NUM
ejpam-6089	481	9	∫	∫	NOUN
ejpam-6089	481	10	1	1	NUM
ejpam-6089	481	11	0	0	NUM
ejpam-6089	481	12	(	(	PUNCT
ejpam-6089	481	13	(	(	PUNCT
ejpam-6089	481	14	1−	1−	NUM
ejpam-6089	481	15	t)(ℵð+℘	t)(ℵð+℘	NOUN
ejpam-6089	481	16	)	)	PUNCT
ejpam-6089	481	17	−	−	PROPN
ejpam-6089	481	18	t(ℵð+℘	t(ℵð+℘	NUM
ejpam-6089	481	19	)	)	PUNCT
ejpam-6089	481	20	)	)	PUNCT
ejpam-6089	482	1	υ′(tℑ1	υ′(tℑ1	NOUN
ejpam-6089	482	2	+	+	CCONJ
ejpam-6089	482	3	(	(	PUNCT
ejpam-6089	482	4	1−	1−	NUM
ejpam-6089	482	5	t)ℑ2)dt	t)ℑ2)dt	NOUN
ejpam-6089	482	6	)	)	PUNCT
ejpam-6089	482	7	,	,	PUNCT
ejpam-6089	482	8	where	where	SCONJ
ejpam-6089	482	9	að	að	PROPN
ejpam-6089	482	10	=	=	SYM
ejpam-6089	482	11	bg(δ+ðs	bg(δ+ðs	PROPN
ejpam-6089	482	12	,	,	PUNCT
ejpam-6089	482	13	b−δ	b−δ	NOUN
ejpam-6089	482	14	)	)	PUNCT
ejpam-6089	482	15	b(δ	b(δ	NOUN
ejpam-6089	482	16	,	,	PUNCT
ejpam-6089	482	17	b−δ	b−δ	NOUN
ejpam-6089	482	18	)	)	PUNCT
ejpam-6089	482	19	(	(	PUNCT
ejpam-6089	482	20	b)ðs	b)ðs	PROPN
ejpam-6089	482	21	♭	♭	PROPN
ejpam-6089	482	22	ð	ð	X
ejpam-6089	482	23	(	(	PUNCT
ejpam-6089	482	24	τ)ðl	τ)ðl	PROPN
ejpam-6089	482	25	and	and	CCONJ
ejpam-6089	482	26	vð	vð	VERB
ejpam-6089	482	27	=	=	SYM
ejpam-6089	482	28	2(ℑ2−ℑ1)(ℵð+℘	2(ℑ2−ℑ1)(ℵð+℘	NUM
ejpam-6089	482	29	)	)	PUNCT
ejpam-6089	482	30	γ((ℵð+℘)+1	γ((ℵð+℘)+1	NOUN
ejpam-6089	482	31	)	)	PUNCT
ejpam-6089	482	32	.	.	PUNCT
ejpam-6089	483	1	proof	proof	NOUN
ejpam-6089	483	2	.	.	PUNCT
ejpam-6089	484	1	replacing	replace	VERB
ejpam-6089	484	2	α∗	α∗	NOUN
ejpam-6089	484	3	by	by	ADP
ejpam-6089	484	4	(	(	PUNCT
ejpam-6089	484	5	ℵð+	ℵð+	ADJ
ejpam-6089	484	6	℘	℘	PROPN
ejpam-6089	484	7	)	)	PUNCT
ejpam-6089	484	8	in	in	ADP
ejpam-6089	484	9	lemma	lemma	PROPN
ejpam-6089	484	10	1	1	NUM
ejpam-6089	484	11	,	,	PUNCT
ejpam-6089	484	12	we	we	PRON
ejpam-6089	484	13	get	get	VERB
ejpam-6089	484	14	(	(	PUNCT
ejpam-6089	484	15	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	484	16	)	)	PUNCT
ejpam-6089	484	17	+	+	CCONJ
ejpam-6089	485	1	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	485	2	)	)	PUNCT
ejpam-6089	485	3	2	2	NUM
ejpam-6089	485	4	)	)	PUNCT
ejpam-6089	486	1	−	−	PROPN
ejpam-6089	486	2	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	486	3	℘	℘	PROPN
ejpam-6089	486	4	)	)	PUNCT
ejpam-6089	486	5	+	+	CCONJ
ejpam-6089	486	6	1	1	NUM
ejpam-6089	486	7	)	)	PUNCT
ejpam-6089	486	8	2(ℑ2	2(ℑ2	NUM
ejpam-6089	486	9	−ℑ1)(ℵð+℘	−ℑ1)(ℵð+℘	NUM
ejpam-6089	486	10	)	)	PUNCT
ejpam-6089	486	11	(	(	PUNCT
ejpam-6089	486	12	r−li	r−li	NOUN
ejpam-6089	486	13	(	(	PUNCT
ejpam-6089	486	14	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	486	15	)	)	PUNCT
ejpam-6089	486	16	ℑ1	ℑ1	NOUN
ejpam-6089	486	17	+	+	CCONJ
ejpam-6089	486	18	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	486	19	)	)	PUNCT
ejpam-6089	487	1	+	+	NUM
ejpam-6089	487	2	r−li	r−li	NOUN
ejpam-6089	487	3	(	(	PUNCT
ejpam-6089	487	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	487	5	)	)	PUNCT
ejpam-6089	487	6	ℑ2−	ℑ2−	NUM
ejpam-6089	488	1	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	488	2	)	)	PUNCT
ejpam-6089	488	3	)	)	PUNCT
ejpam-6089	489	1	=	=	PUNCT
ejpam-6089	489	2	ℑ2	ℑ2	PROPN
ejpam-6089	489	3	−ℑ1	−ℑ1	NOUN
ejpam-6089	489	4	2	2	NUM
ejpam-6089	489	5	∫	∫	NOUN
ejpam-6089	489	6	1	1	NUM
ejpam-6089	489	7	0	0	NUM
ejpam-6089	489	8	(	(	PUNCT
ejpam-6089	489	9	(	(	PUNCT
ejpam-6089	489	10	1−	1−	NUM
ejpam-6089	489	11	t)(ℵð+℘	t)(ℵð+℘	NOUN
ejpam-6089	489	12	)	)	PUNCT
ejpam-6089	489	13	−	−	PROPN
ejpam-6089	489	14	t(ℵð+℘	t(ℵð+℘	NUM
ejpam-6089	489	15	)	)	PUNCT
ejpam-6089	489	16	)	)	PUNCT
ejpam-6089	489	17	υ′(tℑ1	υ′(tℑ1	NOUN
ejpam-6089	489	18	+	+	CCONJ
ejpam-6089	489	19	(	(	PUNCT
ejpam-6089	489	20	1−	1−	NUM
ejpam-6089	489	21	t)ℑ2)dt	t)ℑ2)dt	PROPN
ejpam-6089	489	22	.	.	PUNCT
ejpam-6089	490	1	s.	s.	PROPN
ejpam-6089	490	2	naheed	nahee	VERB
ejpam-6089	490	3	et	et	PROPN
ejpam-6089	490	4	al	al	PROPN
ejpam-6089	490	5	.	.	PUNCT
ejpam-6089	490	6	/	/	SYM
ejpam-6089	490	7	eur	eur	PROPN
ejpam-6089	490	8	.	.	PUNCT
ejpam-6089	491	1	j.	j.	PROPN
ejpam-6089	491	2	pure	pure	PROPN
ejpam-6089	491	3	appl	appl	PROPN
ejpam-6089	491	4	.	.	PROPN
ejpam-6089	491	5	math	math	PROPN
ejpam-6089	491	6	,	,	PUNCT
ejpam-6089	491	7	18	18	NUM
ejpam-6089	491	8	(	(	PUNCT
ejpam-6089	491	9	2	2	NUM
ejpam-6089	491	10	)	)	PUNCT
ejpam-6089	491	11	(	(	PUNCT
ejpam-6089	491	12	2025	2025	NUM
ejpam-6089	491	13	)	)	PUNCT
ejpam-6089	491	14	,	,	PUNCT
ejpam-6089	491	15	6089	6089	NUM
ejpam-6089	491	16	23	23	NUM
ejpam-6089	491	17	of	of	ADP
ejpam-6089	491	18	34	34	NUM
ejpam-6089	491	19	multiplying	multiply	VERB
ejpam-6089	491	20	the	the	DET
ejpam-6089	491	21	above	above	ADJ
ejpam-6089	491	22	equation	equation	NOUN
ejpam-6089	491	23	with	with	ADP
ejpam-6089	491	24	2(ℑ2−ℑ1)(ℵð+℘	2(ℑ2−ℑ1)(ℵð+℘	NUM
ejpam-6089	491	25	)	)	PUNCT
ejpam-6089	491	26	γ((ℵð+℘)+1	γ((ℵð+℘)+1	NOUN
ejpam-6089	491	27	)	)	PUNCT
ejpam-6089	492	1	,	,	PUNCT
ejpam-6089	492	2	we	we	PRON
ejpam-6089	492	3	get	get	VERB
ejpam-6089	492	4	2(ℑ2	2(ℑ2	NUM
ejpam-6089	492	5	−ℑ1	−ℑ1	NOUN
ejpam-6089	492	6	)	)	PUNCT
ejpam-6089	492	7	(	(	PUNCT
ejpam-6089	492	8	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	492	9	)	)	PUNCT
ejpam-6089	492	10	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	492	11	℘	℘	PROPN
ejpam-6089	492	12	)	)	PUNCT
ejpam-6089	492	13	+	+	CCONJ
ejpam-6089	492	14	1	1	X
ejpam-6089	492	15	)	)	PUNCT
ejpam-6089	492	16	(	(	PUNCT
ejpam-6089	492	17	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	492	18	)	)	PUNCT
ejpam-6089	492	19	+	+	CCONJ
ejpam-6089	492	20	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	492	21	)	)	PUNCT
ejpam-6089	492	22	2	2	NUM
ejpam-6089	492	23	)	)	PUNCT
ejpam-6089	492	24	−	−	PROPN
ejpam-6089	492	25	(	(	PUNCT
ejpam-6089	492	26	r−li	r−li	NOUN
ejpam-6089	492	27	(	(	PUNCT
ejpam-6089	492	28	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	492	29	)	)	PUNCT
ejpam-6089	492	30	ℑ1	ℑ1	NOUN
ejpam-6089	492	31	+	+	CCONJ
ejpam-6089	492	32	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	492	33	)	)	PUNCT
ejpam-6089	493	1	+	+	NUM
ejpam-6089	493	2	r−li	r−li	NOUN
ejpam-6089	493	3	(	(	PUNCT
ejpam-6089	493	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	493	5	)	)	PUNCT
ejpam-6089	493	6	ℑ2−	ℑ2−	NUM
ejpam-6089	494	1	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	494	2	)	)	PUNCT
ejpam-6089	494	3	)	)	PUNCT
ejpam-6089	495	1	=	=	PUNCT
ejpam-6089	495	2	2(ℑ2	2(ℑ2	NUM
ejpam-6089	495	3	−ℑ1	−ℑ1	NOUN
ejpam-6089	495	4	)	)	PUNCT
ejpam-6089	495	5	(	(	PUNCT
ejpam-6089	495	6	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	495	7	)	)	PUNCT
ejpam-6089	495	8	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	495	9	℘	℘	PROPN
ejpam-6089	495	10	)	)	PUNCT
ejpam-6089	495	11	+	+	CCONJ
ejpam-6089	495	12	1	1	X
ejpam-6089	495	13	)	)	PUNCT
ejpam-6089	495	14	×	×	NOUN
ejpam-6089	495	15	(	(	PUNCT
ejpam-6089	495	16	ℑ2	ℑ2	PROPN
ejpam-6089	495	17	−ℑ1	−ℑ1	PROPN
ejpam-6089	495	18	2	2	NUM
ejpam-6089	495	19	∫	∫	NOUN
ejpam-6089	495	20	1	1	NUM
ejpam-6089	495	21	0	0	NUM
ejpam-6089	495	22	(	(	PUNCT
ejpam-6089	495	23	(	(	PUNCT
ejpam-6089	495	24	1−	1−	NUM
ejpam-6089	495	25	t)(ℵð+℘	t)(ℵð+℘	NOUN
ejpam-6089	495	26	)	)	PUNCT
ejpam-6089	496	1	−	−	ADP
ejpam-6089	496	2	tℵð+℘	tℵð+℘	PROPN
ejpam-6089	496	3	)	)	PUNCT
ejpam-6089	496	4	υ′(tℑ1	υ′(tℑ1	NOUN
ejpam-6089	496	5	+	+	CCONJ
ejpam-6089	496	6	(	(	PUNCT
ejpam-6089	496	7	1−	1−	NUM
ejpam-6089	496	8	t)ℑ2)dt	t)ℑ2)dt	NOUN
ejpam-6089	496	9	)	)	PUNCT
ejpam-6089	496	10	.	.	PUNCT
ejpam-6089	497	1	again	again	ADV
ejpam-6089	497	2	the	the	DET
ejpam-6089	497	3	above	above	ADJ
ejpam-6089	497	4	expression	expression	NOUN
ejpam-6089	497	5	is	be	AUX
ejpam-6089	497	6	multiplied	multiply	VERB
ejpam-6089	497	7	with	with	ADP
ejpam-6089	497	8	að	að	PRON
ejpam-6089	497	9	to	to	PART
ejpam-6089	497	10	get	get	VERB
ejpam-6089	497	11	að	að	PROPN
ejpam-6089	497	12	2(ℑ2	2(ℑ2	NUM
ejpam-6089	497	13	−ℑ1	−ℑ1	NOUN
ejpam-6089	497	14	)	)	PUNCT
ejpam-6089	497	15	(	(	PUNCT
ejpam-6089	497	16	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	497	17	)	)	PUNCT
ejpam-6089	497	18	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	497	19	℘	℘	PROPN
ejpam-6089	497	20	)	)	PUNCT
ejpam-6089	498	1	+	+	CCONJ
ejpam-6089	498	2	1	1	X
ejpam-6089	498	3	)	)	PUNCT
ejpam-6089	498	4	(	(	PUNCT
ejpam-6089	498	5	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	498	6	)	)	PUNCT
ejpam-6089	498	7	+	+	CCONJ
ejpam-6089	498	8	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	498	9	)	)	PUNCT
ejpam-6089	498	10	2	2	NUM
ejpam-6089	498	11	)	)	PUNCT
ejpam-6089	499	1	−	−	PROPN
ejpam-6089	499	2	að	að	PROPN
ejpam-6089	499	3	(	(	PUNCT
ejpam-6089	499	4	r−li	r−li	NOUN
ejpam-6089	499	5	(	(	PUNCT
ejpam-6089	499	6	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	499	7	)	)	PUNCT
ejpam-6089	499	8	ℑ1	ℑ1	NOUN
ejpam-6089	499	9	+	+	CCONJ
ejpam-6089	499	10	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	499	11	)	)	PUNCT
ejpam-6089	500	1	+	+	NUM
ejpam-6089	500	2	r−li	r−li	NOUN
ejpam-6089	500	3	(	(	PUNCT
ejpam-6089	500	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	500	5	)	)	PUNCT
ejpam-6089	500	6	ℑ2−	ℑ2−	NUM
ejpam-6089	501	1	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	501	2	)	)	PUNCT
ejpam-6089	501	3	)	)	PUNCT
ejpam-6089	502	1	=	=	PUNCT
ejpam-6089	502	2	að	að	X
ejpam-6089	502	3	2(ℑ2	2(ℑ2	NUM
ejpam-6089	502	4	−ℑ1	−ℑ1	NOUN
ejpam-6089	502	5	)	)	PUNCT
ejpam-6089	502	6	(	(	PUNCT
ejpam-6089	502	7	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	502	8	)	)	PUNCT
ejpam-6089	502	9	γ(ℵð+	γ(ℵð+	NOUN
ejpam-6089	502	10	℘+	℘+	ADJ
ejpam-6089	502	11	1	1	NUM
ejpam-6089	502	12	)	)	PUNCT
ejpam-6089	502	13	×	×	NOUN
ejpam-6089	502	14	(	(	PUNCT
ejpam-6089	502	15	ℑ2	ℑ2	PROPN
ejpam-6089	502	16	−ℑ1	−ℑ1	PROPN
ejpam-6089	502	17	2	2	NUM
ejpam-6089	502	18	∫	∫	NOUN
ejpam-6089	502	19	1	1	NUM
ejpam-6089	502	20	0	0	NUM
ejpam-6089	502	21	(	(	PUNCT
ejpam-6089	502	22	(	(	PUNCT
ejpam-6089	502	23	1−	1−	NUM
ejpam-6089	502	24	t)(ℵð+℘	t)(ℵð+℘	NOUN
ejpam-6089	502	25	)	)	PUNCT
ejpam-6089	502	26	−	−	PROPN
ejpam-6089	502	27	t(ℵð+℘	t(ℵð+℘	NUM
ejpam-6089	502	28	)	)	PUNCT
ejpam-6089	502	29	)	)	PUNCT
ejpam-6089	502	30	υ′(tℑ1	υ′(tℑ1	NOUN
ejpam-6089	503	1	+	+	CCONJ
ejpam-6089	503	2	(	(	PUNCT
ejpam-6089	503	3	1−	1−	NUM
ejpam-6089	503	4	t)ℑ2)dt	t)ℑ2)dt	NOUN
ejpam-6089	503	5	)	)	PUNCT
ejpam-6089	503	6	.	.	PUNCT
ejpam-6089	504	1	summing	sum	VERB
ejpam-6089	504	2	over	over	ADP
ejpam-6089	504	3	all	all	DET
ejpam-6089	504	4	ð	ð	NOUN
ejpam-6089	504	5	∞∑	∞∑	NUM
ejpam-6089	504	6	ð=0	ð=0	X
ejpam-6089	504	7	að	að	PROPN
ejpam-6089	504	8	2(ℑ2	2(ℑ2	NUM
ejpam-6089	504	9	−ℑ1	−ℑ1	NOUN
ejpam-6089	504	10	)	)	PUNCT
ejpam-6089	504	11	(	(	PUNCT
ejpam-6089	504	12	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	504	13	)	)	PUNCT
ejpam-6089	504	14	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	504	15	℘	℘	PROPN
ejpam-6089	504	16	)	)	PUNCT
ejpam-6089	504	17	+	+	CCONJ
ejpam-6089	504	18	1	1	X
ejpam-6089	504	19	)	)	PUNCT
ejpam-6089	504	20	(	(	PUNCT
ejpam-6089	504	21	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	504	22	)	)	PUNCT
ejpam-6089	504	23	+	+	CCONJ
ejpam-6089	504	24	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	504	25	)	)	PUNCT
ejpam-6089	504	26	2	2	NUM
ejpam-6089	504	27	)	)	PUNCT
ejpam-6089	504	28	−	−	PROPN
ejpam-6089	505	1	∞∑	∞∑	NUM
ejpam-6089	505	2	ð=0	ð=0	X
ejpam-6089	505	3	að	að	X
ejpam-6089	505	4	(	(	PUNCT
ejpam-6089	505	5	r−li	r−li	NOUN
ejpam-6089	505	6	(	(	PUNCT
ejpam-6089	505	7	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	505	8	)	)	PUNCT
ejpam-6089	505	9	ℑ1	ℑ1	NOUN
ejpam-6089	505	10	+	+	CCONJ
ejpam-6089	505	11	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	505	12	)	)	PUNCT
ejpam-6089	506	1	+	+	NUM
ejpam-6089	506	2	r−li	r−li	NOUN
ejpam-6089	506	3	(	(	PUNCT
ejpam-6089	506	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	506	5	)	)	PUNCT
ejpam-6089	506	6	ℑ2−	ℑ2−	NUM
ejpam-6089	507	1	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	507	2	)	)	PUNCT
ejpam-6089	507	3	)	)	PUNCT
ejpam-6089	508	1	=	=	PUNCT
ejpam-6089	509	1	∞∑	∞∑	NUM
ejpam-6089	509	2	ð=0	ð=0	X
ejpam-6089	509	3	að	að	PROPN
ejpam-6089	509	4	2(ℑ2	2(ℑ2	NUM
ejpam-6089	509	5	−ℑ1	−ℑ1	NOUN
ejpam-6089	509	6	)	)	PUNCT
ejpam-6089	509	7	(	(	PUNCT
ejpam-6089	509	8	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	509	9	)	)	PUNCT
ejpam-6089	509	10	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	509	11	℘	℘	PROPN
ejpam-6089	509	12	)	)	PUNCT
ejpam-6089	509	13	+	+	CCONJ
ejpam-6089	509	14	1	1	X
ejpam-6089	509	15	)	)	PUNCT
ejpam-6089	509	16	×	×	NOUN
ejpam-6089	509	17	(	(	PUNCT
ejpam-6089	509	18	ℑ2	ℑ2	PROPN
ejpam-6089	509	19	−ℑ1	−ℑ1	PROPN
ejpam-6089	509	20	2	2	NUM
ejpam-6089	509	21	∫	∫	NOUN
ejpam-6089	509	22	1	1	NUM
ejpam-6089	509	23	0	0	NUM
ejpam-6089	509	24	(	(	PUNCT
ejpam-6089	509	25	(	(	PUNCT
ejpam-6089	509	26	1−	1−	NUM
ejpam-6089	509	27	t)(ℵð+℘	t)(ℵð+℘	NOUN
ejpam-6089	509	28	)	)	PUNCT
ejpam-6089	509	29	−	−	PROPN
ejpam-6089	509	30	t(ℵð+℘	t(ℵð+℘	NUM
ejpam-6089	509	31	)	)	PUNCT
ejpam-6089	509	32	)	)	PUNCT
ejpam-6089	509	33	υ′(tℑ1	υ′(tℑ1	NOUN
ejpam-6089	510	1	+	+	CCONJ
ejpam-6089	510	2	(	(	PUNCT
ejpam-6089	510	3	1−	1−	NUM
ejpam-6089	510	4	t)ℑ2)dt	t)ℑ2)dt	NOUN
ejpam-6089	510	5	)	)	PUNCT
ejpam-6089	510	6	.	.	PUNCT
ejpam-6089	511	1	using	use	VERB
ejpam-6089	511	2	proposition	proposition	NOUN
ejpam-6089	511	3	1	1	NUM
ejpam-6089	511	4	∞∑	∞∑	NUM
ejpam-6089	511	5	ð=0	ð=0	X
ejpam-6089	511	6	að	að	PROPN
ejpam-6089	511	7	2(ℑ2	2(ℑ2	NUM
ejpam-6089	511	8	−ℑ1	−ℑ1	NOUN
ejpam-6089	511	9	)	)	PUNCT
ejpam-6089	511	10	(	(	PUNCT
ejpam-6089	511	11	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	511	12	)	)	PUNCT
ejpam-6089	511	13	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	511	14	℘	℘	PROPN
ejpam-6089	511	15	)	)	PUNCT
ejpam-6089	511	16	+	+	CCONJ
ejpam-6089	511	17	1	1	X
ejpam-6089	511	18	)	)	PUNCT
ejpam-6089	511	19	(	(	PUNCT
ejpam-6089	511	20	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	511	21	)	)	PUNCT
ejpam-6089	511	22	+	+	CCONJ
ejpam-6089	511	23	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	511	24	)	)	PUNCT
ejpam-6089	511	25	2	2	NUM
ejpam-6089	511	26	)	)	PUNCT
ejpam-6089	511	27	−	−	PROPN
ejpam-6089	511	28	(	(	PUNCT
ejpam-6089	511	29	ε	ε	PROPN
ejpam-6089	511	30	♭	♭	PROPN
ejpam-6089	511	31	,δ	,δ	PUNCT
ejpam-6089	511	32	,	,	PUNCT
ejpam-6089	511	33	b	b	NOUN
ejpam-6089	511	34	,	,	PUNCT
ejpam-6089	511	35	s	s	NOUN
ejpam-6089	511	36	,	,	PUNCT
ejpam-6089	511	37	lℑ1+,ℵ,℘,τυ(ℑ2	lℑ1+,ℵ,℘,τυ(ℑ2	NOUN
ejpam-6089	511	38	;	;	PUNCT
ejpam-6089	511	39	g	g	NOUN
ejpam-6089	511	40	)	)	PUNCT
ejpam-6089	511	41	+	+	CCONJ
ejpam-6089	511	42	(	(	PUNCT
ejpam-6089	511	43	ε	ε	PROPN
ejpam-6089	511	44	♭	♭	PROPN
ejpam-6089	511	45	,δ	,δ	PUNCT
ejpam-6089	511	46	,	,	PUNCT
ejpam-6089	511	47	b	b	NOUN
ejpam-6089	511	48	,	,	PUNCT
ejpam-6089	511	49	s	s	NOUN
ejpam-6089	511	50	,	,	PUNCT
ejpam-6089	511	51	lℑ2−,ℵ,℘,τf	lℑ2−,ℵ,℘,τf	NOUN
ejpam-6089	511	52	)	)	PUNCT
ejpam-6089	511	53	(	(	PUNCT
ejpam-6089	511	54	ℑ1	ℑ1	NOUN
ejpam-6089	511	55	;	;	PUNCT
ejpam-6089	511	56	g	g	NOUN
ejpam-6089	511	57	)	)	PUNCT
ejpam-6089	511	58	)	)	PUNCT
ejpam-6089	512	1	=	=	PUNCT
ejpam-6089	513	1	∞∑	∞∑	NUM
ejpam-6089	513	2	ð=0	ð=0	X
ejpam-6089	513	3	að	að	PROPN
ejpam-6089	513	4	2(ℑ2	2(ℑ2	NUM
ejpam-6089	513	5	−ℑ1	−ℑ1	NOUN
ejpam-6089	513	6	)	)	PUNCT
ejpam-6089	513	7	(	(	PUNCT
ejpam-6089	513	8	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	513	9	)	)	PUNCT
ejpam-6089	513	10	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	513	11	℘	℘	PROPN
ejpam-6089	513	12	)	)	PUNCT
ejpam-6089	513	13	+	+	CCONJ
ejpam-6089	513	14	1	1	X
ejpam-6089	513	15	)	)	PUNCT
ejpam-6089	513	16	×	×	NOUN
ejpam-6089	513	17	(	(	PUNCT
ejpam-6089	513	18	ℑ2	ℑ2	PROPN
ejpam-6089	513	19	−ℑ1	−ℑ1	PROPN
ejpam-6089	513	20	2	2	NUM
ejpam-6089	513	21	∫	∫	NOUN
ejpam-6089	513	22	1	1	NUM
ejpam-6089	513	23	0	0	NUM
ejpam-6089	513	24	(	(	PUNCT
ejpam-6089	513	25	(	(	PUNCT
ejpam-6089	513	26	1−	1−	NUM
ejpam-6089	513	27	t)(ℵð+℘	t)(ℵð+℘	NOUN
ejpam-6089	513	28	)	)	PUNCT
ejpam-6089	513	29	−	−	PROPN
ejpam-6089	513	30	t(ℵð+℘	t(ℵð+℘	NUM
ejpam-6089	513	31	)	)	PUNCT
ejpam-6089	513	32	)	)	PUNCT
ejpam-6089	513	33	υ′(tℑ1	υ′(tℑ1	NOUN
ejpam-6089	514	1	+	+	CCONJ
ejpam-6089	514	2	(	(	PUNCT
ejpam-6089	514	3	1−	1−	NUM
ejpam-6089	514	4	t)ℑ2)dt	t)ℑ2)dt	NOUN
ejpam-6089	514	5	)	)	PUNCT
ejpam-6089	514	6	.	.	PUNCT
ejpam-6089	515	1	after	after	ADP
ejpam-6089	515	2	rearranging	rearrange	VERB
ejpam-6089	515	3	the	the	DET
ejpam-6089	515	4	above	above	ADJ
ejpam-6089	515	5	expression	expression	NOUN
ejpam-6089	515	6	,	,	PUNCT
ejpam-6089	515	7	we	we	PRON
ejpam-6089	515	8	get	get	VERB
ejpam-6089	515	9	ε	ε	PROPN
ejpam-6089	515	10	♭	♭	PROPN
ejpam-6089	515	11	,δ	,δ	PUNCT
ejpam-6089	515	12	,	,	PUNCT
ejpam-6089	515	13	b	b	NOUN
ejpam-6089	515	14	,	,	PUNCT
ejpam-6089	515	15	s	s	NOUN
ejpam-6089	515	16	,	,	PUNCT
ejpam-6089	515	17	lℑ1+,ℵ,℘,τυ(ℑ2	lℑ1+,ℵ,℘,τυ(ℑ2	NOUN
ejpam-6089	515	18	;	;	PUNCT
ejpam-6089	515	19	g	g	NOUN
ejpam-6089	515	20	)	)	PUNCT
ejpam-6089	516	1	+	+	CCONJ
ejpam-6089	516	2	ε	ε	PROPN
ejpam-6089	516	3	♭	♭	PROPN
ejpam-6089	516	4	,δ	,δ	PUNCT
ejpam-6089	516	5	,	,	PUNCT
ejpam-6089	516	6	b	b	NOUN
ejpam-6089	516	7	,	,	PUNCT
ejpam-6089	516	8	s	s	PROPN
ejpam-6089	516	9	,	,	PUNCT
ejpam-6089	516	10	lℑ2−,ℵ,℘,τυ(ℑ1	lℑ2−,ℵ,℘,τυ(ℑ1	PROPN
ejpam-6089	516	11	;	;	PUNCT
ejpam-6089	516	12	g	g	X
ejpam-6089	516	13	)	)	PUNCT
ejpam-6089	516	14	s.	s.	PROPN
ejpam-6089	516	15	naheed	nahee	VERB
ejpam-6089	516	16	et	et	PROPN
ejpam-6089	516	17	al	al	PROPN
ejpam-6089	516	18	.	.	PUNCT
ejpam-6089	516	19	/	/	SYM
ejpam-6089	516	20	eur	eur	PROPN
ejpam-6089	516	21	.	.	PUNCT
ejpam-6089	517	1	j.	j.	PROPN
ejpam-6089	517	2	pure	pure	PROPN
ejpam-6089	517	3	appl	appl	PROPN
ejpam-6089	517	4	.	.	PROPN
ejpam-6089	517	5	math	math	PROPN
ejpam-6089	517	6	,	,	PUNCT
ejpam-6089	517	7	18	18	NUM
ejpam-6089	517	8	(	(	PUNCT
ejpam-6089	517	9	2	2	NUM
ejpam-6089	517	10	)	)	PUNCT
ejpam-6089	517	11	(	(	PUNCT
ejpam-6089	517	12	2025	2025	NUM
ejpam-6089	517	13	)	)	PUNCT
ejpam-6089	517	14	,	,	PUNCT
ejpam-6089	517	15	6089	6089	NUM
ejpam-6089	517	16	24	24	NUM
ejpam-6089	517	17	of	of	ADP
ejpam-6089	517	18	34	34	NUM
ejpam-6089	517	19	=	=	SYM
ejpam-6089	517	20	∞∑	∞∑	NUM
ejpam-6089	517	21	ð=0	ð=0	X
ejpam-6089	517	22	aðvð	aðvð	NOUN
ejpam-6089	517	23	(	(	PUNCT
ejpam-6089	517	24	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	517	25	)	)	PUNCT
ejpam-6089	517	26	+	+	CCONJ
ejpam-6089	517	27	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	517	28	)	)	PUNCT
ejpam-6089	517	29	2	2	NUM
ejpam-6089	517	30	)	)	PUNCT
ejpam-6089	517	31	−	−	PROPN
ejpam-6089	518	1	∞∑	∞∑	NUM
ejpam-6089	518	2	ð=0	ð=0	SYM
ejpam-6089	518	3	aðvð	aðvð	NOUN
ejpam-6089	518	4	×	×	NOUN
ejpam-6089	518	5	(	(	PUNCT
ejpam-6089	518	6	ℑ2	ℑ2	PROPN
ejpam-6089	518	7	−ℑ1	−ℑ1	PROPN
ejpam-6089	518	8	2	2	NUM
ejpam-6089	518	9	∫	∫	NOUN
ejpam-6089	518	10	1	1	NUM
ejpam-6089	518	11	0	0	NUM
ejpam-6089	518	12	(	(	PUNCT
ejpam-6089	518	13	(	(	PUNCT
ejpam-6089	518	14	1−	1−	NUM
ejpam-6089	518	15	t)(ℵð+℘	t)(ℵð+℘	NOUN
ejpam-6089	518	16	)	)	PUNCT
ejpam-6089	518	17	−	−	PROPN
ejpam-6089	518	18	t(ℵð+℘	t(ℵð+℘	NUM
ejpam-6089	518	19	)	)	PUNCT
ejpam-6089	518	20	)	)	PUNCT
ejpam-6089	519	1	υ′(tℑ1	υ′(tℑ1	NOUN
ejpam-6089	519	2	+	+	CCONJ
ejpam-6089	519	3	(	(	PUNCT
ejpam-6089	519	4	1−	1−	NUM
ejpam-6089	519	5	t)ℑ2)dt	t)ℑ2)dt	NOUN
ejpam-6089	519	6	)	)	PUNCT
ejpam-6089	519	7	.	.	PUNCT
ejpam-6089	520	1	thus	thus	ADV
ejpam-6089	520	2	the	the	DET
ejpam-6089	520	3	proof	proof	NOUN
ejpam-6089	520	4	is	be	AUX
ejpam-6089	520	5	completed	complete	VERB
ejpam-6089	520	6	.	.	PUNCT
ejpam-6089	521	1	theorem	theorem	NOUN
ejpam-6089	521	2	9	9	NUM
ejpam-6089	521	3	.	.	PUNCT
ejpam-6089	522	1	let	let	VERB
ejpam-6089	522	2	υ	υ	NOUN
ejpam-6089	522	3	:	:	PUNCT
ejpam-6089	522	4	[	[	X
ejpam-6089	522	5	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	522	6	]	]	PUNCT
ejpam-6089	522	7	→	→	SYM
ejpam-6089	522	8	ℜ	ℜ	PROPN
ejpam-6089	522	9	is	be	AUX
ejpam-6089	522	10	an	an	DET
ejpam-6089	522	11	l1	l1	PROPN
ejpam-6089	522	12	function	function	NOUN
ejpam-6089	522	13	and	and	CCONJ
ejpam-6089	522	14	(	(	PUNCT
ejpam-6089	522	15	ℵð+	ℵð+	ADJ
ejpam-6089	522	16	℘	℘	PROPN
ejpam-6089	522	17	)	)	PUNCT
ejpam-6089	522	18	∈	∈	PROPN
ejpam-6089	522	19	(	(	PUNCT
ejpam-6089	522	20	0	0	NUM
ejpam-6089	522	21	,	,	PUNCT
ejpam-6089	522	22	1	1	NUM
ejpam-6089	522	23	)	)	PUNCT
ejpam-6089	522	24	also	also	ADV
ejpam-6089	522	25	a	a	DET
ejpam-6089	522	26	differentiable	differentiable	ADJ
ejpam-6089	522	27	function	function	NOUN
ejpam-6089	522	28	on	on	ADP
ejpam-6089	522	29	(	(	PUNCT
ejpam-6089	522	30	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	522	31	)	)	PUNCT
ejpam-6089	522	32	with	with	ADP
ejpam-6089	522	33	ℑ1	ℑ1	NOUN
ejpam-6089	522	34	<	<	X
ejpam-6089	522	35	ℑ2	ℑ2	PROPN
ejpam-6089	522	36	and	and	CCONJ
ejpam-6089	522	37	assume	assume	VERB
ejpam-6089	522	38	υ′	υ′	NOUN
ejpam-6089	522	39	∈	∈	NOUN
ejpam-6089	522	40	l1[ℑ1,ℑ2	l1[ℑ1,ℑ2	PROPN
ejpam-6089	522	41	]	]	PUNCT
ejpam-6089	522	42	.	.	PUNCT
ejpam-6089	523	1	consider	consider	VERB
ejpam-6089	523	2	♭	♭	PRON
ejpam-6089	523	3	,	,	PUNCT
ejpam-6089	523	4	ℵ	ℵ	NOUN
ejpam-6089	523	5	,	,	PUNCT
ejpam-6089	523	6	℘	℘	PROPN
ejpam-6089	523	7	,	,	PUNCT
ejpam-6089	523	8	τ	τ	PROPN
ejpam-6089	523	9	,	,	PUNCT
ejpam-6089	523	10	δ	δ	PROPN
ejpam-6089	523	11	,	,	PUNCT
ejpam-6089	523	12	b	b	PROPN
ejpam-6089	523	13	∈	∈	PROPN
ejpam-6089	523	14	c	c	NOUN
ejpam-6089	523	15	with	with	ADP
ejpam-6089	523	16	ℜ(ℵ),ℜ(℘),ℜ(τ	ℜ(ℵ),ℜ(℘),ℜ(τ	PROPN
ejpam-6089	523	17	)	)	PUNCT
ejpam-6089	523	18	>	>	X
ejpam-6089	523	19	0	0	NUM
ejpam-6089	523	20	and	and	CCONJ
ejpam-6089	523	21	ℜ(b	ℜ(b	NOUN
ejpam-6089	523	22	)	)	PUNCT
ejpam-6089	523	23	>	>	X
ejpam-6089	524	1	ℜ(δ	ℜ(δ	X
ejpam-6089	524	2	)	)	PUNCT
ejpam-6089	524	3	>	>	X
ejpam-6089	524	4	0	0	X
ejpam-6089	524	5	.	.	PUNCT
ejpam-6089	525	1	moreover	moreover	ADV
ejpam-6089	525	2	,	,	PUNCT
ejpam-6089	525	3	let	let	VERB
ejpam-6089	525	4	g	g	PROPN
ejpam-6089	525	5	≥	≥	NOUN
ejpam-6089	525	6	0	0	NUM
ejpam-6089	525	7	,	,	PUNCT
ejpam-6089	525	8	l	l	NOUN
ejpam-6089	525	9	>	>	X
ejpam-6089	525	10	0	0	PUNCT
ejpam-6089	525	11	and	and	CCONJ
ejpam-6089	525	12	0	0	NUM
ejpam-6089	525	13	<	<	X
ejpam-6089	525	14	s	s	X
ejpam-6089	525	15	≤	≤	NUM
ejpam-6089	525	16	l	l	NOUN
ejpam-6089	525	17	+	+	CCONJ
ejpam-6089	525	18	ℜ(ℵ	ℜ(ℵ	NOUN
ejpam-6089	525	19	)	)	PUNCT
ejpam-6089	525	20	with	with	ADP
ejpam-6089	525	21	(	(	PUNCT
ejpam-6089	525	22	ℵð+	ℵð+	ADJ
ejpam-6089	525	23	℘	℘	PROPN
ejpam-6089	525	24	)	)	PUNCT
ejpam-6089	525	25	>	>	X
ejpam-6089	525	26	0	0	NUM
ejpam-6089	526	1	∞∑	∞∑	NUM
ejpam-6089	526	2	ð=0	ð=0	X
ejpam-6089	526	3	að	að	PROPN
ejpam-6089	526	4	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	526	5	℘	℘	PROPN
ejpam-6089	526	6	)	)	PUNCT
ejpam-6089	526	7	(	(	PUNCT
ejpam-6089	526	8	ℵð+	ℵð+	ADJ
ejpam-6089	526	9	℘	℘	PROPN
ejpam-6089	526	10	)	)	PUNCT
ejpam-6089	526	11	(	(	PUNCT
ejpam-6089	526	12	a−bi	a−bi	PROPN
ejpam-6089	526	13	(	(	PUNCT
ejpam-6089	526	14	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	526	15	)	)	PUNCT
ejpam-6089	526	16	ℑ1	ℑ1	NOUN
ejpam-6089	526	17	+	+	CCONJ
ejpam-6089	526	18	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	526	19	)	)	PUNCT
ejpam-6089	526	20	+	+	CCONJ
ejpam-6089	526	21	a−bi	a−bi	PROPN
ejpam-6089	526	22	(	(	PUNCT
ejpam-6089	526	23	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	526	24	)	)	PUNCT
ejpam-6089	526	25	ℑ2−	ℑ2−	NUM
ejpam-6089	527	1	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	527	2	)	)	PUNCT
ejpam-6089	527	3	)	)	PUNCT
ejpam-6089	528	1	−	−	PROPN
ejpam-6089	529	1	∞∑	∞∑	NUM
ejpam-6089	529	2	ð=0	ð=0	X
ejpam-6089	529	3	að	að	X
ejpam-6089	529	4	1−	1−	NUM
ejpam-6089	529	5	(	(	PUNCT
ejpam-6089	529	6	ℵð+	ℵð+	ADJ
ejpam-6089	529	7	℘	℘	PROPN
ejpam-6089	529	8	)	)	PUNCT
ejpam-6089	529	9	(	(	PUNCT
ejpam-6089	529	10	ℵð+	ℵð+	ADJ
ejpam-6089	529	11	℘	℘	PROPN
ejpam-6089	529	12	)	)	PUNCT
ejpam-6089	529	13	(	(	PUNCT
ejpam-6089	529	14	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	529	15	)	)	PUNCT
ejpam-6089	529	16	+	+	CCONJ
ejpam-6089	529	17	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	529	18	)	)	PUNCT
ejpam-6089	529	19	)	)	PUNCT
ejpam-6089	530	1	=	=	PUNCT
ejpam-6089	531	1	∞∑	∞∑	NUM
ejpam-6089	531	2	ð=0	ð=0	X
ejpam-6089	531	3	aðvð	aðvð	NOUN
ejpam-6089	531	4	(	(	PUNCT
ejpam-6089	531	5	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	531	6	)	)	PUNCT
ejpam-6089	531	7	+	+	CCONJ
ejpam-6089	531	8	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	531	9	)	)	PUNCT
ejpam-6089	531	10	2	2	NUM
ejpam-6089	531	11	)	)	PUNCT
ejpam-6089	531	12	−	−	PROPN
ejpam-6089	532	1	∞∑	∞∑	NUM
ejpam-6089	532	2	ð=0	ð=0	SYM
ejpam-6089	532	3	aðvð	aðvð	NOUN
ejpam-6089	532	4	×	×	NOUN
ejpam-6089	532	5	(	(	PUNCT
ejpam-6089	532	6	ℑ2	ℑ2	PROPN
ejpam-6089	532	7	−ℑ1	−ℑ1	PROPN
ejpam-6089	532	8	2	2	NUM
ejpam-6089	532	9	∫	∫	NOUN
ejpam-6089	532	10	1	1	NUM
ejpam-6089	532	11	0	0	NUM
ejpam-6089	532	12	(	(	PUNCT
ejpam-6089	532	13	(	(	PUNCT
ejpam-6089	532	14	1−	1−	NUM
ejpam-6089	532	15	t)(ℵð+℘	t)(ℵð+℘	NOUN
ejpam-6089	532	16	)	)	PUNCT
ejpam-6089	532	17	−	−	PROPN
ejpam-6089	532	18	t(ℵð+℘	t(ℵð+℘	NUM
ejpam-6089	532	19	)	)	PUNCT
ejpam-6089	532	20	)	)	PUNCT
ejpam-6089	533	1	υ′(tℑ1	υ′(tℑ1	NOUN
ejpam-6089	533	2	+	+	CCONJ
ejpam-6089	533	3	(	(	PUNCT
ejpam-6089	533	4	1−	1−	NUM
ejpam-6089	533	5	t)ℑ2)dt	t)ℑ2)dt	NOUN
ejpam-6089	533	6	)	)	PUNCT
ejpam-6089	533	7	,	,	PUNCT
ejpam-6089	533	8	where	where	SCONJ
ejpam-6089	533	9	að	að	PROPN
ejpam-6089	533	10	=	=	SYM
ejpam-6089	533	11	bg(δ+ðs	bg(δ+ðs	PROPN
ejpam-6089	533	12	,	,	PUNCT
ejpam-6089	533	13	b−δ	b−δ	NOUN
ejpam-6089	533	14	)	)	PUNCT
ejpam-6089	533	15	b(δ	b(δ	NOUN
ejpam-6089	533	16	,	,	PUNCT
ejpam-6089	533	17	b−δ	b−δ	NOUN
ejpam-6089	533	18	)	)	PUNCT
ejpam-6089	533	19	(	(	PUNCT
ejpam-6089	533	20	b)ðs	b)ðs	PROPN
ejpam-6089	533	21	♭	♭	PROPN
ejpam-6089	533	22	ð	ð	X
ejpam-6089	533	23	(	(	PUNCT
ejpam-6089	533	24	τ)ðl	τ)ðl	PROPN
ejpam-6089	533	25	and	and	CCONJ
ejpam-6089	533	26	vð	vð	VERB
ejpam-6089	533	27	=	=	SYM
ejpam-6089	533	28	2(ℑ2−ℑ1)(ℵð+℘	2(ℑ2−ℑ1)(ℵð+℘	NUM
ejpam-6089	533	29	)	)	PUNCT
ejpam-6089	533	30	γ((ℵð+℘)+1	γ((ℵð+℘)+1	NOUN
ejpam-6089	533	31	)	)	PUNCT
ejpam-6089	533	32	.	.	PUNCT
ejpam-6089	534	1	proof	proof	NOUN
ejpam-6089	534	2	.	.	PUNCT
ejpam-6089	535	1	adding	add	VERB
ejpam-6089	535	2	left	left	ADJ
ejpam-6089	535	3	and	and	CCONJ
ejpam-6089	535	4	right	right	ADV
ejpam-6089	535	5	sided	sided	ADJ
ejpam-6089	535	6	atangana	atangana	PROPN
ejpam-6089	535	7	-	-	PUNCT
ejpam-6089	535	8	baleanu	baleanu	PROPN
ejpam-6089	535	9	integrals	integral	NOUN
ejpam-6089	535	10	(	(	PUNCT
ejpam-6089	535	11	3	3	NUM
ejpam-6089	535	12	)	)	PUNCT
ejpam-6089	535	13	and	and	CCONJ
ejpam-6089	535	14	(	(	PUNCT
ejpam-6089	535	15	4	4	NUM
ejpam-6089	535	16	)	)	PUNCT
ejpam-6089	535	17	,	,	PUNCT
ejpam-6089	535	18	we	we	PRON
ejpam-6089	535	19	have	have	VERB
ejpam-6089	535	20	a−biα	a−biα	NOUN
ejpam-6089	535	21	∗	∗	NOUN
ejpam-6089	535	22	ℑ1+υ(ℑ2	ℑ1+υ(ℑ2	NOUN
ejpam-6089	535	23	)	)	PUNCT
ejpam-6089	535	24	+	+	NUM
ejpam-6089	535	25	a−biα	a−biα	ADJ
ejpam-6089	535	26	∗	∗	NOUN
ejpam-6089	535	27	ℑ2−υ(ℑ1	ℑ2−υ(ℑ1	NOUN
ejpam-6089	535	28	)	)	PUNCT
ejpam-6089	535	29	=	=	PUNCT
ejpam-6089	535	30	α∗	α∗	VERB
ejpam-6089	535	31	b(α∗	b(α∗	NOUN
ejpam-6089	535	32	)	)	PUNCT
ejpam-6089	535	33	(	(	PUNCT
ejpam-6089	535	34	r−liα	r−liα	VERB
ejpam-6089	535	35	∗	∗	NOUN
ejpam-6089	535	36	ℑ1+υ(ℑ2	ℑ1+υ(ℑ2	NOUN
ejpam-6089	535	37	)	)	PUNCT
ejpam-6089	535	38	+	+	NUM
ejpam-6089	535	39	r−liα	r−liα	NOUN
ejpam-6089	535	40	∗	∗	NOUN
ejpam-6089	535	41	ℑ2−υ(ℑ1	ℑ2−υ(ℑ1	NOUN
ejpam-6089	535	42	)	)	PUNCT
ejpam-6089	535	43	)	)	PUNCT
ejpam-6089	536	1	+	+	CCONJ
ejpam-6089	536	2	1−	1−	NUM
ejpam-6089	536	3	α∗	α∗	NOUN
ejpam-6089	536	4	b(α∗	b(α∗	NOUN
ejpam-6089	536	5	)	)	PUNCT
ejpam-6089	536	6	(	(	PUNCT
ejpam-6089	536	7	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	536	8	)	)	PUNCT
ejpam-6089	536	9	+	+	NUM
ejpam-6089	536	10	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	536	11	)	)	PUNCT
ejpam-6089	536	12	.	.	PUNCT
ejpam-6089	537	1	replacing	replace	VERB
ejpam-6089	537	2	α∗	α∗	NOUN
ejpam-6089	537	3	by	by	ADP
ejpam-6089	537	4	(	(	PUNCT
ejpam-6089	537	5	ℵð+	ℵð+	ADJ
ejpam-6089	537	6	℘	℘	PROPN
ejpam-6089	537	7	)	)	PUNCT
ejpam-6089	537	8	and	and	CCONJ
ejpam-6089	537	9	then	then	ADV
ejpam-6089	537	10	rearrange	rearrange	VERB
ejpam-6089	537	11	the	the	DET
ejpam-6089	537	12	above	above	ADJ
ejpam-6089	537	13	equation	equation	NOUN
ejpam-6089	537	14	,	,	PUNCT
ejpam-6089	537	15	we	we	PRON
ejpam-6089	537	16	obtain	obtain	VERB
ejpam-6089	537	17	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	537	18	℘	℘	PROPN
ejpam-6089	537	19	)	)	PUNCT
ejpam-6089	537	20	(	(	PUNCT
ejpam-6089	537	21	ℵð+	ℵð+	ADJ
ejpam-6089	537	22	℘	℘	PROPN
ejpam-6089	537	23	)	)	PUNCT
ejpam-6089	537	24	(	(	PUNCT
ejpam-6089	537	25	a−bi	a−bi	PROPN
ejpam-6089	537	26	(	(	PUNCT
ejpam-6089	537	27	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	537	28	)	)	PUNCT
ejpam-6089	537	29	ℑ1	ℑ1	NOUN
ejpam-6089	537	30	+	+	CCONJ
ejpam-6089	537	31	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	537	32	)	)	PUNCT
ejpam-6089	538	1	+	+	CCONJ
ejpam-6089	538	2	a−bi	a−bi	PROPN
ejpam-6089	538	3	(	(	PUNCT
ejpam-6089	538	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	538	5	)	)	PUNCT
ejpam-6089	538	6	ℑ2−	ℑ2−	NUM
ejpam-6089	538	7	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	538	8	)	)	PUNCT
ejpam-6089	538	9	)	)	PUNCT
ejpam-6089	539	1	−	−	PROPN
ejpam-6089	539	2	1−	1−	NUM
ejpam-6089	539	3	ℵð−	ℵð−	PUNCT
ejpam-6089	539	4	℘	℘	PROPN
ejpam-6089	539	5	(	(	PUNCT
ejpam-6089	539	6	ℵð+	ℵð+	ADJ
ejpam-6089	539	7	℘	℘	PROPN
ejpam-6089	539	8	)	)	PUNCT
ejpam-6089	539	9	(	(	PUNCT
ejpam-6089	539	10	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	539	11	)	)	PUNCT
ejpam-6089	539	12	+	+	CCONJ
ejpam-6089	539	13	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	539	14	)	)	PUNCT
ejpam-6089	539	15	)	)	PUNCT
ejpam-6089	540	1	=	=	PRON
ejpam-6089	540	2	(	(	PUNCT
ejpam-6089	540	3	r−li	r−li	NOUN
ejpam-6089	540	4	(	(	PUNCT
ejpam-6089	540	5	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	540	6	)	)	PUNCT
ejpam-6089	540	7	ℑ1	ℑ1	NOUN
ejpam-6089	540	8	+	+	CCONJ
ejpam-6089	540	9	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	540	10	)	)	PUNCT
ejpam-6089	540	11	+	+	NUM
ejpam-6089	540	12	r−li	r−li	NOUN
ejpam-6089	540	13	(	(	PUNCT
ejpam-6089	540	14	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	540	15	)	)	PUNCT
ejpam-6089	540	16	ℑ2−	ℑ2−	NUM
ejpam-6089	540	17	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	540	18	)	)	PUNCT
ejpam-6089	540	19	)	)	PUNCT
ejpam-6089	540	20	.	.	PUNCT
ejpam-6089	541	1	multiplying	multiply	VERB
ejpam-6089	541	2	the	the	DET
ejpam-6089	541	3	above	above	ADJ
ejpam-6089	541	4	expression	expression	NOUN
ejpam-6089	541	5	with	with	ADP
ejpam-6089	541	6	að	að	ADP
ejpam-6089	541	7	,	,	PUNCT
ejpam-6089	541	8	we	we	PRON
ejpam-6089	541	9	obtain	obtain	VERB
ejpam-6089	541	10	að	að	PROPN
ejpam-6089	541	11	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	541	12	℘	℘	PROPN
ejpam-6089	541	13	)	)	PUNCT
ejpam-6089	541	14	(	(	PUNCT
ejpam-6089	541	15	ℵð+	ℵð+	ADJ
ejpam-6089	541	16	℘	℘	PROPN
ejpam-6089	541	17	)	)	PUNCT
ejpam-6089	541	18	(	(	PUNCT
ejpam-6089	541	19	a−bi	a−bi	PROPN
ejpam-6089	541	20	(	(	PUNCT
ejpam-6089	541	21	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	541	22	)	)	PUNCT
ejpam-6089	541	23	ℑ1	ℑ1	NOUN
ejpam-6089	541	24	+	+	CCONJ
ejpam-6089	541	25	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	541	26	)	)	PUNCT
ejpam-6089	542	1	+	+	CCONJ
ejpam-6089	542	2	a−bi	a−bi	PROPN
ejpam-6089	542	3	(	(	PUNCT
ejpam-6089	542	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	542	5	)	)	PUNCT
ejpam-6089	542	6	ℑ2−	ℑ2−	NUM
ejpam-6089	542	7	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	542	8	)	)	PUNCT
ejpam-6089	542	9	)	)	PUNCT
ejpam-6089	543	1	s.	s.	PROPN
ejpam-6089	543	2	naheed	nahee	VERB
ejpam-6089	543	3	et	et	PROPN
ejpam-6089	543	4	al	al	PROPN
ejpam-6089	543	5	.	.	PUNCT
ejpam-6089	543	6	/	/	SYM
ejpam-6089	543	7	eur	eur	PROPN
ejpam-6089	543	8	.	.	PUNCT
ejpam-6089	544	1	j.	j.	PROPN
ejpam-6089	544	2	pure	pure	PROPN
ejpam-6089	544	3	appl	appl	PROPN
ejpam-6089	544	4	.	.	PROPN
ejpam-6089	544	5	math	math	PROPN
ejpam-6089	544	6	,	,	PUNCT
ejpam-6089	544	7	18	18	NUM
ejpam-6089	544	8	(	(	PUNCT
ejpam-6089	544	9	2	2	NUM
ejpam-6089	544	10	)	)	PUNCT
ejpam-6089	544	11	(	(	PUNCT
ejpam-6089	544	12	2025	2025	NUM
ejpam-6089	544	13	)	)	PUNCT
ejpam-6089	544	14	,	,	PUNCT
ejpam-6089	544	15	6089	6089	NUM
ejpam-6089	544	16	25	25	NUM
ejpam-6089	544	17	of	of	ADP
ejpam-6089	544	18	34	34	NUM
ejpam-6089	544	19	−	−	PROPN
ejpam-6089	544	20	að	að	PROPN
ejpam-6089	544	21	1−	1−	NUM
ejpam-6089	544	22	ℵð−	ℵð−	PUNCT
ejpam-6089	544	23	℘	℘	PROPN
ejpam-6089	544	24	(	(	PUNCT
ejpam-6089	544	25	ℵð+	ℵð+	ADJ
ejpam-6089	544	26	℘	℘	PROPN
ejpam-6089	544	27	)	)	PUNCT
ejpam-6089	544	28	(	(	PUNCT
ejpam-6089	544	29	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	544	30	)	)	PUNCT
ejpam-6089	544	31	+	+	CCONJ
ejpam-6089	544	32	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	544	33	)	)	PUNCT
ejpam-6089	544	34	)	)	PUNCT
ejpam-6089	545	1	=	=	SYM
ejpam-6089	545	2	að	að	PROPN
ejpam-6089	545	3	(	(	PUNCT
ejpam-6089	545	4	r−li	r−li	NOUN
ejpam-6089	545	5	(	(	PUNCT
ejpam-6089	545	6	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	545	7	)	)	PUNCT
ejpam-6089	545	8	ℑ1	ℑ1	NOUN
ejpam-6089	545	9	+	+	CCONJ
ejpam-6089	545	10	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	545	11	)	)	PUNCT
ejpam-6089	546	1	+	+	NUM
ejpam-6089	546	2	r−li	r−li	NOUN
ejpam-6089	546	3	(	(	PUNCT
ejpam-6089	546	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	546	5	)	)	PUNCT
ejpam-6089	546	6	ℑ2−	ℑ2−	NUM
ejpam-6089	547	1	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	547	2	)	)	PUNCT
ejpam-6089	547	3	)	)	PUNCT
ejpam-6089	547	4	.	.	PUNCT
ejpam-6089	548	1	summing	sum	VERB
ejpam-6089	548	2	over	over	ADP
ejpam-6089	548	3	all	all	PRON
ejpam-6089	548	4	ð	ð	NOUN
ejpam-6089	548	5	∞∑	∞∑	NUM
ejpam-6089	548	6	ð=0	ð=0	X
ejpam-6089	548	7	að	að	PROPN
ejpam-6089	548	8	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	548	9	℘	℘	PROPN
ejpam-6089	548	10	)	)	PUNCT
ejpam-6089	548	11	(	(	PUNCT
ejpam-6089	548	12	ℵð+	ℵð+	ADJ
ejpam-6089	548	13	℘	℘	PROPN
ejpam-6089	548	14	)	)	PUNCT
ejpam-6089	548	15	(	(	PUNCT
ejpam-6089	548	16	a−bi	a−bi	PROPN
ejpam-6089	548	17	(	(	PUNCT
ejpam-6089	548	18	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	548	19	)	)	PUNCT
ejpam-6089	548	20	ℑ1	ℑ1	NOUN
ejpam-6089	548	21	+	+	CCONJ
ejpam-6089	548	22	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	548	23	)	)	PUNCT
ejpam-6089	548	24	+	+	CCONJ
ejpam-6089	548	25	a−bi	a−bi	PROPN
ejpam-6089	548	26	(	(	PUNCT
ejpam-6089	548	27	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	548	28	)	)	PUNCT
ejpam-6089	548	29	ℑ2−	ℑ2−	NUM
ejpam-6089	549	1	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	549	2	)	)	PUNCT
ejpam-6089	549	3	)	)	PUNCT
ejpam-6089	550	1	−	−	PROPN
ejpam-6089	551	1	∞∑	∞∑	NUM
ejpam-6089	551	2	ð=0	ð=0	X
ejpam-6089	551	3	að	að	X
ejpam-6089	551	4	1−	1−	NUM
ejpam-6089	551	5	ℵð−	ℵð−	PUNCT
ejpam-6089	551	6	℘	℘	PROPN
ejpam-6089	551	7	(	(	PUNCT
ejpam-6089	551	8	ℵð+	ℵð+	ADJ
ejpam-6089	551	9	℘	℘	PROPN
ejpam-6089	551	10	)	)	PUNCT
ejpam-6089	551	11	(	(	PUNCT
ejpam-6089	551	12	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	551	13	)	)	PUNCT
ejpam-6089	551	14	+	+	CCONJ
ejpam-6089	551	15	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	551	16	)	)	PUNCT
ejpam-6089	551	17	)	)	PUNCT
ejpam-6089	552	1	=	=	PUNCT
ejpam-6089	553	1	∞∑	∞∑	NUM
ejpam-6089	553	2	ð=0	ð=0	X
ejpam-6089	553	3	að	að	X
ejpam-6089	553	4	(	(	PUNCT
ejpam-6089	553	5	r−li	r−li	NOUN
ejpam-6089	553	6	(	(	PUNCT
ejpam-6089	553	7	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	553	8	)	)	PUNCT
ejpam-6089	553	9	ℑ1	ℑ1	NOUN
ejpam-6089	553	10	+	+	CCONJ
ejpam-6089	553	11	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	553	12	)	)	PUNCT
ejpam-6089	553	13	+	+	NUM
ejpam-6089	553	14	r−li	r−li	NOUN
ejpam-6089	553	15	(	(	PUNCT
ejpam-6089	553	16	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	553	17	)	)	PUNCT
ejpam-6089	553	18	ℑ2−	ℑ2−	NUM
ejpam-6089	553	19	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	553	20	)	)	PUNCT
ejpam-6089	553	21	)	)	PUNCT
ejpam-6089	553	22	.	.	PUNCT
ejpam-6089	554	1	using	use	VERB
ejpam-6089	554	2	proposition	proposition	NOUN
ejpam-6089	554	3	1	1	NUM
ejpam-6089	554	4	,	,	PUNCT
ejpam-6089	554	5	we	we	PRON
ejpam-6089	554	6	obtain	obtain	VERB
ejpam-6089	554	7	∞∑	∞∑	PRON
ejpam-6089	554	8	ð=0	ð=0	X
ejpam-6089	554	9	að	að	PROPN
ejpam-6089	554	10	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	554	11	℘	℘	PROPN
ejpam-6089	554	12	)	)	PUNCT
ejpam-6089	554	13	(	(	PUNCT
ejpam-6089	554	14	ℵð+	ℵð+	ADJ
ejpam-6089	554	15	℘	℘	PROPN
ejpam-6089	554	16	)	)	PUNCT
ejpam-6089	554	17	(	(	PUNCT
ejpam-6089	554	18	a−bi	a−bi	PROPN
ejpam-6089	554	19	(	(	PUNCT
ejpam-6089	554	20	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	554	21	)	)	PUNCT
ejpam-6089	554	22	ℑ1	ℑ1	NOUN
ejpam-6089	554	23	+	+	CCONJ
ejpam-6089	554	24	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	554	25	)	)	PUNCT
ejpam-6089	555	1	+	+	CCONJ
ejpam-6089	555	2	a−bi	a−bi	PROPN
ejpam-6089	555	3	(	(	PUNCT
ejpam-6089	555	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	555	5	)	)	PUNCT
ejpam-6089	555	6	ℑ2−	ℑ2−	NUM
ejpam-6089	555	7	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	555	8	)	)	PUNCT
ejpam-6089	555	9	)	)	PUNCT
ejpam-6089	556	1	−	−	PROPN
ejpam-6089	557	1	∞∑	∞∑	NUM
ejpam-6089	557	2	ð=0	ð=0	X
ejpam-6089	557	3	að	að	X
ejpam-6089	557	4	1−	1−	NUM
ejpam-6089	557	5	ℵð−	ℵð−	PUNCT
ejpam-6089	557	6	℘	℘	PROPN
ejpam-6089	557	7	(	(	PUNCT
ejpam-6089	557	8	ℵð+	ℵð+	ADJ
ejpam-6089	557	9	℘	℘	PROPN
ejpam-6089	557	10	)	)	PUNCT
ejpam-6089	557	11	(	(	PUNCT
ejpam-6089	557	12	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	557	13	)	)	PUNCT
ejpam-6089	557	14	+	+	CCONJ
ejpam-6089	557	15	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	557	16	)	)	PUNCT
ejpam-6089	557	17	)	)	PUNCT
ejpam-6089	558	1	=	=	PUNCT
ejpam-6089	558	2	(	(	PUNCT
ejpam-6089	558	3	(	(	PUNCT
ejpam-6089	558	4	ε	ε	PROPN
ejpam-6089	558	5	♭	♭	PROPN
ejpam-6089	558	6	,δ	,δ	PUNCT
ejpam-6089	558	7	,	,	PUNCT
ejpam-6089	558	8	b	b	NOUN
ejpam-6089	558	9	,	,	PUNCT
ejpam-6089	558	10	s	s	NOUN
ejpam-6089	558	11	,	,	PUNCT
ejpam-6089	558	12	lℑ1+,ℵ,℘,τυ	lℑ1+,ℵ,℘,τυ	NOUN
ejpam-6089	558	13	)	)	PUNCT
ejpam-6089	558	14	(	(	PUNCT
ejpam-6089	558	15	ℑ2	ℑ2	VERB
ejpam-6089	558	16	;	;	PUNCT
ejpam-6089	558	17	g	g	NOUN
ejpam-6089	558	18	)	)	PUNCT
ejpam-6089	558	19	+	+	CCONJ
ejpam-6089	558	20	(	(	PUNCT
ejpam-6089	558	21	ε	ε	PROPN
ejpam-6089	558	22	♭	♭	PROPN
ejpam-6089	558	23	,δ	,δ	PUNCT
ejpam-6089	558	24	,	,	PUNCT
ejpam-6089	558	25	b	b	NOUN
ejpam-6089	558	26	,	,	PUNCT
ejpam-6089	558	27	s	s	NOUN
ejpam-6089	558	28	,	,	PUNCT
ejpam-6089	558	29	lℑ2−,ℵ,℘,τυ	lℑ2−,ℵ,℘,τυ	NOUN
ejpam-6089	558	30	)	)	PUNCT
ejpam-6089	558	31	(	(	PUNCT
ejpam-6089	558	32	ℑ1	ℑ1	NOUN
ejpam-6089	558	33	;	;	PUNCT
ejpam-6089	558	34	g	g	NOUN
ejpam-6089	558	35	)	)	PUNCT
ejpam-6089	558	36	)	)	PUNCT
ejpam-6089	558	37	.	.	PUNCT
ejpam-6089	559	1	comparing	compare	VERB
ejpam-6089	559	2	with	with	ADP
ejpam-6089	559	3	lemma	lemma	PROPN
ejpam-6089	559	4	3	3	NUM
ejpam-6089	559	5	,	,	PUNCT
ejpam-6089	559	6	we	we	PRON
ejpam-6089	559	7	get	get	VERB
ejpam-6089	559	8	∞∑	∞∑	NUM
ejpam-6089	559	9	ð=0	ð=0	X
ejpam-6089	559	10	að	að	PROPN
ejpam-6089	559	11	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	559	12	℘	℘	PROPN
ejpam-6089	559	13	)	)	PUNCT
ejpam-6089	559	14	(	(	PUNCT
ejpam-6089	559	15	ℵð+	ℵð+	ADJ
ejpam-6089	559	16	℘	℘	PROPN
ejpam-6089	559	17	)	)	PUNCT
ejpam-6089	559	18	(	(	PUNCT
ejpam-6089	559	19	a−bi	a−bi	PROPN
ejpam-6089	559	20	(	(	PUNCT
ejpam-6089	559	21	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	559	22	)	)	PUNCT
ejpam-6089	559	23	ℑ1	ℑ1	NOUN
ejpam-6089	559	24	+	+	CCONJ
ejpam-6089	559	25	υ(ℑ2	υ(ℑ2	PROPN
ejpam-6089	559	26	)	)	PUNCT
ejpam-6089	560	1	+	+	CCONJ
ejpam-6089	560	2	a−bi	a−bi	PROPN
ejpam-6089	560	3	(	(	PUNCT
ejpam-6089	560	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	560	5	)	)	PUNCT
ejpam-6089	560	6	ℑ2−	ℑ2−	NUM
ejpam-6089	560	7	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	560	8	)	)	PUNCT
ejpam-6089	560	9	)	)	PUNCT
ejpam-6089	561	1	−	−	PROPN
ejpam-6089	562	1	∞∑	∞∑	NUM
ejpam-6089	562	2	ð=0	ð=0	X
ejpam-6089	562	3	að	að	X
ejpam-6089	562	4	1−	1−	NUM
ejpam-6089	562	5	ℵð−	ℵð−	PUNCT
ejpam-6089	562	6	℘	℘	PROPN
ejpam-6089	562	7	(	(	PUNCT
ejpam-6089	562	8	ℵð+	ℵð+	ADJ
ejpam-6089	562	9	℘	℘	PROPN
ejpam-6089	562	10	)	)	PUNCT
ejpam-6089	562	11	(	(	PUNCT
ejpam-6089	562	12	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	562	13	)	)	PUNCT
ejpam-6089	562	14	+	+	CCONJ
ejpam-6089	562	15	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	562	16	)	)	PUNCT
ejpam-6089	562	17	)	)	PUNCT
ejpam-6089	563	1	=	=	PUNCT
ejpam-6089	564	1	∞∑	∞∑	NUM
ejpam-6089	564	2	ð=0	ð=0	X
ejpam-6089	564	3	að	að	PROPN
ejpam-6089	564	4	2(ℑ2	2(ℑ2	NUM
ejpam-6089	564	5	−ℑ1	−ℑ1	NOUN
ejpam-6089	564	6	)	)	PUNCT
ejpam-6089	564	7	(	(	PUNCT
ejpam-6089	564	8	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	564	9	)	)	PUNCT
ejpam-6089	564	10	γ(ℵð+	γ(ℵð+	NOUN
ejpam-6089	564	11	℘+	℘+	ADP
ejpam-6089	564	12	1	1	NUM
ejpam-6089	564	13	)	)	PUNCT
ejpam-6089	564	14	(	(	PUNCT
ejpam-6089	564	15	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	564	16	)	)	PUNCT
ejpam-6089	564	17	+	+	CCONJ
ejpam-6089	564	18	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	564	19	)	)	PUNCT
ejpam-6089	564	20	2	2	NUM
ejpam-6089	564	21	)	)	PUNCT
ejpam-6089	565	1	−	−	PROPN
ejpam-6089	565	2	∞∑	∞∑	NUM
ejpam-6089	565	3	ð=0	ð=0	X
ejpam-6089	565	4	að	að	PROPN
ejpam-6089	565	5	2(ℑ2	2(ℑ2	NUM
ejpam-6089	565	6	−ℑ1	−ℑ1	NOUN
ejpam-6089	565	7	)	)	PUNCT
ejpam-6089	565	8	(	(	PUNCT
ejpam-6089	565	9	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	565	10	)	)	PUNCT
ejpam-6089	565	11	γ((ℵð+	γ((ℵð+	PROPN
ejpam-6089	565	12	℘	℘	PROPN
ejpam-6089	565	13	)	)	PUNCT
ejpam-6089	565	14	+	+	CCONJ
ejpam-6089	565	15	1	1	X
ejpam-6089	565	16	)	)	PUNCT
ejpam-6089	565	17	×	×	NOUN
ejpam-6089	565	18	(	(	PUNCT
ejpam-6089	565	19	ℑ2	ℑ2	PROPN
ejpam-6089	565	20	−ℑ1	−ℑ1	PROPN
ejpam-6089	565	21	2	2	NUM
ejpam-6089	565	22	∫	∫	NOUN
ejpam-6089	565	23	1	1	NUM
ejpam-6089	565	24	0	0	NUM
ejpam-6089	565	25	(	(	PUNCT
ejpam-6089	565	26	(	(	PUNCT
ejpam-6089	565	27	1−	1−	NUM
ejpam-6089	565	28	t)(ℵð+℘	t)(ℵð+℘	NOUN
ejpam-6089	565	29	)	)	PUNCT
ejpam-6089	565	30	−	−	PROPN
ejpam-6089	565	31	t(ℵð+℘	t(ℵð+℘	NUM
ejpam-6089	565	32	)	)	PUNCT
ejpam-6089	565	33	)	)	PUNCT
ejpam-6089	566	1	υ′(tℑ1	υ′(tℑ1	NOUN
ejpam-6089	566	2	+	+	CCONJ
ejpam-6089	566	3	(	(	PUNCT
ejpam-6089	566	4	1−	1−	NUM
ejpam-6089	566	5	t)ℑ2)dt	t)ℑ2)dt	NOUN
ejpam-6089	566	6	)	)	PUNCT
ejpam-6089	566	7	.	.	PUNCT
ejpam-6089	567	1	this	this	PRON
ejpam-6089	567	2	completes	complete	VERB
ejpam-6089	567	3	desired	desire	VERB
ejpam-6089	567	4	result	result	NOUN
ejpam-6089	567	5	.	.	PUNCT
ejpam-6089	568	1	s.	s.	PROPN
ejpam-6089	568	2	naheed	nahee	VERB
ejpam-6089	568	3	et	et	PROPN
ejpam-6089	568	4	al	al	PROPN
ejpam-6089	568	5	.	.	PUNCT
ejpam-6089	568	6	/	/	SYM
ejpam-6089	568	7	eur	eur	PROPN
ejpam-6089	568	8	.	.	PUNCT
ejpam-6089	569	1	j.	j.	PROPN
ejpam-6089	569	2	pure	pure	PROPN
ejpam-6089	569	3	appl	appl	PROPN
ejpam-6089	569	4	.	.	PROPN
ejpam-6089	569	5	math	math	PROPN
ejpam-6089	569	6	,	,	PUNCT
ejpam-6089	569	7	18	18	NUM
ejpam-6089	569	8	(	(	PUNCT
ejpam-6089	569	9	2	2	NUM
ejpam-6089	569	10	)	)	PUNCT
ejpam-6089	569	11	(	(	PUNCT
ejpam-6089	569	12	2025	2025	NUM
ejpam-6089	569	13	)	)	PUNCT
ejpam-6089	569	14	,	,	PUNCT
ejpam-6089	569	15	6089	6089	NUM
ejpam-6089	569	16	26	26	NUM
ejpam-6089	569	17	of	of	ADP
ejpam-6089	569	18	34	34	NUM
ejpam-6089	569	19	3.2	3.2	NUM
ejpam-6089	569	20	.	.	PUNCT
ejpam-6089	570	1	an	an	DET
ejpam-6089	570	2	inequality	inequality	NOUN
ejpam-6089	570	3	of	of	ADP
ejpam-6089	570	4	midpoint	midpoint	NOUN
ejpam-6089	570	5	type	type	NOUN
ejpam-6089	570	6	for	for	ADP
ejpam-6089	570	7	the	the	DET
ejpam-6089	570	8	hermite	hermite	PROPN
ejpam-6089	570	9	-	-	PUNCT
ejpam-6089	570	10	hadamard	hadamard	ADJ
ejpam-6089	570	11	integrals	integral	NOUN
ejpam-6089	570	12	lemma	lemma	PROPN
ejpam-6089	570	13	4	4	X
ejpam-6089	570	14	.	.	PUNCT
ejpam-6089	571	1	let	let	VERB
ejpam-6089	571	2	υ	υ	NOUN
ejpam-6089	571	3	:	:	PUNCT
ejpam-6089	571	4	[	[	X
ejpam-6089	571	5	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	571	6	]	]	PUNCT
ejpam-6089	571	7	→	→	SYM
ejpam-6089	571	8	ℜ	ℜ	PROPN
ejpam-6089	571	9	is	be	AUX
ejpam-6089	571	10	an	an	DET
ejpam-6089	571	11	l1	l1	PROPN
ejpam-6089	571	12	function	function	NOUN
ejpam-6089	571	13	and	and	CCONJ
ejpam-6089	571	14	(	(	PUNCT
ejpam-6089	571	15	ℵð+	ℵð+	ADJ
ejpam-6089	571	16	℘	℘	PROPN
ejpam-6089	571	17	)	)	PUNCT
ejpam-6089	571	18	∈	∈	PROPN
ejpam-6089	571	19	(	(	PUNCT
ejpam-6089	571	20	0	0	NUM
ejpam-6089	571	21	,	,	PUNCT
ejpam-6089	571	22	1	1	NUM
ejpam-6089	571	23	)	)	PUNCT
ejpam-6089	571	24	also	also	ADV
ejpam-6089	571	25	a	a	DET
ejpam-6089	571	26	differentiable	differentiable	ADJ
ejpam-6089	571	27	function	function	NOUN
ejpam-6089	571	28	on	on	ADP
ejpam-6089	571	29	(	(	PUNCT
ejpam-6089	571	30	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	571	31	)	)	PUNCT
ejpam-6089	571	32	with	with	ADP
ejpam-6089	571	33	ℑ1	ℑ1	NOUN
ejpam-6089	571	34	<	<	X
ejpam-6089	571	35	ℑ2	ℑ2	PROPN
ejpam-6089	571	36	and	and	CCONJ
ejpam-6089	571	37	assume	assume	VERB
ejpam-6089	571	38	υ′	υ′	NOUN
ejpam-6089	571	39	∈	∈	NOUN
ejpam-6089	571	40	l1[ℑ1,ℑ2	l1[ℑ1,ℑ2	PROPN
ejpam-6089	571	41	]	]	PUNCT
ejpam-6089	571	42	.	.	PUNCT
ejpam-6089	572	1	consider	consider	VERB
ejpam-6089	572	2	♭	♭	PRON
ejpam-6089	572	3	,	,	PUNCT
ejpam-6089	572	4	ℵ	ℵ	NOUN
ejpam-6089	572	5	,	,	PUNCT
ejpam-6089	572	6	℘	℘	PROPN
ejpam-6089	572	7	,	,	PUNCT
ejpam-6089	572	8	τ	τ	PROPN
ejpam-6089	572	9	,	,	PUNCT
ejpam-6089	572	10	δ	δ	PROPN
ejpam-6089	572	11	,	,	PUNCT
ejpam-6089	572	12	b	b	PROPN
ejpam-6089	572	13	∈	∈	PROPN
ejpam-6089	572	14	c	c	NOUN
ejpam-6089	572	15	with	with	ADP
ejpam-6089	572	16	ℜ(ℵ),ℜ(℘),ℜ(τ	ℜ(ℵ),ℜ(℘),ℜ(τ	PROPN
ejpam-6089	572	17	)	)	PUNCT
ejpam-6089	572	18	>	>	X
ejpam-6089	572	19	0	0	NUM
ejpam-6089	572	20	and	and	CCONJ
ejpam-6089	572	21	ℜ(b	ℜ(b	NOUN
ejpam-6089	572	22	)	)	PUNCT
ejpam-6089	572	23	>	>	X
ejpam-6089	573	1	ℜ(δ	ℜ(δ	X
ejpam-6089	573	2	)	)	PUNCT
ejpam-6089	573	3	>	>	X
ejpam-6089	573	4	0	0	X
ejpam-6089	573	5	.	.	PUNCT
ejpam-6089	574	1	moreover	moreover	ADV
ejpam-6089	574	2	,	,	PUNCT
ejpam-6089	574	3	let	let	VERB
ejpam-6089	574	4	g	g	PROPN
ejpam-6089	574	5	≥	≥	NOUN
ejpam-6089	574	6	0	0	NUM
ejpam-6089	574	7	,	,	PUNCT
ejpam-6089	574	8	l	l	NOUN
ejpam-6089	574	9	>	>	X
ejpam-6089	574	10	0	0	PUNCT
ejpam-6089	574	11	and	and	CCONJ
ejpam-6089	574	12	0	0	NUM
ejpam-6089	574	13	<	<	X
ejpam-6089	574	14	s	s	X
ejpam-6089	574	15	≤	≤	NUM
ejpam-6089	574	16	l	l	NOUN
ejpam-6089	574	17	+	+	CCONJ
ejpam-6089	574	18	ℜ(ℵ	ℜ(ℵ	NOUN
ejpam-6089	574	19	)	)	PUNCT
ejpam-6089	574	20	.	.	PUNCT
ejpam-6089	575	1	under	under	ADP
ejpam-6089	575	2	these	these	DET
ejpam-6089	575	3	conditions	condition	NOUN
ejpam-6089	575	4	,	,	PUNCT
ejpam-6089	575	5	the	the	DET
ejpam-6089	575	6	following	follow	VERB
ejpam-6089	575	7	equality	equality	NOUN
ejpam-6089	575	8	for	for	ADP
ejpam-6089	575	9	fractional	fractional	ADJ
ejpam-6089	575	10	integrals	integral	NOUN
ejpam-6089	575	11	holds	hold	VERB
ejpam-6089	575	12	ε	ε	PROPN
ejpam-6089	575	13	♭	♭	PROPN
ejpam-6089	575	14	,δ	,δ	PUNCT
ejpam-6089	575	15	,	,	PUNCT
ejpam-6089	575	16	b	b	NOUN
ejpam-6089	575	17	,	,	PUNCT
ejpam-6089	575	18	s	s	X
ejpam-6089	575	19	,	,	PUNCT
ejpam-6089	575	20	l	l	NOUN
ejpam-6089	575	21	(	(	PUNCT
ejpam-6089	575	22	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	575	23	2	2	NUM
ejpam-6089	575	24	)	)	PUNCT
ejpam-6089	575	25	+	+	ADV
ejpam-6089	575	26	,	,	PUNCT
ejpam-6089	575	27	ℵ,℘,τ	ℵ,℘,τ	PROPN
ejpam-6089	575	28	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	575	29	;	;	PUNCT
ejpam-6089	575	30	g	g	NOUN
ejpam-6089	575	31	)	)	PUNCT
ejpam-6089	576	1	+	+	CCONJ
ejpam-6089	576	2	ε	ε	PROPN
ejpam-6089	576	3	♭	♭	PROPN
ejpam-6089	576	4	,δ	,δ	PUNCT
ejpam-6089	576	5	,	,	PUNCT
ejpam-6089	576	6	b	b	NOUN
ejpam-6089	576	7	,	,	PUNCT
ejpam-6089	576	8	s	s	X
ejpam-6089	576	9	,	,	PUNCT
ejpam-6089	576	10	l	l	NOUN
ejpam-6089	576	11	(	(	PUNCT
ejpam-6089	576	12	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	576	13	2	2	NUM
ejpam-6089	576	14	)	)	PUNCT
ejpam-6089	576	15	−,ℵ,℘,τ	−,ℵ,℘,τ	NOUN
ejpam-6089	576	16	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	576	17	;	;	PUNCT
ejpam-6089	576	18	g	g	NOUN
ejpam-6089	576	19	)	)	PUNCT
ejpam-6089	576	20	=	=	PUNCT
ejpam-6089	577	1	∞∑	∞∑	NUM
ejpam-6089	577	2	ð=0	ð=0	X
ejpam-6089	577	3	aðoð	aðoð	ADJ
ejpam-6089	577	4	×	×	NOUN
ejpam-6089	577	5	(	(	PUNCT
ejpam-6089	577	6	ℑ2	ℑ2	PROPN
ejpam-6089	577	7	−ℑ1	−ℑ1	PROPN
ejpam-6089	577	8	4	4	NUM
ejpam-6089	577	9	∫	∫	PROPN
ejpam-6089	577	10	1	1	NUM
ejpam-6089	577	11	0	0	NUM
ejpam-6089	577	12	t(ℵð+℘	t(ℵð+℘	NUM
ejpam-6089	577	13	)	)	PUNCT
ejpam-6089	577	14	(	(	PUNCT
ejpam-6089	577	15	υ′	υ′	X
ejpam-6089	577	16	(	(	PUNCT
ejpam-6089	577	17	t	t	PROPN
ejpam-6089	577	18	2	2	NUM
ejpam-6089	577	19	ℑ1	ℑ1	NOUN
ejpam-6089	577	20	+	+	CCONJ
ejpam-6089	577	21	2−	2−	NUM
ejpam-6089	577	22	t	t	NOUN
ejpam-6089	577	23	2	2	NUM
ejpam-6089	577	24	ℑ2	ℑ2	ADJ
ejpam-6089	577	25	)	)	PUNCT
ejpam-6089	577	26	−υ′	−υ′	NOUN
ejpam-6089	577	27	(	(	PUNCT
ejpam-6089	577	28	2−	2−	NUM
ejpam-6089	577	29	t	t	NOUN
ejpam-6089	577	30	2	2	NUM
ejpam-6089	577	31	ℑ1	ℑ1	NOUN
ejpam-6089	577	32	+	+	CCONJ
ejpam-6089	577	33	t	t	PROPN
ejpam-6089	577	34	2	2	NUM
ejpam-6089	577	35	ℑ2	ℑ2	PROPN
ejpam-6089	577	36	)	)	PUNCT
ejpam-6089	577	37	)	)	PUNCT
ejpam-6089	577	38	dt	dt	PUNCT
ejpam-6089	577	39	)	)	PUNCT
ejpam-6089	578	1	+	+	CCONJ
ejpam-6089	578	2	∞∑	∞∑	NUM
ejpam-6089	578	3	ð=0	ð=0	X
ejpam-6089	578	4	aðoðυ	aðoðυ	NOUN
ejpam-6089	578	5	(	(	PUNCT
ejpam-6089	578	6	ℑ1	ℑ1	PROPN
ejpam-6089	578	7	+	+	CCONJ
ejpam-6089	578	8	ℑ2	ℑ2	PROPN
ejpam-6089	578	9	2	2	NUM
ejpam-6089	578	10	)	)	PUNCT
ejpam-6089	578	11	,	,	PUNCT
ejpam-6089	578	12	where	where	SCONJ
ejpam-6089	578	13	að	að	PROPN
ejpam-6089	578	14	=	=	SYM
ejpam-6089	578	15	bg(δ+ðs	bg(δ+ðs	PROPN
ejpam-6089	578	16	,	,	PUNCT
ejpam-6089	578	17	b−δ	b−δ	NOUN
ejpam-6089	578	18	)	)	PUNCT
ejpam-6089	578	19	b(δ	b(δ	NOUN
ejpam-6089	578	20	,	,	PUNCT
ejpam-6089	578	21	b−δ	b−δ	NOUN
ejpam-6089	578	22	)	)	PUNCT
ejpam-6089	578	23	(	(	PUNCT
ejpam-6089	578	24	b)ðs	b)ðs	PROPN
ejpam-6089	578	25	♭	♭	PROPN
ejpam-6089	578	26	ð	ð	X
ejpam-6089	578	27	(	(	PUNCT
ejpam-6089	578	28	τ)ðl	τ)ðl	PROPN
ejpam-6089	578	29	and	and	CCONJ
ejpam-6089	578	30	oð	oð	X
ejpam-6089	578	31	=	=	SYM
ejpam-6089	578	32	(	(	PUNCT
ejpam-6089	578	33	ℑ2−ℑ1)(ℵð+℘	ℑ2−ℑ1)(ℵð+℘	PROPN
ejpam-6089	578	34	)	)	PUNCT
ejpam-6089	578	35	2(ℵð+℘)−1γ((ℵð+℘)+1	2(ℵð+℘)−1γ((ℵð+℘)+1	NUM
ejpam-6089	578	36	)	)	PUNCT
ejpam-6089	578	37	with	with	ADP
ejpam-6089	578	38	(	(	PUNCT
ejpam-6089	578	39	ℵð+	ℵð+	ADJ
ejpam-6089	578	40	℘	℘	PROPN
ejpam-6089	578	41	)	)	PUNCT
ejpam-6089	578	42	>	>	X
ejpam-6089	578	43	0	0	X
ejpam-6089	578	44	.	.	PUNCT
ejpam-6089	579	1	proof	proof	NOUN
ejpam-6089	579	2	.	.	PUNCT
ejpam-6089	580	1	replacing	replace	VERB
ejpam-6089	580	2	α∗	α∗	NOUN
ejpam-6089	580	3	by	by	ADP
ejpam-6089	580	4	(	(	PUNCT
ejpam-6089	580	5	ℵð+	ℵð+	ADJ
ejpam-6089	580	6	℘	℘	PROPN
ejpam-6089	580	7	)	)	PUNCT
ejpam-6089	580	8	in	in	ADP
ejpam-6089	580	9	lemma	lemma	PROPN
ejpam-6089	580	10	2	2	NUM
ejpam-6089	580	11	,	,	PUNCT
ejpam-6089	580	12	we	we	PRON
ejpam-6089	580	13	get	get	VERB
ejpam-6089	580	14	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	580	15	℘	℘	NOUN
ejpam-6089	580	16	)	)	PUNCT
ejpam-6089	580	17	+	+	NUM
ejpam-6089	580	18	1	1	X
ejpam-6089	580	19	)	)	PUNCT
ejpam-6089	580	20	(	(	PUNCT
ejpam-6089	580	21	ℑ2	ℑ2	ADP
ejpam-6089	580	22	−ℑ1)(ℵð+℘	−ℑ1)(ℵð+℘	NUM
ejpam-6089	580	23	)	)	PUNCT
ejpam-6089	580	24	(	(	PUNCT
ejpam-6089	580	25	r−li	r−li	NOUN
ejpam-6089	580	26	(	(	PUNCT
ejpam-6089	580	27	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	580	28	)	)	PUNCT
ejpam-6089	580	29	(	(	PUNCT
ejpam-6089	580	30	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	580	31	2	2	NUM
ejpam-6089	580	32	)	)	PUNCT
ejpam-6089	580	33	+	+	CCONJ
ejpam-6089	581	1	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	581	2	)	)	PUNCT
ejpam-6089	581	3	+	+	NUM
ejpam-6089	581	4	r−li	r−li	NOUN
ejpam-6089	581	5	(	(	PUNCT
ejpam-6089	581	6	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	581	7	)	)	PUNCT
ejpam-6089	581	8	(	(	PUNCT
ejpam-6089	581	9	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	581	10	2	2	NUM
ejpam-6089	581	11	)	)	PUNCT
ejpam-6089	581	12	−	−	PROPN
ejpam-6089	581	13	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	581	14	)	)	PUNCT
ejpam-6089	581	15	)	)	PUNCT
ejpam-6089	581	16	−υ	−υ	NOUN
ejpam-6089	581	17	(	(	PUNCT
ejpam-6089	581	18	ℑ1	ℑ1	PROPN
ejpam-6089	581	19	+	+	CCONJ
ejpam-6089	581	20	ℑ2	ℑ2	PROPN
ejpam-6089	581	21	2	2	NUM
ejpam-6089	581	22	)	)	PUNCT
ejpam-6089	581	23	=	=	VERB
ejpam-6089	582	1	ℑ2	ℑ2	PROPN
ejpam-6089	582	2	−ℑ1	−ℑ1	NOUN
ejpam-6089	582	3	4	4	NUM
ejpam-6089	582	4	∫	∫	PROPN
ejpam-6089	582	5	1	1	NUM
ejpam-6089	582	6	0	0	NUM
ejpam-6089	582	7	t(ℵð+℘	t(ℵð+℘	NOUN
ejpam-6089	582	8	)	)	PUNCT
ejpam-6089	582	9	×	×	NOUN
ejpam-6089	582	10	(	(	PUNCT
ejpam-6089	582	11	υ′	υ′	X
ejpam-6089	582	12	(	(	PUNCT
ejpam-6089	582	13	t	t	PROPN
ejpam-6089	582	14	2	2	NUM
ejpam-6089	582	15	ℑ1	ℑ1	NOUN
ejpam-6089	582	16	+	+	CCONJ
ejpam-6089	582	17	2−	2−	NUM
ejpam-6089	582	18	t	t	NOUN
ejpam-6089	582	19	2	2	NUM
ejpam-6089	582	20	ℑ2	ℑ2	ADJ
ejpam-6089	582	21	)	)	PUNCT
ejpam-6089	582	22	−υ′	−υ′	NOUN
ejpam-6089	582	23	(	(	PUNCT
ejpam-6089	582	24	2−	2−	NUM
ejpam-6089	582	25	t	t	NOUN
ejpam-6089	582	26	2	2	NUM
ejpam-6089	582	27	ℑ1	ℑ1	NOUN
ejpam-6089	582	28	+	+	CCONJ
ejpam-6089	582	29	t	t	PROPN
ejpam-6089	582	30	2	2	NUM
ejpam-6089	582	31	ℑ2	ℑ2	PROPN
ejpam-6089	582	32	)	)	PUNCT
ejpam-6089	582	33	)	)	PUNCT
ejpam-6089	583	1	dt	dt	X
ejpam-6089	583	2	.	.	PUNCT
ejpam-6089	584	1	multiplying	multiply	VERB
ejpam-6089	584	2	the	the	DET
ejpam-6089	584	3	above	above	ADJ
ejpam-6089	584	4	expression	expression	NOUN
ejpam-6089	584	5	with	with	ADP
ejpam-6089	584	6	(	(	PUNCT
ejpam-6089	584	7	ℑ2−ℑ1)(ℵð+℘	ℑ2−ℑ1)(ℵð+℘	NOUN
ejpam-6089	584	8	)	)	PUNCT
ejpam-6089	584	9	2(ℵð+℘)−1γ((ℵð+℘)+1	2(ℵð+℘)−1γ((ℵð+℘)+1	NUM
ejpam-6089	584	10	)	)	PUNCT
ejpam-6089	584	11	,	,	PUNCT
ejpam-6089	584	12	we	we	PRON
ejpam-6089	584	13	get	get	VERB
ejpam-6089	584	14	(	(	PUNCT
ejpam-6089	584	15	r−li	r−li	NOUN
ejpam-6089	584	16	(	(	PUNCT
ejpam-6089	584	17	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	584	18	)	)	PUNCT
ejpam-6089	584	19	(	(	PUNCT
ejpam-6089	584	20	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	584	21	2	2	NUM
ejpam-6089	584	22	)	)	PUNCT
ejpam-6089	584	23	+	+	CCONJ
ejpam-6089	585	1	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	585	2	)	)	PUNCT
ejpam-6089	585	3	+	+	NUM
ejpam-6089	585	4	r−li	r−li	NOUN
ejpam-6089	585	5	(	(	PUNCT
ejpam-6089	585	6	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	585	7	)	)	PUNCT
ejpam-6089	585	8	(	(	PUNCT
ejpam-6089	585	9	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	585	10	2	2	NUM
ejpam-6089	585	11	)	)	PUNCT
ejpam-6089	585	12	−	−	PROPN
ejpam-6089	585	13	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	585	14	)	)	PUNCT
ejpam-6089	585	15	)	)	PUNCT
ejpam-6089	586	1	=	=	PRON
ejpam-6089	586	2	(	(	PUNCT
ejpam-6089	586	3	ℑ2	ℑ2	PROPN
ejpam-6089	586	4	−ℑ1	−ℑ1	PROPN
ejpam-6089	586	5	)	)	PUNCT
ejpam-6089	586	6	(	(	PUNCT
ejpam-6089	586	7	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	586	8	)	)	PUNCT
ejpam-6089	586	9	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	586	10	℘	℘	NOUN
ejpam-6089	586	11	)	)	PUNCT
ejpam-6089	586	12	+	+	CCONJ
ejpam-6089	586	13	1	1	X
ejpam-6089	586	14	)	)	PUNCT
ejpam-6089	586	15	×	×	NOUN
ejpam-6089	586	16	(	(	PUNCT
ejpam-6089	586	17	ℑ2	ℑ2	PROPN
ejpam-6089	586	18	−ℑ1	−ℑ1	PROPN
ejpam-6089	586	19	4	4	NUM
ejpam-6089	586	20	∫	∫	PROPN
ejpam-6089	586	21	1	1	NUM
ejpam-6089	586	22	0	0	NUM
ejpam-6089	586	23	t(ℵð+℘	t(ℵð+℘	NUM
ejpam-6089	586	24	)	)	PUNCT
ejpam-6089	586	25	(	(	PUNCT
ejpam-6089	586	26	υ′	υ′	X
ejpam-6089	586	27	(	(	PUNCT
ejpam-6089	586	28	t	t	PROPN
ejpam-6089	586	29	2	2	NUM
ejpam-6089	586	30	ℑ1	ℑ1	NOUN
ejpam-6089	586	31	+	+	CCONJ
ejpam-6089	586	32	2−	2−	NUM
ejpam-6089	586	33	t	t	NOUN
ejpam-6089	586	34	2	2	NUM
ejpam-6089	586	35	ℑ2	ℑ2	ADJ
ejpam-6089	586	36	)	)	PUNCT
ejpam-6089	586	37	−υ′	−υ′	NOUN
ejpam-6089	586	38	(	(	PUNCT
ejpam-6089	586	39	2−	2−	NUM
ejpam-6089	586	40	t	t	NOUN
ejpam-6089	586	41	2	2	NUM
ejpam-6089	586	42	ℑ1	ℑ1	NOUN
ejpam-6089	586	43	+	+	CCONJ
ejpam-6089	586	44	t	t	PROPN
ejpam-6089	586	45	2	2	NUM
ejpam-6089	586	46	ℑ2	ℑ2	PROPN
ejpam-6089	586	47	)	)	PUNCT
ejpam-6089	586	48	)	)	PUNCT
ejpam-6089	586	49	dt	dt	PUNCT
ejpam-6089	586	50	)	)	PUNCT
ejpam-6089	587	1	+	+	CCONJ
ejpam-6089	587	2	(	(	PUNCT
ejpam-6089	587	3	ℑ2	ℑ2	PROPN
ejpam-6089	587	4	−ℑ1	−ℑ1	PROPN
ejpam-6089	587	5	)	)	PUNCT
ejpam-6089	587	6	(	(	PUNCT
ejpam-6089	587	7	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	587	8	)	)	PUNCT
ejpam-6089	587	9	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	587	10	℘	℘	NOUN
ejpam-6089	587	11	)	)	PUNCT
ejpam-6089	587	12	+	+	NUM
ejpam-6089	587	13	1	1	X
ejpam-6089	587	14	)	)	PUNCT
ejpam-6089	587	15	υ	υ	NOUN
ejpam-6089	587	16	(	(	PUNCT
ejpam-6089	587	17	ℑ1	ℑ1	PROPN
ejpam-6089	587	18	+	+	CCONJ
ejpam-6089	587	19	ℑ2	ℑ2	PROPN
ejpam-6089	587	20	2	2	NUM
ejpam-6089	587	21	)	)	PUNCT
ejpam-6089	587	22	.	.	PUNCT
ejpam-6089	588	1	again	again	ADV
ejpam-6089	588	2	we	we	PRON
ejpam-6089	588	3	multiply	multiply	VERB
ejpam-6089	588	4	the	the	DET
ejpam-6089	588	5	above	above	ADJ
ejpam-6089	588	6	equation	equation	NOUN
ejpam-6089	588	7	with	with	ADP
ejpam-6089	588	8	að	að	PROPN
ejpam-6089	588	9	að	að	PROPN
ejpam-6089	588	10	(	(	PUNCT
ejpam-6089	588	11	r−li	r−li	NOUN
ejpam-6089	588	12	(	(	PUNCT
ejpam-6089	588	13	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	588	14	)	)	PUNCT
ejpam-6089	588	15	(	(	PUNCT
ejpam-6089	588	16	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	588	17	2	2	NUM
ejpam-6089	588	18	)	)	PUNCT
ejpam-6089	588	19	+	+	CCONJ
ejpam-6089	589	1	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	589	2	)	)	PUNCT
ejpam-6089	589	3	+	+	NUM
ejpam-6089	589	4	r−li	r−li	NOUN
ejpam-6089	589	5	(	(	PUNCT
ejpam-6089	589	6	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	589	7	)	)	PUNCT
ejpam-6089	589	8	(	(	PUNCT
ejpam-6089	589	9	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	589	10	2	2	NUM
ejpam-6089	589	11	)	)	PUNCT
ejpam-6089	589	12	−	−	PROPN
ejpam-6089	589	13	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	589	14	)	)	PUNCT
ejpam-6089	589	15	)	)	PUNCT
ejpam-6089	590	1	=	=	SYM
ejpam-6089	590	2	að	að	PROPN
ejpam-6089	590	3	(	(	PUNCT
ejpam-6089	590	4	ℑ2	ℑ2	PROPN
ejpam-6089	590	5	−ℑ1	−ℑ1	PROPN
ejpam-6089	590	6	)	)	PUNCT
ejpam-6089	590	7	(	(	PUNCT
ejpam-6089	590	8	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	590	9	)	)	PUNCT
ejpam-6089	590	10	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	590	11	℘	℘	NOUN
ejpam-6089	590	12	)	)	PUNCT
ejpam-6089	590	13	+	+	NUM
ejpam-6089	590	14	1	1	X
ejpam-6089	590	15	)	)	PUNCT
ejpam-6089	590	16	s.	s.	PROPN
ejpam-6089	590	17	naheed	nahee	VERB
ejpam-6089	590	18	et	et	PROPN
ejpam-6089	590	19	al	al	PROPN
ejpam-6089	590	20	.	.	PUNCT
ejpam-6089	590	21	/	/	SYM
ejpam-6089	590	22	eur	eur	PROPN
ejpam-6089	590	23	.	.	PUNCT
ejpam-6089	591	1	j.	j.	PROPN
ejpam-6089	591	2	pure	pure	PROPN
ejpam-6089	591	3	appl	appl	PROPN
ejpam-6089	591	4	.	.	PROPN
ejpam-6089	591	5	math	math	PROPN
ejpam-6089	591	6	,	,	PUNCT
ejpam-6089	591	7	18	18	NUM
ejpam-6089	591	8	(	(	PUNCT
ejpam-6089	591	9	2	2	NUM
ejpam-6089	591	10	)	)	PUNCT
ejpam-6089	591	11	(	(	PUNCT
ejpam-6089	591	12	2025	2025	NUM
ejpam-6089	591	13	)	)	PUNCT
ejpam-6089	591	14	,	,	PUNCT
ejpam-6089	591	15	6089	6089	NUM
ejpam-6089	591	16	27	27	NUM
ejpam-6089	591	17	of	of	ADP
ejpam-6089	591	18	34	34	NUM
ejpam-6089	591	19	×	×	NOUN
ejpam-6089	591	20	(	(	PUNCT
ejpam-6089	591	21	ℑ2	ℑ2	PROPN
ejpam-6089	591	22	−ℑ1	−ℑ1	PROPN
ejpam-6089	591	23	4	4	NUM
ejpam-6089	591	24	∫	∫	PROPN
ejpam-6089	591	25	1	1	NUM
ejpam-6089	591	26	0	0	NUM
ejpam-6089	591	27	t(ℵð+℘	t(ℵð+℘	NUM
ejpam-6089	591	28	)	)	PUNCT
ejpam-6089	591	29	(	(	PUNCT
ejpam-6089	591	30	υ′	υ′	X
ejpam-6089	591	31	(	(	PUNCT
ejpam-6089	591	32	t	t	PROPN
ejpam-6089	591	33	2	2	NUM
ejpam-6089	591	34	ℑ1	ℑ1	NOUN
ejpam-6089	591	35	+	+	CCONJ
ejpam-6089	591	36	2−	2−	NUM
ejpam-6089	591	37	t	t	NOUN
ejpam-6089	591	38	2	2	NUM
ejpam-6089	591	39	ℑ2	ℑ2	ADJ
ejpam-6089	591	40	)	)	PUNCT
ejpam-6089	591	41	−υ′	−υ′	NOUN
ejpam-6089	591	42	(	(	PUNCT
ejpam-6089	591	43	2−	2−	NUM
ejpam-6089	591	44	t	t	NOUN
ejpam-6089	591	45	2	2	NUM
ejpam-6089	591	46	ℑ1	ℑ1	NOUN
ejpam-6089	591	47	+	+	CCONJ
ejpam-6089	591	48	t	t	PROPN
ejpam-6089	591	49	2	2	NUM
ejpam-6089	591	50	ℑ2	ℑ2	PROPN
ejpam-6089	591	51	)	)	PUNCT
ejpam-6089	591	52	)	)	PUNCT
ejpam-6089	591	53	dt	dt	PUNCT
ejpam-6089	591	54	)	)	PUNCT
ejpam-6089	592	1	+	+	CCONJ
ejpam-6089	592	2	að	að	X
ejpam-6089	592	3	(	(	PUNCT
ejpam-6089	592	4	ℑ2	ℑ2	PROPN
ejpam-6089	592	5	−ℑ1	−ℑ1	PROPN
ejpam-6089	592	6	)	)	PUNCT
ejpam-6089	592	7	(	(	PUNCT
ejpam-6089	592	8	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	592	9	)	)	PUNCT
ejpam-6089	592	10	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	592	11	℘	℘	NOUN
ejpam-6089	592	12	)	)	PUNCT
ejpam-6089	592	13	+	+	NUM
ejpam-6089	592	14	1	1	X
ejpam-6089	592	15	)	)	PUNCT
ejpam-6089	592	16	υ	υ	NOUN
ejpam-6089	592	17	(	(	PUNCT
ejpam-6089	592	18	ℑ1	ℑ1	PROPN
ejpam-6089	592	19	+	+	CCONJ
ejpam-6089	592	20	ℑ2	ℑ2	PROPN
ejpam-6089	592	21	2	2	NUM
ejpam-6089	592	22	)	)	PUNCT
ejpam-6089	592	23	.	.	PUNCT
ejpam-6089	593	1	summing	sum	VERB
ejpam-6089	593	2	over	over	ADP
ejpam-6089	593	3	all	all	PRON
ejpam-6089	593	4	ð	ð	NOUN
ejpam-6089	593	5	∞∑	∞∑	NUM
ejpam-6089	593	6	ð=0	ð=0	X
ejpam-6089	593	7	að	að	X
ejpam-6089	593	8	(	(	PUNCT
ejpam-6089	593	9	r−li	r−li	NOUN
ejpam-6089	593	10	(	(	PUNCT
ejpam-6089	593	11	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	593	12	)	)	PUNCT
ejpam-6089	593	13	(	(	PUNCT
ejpam-6089	593	14	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	593	15	2	2	NUM
ejpam-6089	593	16	)	)	PUNCT
ejpam-6089	593	17	+	+	CCONJ
ejpam-6089	593	18	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	593	19	)	)	PUNCT
ejpam-6089	593	20	+	+	NUM
ejpam-6089	593	21	r−li	r−li	NOUN
ejpam-6089	593	22	(	(	PUNCT
ejpam-6089	593	23	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	593	24	)	)	PUNCT
ejpam-6089	593	25	(	(	PUNCT
ejpam-6089	593	26	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	593	27	2	2	NUM
ejpam-6089	593	28	)	)	PUNCT
ejpam-6089	593	29	−	−	PROPN
ejpam-6089	593	30	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	593	31	)	)	PUNCT
ejpam-6089	593	32	)	)	PUNCT
ejpam-6089	594	1	=	=	PUNCT
ejpam-6089	595	1	∞∑	∞∑	NUM
ejpam-6089	595	2	ð=0	ð=0	X
ejpam-6089	595	3	að	að	X
ejpam-6089	595	4	(	(	PUNCT
ejpam-6089	595	5	ℑ2	ℑ2	PROPN
ejpam-6089	595	6	−ℑ1	−ℑ1	PROPN
ejpam-6089	595	7	)	)	PUNCT
ejpam-6089	595	8	(	(	PUNCT
ejpam-6089	595	9	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	595	10	)	)	PUNCT
ejpam-6089	595	11	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	595	12	℘	℘	NOUN
ejpam-6089	595	13	)	)	PUNCT
ejpam-6089	595	14	+	+	CCONJ
ejpam-6089	595	15	1	1	X
ejpam-6089	595	16	)	)	PUNCT
ejpam-6089	595	17	×	×	NOUN
ejpam-6089	595	18	(	(	PUNCT
ejpam-6089	595	19	ℑ2	ℑ2	PROPN
ejpam-6089	595	20	−ℑ1	−ℑ1	PROPN
ejpam-6089	595	21	4	4	NUM
ejpam-6089	595	22	∫	∫	PROPN
ejpam-6089	595	23	1	1	NUM
ejpam-6089	595	24	0	0	NUM
ejpam-6089	595	25	t(ℵð+℘	t(ℵð+℘	NUM
ejpam-6089	595	26	)	)	PUNCT
ejpam-6089	595	27	(	(	PUNCT
ejpam-6089	595	28	υ′	υ′	X
ejpam-6089	595	29	(	(	PUNCT
ejpam-6089	595	30	t	t	PROPN
ejpam-6089	595	31	2	2	NUM
ejpam-6089	595	32	ℑ1	ℑ1	NOUN
ejpam-6089	595	33	+	+	CCONJ
ejpam-6089	595	34	2−	2−	NUM
ejpam-6089	595	35	t	t	NOUN
ejpam-6089	595	36	2	2	NUM
ejpam-6089	595	37	ℑ2	ℑ2	ADJ
ejpam-6089	595	38	)	)	PUNCT
ejpam-6089	595	39	−υ′	−υ′	NOUN
ejpam-6089	595	40	(	(	PUNCT
ejpam-6089	595	41	2−	2−	NUM
ejpam-6089	595	42	t	t	NOUN
ejpam-6089	595	43	2	2	NUM
ejpam-6089	595	44	ℑ1	ℑ1	NOUN
ejpam-6089	595	45	+	+	CCONJ
ejpam-6089	595	46	t	t	PROPN
ejpam-6089	595	47	2	2	NUM
ejpam-6089	595	48	ℑ2	ℑ2	PROPN
ejpam-6089	595	49	)	)	PUNCT
ejpam-6089	595	50	)	)	PUNCT
ejpam-6089	595	51	dt	dt	PUNCT
ejpam-6089	595	52	)	)	PUNCT
ejpam-6089	596	1	+	+	CCONJ
ejpam-6089	596	2	∞∑	∞∑	NUM
ejpam-6089	596	3	ð=0	ð=0	X
ejpam-6089	596	4	að	að	X
ejpam-6089	596	5	(	(	PUNCT
ejpam-6089	596	6	ℑ2	ℑ2	PROPN
ejpam-6089	596	7	−ℑ1	−ℑ1	PROPN
ejpam-6089	596	8	)	)	PUNCT
ejpam-6089	596	9	(	(	PUNCT
ejpam-6089	596	10	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	596	11	)	)	PUNCT
ejpam-6089	596	12	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	596	13	℘	℘	NOUN
ejpam-6089	596	14	)	)	PUNCT
ejpam-6089	596	15	+	+	NUM
ejpam-6089	596	16	1	1	X
ejpam-6089	596	17	)	)	PUNCT
ejpam-6089	596	18	υ	υ	NOUN
ejpam-6089	596	19	(	(	PUNCT
ejpam-6089	596	20	ℑ1	ℑ1	PROPN
ejpam-6089	596	21	+	+	CCONJ
ejpam-6089	596	22	ℑ2	ℑ2	PROPN
ejpam-6089	596	23	2	2	NUM
ejpam-6089	596	24	)	)	PUNCT
ejpam-6089	596	25	.	.	PUNCT
ejpam-6089	597	1	using	use	VERB
ejpam-6089	597	2	proposition	proposition	NOUN
ejpam-6089	597	3	1	1	NUM
ejpam-6089	597	4	from	from	ADP
ejpam-6089	597	5	the	the	DET
ejpam-6089	597	6	middle	middle	NOUN
ejpam-6089	597	7	of	of	ADP
ejpam-6089	597	8	interval	interval	NOUN
ejpam-6089	597	9	[	[	X
ejpam-6089	597	10	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	597	11	]	]	PUNCT
ejpam-6089	597	12	,	,	PUNCT
ejpam-6089	597	13	we	we	PRON
ejpam-6089	597	14	obtain	obtain	VERB
ejpam-6089	597	15	ε	ε	PROPN
ejpam-6089	597	16	♭	♭	PROPN
ejpam-6089	597	17	,δ	,δ	PUNCT
ejpam-6089	597	18	,	,	PUNCT
ejpam-6089	597	19	b	b	NOUN
ejpam-6089	597	20	,	,	PUNCT
ejpam-6089	597	21	s	s	X
ejpam-6089	597	22	,	,	PUNCT
ejpam-6089	597	23	l	l	NOUN
ejpam-6089	597	24	(	(	PUNCT
ejpam-6089	597	25	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	597	26	2	2	NUM
ejpam-6089	597	27	)	)	PUNCT
ejpam-6089	598	1	+	+	ADV
ejpam-6089	598	2	,	,	PUNCT
ejpam-6089	598	3	ℵ,℘,τ	ℵ,℘,τ	PROPN
ejpam-6089	598	4	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	598	5	;	;	PUNCT
ejpam-6089	598	6	g	g	NOUN
ejpam-6089	598	7	)	)	PUNCT
ejpam-6089	599	1	+	+	CCONJ
ejpam-6089	599	2	ε	ε	PROPN
ejpam-6089	599	3	♭	♭	PROPN
ejpam-6089	599	4	,δ	,δ	PUNCT
ejpam-6089	599	5	,	,	PUNCT
ejpam-6089	599	6	b	b	NOUN
ejpam-6089	599	7	,	,	PUNCT
ejpam-6089	599	8	s	s	X
ejpam-6089	599	9	,	,	PUNCT
ejpam-6089	599	10	l	l	NOUN
ejpam-6089	599	11	(	(	PUNCT
ejpam-6089	599	12	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	599	13	2	2	NUM
ejpam-6089	599	14	)	)	PUNCT
ejpam-6089	599	15	−,ℵ,℘,τ	−,ℵ,℘,τ	NOUN
ejpam-6089	599	16	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	599	17	;	;	PUNCT
ejpam-6089	599	18	g	g	NOUN
ejpam-6089	599	19	)	)	PUNCT
ejpam-6089	599	20	=	=	PUNCT
ejpam-6089	600	1	∞∑	∞∑	NUM
ejpam-6089	600	2	ð=0	ð=0	X
ejpam-6089	600	3	aðoð	aðoð	ADJ
ejpam-6089	600	4	×	×	NOUN
ejpam-6089	600	5	(	(	PUNCT
ejpam-6089	600	6	ℑ2	ℑ2	PROPN
ejpam-6089	600	7	−ℑ1	−ℑ1	PROPN
ejpam-6089	600	8	4	4	NUM
ejpam-6089	600	9	∫	∫	PROPN
ejpam-6089	600	10	1	1	NUM
ejpam-6089	600	11	0	0	NUM
ejpam-6089	600	12	t(ℵð+℘	t(ℵð+℘	NUM
ejpam-6089	600	13	)	)	PUNCT
ejpam-6089	600	14	(	(	PUNCT
ejpam-6089	600	15	υ′	υ′	X
ejpam-6089	600	16	(	(	PUNCT
ejpam-6089	600	17	t	t	PROPN
ejpam-6089	600	18	2	2	NUM
ejpam-6089	600	19	ℑ1	ℑ1	NOUN
ejpam-6089	600	20	+	+	CCONJ
ejpam-6089	600	21	2−	2−	NUM
ejpam-6089	600	22	t	t	NOUN
ejpam-6089	600	23	2	2	NUM
ejpam-6089	600	24	ℑ2	ℑ2	PROPN
ejpam-6089	600	25	)	)	PUNCT
ejpam-6089	600	26	−	−	PROPN
ejpam-6089	601	1	f	f	X
ejpam-6089	601	2	′	′	NUM
ejpam-6089	602	1	(	(	PUNCT
ejpam-6089	602	2	2−	2−	NUM
ejpam-6089	602	3	t	t	NOUN
ejpam-6089	602	4	2	2	NUM
ejpam-6089	602	5	ℑ1	ℑ1	NOUN
ejpam-6089	602	6	+	+	CCONJ
ejpam-6089	602	7	t	t	PROPN
ejpam-6089	602	8	2	2	NUM
ejpam-6089	602	9	ℑ2	ℑ2	PROPN
ejpam-6089	602	10	)	)	PUNCT
ejpam-6089	602	11	)	)	PUNCT
ejpam-6089	602	12	dt	dt	PUNCT
ejpam-6089	602	13	)	)	PUNCT
ejpam-6089	603	1	+	+	CCONJ
ejpam-6089	603	2	∞∑	∞∑	NUM
ejpam-6089	603	3	ð=0	ð=0	X
ejpam-6089	603	4	aðoðυ	aðoðυ	NOUN
ejpam-6089	603	5	(	(	PUNCT
ejpam-6089	603	6	ℑ1	ℑ1	PROPN
ejpam-6089	603	7	+	+	CCONJ
ejpam-6089	603	8	ℑ2	ℑ2	PROPN
ejpam-6089	603	9	2	2	NUM
ejpam-6089	603	10	)	)	PUNCT
ejpam-6089	603	11	.	.	PUNCT
ejpam-6089	604	1	this	this	PRON
ejpam-6089	604	2	is	be	AUX
ejpam-6089	604	3	our	our	PRON
ejpam-6089	604	4	required	required	ADJ
ejpam-6089	604	5	result	result	NOUN
ejpam-6089	604	6	.	.	PUNCT
ejpam-6089	605	1	theorem	theorem	ADJ
ejpam-6089	605	2	10	10	NUM
ejpam-6089	605	3	.	.	PUNCT
ejpam-6089	606	1	let	let	VERB
ejpam-6089	606	2	υ	υ	NOUN
ejpam-6089	606	3	:	:	PUNCT
ejpam-6089	606	4	[	[	X
ejpam-6089	606	5	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	606	6	]	]	PUNCT
ejpam-6089	606	7	→	→	SYM
ejpam-6089	606	8	ℜ	ℜ	PROPN
ejpam-6089	606	9	is	be	AUX
ejpam-6089	606	10	an	an	DET
ejpam-6089	606	11	l1	l1	PROPN
ejpam-6089	606	12	function	function	NOUN
ejpam-6089	606	13	and	and	CCONJ
ejpam-6089	606	14	(	(	PUNCT
ejpam-6089	606	15	ℵð+	ℵð+	ADJ
ejpam-6089	606	16	℘	℘	PROPN
ejpam-6089	606	17	)	)	PUNCT
ejpam-6089	606	18	∈	∈	PROPN
ejpam-6089	606	19	(	(	PUNCT
ejpam-6089	606	20	0	0	NUM
ejpam-6089	606	21	,	,	PUNCT
ejpam-6089	606	22	1	1	NUM
ejpam-6089	606	23	)	)	PUNCT
ejpam-6089	606	24	also	also	ADV
ejpam-6089	606	25	a	a	DET
ejpam-6089	606	26	differentiable	differentiable	ADJ
ejpam-6089	606	27	function	function	NOUN
ejpam-6089	606	28	on	on	ADP
ejpam-6089	606	29	(	(	PUNCT
ejpam-6089	606	30	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	606	31	)	)	PUNCT
ejpam-6089	606	32	with	with	ADP
ejpam-6089	606	33	ℑ1	ℑ1	NOUN
ejpam-6089	606	34	<	<	X
ejpam-6089	606	35	ℑ2	ℑ2	PROPN
ejpam-6089	606	36	and	and	CCONJ
ejpam-6089	606	37	assume	assume	VERB
ejpam-6089	606	38	υ′	υ′	NOUN
ejpam-6089	606	39	∈	∈	NOUN
ejpam-6089	606	40	l1[ℑ1,ℑ2	l1[ℑ1,ℑ2	PROPN
ejpam-6089	606	41	]	]	PUNCT
ejpam-6089	606	42	.	.	PUNCT
ejpam-6089	607	1	consider	consider	VERB
ejpam-6089	607	2	♭	♭	PRON
ejpam-6089	607	3	,	,	PUNCT
ejpam-6089	607	4	ℵ	ℵ	NOUN
ejpam-6089	607	5	,	,	PUNCT
ejpam-6089	607	6	℘	℘	PROPN
ejpam-6089	607	7	,	,	PUNCT
ejpam-6089	607	8	τ	τ	PROPN
ejpam-6089	607	9	,	,	PUNCT
ejpam-6089	607	10	δ	δ	PROPN
ejpam-6089	607	11	,	,	PUNCT
ejpam-6089	607	12	b	b	PROPN
ejpam-6089	607	13	∈	∈	PROPN
ejpam-6089	607	14	c	c	NOUN
ejpam-6089	607	15	with	with	ADP
ejpam-6089	607	16	ℜ(ℵ),ℜ(℘),ℜ(τ	ℜ(ℵ),ℜ(℘),ℜ(τ	PROPN
ejpam-6089	607	17	)	)	PUNCT
ejpam-6089	607	18	>	>	X
ejpam-6089	607	19	0	0	NUM
ejpam-6089	607	20	and	and	CCONJ
ejpam-6089	607	21	ℜ(b	ℜ(b	NOUN
ejpam-6089	607	22	)	)	PUNCT
ejpam-6089	607	23	>	>	X
ejpam-6089	608	1	ℜ(δ	ℜ(δ	X
ejpam-6089	608	2	)	)	PUNCT
ejpam-6089	608	3	>	>	X
ejpam-6089	608	4	0	0	X
ejpam-6089	608	5	.	.	PUNCT
ejpam-6089	609	1	moreover	moreover	ADV
ejpam-6089	609	2	,	,	PUNCT
ejpam-6089	609	3	let	let	VERB
ejpam-6089	609	4	g	g	PROPN
ejpam-6089	609	5	≥	≥	NOUN
ejpam-6089	609	6	0	0	NUM
ejpam-6089	609	7	,	,	PUNCT
ejpam-6089	609	8	l	l	NOUN
ejpam-6089	609	9	>	>	X
ejpam-6089	609	10	0	0	PUNCT
ejpam-6089	609	11	and	and	CCONJ
ejpam-6089	609	12	0	0	NUM
ejpam-6089	609	13	<	<	X
ejpam-6089	609	14	s	s	X
ejpam-6089	609	15	≤	≤	NUM
ejpam-6089	609	16	l	l	NOUN
ejpam-6089	609	17	+	+	CCONJ
ejpam-6089	609	18	ℜ(ℵ	ℜ(ℵ	NOUN
ejpam-6089	609	19	)	)	PUNCT
ejpam-6089	609	20	(	(	PUNCT
ejpam-6089	609	21	ε	ε	PROPN
ejpam-6089	609	22	♭	♭	PROPN
ejpam-6089	609	23	,δ	,δ	PUNCT
ejpam-6089	609	24	,	,	PUNCT
ejpam-6089	609	25	b	b	NOUN
ejpam-6089	609	26	,	,	PUNCT
ejpam-6089	609	27	s	s	X
ejpam-6089	609	28	,	,	PUNCT
ejpam-6089	609	29	l	l	NOUN
ejpam-6089	609	30	(	(	PUNCT
ejpam-6089	609	31	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	609	32	2	2	NUM
ejpam-6089	609	33	)	)	PUNCT
ejpam-6089	610	1	+	+	ADP
ejpam-6089	610	2	,	,	PUNCT
ejpam-6089	610	3	ℵ,℘,τ	ℵ,℘,τ	NOUN
ejpam-6089	610	4	υ	υ	NOUN
ejpam-6089	610	5	)	)	PUNCT
ejpam-6089	610	6	(	(	PUNCT
ejpam-6089	610	7	ℑ2	ℑ2	PROPN
ejpam-6089	610	8	;	;	PUNCT
ejpam-6089	610	9	g	g	NOUN
ejpam-6089	610	10	)	)	PUNCT
ejpam-6089	610	11	+	+	CCONJ
ejpam-6089	610	12	(	(	PUNCT
ejpam-6089	610	13	ε	ε	PROPN
ejpam-6089	610	14	♭	♭	PROPN
ejpam-6089	610	15	,δ	,δ	PUNCT
ejpam-6089	610	16	,	,	PUNCT
ejpam-6089	610	17	b	b	NOUN
ejpam-6089	610	18	,	,	PUNCT
ejpam-6089	610	19	s	s	X
ejpam-6089	610	20	,	,	PUNCT
ejpam-6089	610	21	l	l	NOUN
ejpam-6089	610	22	(	(	PUNCT
ejpam-6089	610	23	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	610	24	2	2	NUM
ejpam-6089	610	25	)	)	PUNCT
ejpam-6089	610	26	−,ℵ,℘,τ	−,ℵ,℘,τ	NOUN
ejpam-6089	610	27	υ	υ	PROPN
ejpam-6089	610	28	)	)	PUNCT
ejpam-6089	610	29	(	(	PUNCT
ejpam-6089	610	30	ℑ1	ℑ1	NOUN
ejpam-6089	610	31	;	;	PUNCT
ejpam-6089	610	32	g	g	NOUN
ejpam-6089	610	33	)	)	PUNCT
ejpam-6089	610	34	−	−	PROPN
ejpam-6089	611	1	∞∑	∞∑	NUM
ejpam-6089	611	2	ð=0	ð=0	X
ejpam-6089	611	3	að	að	X
ejpam-6089	611	4	(	(	PUNCT
ejpam-6089	611	5	oð	oð	PROPN
ejpam-6089	611	6	−	−	PROPN
ejpam-6089	611	7	1)υ	1)υ	NUM
ejpam-6089	611	8	(	(	PUNCT
ejpam-6089	611	9	ℑ1	ℑ1	PROPN
ejpam-6089	611	10	+	+	CCONJ
ejpam-6089	611	11	ℑ2	ℑ2	PROPN
ejpam-6089	611	12	2	2	NUM
ejpam-6089	611	13	)	)	PUNCT
ejpam-6089	611	14	≥	≥	NOUN
ejpam-6089	611	15	∞∑	∞∑	NUM
ejpam-6089	611	16	ð=0	ð=0	X
ejpam-6089	611	17	aðoð	aðoð	ADJ
ejpam-6089	611	18	s.	s.	PROPN
ejpam-6089	611	19	naheed	nahee	VERB
ejpam-6089	611	20	et	et	PROPN
ejpam-6089	611	21	al	al	PROPN
ejpam-6089	611	22	.	.	PUNCT
ejpam-6089	611	23	/	/	SYM
ejpam-6089	611	24	eur	eur	PROPN
ejpam-6089	611	25	.	.	PUNCT
ejpam-6089	612	1	j.	j.	PROPN
ejpam-6089	612	2	pure	pure	PROPN
ejpam-6089	612	3	appl	appl	PROPN
ejpam-6089	612	4	.	.	PROPN
ejpam-6089	612	5	math	math	PROPN
ejpam-6089	612	6	,	,	PUNCT
ejpam-6089	612	7	18	18	NUM
ejpam-6089	612	8	(	(	PUNCT
ejpam-6089	612	9	2	2	NUM
ejpam-6089	612	10	)	)	PUNCT
ejpam-6089	612	11	(	(	PUNCT
ejpam-6089	612	12	2025	2025	NUM
ejpam-6089	612	13	)	)	PUNCT
ejpam-6089	612	14	,	,	PUNCT
ejpam-6089	612	15	6089	6089	NUM
ejpam-6089	612	16	28	28	NUM
ejpam-6089	612	17	of	of	ADP
ejpam-6089	612	18	34	34	NUM
ejpam-6089	612	19	×	×	NOUN
ejpam-6089	612	20	(	(	PUNCT
ejpam-6089	612	21	ℑ2	ℑ2	PROPN
ejpam-6089	612	22	−ℑ1	−ℑ1	PROPN
ejpam-6089	612	23	4	4	NUM
ejpam-6089	612	24	∫	∫	PROPN
ejpam-6089	612	25	1	1	NUM
ejpam-6089	612	26	0	0	NUM
ejpam-6089	612	27	t(ℵð+℘	t(ℵð+℘	NUM
ejpam-6089	612	28	)	)	PUNCT
ejpam-6089	612	29	{	{	PUNCT
ejpam-6089	612	30	υ′	υ′	X
ejpam-6089	612	31	(	(	PUNCT
ejpam-6089	612	32	t	t	PROPN
ejpam-6089	612	33	2	2	NUM
ejpam-6089	612	34	ℑ1	ℑ1	NOUN
ejpam-6089	612	35	+	+	CCONJ
ejpam-6089	612	36	2−	2−	NUM
ejpam-6089	612	37	t	t	NOUN
ejpam-6089	612	38	2	2	NUM
ejpam-6089	612	39	ℑ2	ℑ2	ADJ
ejpam-6089	612	40	)	)	PUNCT
ejpam-6089	612	41	−υ′	−υ′	NOUN
ejpam-6089	612	42	(	(	PUNCT
ejpam-6089	612	43	2−	2−	NUM
ejpam-6089	612	44	t	t	NOUN
ejpam-6089	612	45	2	2	NUM
ejpam-6089	612	46	ℑ1	ℑ1	NOUN
ejpam-6089	612	47	+	+	CCONJ
ejpam-6089	612	48	t	t	PROPN
ejpam-6089	612	49	2	2	NUM
ejpam-6089	612	50	ℑ2	ℑ2	PROPN
ejpam-6089	612	51	)	)	PUNCT
ejpam-6089	612	52	}	}	PUNCT
ejpam-6089	612	53	dt	dt	PUNCT
ejpam-6089	612	54	)	)	PUNCT
ejpam-6089	613	1	+	+	CCONJ
ejpam-6089	613	2	∞∑	∞∑	NUM
ejpam-6089	613	3	ð=0	ð=0	X
ejpam-6089	613	4	aðυ	aðυ	ADJ
ejpam-6089	613	5	(	(	PUNCT
ejpam-6089	613	6	ℑ1	ℑ1	PROPN
ejpam-6089	613	7	+	+	CCONJ
ejpam-6089	613	8	ℑ2	ℑ2	PROPN
ejpam-6089	613	9	2	2	NUM
ejpam-6089	613	10	)	)	PUNCT
ejpam-6089	613	11	.	.	PUNCT
ejpam-6089	614	1	where	where	SCONJ
ejpam-6089	614	2	að	að	PROPN
ejpam-6089	614	3	=	=	SYM
ejpam-6089	614	4	bg(δ+ðs	bg(δ+ðs	PROPN
ejpam-6089	614	5	,	,	PUNCT
ejpam-6089	614	6	b−δ	b−δ	NOUN
ejpam-6089	614	7	)	)	PUNCT
ejpam-6089	614	8	b(δ	b(δ	NOUN
ejpam-6089	614	9	,	,	PUNCT
ejpam-6089	614	10	b−δ	b−δ	NOUN
ejpam-6089	614	11	)	)	PUNCT
ejpam-6089	614	12	(	(	PUNCT
ejpam-6089	614	13	b)ðs	b)ðs	PROPN
ejpam-6089	614	14	♭	♭	PROPN
ejpam-6089	614	15	ð	ð	X
ejpam-6089	614	16	(	(	PUNCT
ejpam-6089	614	17	τ)ðl	τ)ðl	PROPN
ejpam-6089	614	18	and	and	CCONJ
ejpam-6089	614	19	oð	oð	X
ejpam-6089	614	20	=	=	SYM
ejpam-6089	614	21	(	(	PUNCT
ejpam-6089	614	22	ℑ2−ℑ1)(ℵð+℘	ℑ2−ℑ1)(ℵð+℘	PROPN
ejpam-6089	614	23	)	)	PUNCT
ejpam-6089	614	24	2(ℵð+℘)−1γ((ℵð+℘)+1	2(ℵð+℘)−1γ((ℵð+℘)+1	NUM
ejpam-6089	614	25	)	)	PUNCT
ejpam-6089	614	26	with	with	ADP
ejpam-6089	614	27	(	(	PUNCT
ejpam-6089	614	28	ℵð+	ℵð+	ADJ
ejpam-6089	614	29	℘	℘	PROPN
ejpam-6089	614	30	)	)	PUNCT
ejpam-6089	614	31	>	>	X
ejpam-6089	614	32	0	0	X
ejpam-6089	614	33	.	.	PUNCT
ejpam-6089	614	34	proof	proof	NOUN
ejpam-6089	614	35	.	.	PUNCT
ejpam-6089	615	1	adding	add	VERB
ejpam-6089	615	2	left	left	ADJ
ejpam-6089	615	3	and	and	CCONJ
ejpam-6089	615	4	right	right	ADV
ejpam-6089	615	5	sided	sided	ADJ
ejpam-6089	615	6	atangana	atangana	PROPN
ejpam-6089	615	7	-	-	PUNCT
ejpam-6089	615	8	baleanu	baleanu	PROPN
ejpam-6089	615	9	integrals	integral	NOUN
ejpam-6089	615	10	(	(	PUNCT
ejpam-6089	615	11	3	3	NUM
ejpam-6089	615	12	)	)	PUNCT
ejpam-6089	615	13	and	and	CCONJ
ejpam-6089	615	14	(	(	PUNCT
ejpam-6089	615	15	4	4	NUM
ejpam-6089	615	16	)	)	PUNCT
ejpam-6089	615	17	from	from	ADP
ejpam-6089	615	18	the	the	DET
ejpam-6089	615	19	middle	middle	NOUN
ejpam-6089	615	20	of	of	ADP
ejpam-6089	615	21	interval	interval	NOUN
ejpam-6089	615	22	[	[	X
ejpam-6089	615	23	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	615	24	]	]	PUNCT
ejpam-6089	615	25	,	,	PUNCT
ejpam-6089	615	26	we	we	PRON
ejpam-6089	615	27	have	have	VERB
ejpam-6089	615	28	(	(	PUNCT
ejpam-6089	615	29	a−biα	a−biα	ADJ
ejpam-6089	615	30	∗	∗	NOUN
ejpam-6089	615	31	(	(	PUNCT
ejpam-6089	615	32	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	615	33	2	2	NUM
ejpam-6089	615	34	)	)	PUNCT
ejpam-6089	615	35	+	+	CCONJ
ejpam-6089	616	1	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	616	2	)	)	PUNCT
ejpam-6089	616	3	+	+	NUM
ejpam-6089	616	4	a−biα	a−biα	ADJ
ejpam-6089	616	5	∗	∗	NOUN
ejpam-6089	616	6	(	(	PUNCT
ejpam-6089	616	7	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	616	8	2	2	NUM
ejpam-6089	616	9	)	)	PUNCT
ejpam-6089	616	10	−	−	PROPN
ejpam-6089	616	11	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	616	12	)	)	PUNCT
ejpam-6089	616	13	)	)	PUNCT
ejpam-6089	617	1	=	=	PUNCT
ejpam-6089	617	2	α∗	α∗	NOUN
ejpam-6089	617	3	b(α∗	b(α∗	NOUN
ejpam-6089	617	4	)	)	PUNCT
ejpam-6089	617	5	(	(	PUNCT
ejpam-6089	617	6	r−liα	r−liα	NOUN
ejpam-6089	617	7	∗	∗	NOUN
ejpam-6089	617	8	(	(	PUNCT
ejpam-6089	617	9	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	617	10	2	2	NUM
ejpam-6089	617	11	)	)	PUNCT
ejpam-6089	617	12	+	+	CCONJ
ejpam-6089	618	1	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	618	2	)	)	PUNCT
ejpam-6089	618	3	+	+	NUM
ejpam-6089	618	4	r−liα	r−liα	NOUN
ejpam-6089	618	5	∗	∗	NOUN
ejpam-6089	618	6	(	(	PUNCT
ejpam-6089	618	7	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	618	8	2	2	NUM
ejpam-6089	618	9	)	)	PUNCT
ejpam-6089	618	10	−	−	PROPN
ejpam-6089	618	11	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	618	12	)	)	PUNCT
ejpam-6089	618	13	)	)	PUNCT
ejpam-6089	619	1	+	+	CCONJ
ejpam-6089	619	2	1−	1−	NUM
ejpam-6089	619	3	α∗	α∗	NOUN
ejpam-6089	619	4	b(α∗	b(α∗	NOUN
ejpam-6089	619	5	)	)	PUNCT
ejpam-6089	619	6	(	(	PUNCT
ejpam-6089	619	7	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	619	8	)	)	PUNCT
ejpam-6089	619	9	+	+	CCONJ
ejpam-6089	619	10	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	619	11	)	)	PUNCT
ejpam-6089	619	12	)	)	PUNCT
ejpam-6089	619	13	.	.	PUNCT
ejpam-6089	620	1	using	use	VERB
ejpam-6089	620	2	α∗	α∗	NOUN
ejpam-6089	620	3	=	=	SYM
ejpam-6089	620	4	(	(	PUNCT
ejpam-6089	620	5	ℵð+	ℵð+	ADJ
ejpam-6089	620	6	℘	℘	PROPN
ejpam-6089	620	7	)	)	PUNCT
ejpam-6089	620	8	in	in	ADP
ejpam-6089	620	9	the	the	DET
ejpam-6089	620	10	above	above	ADJ
ejpam-6089	620	11	expression	expression	NOUN
ejpam-6089	620	12	,	,	PUNCT
ejpam-6089	620	13	we	we	PRON
ejpam-6089	620	14	get	get	VERB
ejpam-6089	620	15	ℵð+	ℵð+	ADJ
ejpam-6089	620	16	℘	℘	PROPN
ejpam-6089	620	17	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	620	18	℘	℘	PROPN
ejpam-6089	620	19	)	)	PUNCT
ejpam-6089	620	20	(	(	PUNCT
ejpam-6089	620	21	r−li	r−li	NOUN
ejpam-6089	620	22	(	(	PUNCT
ejpam-6089	620	23	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	620	24	)	)	PUNCT
ejpam-6089	620	25	(	(	PUNCT
ejpam-6089	620	26	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	620	27	2	2	NUM
ejpam-6089	620	28	)	)	PUNCT
ejpam-6089	620	29	+	+	CCONJ
ejpam-6089	621	1	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	621	2	)	)	PUNCT
ejpam-6089	621	3	+	+	NUM
ejpam-6089	621	4	r−li	r−li	NOUN
ejpam-6089	621	5	(	(	PUNCT
ejpam-6089	621	6	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	621	7	)	)	PUNCT
ejpam-6089	621	8	(	(	PUNCT
ejpam-6089	621	9	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	621	10	2	2	NUM
ejpam-6089	621	11	)	)	PUNCT
ejpam-6089	621	12	−	−	PROPN
ejpam-6089	621	13	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	621	14	)	)	PUNCT
ejpam-6089	621	15	)	)	PUNCT
ejpam-6089	622	1	=	=	PRON
ejpam-6089	622	2	(	(	PUNCT
ejpam-6089	622	3	a−bi	a−bi	PROPN
ejpam-6089	622	4	(	(	PUNCT
ejpam-6089	622	5	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	622	6	)	)	PUNCT
ejpam-6089	622	7	(	(	PUNCT
ejpam-6089	622	8	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	622	9	2	2	NUM
ejpam-6089	622	10	)	)	PUNCT
ejpam-6089	622	11	+	+	CCONJ
ejpam-6089	623	1	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	623	2	)	)	PUNCT
ejpam-6089	623	3	+	+	CCONJ
ejpam-6089	623	4	a−bi	a−bi	PROPN
ejpam-6089	623	5	(	(	PUNCT
ejpam-6089	623	6	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	623	7	)	)	PUNCT
ejpam-6089	623	8	(	(	PUNCT
ejpam-6089	623	9	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	623	10	2	2	NUM
ejpam-6089	623	11	)	)	PUNCT
ejpam-6089	623	12	−	−	PROPN
ejpam-6089	623	13	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	623	14	)	)	PUNCT
ejpam-6089	623	15	)	)	PUNCT
ejpam-6089	624	1	−	−	PROPN
ejpam-6089	624	2	1−	1−	NUM
ejpam-6089	624	3	ℵð−	ℵð−	PUNCT
ejpam-6089	624	4	℘	℘	PROPN
ejpam-6089	624	5	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	624	6	℘	℘	PROPN
ejpam-6089	624	7	)	)	PUNCT
ejpam-6089	624	8	(	(	PUNCT
ejpam-6089	624	9	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	624	10	)	)	PUNCT
ejpam-6089	624	11	+	+	CCONJ
ejpam-6089	624	12	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	624	13	)	)	PUNCT
ejpam-6089	624	14	)	)	PUNCT
ejpam-6089	624	15	.	.	PUNCT
ejpam-6089	625	1	multiplying	multiply	VERB
ejpam-6089	625	2	the	the	DET
ejpam-6089	625	3	above	above	ADJ
ejpam-6089	625	4	equality	equality	NOUN
ejpam-6089	625	5	with	with	ADP
ejpam-6089	625	6	b(ℵð+℘	b(ℵð+℘	NOUN
ejpam-6089	625	7	)	)	PUNCT
ejpam-6089	625	8	(	(	PUNCT
ejpam-6089	625	9	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	625	10	)	)	PUNCT
ejpam-6089	625	11	and	and	CCONJ
ejpam-6089	625	12	then	then	ADV
ejpam-6089	625	13	subtracting	subtract	VERB
ejpam-6089	625	14	υ	υ	PROPN
ejpam-6089	625	15	(	(	PUNCT
ejpam-6089	625	16	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	625	17	2	2	NUM
ejpam-6089	625	18	)	)	PUNCT
ejpam-6089	625	19	,	,	PUNCT
ejpam-6089	625	20	we	we	PRON
ejpam-6089	625	21	obtain	obtain	VERB
ejpam-6089	625	22	(	(	PUNCT
ejpam-6089	625	23	r−li	r−li	NOUN
ejpam-6089	625	24	(	(	PUNCT
ejpam-6089	625	25	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	625	26	)	)	PUNCT
ejpam-6089	625	27	(	(	PUNCT
ejpam-6089	625	28	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	625	29	2	2	NUM
ejpam-6089	625	30	)	)	PUNCT
ejpam-6089	625	31	+	+	CCONJ
ejpam-6089	626	1	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	626	2	)	)	PUNCT
ejpam-6089	626	3	+	+	X
ejpam-6089	626	4	r−liℵð+℘	r−liℵð+℘	ADJ
ejpam-6089	626	5	(	(	PUNCT
ejpam-6089	626	6	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	626	7	2	2	NUM
ejpam-6089	626	8	)	)	PUNCT
ejpam-6089	626	9	−	−	PROPN
ejpam-6089	626	10	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	626	11	)	)	PUNCT
ejpam-6089	626	12	)	)	PUNCT
ejpam-6089	627	1	−υ	−υ	NOUN
ejpam-6089	627	2	(	(	PUNCT
ejpam-6089	627	3	ℑ1	ℑ1	PROPN
ejpam-6089	627	4	+	+	CCONJ
ejpam-6089	627	5	ℑ2	ℑ2	PROPN
ejpam-6089	627	6	2	2	NUM
ejpam-6089	627	7	)	)	PUNCT
ejpam-6089	627	8	=	=	SYM
ejpam-6089	627	9	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	627	10	℘	℘	PROPN
ejpam-6089	627	11	)	)	PUNCT
ejpam-6089	627	12	(	(	PUNCT
ejpam-6089	627	13	ℵð+	ℵð+	ADJ
ejpam-6089	627	14	℘	℘	PROPN
ejpam-6089	627	15	)	)	PUNCT
ejpam-6089	627	16	(	(	PUNCT
ejpam-6089	627	17	a−bi	a−bi	PROPN
ejpam-6089	627	18	(	(	PUNCT
ejpam-6089	627	19	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	627	20	)	)	PUNCT
ejpam-6089	627	21	(	(	PUNCT
ejpam-6089	627	22	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	627	23	2	2	NUM
ejpam-6089	627	24	)	)	PUNCT
ejpam-6089	627	25	+	+	CCONJ
ejpam-6089	627	26	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	627	27	)	)	PUNCT
ejpam-6089	627	28	+	+	SYM
ejpam-6089	627	29	a−biℵð+℘	a−biℵð+℘	ADJ
ejpam-6089	627	30	(	(	PUNCT
ejpam-6089	627	31	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	627	32	2	2	NUM
ejpam-6089	627	33	)	)	PUNCT
ejpam-6089	627	34	−	−	PROPN
ejpam-6089	627	35	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	627	36	)	)	PUNCT
ejpam-6089	627	37	)	)	PUNCT
ejpam-6089	628	1	−	−	PROPN
ejpam-6089	629	1	2(1−	2(1−	X
ejpam-6089	629	2	ℵð−	ℵð−	PUNCT
ejpam-6089	629	3	℘	℘	NUM
ejpam-6089	629	4	)	)	PUNCT
ejpam-6089	629	5	(	(	PUNCT
ejpam-6089	629	6	ℵð+	ℵð+	ADJ
ejpam-6089	629	7	℘	℘	PROPN
ejpam-6089	629	8	)	)	PUNCT
ejpam-6089	629	9	(	(	PUNCT
ejpam-6089	629	10	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	629	11	)	)	PUNCT
ejpam-6089	629	12	+	+	CCONJ
ejpam-6089	629	13	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	629	14	)	)	PUNCT
ejpam-6089	629	15	)	)	PUNCT
ejpam-6089	629	16	2	2	NUM
ejpam-6089	629	17	−υ	−υ	NOUN
ejpam-6089	629	18	(	(	PUNCT
ejpam-6089	629	19	ℑ1	ℑ1	PROPN
ejpam-6089	629	20	+	+	CCONJ
ejpam-6089	629	21	ℑ2	ℑ2	PROPN
ejpam-6089	629	22	2	2	NUM
ejpam-6089	629	23	)	)	PUNCT
ejpam-6089	629	24	.	.	PUNCT
ejpam-6089	630	1	again	again	ADV
ejpam-6089	630	2	we	we	PRON
ejpam-6089	630	3	multiply	multiply	VERB
ejpam-6089	630	4	the	the	DET
ejpam-6089	630	5	above	above	ADJ
ejpam-6089	630	6	equality	equality	NOUN
ejpam-6089	630	7	with	with	ADP
ejpam-6089	630	8	að	að	PRON
ejpam-6089	630	9	to	to	PART
ejpam-6089	630	10	get	get	VERB
ejpam-6089	630	11	að	að	PROPN
ejpam-6089	630	12	(	(	PUNCT
ejpam-6089	630	13	r−liℵð+℘	r−liℵð+℘	PROPN
ejpam-6089	630	14	(	(	PUNCT
ejpam-6089	630	15	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	630	16	2	2	NUM
ejpam-6089	630	17	)	)	PUNCT
ejpam-6089	630	18	+	+	CCONJ
ejpam-6089	631	1	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	631	2	)	)	PUNCT
ejpam-6089	631	3	+	+	NUM
ejpam-6089	631	4	r−li	r−li	NOUN
ejpam-6089	631	5	(	(	PUNCT
ejpam-6089	631	6	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	631	7	)	)	PUNCT
ejpam-6089	631	8	(	(	PUNCT
ejpam-6089	631	9	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	631	10	2	2	NUM
ejpam-6089	631	11	)	)	PUNCT
ejpam-6089	631	12	−	−	PROPN
ejpam-6089	631	13	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	631	14	)	)	PUNCT
ejpam-6089	631	15	)	)	PUNCT
ejpam-6089	632	1	−	−	PROPN
ejpam-6089	632	2	aðυ	aðυ	ADJ
ejpam-6089	632	3	(	(	PUNCT
ejpam-6089	632	4	ℑ1	ℑ1	PROPN
ejpam-6089	632	5	+	+	CCONJ
ejpam-6089	632	6	ℑ2	ℑ2	PROPN
ejpam-6089	632	7	2	2	NUM
ejpam-6089	632	8	)	)	PUNCT
ejpam-6089	633	1	=	=	SYM
ejpam-6089	633	2	að	að	PROPN
ejpam-6089	633	3	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	633	4	℘	℘	PROPN
ejpam-6089	633	5	)	)	PUNCT
ejpam-6089	633	6	(	(	PUNCT
ejpam-6089	633	7	ℵð+	ℵð+	ADJ
ejpam-6089	633	8	℘	℘	PROPN
ejpam-6089	633	9	)	)	PUNCT
ejpam-6089	633	10	(	(	PUNCT
ejpam-6089	633	11	a−bi	a−bi	PROPN
ejpam-6089	633	12	(	(	PUNCT
ejpam-6089	633	13	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	633	14	)	)	PUNCT
ejpam-6089	633	15	(	(	PUNCT
ejpam-6089	633	16	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	633	17	2	2	NUM
ejpam-6089	633	18	)	)	PUNCT
ejpam-6089	633	19	+	+	CCONJ
ejpam-6089	633	20	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	633	21	)	)	PUNCT
ejpam-6089	633	22	+	+	SYM
ejpam-6089	633	23	a−biℵð+℘	a−biℵð+℘	ADJ
ejpam-6089	633	24	(	(	PUNCT
ejpam-6089	633	25	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	633	26	2	2	NUM
ejpam-6089	633	27	)	)	PUNCT
ejpam-6089	633	28	−	−	PROPN
ejpam-6089	633	29	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	633	30	)	)	PUNCT
ejpam-6089	633	31	)	)	PUNCT
ejpam-6089	634	1	s.	s.	PROPN
ejpam-6089	634	2	naheed	nahee	VERB
ejpam-6089	634	3	et	et	PROPN
ejpam-6089	634	4	al	al	PROPN
ejpam-6089	634	5	.	.	PUNCT
ejpam-6089	634	6	/	/	SYM
ejpam-6089	634	7	eur	eur	PROPN
ejpam-6089	634	8	.	.	PUNCT
ejpam-6089	635	1	j.	j.	PROPN
ejpam-6089	635	2	pure	pure	PROPN
ejpam-6089	635	3	appl	appl	PROPN
ejpam-6089	635	4	.	.	PROPN
ejpam-6089	635	5	math	math	PROPN
ejpam-6089	635	6	,	,	PUNCT
ejpam-6089	635	7	18	18	NUM
ejpam-6089	635	8	(	(	PUNCT
ejpam-6089	635	9	2	2	NUM
ejpam-6089	635	10	)	)	PUNCT
ejpam-6089	635	11	(	(	PUNCT
ejpam-6089	635	12	2025	2025	NUM
ejpam-6089	635	13	)	)	PUNCT
ejpam-6089	635	14	,	,	PUNCT
ejpam-6089	635	15	6089	6089	NUM
ejpam-6089	635	16	29	29	NUM
ejpam-6089	635	17	of	of	ADP
ejpam-6089	635	18	34	34	NUM
ejpam-6089	635	19	−	−	NOUN
ejpam-6089	635	20	að	að	PROPN
ejpam-6089	635	21	2(1−	2(1−	X
ejpam-6089	635	22	ℵð−	ℵð−	PUNCT
ejpam-6089	635	23	℘	℘	PROPN
ejpam-6089	635	24	)	)	PUNCT
ejpam-6089	635	25	(	(	PUNCT
ejpam-6089	635	26	ℵð+	ℵð+	ADJ
ejpam-6089	635	27	℘	℘	PROPN
ejpam-6089	635	28	)	)	PUNCT
ejpam-6089	635	29	(	(	PUNCT
ejpam-6089	635	30	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	635	31	)	)	PUNCT
ejpam-6089	635	32	+	+	CCONJ
ejpam-6089	635	33	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	635	34	)	)	PUNCT
ejpam-6089	635	35	)	)	PUNCT
ejpam-6089	635	36	2	2	NUM
ejpam-6089	635	37	−	−	NOUN
ejpam-6089	635	38	aðυ	aðυ	ADJ
ejpam-6089	635	39	(	(	PUNCT
ejpam-6089	635	40	ℑ1	ℑ1	PROPN
ejpam-6089	635	41	+	+	CCONJ
ejpam-6089	635	42	ℑ2	ℑ2	PROPN
ejpam-6089	635	43	2	2	NUM
ejpam-6089	635	44	)	)	PUNCT
ejpam-6089	635	45	.	.	PUNCT
ejpam-6089	636	1	summing	sum	VERB
ejpam-6089	636	2	over	over	ADP
ejpam-6089	636	3	all	all	PRON
ejpam-6089	636	4	ð	ð	NOUN
ejpam-6089	636	5	∞∑	∞∑	NUM
ejpam-6089	636	6	ð=0	ð=0	X
ejpam-6089	636	7	að	að	X
ejpam-6089	636	8	(	(	PUNCT
ejpam-6089	636	9	r−li	r−li	NOUN
ejpam-6089	636	10	(	(	PUNCT
ejpam-6089	636	11	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	636	12	)	)	PUNCT
ejpam-6089	636	13	(	(	PUNCT
ejpam-6089	636	14	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	636	15	2	2	NUM
ejpam-6089	636	16	)	)	PUNCT
ejpam-6089	636	17	+	+	CCONJ
ejpam-6089	636	18	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	636	19	)	)	PUNCT
ejpam-6089	636	20	+	+	NUM
ejpam-6089	636	21	r−li	r−li	NOUN
ejpam-6089	636	22	(	(	PUNCT
ejpam-6089	636	23	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	636	24	)	)	PUNCT
ejpam-6089	636	25	(	(	PUNCT
ejpam-6089	636	26	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	636	27	2	2	NUM
ejpam-6089	636	28	)	)	PUNCT
ejpam-6089	636	29	−	−	PROPN
ejpam-6089	636	30	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	636	31	)	)	PUNCT
ejpam-6089	636	32	)	)	PUNCT
ejpam-6089	637	1	−	−	PROPN
ejpam-6089	638	1	∞∑	∞∑	NUM
ejpam-6089	638	2	ð=0	ð=0	X
ejpam-6089	638	3	aðυ	aðυ	ADJ
ejpam-6089	638	4	(	(	PUNCT
ejpam-6089	638	5	ℑ1	ℑ1	PROPN
ejpam-6089	638	6	+	+	CCONJ
ejpam-6089	638	7	ℑ2	ℑ2	PROPN
ejpam-6089	638	8	2	2	NUM
ejpam-6089	638	9	)	)	PUNCT
ejpam-6089	638	10	=	=	NOUN
ejpam-6089	639	1	∞∑	∞∑	NUM
ejpam-6089	639	2	ð=0	ð=0	PUNCT
ejpam-6089	639	3	að	að	PROPN
ejpam-6089	639	4	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	639	5	℘	℘	PROPN
ejpam-6089	639	6	)	)	PUNCT
ejpam-6089	639	7	(	(	PUNCT
ejpam-6089	639	8	ℵð+	ℵð+	ADJ
ejpam-6089	639	9	℘	℘	PROPN
ejpam-6089	639	10	)	)	PUNCT
ejpam-6089	639	11	(	(	PUNCT
ejpam-6089	639	12	a−bi	a−bi	PROPN
ejpam-6089	639	13	(	(	PUNCT
ejpam-6089	639	14	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	639	15	)	)	PUNCT
ejpam-6089	639	16	(	(	PUNCT
ejpam-6089	639	17	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	639	18	2	2	NUM
ejpam-6089	639	19	)	)	PUNCT
ejpam-6089	639	20	+	+	CCONJ
ejpam-6089	639	21	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	639	22	)	)	PUNCT
ejpam-6089	639	23	+	+	CCONJ
ejpam-6089	639	24	a−bi	a−bi	PROPN
ejpam-6089	639	25	(	(	PUNCT
ejpam-6089	639	26	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	639	27	)	)	PUNCT
ejpam-6089	639	28	(	(	PUNCT
ejpam-6089	639	29	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	639	30	2	2	NUM
ejpam-6089	639	31	)	)	PUNCT
ejpam-6089	639	32	−	−	PROPN
ejpam-6089	639	33	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	639	34	)	)	PUNCT
ejpam-6089	639	35	)	)	PUNCT
ejpam-6089	640	1	−	−	PROPN
ejpam-6089	641	1	∞∑	∞∑	NUM
ejpam-6089	641	2	ð=0	ð=0	X
ejpam-6089	641	3	að	að	X
ejpam-6089	641	4	2(1−	2(1−	X
ejpam-6089	641	5	ℵð−	ℵð−	NUM
ejpam-6089	641	6	℘	℘	PROPN
ejpam-6089	641	7	)	)	PUNCT
ejpam-6089	641	8	ℵð+	ℵð+	NOUN
ejpam-6089	641	9	℘	℘	PROPN
ejpam-6089	641	10	(	(	PUNCT
ejpam-6089	641	11	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	641	12	)	)	PUNCT
ejpam-6089	641	13	+	+	CCONJ
ejpam-6089	641	14	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	641	15	)	)	PUNCT
ejpam-6089	641	16	)	)	PUNCT
ejpam-6089	642	1	2	2	NUM
ejpam-6089	642	2	−	−	PROPN
ejpam-6089	642	3	∞∑	∞∑	NUM
ejpam-6089	642	4	ð=0	ð=0	X
ejpam-6089	642	5	aðυ	aðυ	ADJ
ejpam-6089	642	6	(	(	PUNCT
ejpam-6089	642	7	ℑ1	ℑ1	PROPN
ejpam-6089	642	8	+	+	CCONJ
ejpam-6089	642	9	ℑ2	ℑ2	PROPN
ejpam-6089	642	10	2	2	NUM
ejpam-6089	642	11	)	)	PUNCT
ejpam-6089	642	12	.	.	PUNCT
ejpam-6089	643	1	(	(	PUNCT
ejpam-6089	643	2	34	34	NUM
ejpam-6089	643	3	)	)	PUNCT
ejpam-6089	643	4	by	by	ADP
ejpam-6089	643	5	convexity	convexity	NOUN
ejpam-6089	643	6	of	of	ADP
ejpam-6089	643	7	υ	υ	NOUN
ejpam-6089	643	8	we	we	PRON
ejpam-6089	643	9	have	have	VERB
ejpam-6089	643	10	,	,	PUNCT
ejpam-6089	643	11	υ	υ	PROPN
ejpam-6089	643	12	(	(	PUNCT
ejpam-6089	643	13	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	643	14	2	2	NUM
ejpam-6089	643	15	)	)	PUNCT
ejpam-6089	643	16	≤	≤	NOUN
ejpam-6089	643	17	(	(	PUNCT
ejpam-6089	643	18	υ(ℑ1)+υ(ℑ2	υ(ℑ1)+υ(ℑ2	PROPN
ejpam-6089	643	19	)	)	PUNCT
ejpam-6089	643	20	2	2	NUM
ejpam-6089	643	21	)	)	PUNCT
ejpam-6089	643	22	with	with	ADP
ejpam-6089	643	23	positive	positive	ADJ
ejpam-6089	643	24	multiplier	multipli	ADJ
ejpam-6089	643	25	að	að	NOUN
ejpam-6089	643	26	∞∑	∞∑	PROPN
ejpam-6089	643	27	ð=0	ð=0	X
ejpam-6089	643	28	að	að	X
ejpam-6089	643	29	(	(	PUNCT
ejpam-6089	643	30	r−li	r−li	NOUN
ejpam-6089	643	31	(	(	PUNCT
ejpam-6089	643	32	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	643	33	)	)	PUNCT
ejpam-6089	643	34	(	(	PUNCT
ejpam-6089	643	35	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	643	36	2	2	NUM
ejpam-6089	643	37	)	)	PUNCT
ejpam-6089	643	38	+	+	CCONJ
ejpam-6089	643	39	+	+	CCONJ
ejpam-6089	643	40	r−li	r−li	NOUN
ejpam-6089	643	41	(	(	PUNCT
ejpam-6089	643	42	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	643	43	)	)	PUNCT
ejpam-6089	643	44	(	(	PUNCT
ejpam-6089	643	45	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	643	46	2	2	NUM
ejpam-6089	643	47	)	)	PUNCT
ejpam-6089	643	48	−	−	PROPN
ejpam-6089	643	49	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	643	50	)	)	PUNCT
ejpam-6089	643	51	)	)	PUNCT
ejpam-6089	644	1	−	−	PROPN
ejpam-6089	645	1	∞∑	∞∑	NUM
ejpam-6089	645	2	ð=0	ð=0	X
ejpam-6089	645	3	aðυ	aðυ	ADJ
ejpam-6089	645	4	(	(	PUNCT
ejpam-6089	645	5	ℑ1	ℑ1	PROPN
ejpam-6089	645	6	+	+	CCONJ
ejpam-6089	645	7	ℑ2	ℑ2	PROPN
ejpam-6089	645	8	2	2	NUM
ejpam-6089	645	9	)	)	PUNCT
ejpam-6089	645	10	≤	≤	NOUN
ejpam-6089	645	11	∞∑	∞∑	NUM
ejpam-6089	645	12	ð=0	ð=0	SYM
ejpam-6089	645	13	að	að	PROPN
ejpam-6089	645	14	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	645	15	℘	℘	PROPN
ejpam-6089	645	16	)	)	PUNCT
ejpam-6089	645	17	(	(	PUNCT
ejpam-6089	645	18	ℵð+	ℵð+	ADJ
ejpam-6089	645	19	℘	℘	PROPN
ejpam-6089	645	20	)	)	PUNCT
ejpam-6089	645	21	(	(	PUNCT
ejpam-6089	645	22	a−bi	a−bi	PROPN
ejpam-6089	645	23	(	(	PUNCT
ejpam-6089	645	24	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	645	25	)	)	PUNCT
ejpam-6089	645	26	(	(	PUNCT
ejpam-6089	645	27	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	645	28	2	2	NUM
ejpam-6089	645	29	)	)	PUNCT
ejpam-6089	645	30	+	+	CCONJ
ejpam-6089	645	31	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	645	32	)	)	PUNCT
ejpam-6089	646	1	+	+	CCONJ
ejpam-6089	646	2	a−bi	a−bi	PROPN
ejpam-6089	646	3	(	(	PUNCT
ejpam-6089	646	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	646	5	)	)	PUNCT
ejpam-6089	646	6	(	(	PUNCT
ejpam-6089	646	7	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	646	8	2	2	NUM
ejpam-6089	646	9	)	)	PUNCT
ejpam-6089	646	10	−	−	PROPN
ejpam-6089	646	11	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	646	12	)	)	PUNCT
ejpam-6089	646	13	)	)	PUNCT
ejpam-6089	647	1	−	−	PROPN
ejpam-6089	648	1	∞∑	∞∑	NUM
ejpam-6089	648	2	ð=0	ð=0	X
ejpam-6089	648	3	að	að	X
ejpam-6089	648	4	(	(	PUNCT
ejpam-6089	648	5	2(1−	2(1−	X
ejpam-6089	648	6	ℵð−	ℵð−	NUM
ejpam-6089	648	7	℘	℘	NUM
ejpam-6089	648	8	)	)	PUNCT
ejpam-6089	648	9	(	(	PUNCT
ejpam-6089	648	10	ℵð+	ℵð+	ADJ
ejpam-6089	648	11	℘	℘	PROPN
ejpam-6089	648	12	)	)	PUNCT
ejpam-6089	648	13	+	+	CCONJ
ejpam-6089	648	14	1	1	NUM
ejpam-6089	648	15	)	)	PUNCT
ejpam-6089	648	16	(	(	PUNCT
ejpam-6089	648	17	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	648	18	)	)	PUNCT
ejpam-6089	648	19	+	+	CCONJ
ejpam-6089	648	20	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	648	21	)	)	PUNCT
ejpam-6089	648	22	2	2	NUM
ejpam-6089	648	23	)	)	PUNCT
ejpam-6089	648	24	.	.	PUNCT
ejpam-6089	649	1	using	use	VERB
ejpam-6089	649	2	proposition	proposition	NOUN
ejpam-6089	649	3	1	1	NUM
ejpam-6089	649	4	from	from	ADP
ejpam-6089	649	5	the	the	DET
ejpam-6089	649	6	middle	middle	NOUN
ejpam-6089	649	7	of	of	ADP
ejpam-6089	649	8	interval	interval	NOUN
ejpam-6089	649	9	[	[	X
ejpam-6089	649	10	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	649	11	]	]	PUNCT
ejpam-6089	649	12	,	,	PUNCT
ejpam-6089	649	13	we	we	PRON
ejpam-6089	649	14	acquire	acquire	VERB
ejpam-6089	649	15	ε	ε	PROPN
ejpam-6089	649	16	♭	♭	PROPN
ejpam-6089	649	17	,δ	,δ	PUNCT
ejpam-6089	649	18	,	,	PUNCT
ejpam-6089	649	19	b	b	NOUN
ejpam-6089	649	20	,	,	PUNCT
ejpam-6089	649	21	s	s	X
ejpam-6089	649	22	,	,	PUNCT
ejpam-6089	649	23	l	l	NOUN
ejpam-6089	649	24	(	(	PUNCT
ejpam-6089	649	25	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	649	26	2	2	NUM
ejpam-6089	649	27	)	)	PUNCT
ejpam-6089	650	1	+	+	ADV
ejpam-6089	650	2	,	,	PUNCT
ejpam-6089	650	3	ℵ,℘,τ	ℵ,℘,τ	PROPN
ejpam-6089	650	4	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	650	5	;	;	PUNCT
ejpam-6089	650	6	g	g	NOUN
ejpam-6089	650	7	)	)	PUNCT
ejpam-6089	651	1	+	+	CCONJ
ejpam-6089	651	2	ε	ε	PROPN
ejpam-6089	651	3	♭	♭	PROPN
ejpam-6089	651	4	,δ	,δ	PUNCT
ejpam-6089	651	5	,	,	PUNCT
ejpam-6089	651	6	b	b	NOUN
ejpam-6089	651	7	,	,	PUNCT
ejpam-6089	651	8	s	s	X
ejpam-6089	651	9	,	,	PUNCT
ejpam-6089	651	10	l	l	NOUN
ejpam-6089	651	11	(	(	PUNCT
ejpam-6089	651	12	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	651	13	2	2	NUM
ejpam-6089	651	14	)	)	PUNCT
ejpam-6089	651	15	−,ℵ,℘,τ	−,ℵ,℘,τ	NOUN
ejpam-6089	651	16	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	651	17	;	;	PUNCT
ejpam-6089	651	18	g)−	g)−	VERB
ejpam-6089	651	19	∞∑	∞∑	NUM
ejpam-6089	651	20	ð=0	ð=0	X
ejpam-6089	651	21	aðυ	aðυ	ADJ
ejpam-6089	651	22	(	(	PUNCT
ejpam-6089	651	23	ℑ1	ℑ1	PROPN
ejpam-6089	651	24	+	+	CCONJ
ejpam-6089	651	25	ℑ2	ℑ2	PROPN
ejpam-6089	651	26	2	2	NUM
ejpam-6089	651	27	)	)	PUNCT
ejpam-6089	651	28	≤	≤	NOUN
ejpam-6089	652	1	∞∑	∞∑	NUM
ejpam-6089	652	2	ð=0	ð=0	SYM
ejpam-6089	652	3	að	að	PROPN
ejpam-6089	652	4	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	652	5	℘	℘	PROPN
ejpam-6089	652	6	)	)	PUNCT
ejpam-6089	652	7	(	(	PUNCT
ejpam-6089	652	8	ℵð+	ℵð+	ADJ
ejpam-6089	652	9	℘	℘	PROPN
ejpam-6089	652	10	)	)	PUNCT
ejpam-6089	652	11	(	(	PUNCT
ejpam-6089	652	12	a−bi	a−bi	PROPN
ejpam-6089	652	13	(	(	PUNCT
ejpam-6089	652	14	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	652	15	)	)	PUNCT
ejpam-6089	652	16	(	(	PUNCT
ejpam-6089	652	17	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	652	18	2	2	NUM
ejpam-6089	652	19	)	)	PUNCT
ejpam-6089	652	20	+	+	CCONJ
ejpam-6089	652	21	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	652	22	)	)	PUNCT
ejpam-6089	653	1	+	+	CCONJ
ejpam-6089	653	2	a−bi	a−bi	PROPN
ejpam-6089	653	3	(	(	PUNCT
ejpam-6089	653	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	653	5	)	)	PUNCT
ejpam-6089	653	6	(	(	PUNCT
ejpam-6089	653	7	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	653	8	2	2	NUM
ejpam-6089	653	9	)	)	PUNCT
ejpam-6089	653	10	−	−	PROPN
ejpam-6089	653	11	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	653	12	)	)	PUNCT
ejpam-6089	653	13	)	)	PUNCT
ejpam-6089	654	1	−	−	PROPN
ejpam-6089	655	1	∞∑	∞∑	NUM
ejpam-6089	655	2	ð=0	ð=0	X
ejpam-6089	655	3	að	að	X
ejpam-6089	655	4	(	(	PUNCT
ejpam-6089	655	5	2(1−	2(1−	X
ejpam-6089	655	6	ℵð−	ℵð−	NUM
ejpam-6089	655	7	℘	℘	NUM
ejpam-6089	655	8	)	)	PUNCT
ejpam-6089	655	9	(	(	PUNCT
ejpam-6089	655	10	ℵð+	ℵð+	ADJ
ejpam-6089	655	11	℘	℘	PROPN
ejpam-6089	655	12	)	)	PUNCT
ejpam-6089	655	13	+	+	CCONJ
ejpam-6089	655	14	1	1	NUM
ejpam-6089	655	15	)	)	PUNCT
ejpam-6089	655	16	(	(	PUNCT
ejpam-6089	655	17	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	655	18	)	)	PUNCT
ejpam-6089	655	19	+	+	CCONJ
ejpam-6089	655	20	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	655	21	)	)	PUNCT
ejpam-6089	655	22	2	2	NUM
ejpam-6089	655	23	)	)	PUNCT
ejpam-6089	655	24	.	.	PUNCT
ejpam-6089	656	1	using	use	VERB
ejpam-6089	656	2	lemma	lemma	PROPN
ejpam-6089	656	3	4	4	NUM
ejpam-6089	656	4	in	in	ADP
ejpam-6089	656	5	the	the	DET
ejpam-6089	656	6	above	above	ADJ
ejpam-6089	656	7	inequality	inequality	NOUN
ejpam-6089	656	8	,	,	PUNCT
ejpam-6089	656	9	we	we	PRON
ejpam-6089	656	10	get	get	VERB
ejpam-6089	656	11	∞∑	∞∑	NUM
ejpam-6089	656	12	ð=0	ð=0	X
ejpam-6089	656	13	að	að	X
ejpam-6089	656	14	(	(	PUNCT
ejpam-6089	656	15	ℑ2	ℑ2	PROPN
ejpam-6089	656	16	−ℑ1	−ℑ1	PROPN
ejpam-6089	656	17	)	)	PUNCT
ejpam-6089	656	18	(	(	PUNCT
ejpam-6089	656	19	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	656	20	)	)	PUNCT
ejpam-6089	656	21	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	656	22	℘	℘	NOUN
ejpam-6089	656	23	)	)	PUNCT
ejpam-6089	657	1	+	+	CCONJ
ejpam-6089	657	2	1	1	X
ejpam-6089	657	3	)	)	PUNCT
ejpam-6089	657	4	×	×	NOUN
ejpam-6089	657	5	(	(	PUNCT
ejpam-6089	657	6	ℑ2	ℑ2	PROPN
ejpam-6089	657	7	−ℑ1	−ℑ1	PROPN
ejpam-6089	657	8	4	4	NUM
ejpam-6089	657	9	∫	∫	PROPN
ejpam-6089	657	10	1	1	NUM
ejpam-6089	657	11	0	0	NUM
ejpam-6089	657	12	t(ℵð+℘	t(ℵð+℘	NUM
ejpam-6089	657	13	)	)	PUNCT
ejpam-6089	657	14	{	{	PUNCT
ejpam-6089	657	15	υ′	υ′	X
ejpam-6089	657	16	(	(	PUNCT
ejpam-6089	657	17	t	t	PROPN
ejpam-6089	657	18	2	2	NUM
ejpam-6089	657	19	ℑ1	ℑ1	NOUN
ejpam-6089	657	20	+	+	CCONJ
ejpam-6089	657	21	2−	2−	NUM
ejpam-6089	657	22	t	t	NOUN
ejpam-6089	657	23	2	2	NUM
ejpam-6089	657	24	ℑ2	ℑ2	ADJ
ejpam-6089	657	25	)	)	PUNCT
ejpam-6089	657	26	−υ′	−υ′	NOUN
ejpam-6089	657	27	(	(	PUNCT
ejpam-6089	657	28	2−	2−	NUM
ejpam-6089	657	29	t	t	NOUN
ejpam-6089	657	30	2	2	NUM
ejpam-6089	657	31	ℑ1	ℑ1	NOUN
ejpam-6089	657	32	+	+	CCONJ
ejpam-6089	657	33	t	t	PROPN
ejpam-6089	657	34	2	2	NUM
ejpam-6089	657	35	ℑ2	ℑ2	PROPN
ejpam-6089	657	36	)	)	PUNCT
ejpam-6089	657	37	}	}	PUNCT
ejpam-6089	657	38	dt	dt	PUNCT
ejpam-6089	657	39	)	)	PUNCT
ejpam-6089	658	1	+	+	CCONJ
ejpam-6089	658	2	∞∑	∞∑	NUM
ejpam-6089	658	3	ð=0	ð=0	X
ejpam-6089	658	4	að	að	X
ejpam-6089	658	5	(	(	PUNCT
ejpam-6089	658	6	(	(	PUNCT
ejpam-6089	658	7	ℑ2	ℑ2	PROPN
ejpam-6089	658	8	−ℑ1	−ℑ1	PROPN
ejpam-6089	658	9	)	)	PUNCT
ejpam-6089	658	10	(	(	PUNCT
ejpam-6089	658	11	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	658	12	)	)	PUNCT
ejpam-6089	658	13	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	658	14	℘	℘	NOUN
ejpam-6089	658	15	)	)	PUNCT
ejpam-6089	658	16	+	+	CCONJ
ejpam-6089	658	17	1	1	X
ejpam-6089	658	18	)	)	PUNCT
ejpam-6089	658	19	−	−	PROPN
ejpam-6089	658	20	1	1	NUM
ejpam-6089	658	21	)	)	PUNCT
ejpam-6089	658	22	υ	υ	NOUN
ejpam-6089	658	23	(	(	PUNCT
ejpam-6089	658	24	ℑ1	ℑ1	PROPN
ejpam-6089	658	25	+	+	CCONJ
ejpam-6089	658	26	ℑ2	ℑ2	PROPN
ejpam-6089	658	27	2	2	NUM
ejpam-6089	658	28	)	)	PUNCT
ejpam-6089	658	29	s.	s.	PROPN
ejpam-6089	658	30	naheed	nahee	VERB
ejpam-6089	658	31	et	et	PROPN
ejpam-6089	658	32	al	al	PROPN
ejpam-6089	658	33	.	.	PUNCT
ejpam-6089	658	34	/	/	SYM
ejpam-6089	658	35	eur	eur	PROPN
ejpam-6089	658	36	.	.	PUNCT
ejpam-6089	659	1	j.	j.	PROPN
ejpam-6089	659	2	pure	pure	PROPN
ejpam-6089	659	3	appl	appl	PROPN
ejpam-6089	659	4	.	.	PROPN
ejpam-6089	659	5	math	math	PROPN
ejpam-6089	659	6	,	,	PUNCT
ejpam-6089	659	7	18	18	NUM
ejpam-6089	659	8	(	(	PUNCT
ejpam-6089	659	9	2	2	NUM
ejpam-6089	659	10	)	)	PUNCT
ejpam-6089	659	11	(	(	PUNCT
ejpam-6089	659	12	2025	2025	NUM
ejpam-6089	659	13	)	)	PUNCT
ejpam-6089	659	14	,	,	PUNCT
ejpam-6089	659	15	6089	6089	NUM
ejpam-6089	659	16	30	30	NUM
ejpam-6089	659	17	of	of	ADP
ejpam-6089	659	18	34	34	NUM
ejpam-6089	659	19	≤	≤	NOUN
ejpam-6089	659	20	∞∑	∞∑	NUM
ejpam-6089	659	21	ð=0	ð=0	X
ejpam-6089	659	22	að	að	PROPN
ejpam-6089	659	23	b(ℵð+	b(ℵð+	NOUN
ejpam-6089	659	24	℘	℘	PROPN
ejpam-6089	659	25	)	)	PUNCT
ejpam-6089	659	26	(	(	PUNCT
ejpam-6089	659	27	ℵð+	ℵð+	ADJ
ejpam-6089	659	28	℘	℘	PROPN
ejpam-6089	659	29	)	)	PUNCT
ejpam-6089	659	30	(	(	PUNCT
ejpam-6089	659	31	a−bi	a−bi	PROPN
ejpam-6089	659	32	(	(	PUNCT
ejpam-6089	659	33	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	659	34	)	)	PUNCT
ejpam-6089	659	35	(	(	PUNCT
ejpam-6089	659	36	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	659	37	2	2	NUM
ejpam-6089	659	38	)	)	PUNCT
ejpam-6089	659	39	+	+	CCONJ
ejpam-6089	659	40	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	659	41	)	)	PUNCT
ejpam-6089	660	1	+	+	CCONJ
ejpam-6089	660	2	a−bi	a−bi	PROPN
ejpam-6089	660	3	(	(	PUNCT
ejpam-6089	660	4	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	660	5	)	)	PUNCT
ejpam-6089	660	6	(	(	PUNCT
ejpam-6089	660	7	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	660	8	2	2	NUM
ejpam-6089	660	9	)	)	PUNCT
ejpam-6089	660	10	−	−	PROPN
ejpam-6089	660	11	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	660	12	)	)	PUNCT
ejpam-6089	660	13	)	)	PUNCT
ejpam-6089	661	1	−	−	PROPN
ejpam-6089	662	1	∞∑	∞∑	NUM
ejpam-6089	662	2	ð=0	ð=0	X
ejpam-6089	662	3	að	að	X
ejpam-6089	662	4	(	(	PUNCT
ejpam-6089	662	5	2(1−	2(1−	X
ejpam-6089	662	6	ℵð−	ℵð−	NUM
ejpam-6089	662	7	℘	℘	NUM
ejpam-6089	662	8	)	)	PUNCT
ejpam-6089	662	9	(	(	PUNCT
ejpam-6089	662	10	ℵð+	ℵð+	ADJ
ejpam-6089	662	11	℘	℘	PROPN
ejpam-6089	662	12	)	)	PUNCT
ejpam-6089	662	13	+	+	CCONJ
ejpam-6089	662	14	1	1	NUM
ejpam-6089	662	15	)	)	PUNCT
ejpam-6089	662	16	(	(	PUNCT
ejpam-6089	662	17	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	662	18	)	)	PUNCT
ejpam-6089	662	19	+	+	CCONJ
ejpam-6089	662	20	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	662	21	)	)	PUNCT
ejpam-6089	662	22	2	2	NUM
ejpam-6089	662	23	)	)	PUNCT
ejpam-6089	662	24	.	.	PUNCT
ejpam-6089	663	1	using	use	VERB
ejpam-6089	663	2	(	(	PUNCT
ejpam-6089	663	3	34	34	NUM
ejpam-6089	663	4	)	)	PUNCT
ejpam-6089	663	5	in	in	ADP
ejpam-6089	663	6	the	the	DET
ejpam-6089	663	7	above	above	ADJ
ejpam-6089	663	8	expression	expression	NOUN
ejpam-6089	663	9	∞∑	∞∑	NUM
ejpam-6089	663	10	ð=0	ð=0	X
ejpam-6089	663	11	að	að	X
ejpam-6089	663	12	(	(	PUNCT
ejpam-6089	663	13	ℑ2	ℑ2	PROPN
ejpam-6089	663	14	−ℑ1	−ℑ1	PROPN
ejpam-6089	663	15	)	)	PUNCT
ejpam-6089	663	16	(	(	PUNCT
ejpam-6089	663	17	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	663	18	)	)	PUNCT
ejpam-6089	663	19	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	663	20	℘	℘	NOUN
ejpam-6089	663	21	)	)	PUNCT
ejpam-6089	663	22	+	+	CCONJ
ejpam-6089	663	23	1	1	X
ejpam-6089	663	24	)	)	PUNCT
ejpam-6089	663	25	×	×	NOUN
ejpam-6089	663	26	(	(	PUNCT
ejpam-6089	663	27	ℑ2	ℑ2	PROPN
ejpam-6089	663	28	−ℑ1	−ℑ1	PROPN
ejpam-6089	663	29	4	4	NUM
ejpam-6089	663	30	∫	∫	PROPN
ejpam-6089	663	31	1	1	NUM
ejpam-6089	663	32	0	0	NUM
ejpam-6089	663	33	t(ℵð+℘	t(ℵð+℘	NUM
ejpam-6089	663	34	)	)	PUNCT
ejpam-6089	663	35	{	{	PUNCT
ejpam-6089	663	36	υ′	υ′	X
ejpam-6089	663	37	(	(	PUNCT
ejpam-6089	663	38	t	t	PROPN
ejpam-6089	663	39	2	2	NUM
ejpam-6089	663	40	ℑ1	ℑ1	NOUN
ejpam-6089	663	41	+	+	CCONJ
ejpam-6089	663	42	2−	2−	NUM
ejpam-6089	663	43	t	t	NOUN
ejpam-6089	663	44	2	2	NUM
ejpam-6089	663	45	b	b	NOUN
ejpam-6089	663	46	)	)	PUNCT
ejpam-6089	663	47	−υ′	−υ′	NOUN
ejpam-6089	663	48	(	(	PUNCT
ejpam-6089	663	49	2−	2−	NUM
ejpam-6089	663	50	t	t	NOUN
ejpam-6089	663	51	2	2	NUM
ejpam-6089	663	52	ℑ1	ℑ1	NOUN
ejpam-6089	663	53	+	+	CCONJ
ejpam-6089	663	54	t	t	PROPN
ejpam-6089	663	55	2	2	NUM
ejpam-6089	663	56	ℑ2	ℑ2	PROPN
ejpam-6089	663	57	)	)	PUNCT
ejpam-6089	663	58	}	}	PUNCT
ejpam-6089	663	59	dt	dt	PUNCT
ejpam-6089	663	60	)	)	PUNCT
ejpam-6089	664	1	+	+	CCONJ
ejpam-6089	664	2	∞∑	∞∑	NUM
ejpam-6089	664	3	ð=0	ð=0	X
ejpam-6089	664	4	að	að	X
ejpam-6089	664	5	(	(	PUNCT
ejpam-6089	664	6	(	(	PUNCT
ejpam-6089	664	7	ℑ2	ℑ2	PROPN
ejpam-6089	664	8	−ℑ1	−ℑ1	PROPN
ejpam-6089	664	9	)	)	PUNCT
ejpam-6089	664	10	(	(	PUNCT
ejpam-6089	664	11	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	664	12	)	)	PUNCT
ejpam-6089	664	13	2(ℵð+℘)−1γ((ℵð+	2(ℵð+℘)−1γ((ℵð+	NUM
ejpam-6089	664	14	℘	℘	NOUN
ejpam-6089	664	15	)	)	PUNCT
ejpam-6089	664	16	+	+	CCONJ
ejpam-6089	664	17	1	1	X
ejpam-6089	664	18	)	)	PUNCT
ejpam-6089	664	19	−	−	PROPN
ejpam-6089	664	20	1	1	NUM
ejpam-6089	664	21	)	)	PUNCT
ejpam-6089	665	1	υ	υ	NOUN
ejpam-6089	665	2	(	(	PUNCT
ejpam-6089	665	3	ℑ1	ℑ1	PROPN
ejpam-6089	665	4	+	+	CCONJ
ejpam-6089	665	5	ℑ2	ℑ2	PROPN
ejpam-6089	665	6	2	2	NUM
ejpam-6089	665	7	)	)	PUNCT
ejpam-6089	665	8	≤	≤	NOUN
ejpam-6089	665	9	∞∑	∞∑	NUM
ejpam-6089	665	10	ð=0	ð=0	X
ejpam-6089	665	11	að	að	X
ejpam-6089	665	12	(	(	PUNCT
ejpam-6089	665	13	r−li	r−li	NOUN
ejpam-6089	665	14	(	(	PUNCT
ejpam-6089	665	15	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	665	16	)	)	PUNCT
ejpam-6089	665	17	(	(	PUNCT
ejpam-6089	665	18	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	665	19	2	2	NUM
ejpam-6089	665	20	)	)	PUNCT
ejpam-6089	666	1	+	+	CCONJ
ejpam-6089	667	1	υ(ℑ2	υ(ℑ2	NOUN
ejpam-6089	667	2	)	)	PUNCT
ejpam-6089	667	3	+	+	NUM
ejpam-6089	667	4	r−li	r−li	NOUN
ejpam-6089	667	5	(	(	PUNCT
ejpam-6089	667	6	ℵð+℘	ℵð+℘	NOUN
ejpam-6089	667	7	)	)	PUNCT
ejpam-6089	667	8	(	(	PUNCT
ejpam-6089	667	9	ℑ̇1+ℑ2	ℑ̇1+ℑ2	ADJ
ejpam-6089	667	10	2	2	NUM
ejpam-6089	667	11	)	)	PUNCT
ejpam-6089	667	12	−	−	PROPN
ejpam-6089	667	13	υ(ℑ1	υ(ℑ1	PROPN
ejpam-6089	667	14	)	)	PUNCT
ejpam-6089	667	15	)	)	PUNCT
ejpam-6089	668	1	−	−	PROPN
ejpam-6089	669	1	∞∑	∞∑	NUM
ejpam-6089	669	2	ð=0	ð=0	X
ejpam-6089	669	3	aðυ	aðυ	ADJ
ejpam-6089	669	4	(	(	PUNCT
ejpam-6089	669	5	ℑ1	ℑ1	PROPN
ejpam-6089	669	6	+	+	CCONJ
ejpam-6089	669	7	ℑ2	ℑ2	PROPN
ejpam-6089	669	8	2	2	NUM
ejpam-6089	669	9	)	)	PUNCT
ejpam-6089	669	10	.	.	PUNCT
ejpam-6089	670	1	using	use	VERB
ejpam-6089	670	2	proposition	proposition	NOUN
ejpam-6089	670	3	1	1	NUM
ejpam-6089	670	4	from	from	ADP
ejpam-6089	670	5	the	the	DET
ejpam-6089	670	6	middle	middle	NOUN
ejpam-6089	670	7	of	of	ADP
ejpam-6089	670	8	interval	interval	NOUN
ejpam-6089	670	9	[	[	X
ejpam-6089	670	10	ℑ1,ℑ2	ℑ1,ℑ2	NOUN
ejpam-6089	670	11	]	]	PUNCT
ejpam-6089	670	12	,	,	PUNCT
ejpam-6089	670	13	we	we	PRON
ejpam-6089	670	14	have	have	VERB
ejpam-6089	670	15	(	(	PUNCT
ejpam-6089	670	16	ε	ε	PROPN
ejpam-6089	670	17	♭	♭	PROPN
ejpam-6089	670	18	,δ	,δ	PUNCT
ejpam-6089	670	19	,	,	PUNCT
ejpam-6089	670	20	b	b	NOUN
ejpam-6089	670	21	,	,	PUNCT
ejpam-6089	670	22	s	s	X
ejpam-6089	670	23	,	,	PUNCT
ejpam-6089	670	24	l	l	NOUN
ejpam-6089	670	25	(	(	PUNCT
ejpam-6089	670	26	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	670	27	2	2	NUM
ejpam-6089	670	28	)	)	PUNCT
ejpam-6089	671	1	+	+	ADP
ejpam-6089	671	2	,	,	PUNCT
ejpam-6089	671	3	ℵ,℘,τ	ℵ,℘,τ	NOUN
ejpam-6089	671	4	υ	υ	NOUN
ejpam-6089	671	5	)	)	PUNCT
ejpam-6089	671	6	(	(	PUNCT
ejpam-6089	671	7	ℑ2	ℑ2	PROPN
ejpam-6089	671	8	;	;	PUNCT
ejpam-6089	671	9	g	g	NOUN
ejpam-6089	671	10	)	)	PUNCT
ejpam-6089	671	11	+	+	CCONJ
ejpam-6089	671	12	(	(	PUNCT
ejpam-6089	671	13	ε	ε	PROPN
ejpam-6089	671	14	♭	♭	PROPN
ejpam-6089	671	15	,δ	,δ	PUNCT
ejpam-6089	671	16	,	,	PUNCT
ejpam-6089	671	17	b	b	NOUN
ejpam-6089	671	18	,	,	PUNCT
ejpam-6089	671	19	s	s	X
ejpam-6089	671	20	,	,	PUNCT
ejpam-6089	671	21	l	l	NOUN
ejpam-6089	671	22	(	(	PUNCT
ejpam-6089	671	23	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	671	24	2	2	NUM
ejpam-6089	671	25	)	)	PUNCT
ejpam-6089	671	26	−,ℵ,℘,τ	−,ℵ,℘,τ	NOUN
ejpam-6089	671	27	υ	υ	PROPN
ejpam-6089	671	28	)	)	PUNCT
ejpam-6089	671	29	(	(	PUNCT
ejpam-6089	671	30	ℑ1	ℑ1	NOUN
ejpam-6089	671	31	;	;	PUNCT
ejpam-6089	671	32	g	g	NOUN
ejpam-6089	671	33	)	)	PUNCT
ejpam-6089	671	34	−	−	PROPN
ejpam-6089	672	1	∞∑	∞∑	NUM
ejpam-6089	672	2	ð=0	ð=0	X
ejpam-6089	672	3	að	að	X
ejpam-6089	672	4	(	(	PUNCT
ejpam-6089	672	5	oð	oð	PROPN
ejpam-6089	672	6	−	−	PROPN
ejpam-6089	672	7	1)υ	1)υ	NUM
ejpam-6089	672	8	(	(	PUNCT
ejpam-6089	672	9	ℑ1	ℑ1	PROPN
ejpam-6089	672	10	+	+	CCONJ
ejpam-6089	672	11	ℑ2	ℑ2	PROPN
ejpam-6089	672	12	2	2	NUM
ejpam-6089	672	13	)	)	PUNCT
ejpam-6089	672	14	≥	≥	NOUN
ejpam-6089	672	15	∞∑	∞∑	NUM
ejpam-6089	672	16	ð=0	ð=0	X
ejpam-6089	672	17	aðoð	aðoð	ADJ
ejpam-6089	672	18	×	×	NOUN
ejpam-6089	672	19	(	(	PUNCT
ejpam-6089	672	20	ℑ2	ℑ2	PROPN
ejpam-6089	672	21	−ℑ1	−ℑ1	PROPN
ejpam-6089	672	22	4	4	NUM
ejpam-6089	672	23	∫	∫	PROPN
ejpam-6089	672	24	1	1	NUM
ejpam-6089	672	25	0	0	NUM
ejpam-6089	672	26	t(ℵð+℘	t(ℵð+℘	NUM
ejpam-6089	672	27	)	)	PUNCT
ejpam-6089	672	28	{	{	PUNCT
ejpam-6089	672	29	υ′	υ′	X
ejpam-6089	672	30	(	(	PUNCT
ejpam-6089	672	31	t	t	PROPN
ejpam-6089	672	32	2	2	NUM
ejpam-6089	672	33	ℑ1	ℑ1	NOUN
ejpam-6089	672	34	+	+	CCONJ
ejpam-6089	672	35	2−	2−	NUM
ejpam-6089	672	36	t	t	NOUN
ejpam-6089	672	37	2	2	NUM
ejpam-6089	672	38	ℑ2	ℑ2	ADJ
ejpam-6089	672	39	)	)	PUNCT
ejpam-6089	672	40	−υ′	−υ′	NOUN
ejpam-6089	672	41	(	(	PUNCT
ejpam-6089	672	42	2−	2−	NUM
ejpam-6089	672	43	t	t	NOUN
ejpam-6089	672	44	2	2	NUM
ejpam-6089	672	45	ℑ1	ℑ1	NOUN
ejpam-6089	672	46	+	+	CCONJ
ejpam-6089	672	47	t	t	PROPN
ejpam-6089	672	48	2	2	NUM
ejpam-6089	672	49	ℑ2	ℑ2	PROPN
ejpam-6089	672	50	)	)	PUNCT
ejpam-6089	672	51	}	}	PUNCT
ejpam-6089	672	52	dt	dt	PUNCT
ejpam-6089	672	53	)	)	PUNCT
ejpam-6089	673	1	+	+	CCONJ
ejpam-6089	673	2	∞∑	∞∑	NUM
ejpam-6089	673	3	ð=0	ð=0	X
ejpam-6089	673	4	aðυ	aðυ	ADJ
ejpam-6089	673	5	(	(	PUNCT
ejpam-6089	673	6	ℑ1	ℑ1	PROPN
ejpam-6089	673	7	+	+	CCONJ
ejpam-6089	673	8	ℑ2	ℑ2	PROPN
ejpam-6089	673	9	2	2	NUM
ejpam-6089	673	10	)	)	PUNCT
ejpam-6089	673	11	.	.	PUNCT
ejpam-6089	674	1	hence	hence	ADV
ejpam-6089	674	2	the	the	DET
ejpam-6089	674	3	required	require	VERB
ejpam-6089	674	4	result	result	NOUN
ejpam-6089	674	5	is	be	AUX
ejpam-6089	674	6	obtained	obtain	VERB
ejpam-6089	674	7	.	.	PUNCT
ejpam-6089	675	1	4	4	X
ejpam-6089	675	2	.	.	X
ejpam-6089	675	3	conclusion	conclusion	VERB
ejpam-6089	675	4	hermite	hermite	PROPN
ejpam-6089	675	5	-	-	PUNCT
ejpam-6089	675	6	hadamard	hadamard	ADJ
ejpam-6089	675	7	inequalities	inequality	NOUN
ejpam-6089	675	8	are	be	AUX
ejpam-6089	675	9	essential	essential	ADJ
ejpam-6089	675	10	to	to	ADP
ejpam-6089	675	11	many	many	ADJ
ejpam-6089	675	12	areas	area	NOUN
ejpam-6089	675	13	of	of	ADP
ejpam-6089	675	14	mathematics	mathematic	NOUN
ejpam-6089	675	15	,	,	PUNCT
ejpam-6089	675	16	such	such	ADJ
ejpam-6089	675	17	as	as	ADP
ejpam-6089	675	18	calculus	calculus	NOUN
ejpam-6089	675	19	,	,	PUNCT
ejpam-6089	675	20	real	real	ADJ
ejpam-6089	675	21	analysis	analysis	NOUN
ejpam-6089	675	22	,	,	PUNCT
ejpam-6089	675	23	and	and	CCONJ
ejpam-6089	675	24	convex	convex	NOUN
ejpam-6089	675	25	functions	function	NOUN
ejpam-6089	675	26	with	with	ADP
ejpam-6089	675	27	practical	practical	ADJ
ejpam-6089	675	28	applications	application	NOUN
ejpam-6089	675	29	in	in	ADP
ejpam-6089	675	30	diverse	diverse	ADJ
ejpam-6089	675	31	areas	area	NOUN
ejpam-6089	675	32	s.	s.	PROPN
ejpam-6089	675	33	naheed	nahee	VERB
ejpam-6089	675	34	et	et	PROPN
ejpam-6089	675	35	al	al	PROPN
ejpam-6089	675	36	.	.	PUNCT
ejpam-6089	675	37	/	/	SYM
ejpam-6089	675	38	eur	eur	PROPN
ejpam-6089	675	39	.	.	PUNCT
ejpam-6089	676	1	j.	j.	PROPN
ejpam-6089	676	2	pure	pure	PROPN
ejpam-6089	676	3	appl	appl	PROPN
ejpam-6089	676	4	.	.	PROPN
ejpam-6089	676	5	math	math	PROPN
ejpam-6089	676	6	,	,	PUNCT
ejpam-6089	676	7	18	18	NUM
ejpam-6089	676	8	(	(	PUNCT
ejpam-6089	676	9	2	2	NUM
ejpam-6089	676	10	)	)	PUNCT
ejpam-6089	676	11	(	(	PUNCT
ejpam-6089	676	12	2025	2025	NUM
ejpam-6089	676	13	)	)	PUNCT
ejpam-6089	676	14	,	,	PUNCT
ejpam-6089	676	15	6089	6089	NUM
ejpam-6089	676	16	31	31	NUM
ejpam-6089	676	17	of	of	ADP
ejpam-6089	676	18	34	34	NUM
ejpam-6089	676	19	such	such	ADJ
ejpam-6089	676	20	as	as	ADP
ejpam-6089	676	21	physics	physics	NOUN
ejpam-6089	676	22	,	,	PUNCT
ejpam-6089	676	23	economics	economic	NOUN
ejpam-6089	676	24	,	,	PUNCT
ejpam-6089	676	25	optimization	optimization	NOUN
ejpam-6089	676	26	and	and	CCONJ
ejpam-6089	676	27	engineering	engineering	NOUN
ejpam-6089	676	28	.	.	PUNCT
ejpam-6089	677	1	in	in	ADP
ejpam-6089	677	2	this	this	DET
ejpam-6089	677	3	article	article	NOUN
ejpam-6089	677	4	,	,	PUNCT
ejpam-6089	677	5	we	we	PRON
ejpam-6089	677	6	look	look	VERB
ejpam-6089	677	7	into	into	ADP
ejpam-6089	677	8	fractional	fractional	ADJ
ejpam-6089	677	9	integral	integral	ADJ
ejpam-6089	677	10	inequalities	inequality	NOUN
ejpam-6089	677	11	to	to	ADP
ejpam-6089	677	12	atangana	atangana	PROPN
ejpam-6089	677	13	-	-	PUNCT
ejpam-6089	677	14	baleanu	baleanu	PROPN
ejpam-6089	677	15	and	and	CCONJ
ejpam-6089	677	16	prabhakar	prabhakar	PROPN
ejpam-6089	677	17	fractional	fractional	PROPN
ejpam-6089	677	18	calculus	calculus	NOUN
ejpam-6089	677	19	operators	operator	NOUN
ejpam-6089	677	20	.	.	PUNCT
ejpam-6089	678	1	using	use	VERB
ejpam-6089	678	2	extended	extended	ADJ
ejpam-6089	678	3	generalized	generalize	VERB
ejpam-6089	678	4	mittag	mittag	ADJ
ejpam-6089	678	5	-	-	PUNCT
ejpam-6089	678	6	leffler	leffler	NOUN
ejpam-6089	678	7	functions	function	NOUN
ejpam-6089	678	8	as	as	ADP
ejpam-6089	678	9	their	their	PRON
ejpam-6089	678	10	kernel	kernel	NOUN
ejpam-6089	678	11	,	,	PUNCT
ejpam-6089	678	12	we	we	PRON
ejpam-6089	678	13	present	present	VERB
ejpam-6089	678	14	several	several	ADJ
ejpam-6089	678	15	hermite	hermite	ADJ
ejpam-6089	678	16	-	-	PUNCT
ejpam-6089	678	17	hadamard	hadamard	ADJ
ejpam-6089	678	18	type	type	NOUN
ejpam-6089	678	19	fractional	fractional	ADJ
ejpam-6089	678	20	integral	integral	ADJ
ejpam-6089	678	21	inequalities	inequality	NOUN
ejpam-6089	678	22	for	for	ADP
ejpam-6089	678	23	the	the	DET
ejpam-6089	678	24	atangana	atangana	PROPN
ejpam-6089	678	25	-	-	PUNCT
ejpam-6089	678	26	baleanu	baleanu	PROPN
ejpam-6089	678	27	and	and	CCONJ
ejpam-6089	678	28	prabhakar	prabhakar	PROPN
ejpam-6089	678	29	fractional	fractional	ADJ
ejpam-6089	678	30	operators	operator	NOUN
ejpam-6089	678	31	.	.	PUNCT
ejpam-6089	679	1	for	for	ADP
ejpam-6089	679	2	the	the	DET
ejpam-6089	679	3	integral	integral	ADJ
ejpam-6089	679	4	inequalities	inequality	NOUN
ejpam-6089	679	5	involving	involve	VERB
ejpam-6089	679	6	fractional	fractional	ADJ
ejpam-6089	679	7	integral	integral	ADJ
ejpam-6089	679	8	of	of	ADP
ejpam-6089	679	9	the	the	DET
ejpam-6089	679	10	kind	kind	NOUN
ejpam-6089	679	11	(	(	PUNCT
ejpam-6089	679	12	ℑ1+,ℑ2−	ℑ1+,ℑ2−	PROPN
ejpam-6089	679	13	)	)	PUNCT
ejpam-6089	679	14	and	and	CCONJ
ejpam-6089	679	15	(	(	PUNCT
ejpam-6089	679	16	ℑ1+ℑ2	ℑ1+ℑ2	NOUN
ejpam-6089	679	17	2	2	NUM
ejpam-6089	679	18	)	)	PUNCT
ejpam-6089	679	19	,	,	PUNCT
ejpam-6089	679	20	important	important	ADJ
ejpam-6089	679	21	results	result	NOUN
ejpam-6089	679	22	are	be	AUX
ejpam-6089	679	23	given	give	VERB
ejpam-6089	679	24	.	.	PUNCT
ejpam-6089	680	1	we	we	PRON
ejpam-6089	680	2	demonstrate	demonstrate	VERB
ejpam-6089	680	3	the	the	DET
ejpam-6089	680	4	validity	validity	NOUN
ejpam-6089	680	5	of	of	ADP
ejpam-6089	680	6	our	our	PRON
ejpam-6089	680	7	results	result	NOUN
ejpam-6089	680	8	by	by	ADP
ejpam-6089	680	9	using	use	VERB
ejpam-6089	680	10	certain	certain	ADJ
ejpam-6089	680	11	functions	function	NOUN
ejpam-6089	680	12	to	to	PART
ejpam-6089	680	13	generate	generate	VERB
ejpam-6089	680	14	visual	visual	ADJ
ejpam-6089	680	15	graphs	graph	NOUN
ejpam-6089	680	16	that	that	PRON
ejpam-6089	680	17	illustrate	illustrate	VERB
ejpam-6089	680	18	the	the	DET
ejpam-6089	680	19	inequalities	inequality	NOUN
ejpam-6089	680	20	with	with	ADP
ejpam-6089	680	21	corresponding	corresponding	ADJ
ejpam-6089	680	22	numerical	numerical	ADJ
ejpam-6089	680	23	entries	entry	NOUN
ejpam-6089	680	24	.	.	PUNCT
ejpam-6089	681	1	this	this	DET
ejpam-6089	681	2	article	article	NOUN
ejpam-6089	681	3	seeks	seek	VERB
ejpam-6089	681	4	to	to	PART
ejpam-6089	681	5	provide	provide	VERB
ejpam-6089	681	6	more	more	ADV
ejpam-6089	681	7	precise	precise	ADJ
ejpam-6089	681	8	bounds	bound	NOUN
ejpam-6089	681	9	and	and	CCONJ
ejpam-6089	681	10	enhance	enhance	VERB
ejpam-6089	681	11	the	the	DET
ejpam-6089	681	12	theoretical	theoretical	ADJ
ejpam-6089	681	13	foundation	foundation	NOUN
ejpam-6089	681	14	for	for	ADP
ejpam-6089	681	15	further	further	ADJ
ejpam-6089	681	16	studies	study	NOUN
ejpam-6089	681	17	to	to	PART
ejpam-6089	681	18	broaden	broaden	VERB
ejpam-6089	681	19	the	the	DET
ejpam-6089	681	20	classical	classical	ADJ
ejpam-6089	681	21	(	(	PUNCT
ejpam-6089	681	22	h−h	h−h	NOUN
ejpam-6089	681	23	)	)	PUNCT
ejpam-6089	681	24	inequality	inequality	NOUN
ejpam-6089	681	25	with	with	ADP
ejpam-6089	681	26	generalized	generalized	ADJ
ejpam-6089	681	27	fractional	fractional	ADJ
ejpam-6089	681	28	integral	integral	ADJ
ejpam-6089	681	29	operators	operator	NOUN
ejpam-6089	681	30	.	.	PUNCT
ejpam-6089	682	1	the	the	DET
ejpam-6089	682	2	latest	late	ADJ
ejpam-6089	682	3	inequalities	inequality	NOUN
ejpam-6089	682	4	will	will	AUX
ejpam-6089	682	5	assist	assist	VERB
ejpam-6089	682	6	to	to	PART
ejpam-6089	682	7	boost	boost	VERB
ejpam-6089	682	8	comprehension	comprehension	NOUN
ejpam-6089	682	9	in	in	ADP
ejpam-6089	682	10	fractional	fractional	ADJ
ejpam-6089	682	11	calculus	calculus	NOUN
ejpam-6089	682	12	and	and	CCONJ
ejpam-6089	682	13	convex	convex	ADJ
ejpam-6089	682	14	analysis	analysis	NOUN
ejpam-6089	682	15	,	,	PUNCT
ejpam-6089	682	16	with	with	ADP
ejpam-6089	682	17	inference	inference	NOUN
ejpam-6089	682	18	through	through	ADP
ejpam-6089	682	19	several	several	ADJ
ejpam-6089	682	20	domains	domain	NOUN
ejpam-6089	682	21	.	.	PUNCT
ejpam-6089	683	1	acknowledgements	acknowledgement	NOUN
ejpam-6089	683	2	the	the	DET
ejpam-6089	683	3	authors	author	NOUN
ejpam-6089	683	4	i.	i.	PROPN
ejpam-6089	683	5	ayoob	ayoob	PROPN
ejpam-6089	683	6	and	and	CCONJ
ejpam-6089	683	7	n.	n.	PROPN
ejpam-6089	683	8	mlaiki	mlaiki	PROPN
ejpam-6089	683	9	would	would	AUX
ejpam-6089	683	10	like	like	VERB
ejpam-6089	683	11	to	to	PART
ejpam-6089	683	12	thank	thank	VERB
ejpam-6089	683	13	prince	prince	PROPN
ejpam-6089	683	14	sultan	sultan	PROPN
ejpam-6089	683	15	university	university	PROPN
ejpam-6089	683	16	for	for	ADP
ejpam-6089	683	17	paying	pay	VERB
ejpam-6089	683	18	the	the	DET
ejpam-6089	683	19	publication	publication	NOUN
ejpam-6089	683	20	fees	fee	NOUN
ejpam-6089	683	21	for	for	ADP
ejpam-6089	683	22	this	this	DET
ejpam-6089	683	23	work	work	NOUN
ejpam-6089	683	24	through	through	ADP
ejpam-6089	683	25	tas	ta	NOUN
ejpam-6089	683	26	lab	lab	PROPN
ejpam-6089	683	27	.	.	PUNCT
ejpam-6089	684	1	declarations	declaration	NOUN
ejpam-6089	684	2	:	:	PUNCT
ejpam-6089	684	3	availability	availability	NOUN
ejpam-6089	684	4	of	of	ADP
ejpam-6089	684	5	data	datum	NOUN
ejpam-6089	684	6	and	and	CCONJ
ejpam-6089	684	7	material	material	NOUN
ejpam-6089	684	8	the	the	DET
ejpam-6089	684	9	data	datum	NOUN
ejpam-6089	684	10	used	use	VERB
ejpam-6089	684	11	to	to	PART
ejpam-6089	684	12	support	support	VERB
ejpam-6089	684	13	the	the	DET
ejpam-6089	684	14	findings	finding	NOUN
ejpam-6089	684	15	of	of	ADP
ejpam-6089	684	16	this	this	DET
ejpam-6089	684	17	study	study	NOUN
ejpam-6089	684	18	are	be	AUX
ejpam-6089	684	19	available	available	ADJ
ejpam-6089	684	20	from	from	ADP
ejpam-6089	684	21	the	the	DET
ejpam-6089	684	22	corresponding	corresponding	ADJ
ejpam-6089	684	23	author	author	NOUN
ejpam-6089	684	24	upon	upon	SCONJ
ejpam-6089	684	25	request	request	NOUN
ejpam-6089	684	26	.	.	PUNCT
ejpam-6089	685	1	authors	author	NOUN
ejpam-6089	685	2	’	'	PUNCT
ejpam-6089	685	3	contributions	contribution	NOUN
ejpam-6089	685	4	all	all	DET
ejpam-6089	685	5	authors	author	NOUN
ejpam-6089	685	6	contributed	contribute	VERB
ejpam-6089	685	7	equally	equally	ADV
ejpam-6089	685	8	and	and	CCONJ
ejpam-6089	685	9	significantly	significantly	ADV
ejpam-6089	685	10	in	in	ADP
ejpam-6089	685	11	writing	write	VERB
ejpam-6089	685	12	this	this	DET
ejpam-6089	685	13	article	article	NOUN
ejpam-6089	685	14	.	.	PUNCT
ejpam-6089	686	1	all	all	DET
ejpam-6089	686	2	authors	author	NOUN
ejpam-6089	686	3	read	read	VERB
ejpam-6089	686	4	and	and	CCONJ
ejpam-6089	686	5	approved	approve	VERB
ejpam-6089	686	6	the	the	DET
ejpam-6089	686	7	final	final	ADJ
ejpam-6089	686	8	version	version	NOUN
ejpam-6089	686	9	.	.	PUNCT
ejpam-6089	687	1	competing	compete	VERB
ejpam-6089	687	2	interests	interest	NOUN
ejpam-6089	687	3	the	the	DET
ejpam-6089	687	4	authors	author	NOUN
ejpam-6089	687	5	declare	declare	VERB
ejpam-6089	687	6	that	that	SCONJ
ejpam-6089	687	7	they	they	PRON
ejpam-6089	687	8	have	have	VERB
ejpam-6089	687	9	no	no	DET
ejpam-6089	687	10	conflicts	conflict	NOUN
ejpam-6089	687	11	of	of	ADP
ejpam-6089	687	12	interest	interest	NOUN
ejpam-6089	687	13	.	.	PUNCT
ejpam-6089	688	1	references	reference	NOUN
ejpam-6089	688	2	[	[	X
ejpam-6089	688	3	1	1	NUM
ejpam-6089	688	4	]	]	PUNCT
ejpam-6089	688	5	i.	i.	PROPN
ejpam-6089	688	6	k.	k.	PROPN
ejpam-6089	688	7	guce	guce	PROPN
ejpam-6089	688	8	.	.	PUNCT
ejpam-6089	689	1	on	on	ADP
ejpam-6089	689	2	fractional	fractional	ADJ
ejpam-6089	689	3	derivatives	derivative	NOUN
ejpam-6089	689	4	:	:	PUNCT
ejpam-6089	689	5	the	the	DET
ejpam-6089	689	6	non	non	ADJ
ejpam-6089	689	7	-	-	ADJ
ejpam-6089	689	8	integer	integer	ADJ
ejpam-6089	689	9	order	order	NOUN
ejpam-6089	689	10	of	of	ADP
ejpam-6089	689	11	the	the	DET
ejpam-6089	689	12	derivative	derivative	NOUN
ejpam-6089	689	13	.	.	PUNCT
ejpam-6089	690	1	international	international	ADJ
ejpam-6089	690	2	journal	journal	PROPN
ejpam-6089	690	3	of	of	ADP
ejpam-6089	690	4	scientific	scientific	PROPN
ejpam-6089	690	5	&	&	CCONJ
ejpam-6089	690	6	engineering	engineering	PROPN
ejpam-6089	690	7	research	research	NOUN
ejpam-6089	690	8	,	,	PUNCT
ejpam-6089	690	9	4(3):1–5	4(3):1–5	X
ejpam-6089	690	10	,	,	PUNCT
ejpam-6089	690	11	2013	2013	NUM
ejpam-6089	690	12	.	.	PUNCT
ejpam-6089	691	1	[	[	X
ejpam-6089	691	2	2	2	X
ejpam-6089	691	3	]	]	PUNCT
ejpam-6089	691	4	s.	s.	PROPN
ejpam-6089	691	5	a.	a.	PROPN
ejpam-6089	691	6	david	david	PROPN
ejpam-6089	691	7	,	,	PUNCT
ejpam-6089	691	8	j.	j.	PROPN
ejpam-6089	691	9	l.	l.	PROPN
ejpam-6089	691	10	linares	linares	PROPN
ejpam-6089	691	11	,	,	PUNCT
ejpam-6089	691	12	and	and	CCONJ
ejpam-6089	691	13	e.	e.	PROPN
ejpam-6089	691	14	m.	m.	PROPN
ejpam-6089	691	15	j.	j.	PROPN
ejpam-6089	691	16	a.	a.	PROPN
ejpam-6089	691	17	pallone	pallone	PROPN
ejpam-6089	691	18	.	.	PUNCT
ejpam-6089	691	19	fractional	fractional	ADJ
ejpam-6089	691	20	order	order	NOUN
ejpam-6089	691	21	calculus	calculus	NOUN
ejpam-6089	691	22	:	:	PUNCT
ejpam-6089	691	23	historical	historical	ADJ
ejpam-6089	691	24	apologia	apologia	ADJ
ejpam-6089	691	25	,	,	PUNCT
ejpam-6089	691	26	basic	basic	ADJ
ejpam-6089	691	27	concepts	concept	NOUN
ejpam-6089	691	28	and	and	CCONJ
ejpam-6089	691	29	some	some	DET
ejpam-6089	691	30	applications	application	NOUN
ejpam-6089	691	31	.	.	PUNCT
ejpam-6089	692	1	revista	revista	PROPN
ejpam-6089	692	2	brasileira	brasileira	PROPN
ejpam-6089	692	3	de	de	PROPN
ejpam-6089	692	4	ensino	ensino	PROPN
ejpam-6089	692	5	de	de	PROPN
ejpam-6089	692	6	f́ısica	f́ısica	PROPN
ejpam-6089	692	7	,	,	PUNCT
ejpam-6089	692	8	33(4):4302–4309	33(4):4302–4309	NUM
ejpam-6089	692	9	,	,	PUNCT
ejpam-6089	692	10	2011	2011	NUM
ejpam-6089	692	11	.	.	PUNCT
ejpam-6089	693	1	[	[	X
ejpam-6089	693	2	3	3	NUM
ejpam-6089	693	3	]	]	X
ejpam-6089	693	4	r.	r.	PROPN
ejpam-6089	693	5	gorenflo	gorenflo	PROPN
ejpam-6089	693	6	and	and	CCONJ
ejpam-6089	693	7	f.	f.	PROPN
ejpam-6089	693	8	mainardi	mainardi	PROPN
ejpam-6089	693	9	.	.	PUNCT
ejpam-6089	694	1	fractional	fractional	ADJ
ejpam-6089	694	2	calculus	calculus	NOUN
ejpam-6089	694	3	:	:	PUNCT
ejpam-6089	694	4	integral	integral	ADJ
ejpam-6089	694	5	and	and	CCONJ
ejpam-6089	694	6	differential	differential	ADJ
ejpam-6089	694	7	equations	equation	NOUN
ejpam-6089	694	8	of	of	ADP
ejpam-6089	694	9	fractional	fractional	ADJ
ejpam-6089	694	10	order	order	NOUN
ejpam-6089	694	11	.	.	PUNCT
ejpam-6089	695	1	fractals	fractal	NOUN
ejpam-6089	695	2	,	,	PUNCT
ejpam-6089	695	3	5(4):411–424	5(4):411–424	NUM
ejpam-6089	695	4	,	,	PUNCT
ejpam-6089	695	5	1997	1997	NUM
ejpam-6089	695	6	.	.	PUNCT
ejpam-6089	696	1	s.	s.	PROPN
ejpam-6089	696	2	naheed	nahee	VERB
ejpam-6089	696	3	et	et	PROPN
ejpam-6089	696	4	al	al	PROPN
ejpam-6089	696	5	.	.	PUNCT
ejpam-6089	696	6	/	/	SYM
ejpam-6089	696	7	eur	eur	PROPN
ejpam-6089	696	8	.	.	PUNCT
ejpam-6089	697	1	j.	j.	PROPN
ejpam-6089	697	2	pure	pure	PROPN
ejpam-6089	697	3	appl	appl	PROPN
ejpam-6089	697	4	.	.	PROPN
ejpam-6089	697	5	math	math	PROPN
ejpam-6089	697	6	,	,	PUNCT
ejpam-6089	697	7	18	18	NUM
ejpam-6089	697	8	(	(	PUNCT
ejpam-6089	697	9	2	2	NUM
ejpam-6089	697	10	)	)	PUNCT
ejpam-6089	697	11	(	(	PUNCT
ejpam-6089	697	12	2025	2025	NUM
ejpam-6089	697	13	)	)	PUNCT
ejpam-6089	697	14	,	,	PUNCT
ejpam-6089	697	15	6089	6089	NUM
ejpam-6089	697	16	32	32	NUM
ejpam-6089	697	17	of	of	ADP
ejpam-6089	697	18	34	34	NUM
ejpam-6089	697	19	[	[	X
ejpam-6089	697	20	4	4	NUM
ejpam-6089	697	21	]	]	PUNCT
ejpam-6089	697	22	k.	k.	PROPN
ejpam-6089	697	23	s.	s.	PROPN
ejpam-6089	697	24	miller	miller	PROPN
ejpam-6089	697	25	and	and	CCONJ
ejpam-6089	697	26	b.	b.	PROPN
ejpam-6089	697	27	ross	ross	PROPN
ejpam-6089	697	28	.	.	PUNCT
ejpam-6089	698	1	an	an	DET
ejpam-6089	698	2	introduction	introduction	NOUN
ejpam-6089	698	3	to	to	ADP
ejpam-6089	698	4	the	the	DET
ejpam-6089	698	5	fractional	fractional	ADJ
ejpam-6089	698	6	calculus	calculus	NOUN
ejpam-6089	698	7	and	and	CCONJ
ejpam-6089	698	8	fractional	fractional	ADJ
ejpam-6089	698	9	differential	differential	ADJ
ejpam-6089	698	10	equations	equation	NOUN
ejpam-6089	698	11	.	.	PUNCT
ejpam-6089	699	1	wiley	wiley	PROPN
ejpam-6089	699	2	,	,	PUNCT
ejpam-6089	699	3	new	new	PROPN
ejpam-6089	699	4	york	york	PROPN
ejpam-6089	699	5	,	,	PUNCT
ejpam-6089	699	6	1993	1993	NUM
ejpam-6089	699	7	.	.	PUNCT
ejpam-6089	700	1	[	[	X
ejpam-6089	700	2	5	5	X
ejpam-6089	700	3	]	]	PUNCT
ejpam-6089	700	4	k.	k.	PROPN
ejpam-6089	700	5	b.	b.	PROPN
ejpam-6089	700	6	oldham	oldham	PROPN
ejpam-6089	700	7	and	and	CCONJ
ejpam-6089	700	8	j.	j.	PROPN
ejpam-6089	700	9	spanier	spanier	PROPN
ejpam-6089	700	10	.	.	PUNCT
ejpam-6089	701	1	the	the	DET
ejpam-6089	701	2	fractional	fractional	ADJ
ejpam-6089	701	3	calculus	calculus	NOUN
ejpam-6089	701	4	.	.	PUNCT
ejpam-6089	702	1	academic	academic	ADJ
ejpam-6089	702	2	press	press	NOUN
ejpam-6089	702	3	,	,	PUNCT
ejpam-6089	702	4	san	san	PROPN
ejpam-6089	702	5	diego	diego	PROPN
ejpam-6089	702	6	,	,	PUNCT
ejpam-6089	702	7	1974	1974	NUM
ejpam-6089	702	8	.	.	PUNCT
ejpam-6089	703	1	[	[	X
ejpam-6089	703	2	6	6	NUM
ejpam-6089	703	3	]	]	PUNCT
ejpam-6089	703	4	h.	h.	PROPN
ejpam-6089	703	5	m.	m.	PROPN
ejpam-6089	703	6	srivastava	srivastava	PROPN
ejpam-6089	703	7	and	and	CCONJ
ejpam-6089	703	8	a.	a.	PROPN
ejpam-6089	703	9	k.	k.	PROPN
ejpam-6089	703	10	mishra	mishra	PROPN
ejpam-6089	703	11	.	.	PROPN
ejpam-6089	703	12	applications	application	NOUN
ejpam-6089	703	13	of	of	ADP
ejpam-6089	703	14	fractional	fractional	ADJ
ejpam-6089	703	15	calculus	calculus	NOUN
ejpam-6089	703	16	to	to	PART
ejpam-6089	703	17	parabolic	parabolic	VERB
ejpam-6089	703	18	starlike	starlike	NOUN
ejpam-6089	703	19	and	and	CCONJ
ejpam-6089	703	20	uniformly	uniformly	ADV
ejpam-6089	703	21	convex	convex	NOUN
ejpam-6089	703	22	functions	function	NOUN
ejpam-6089	703	23	.	.	PUNCT
ejpam-6089	704	1	computers	computer	NOUN
ejpam-6089	704	2	&	&	CCONJ
ejpam-6089	704	3	mathematics	mathematics	PROPN
ejpam-6089	704	4	with	with	ADP
ejpam-6089	704	5	applications	application	NOUN
ejpam-6089	704	6	,	,	PUNCT
ejpam-6089	704	7	39(3	39(3	NUM
ejpam-6089	704	8	-	-	SYM
ejpam-6089	704	9	4):57–69	4):57–69	NUM
ejpam-6089	704	10	,	,	PUNCT
ejpam-6089	704	11	2000	2000	NUM
ejpam-6089	704	12	.	.	PUNCT
ejpam-6089	705	1	[	[	X
ejpam-6089	705	2	7	7	X
ejpam-6089	705	3	]	]	X
ejpam-6089	705	4	d.	d.	PROPN
ejpam-6089	705	5	bertsekas	bertsekas	PROPN
ejpam-6089	705	6	.	.	PUNCT
ejpam-6089	706	1	convex	convex	PROPN
ejpam-6089	706	2	optimization	optimization	NOUN
ejpam-6089	706	3	theory	theory	NOUN
ejpam-6089	706	4	.	.	PUNCT
ejpam-6089	707	1	athena	athena	PROPN
ejpam-6089	707	2	scientific	scientific	PROPN
ejpam-6089	707	3	,	,	PUNCT
ejpam-6089	707	4	belmont	belmont	PROPN
ejpam-6089	707	5	,	,	PUNCT
ejpam-6089	707	6	ma	ma	PROPN
ejpam-6089	707	7	,	,	PUNCT
ejpam-6089	707	8	2009	2009	NUM
ejpam-6089	707	9	.	.	PUNCT
ejpam-6089	708	1	[	[	X
ejpam-6089	708	2	8	8	NUM
ejpam-6089	708	3	]	]	X
ejpam-6089	708	4	a.	a.	PROPN
ejpam-6089	708	5	ben	ben	PROPN
ejpam-6089	708	6	-	-	PROPN
ejpam-6089	708	7	tal	tal	PROPN
ejpam-6089	708	8	and	and	CCONJ
ejpam-6089	708	9	a.	a.	NOUN
ejpam-6089	708	10	nemirovski	nemirovski	PROPN
ejpam-6089	708	11	.	.	PUNCT
ejpam-6089	709	1	lectures	lecture	NOUN
ejpam-6089	709	2	on	on	ADP
ejpam-6089	709	3	modern	modern	ADJ
ejpam-6089	709	4	convex	convex	NOUN
ejpam-6089	709	5	optimization	optimization	NOUN
ejpam-6089	709	6	:	:	PUNCT
ejpam-6089	709	7	analysis	analysis	NOUN
ejpam-6089	709	8	,	,	PUNCT
ejpam-6089	709	9	algorithms	algorithm	NOUN
ejpam-6089	709	10	,	,	PUNCT
ejpam-6089	709	11	and	and	CCONJ
ejpam-6089	709	12	engineering	engineering	NOUN
ejpam-6089	709	13	applications	application	NOUN
ejpam-6089	709	14	.	.	PUNCT
ejpam-6089	710	1	society	society	NOUN
ejpam-6089	710	2	for	for	ADP
ejpam-6089	710	3	industrial	industrial	ADJ
ejpam-6089	710	4	and	and	CCONJ
ejpam-6089	710	5	applied	applied	ADJ
ejpam-6089	710	6	mathematics	mathematic	NOUN
ejpam-6089	710	7	,	,	PUNCT
ejpam-6089	710	8	philadelphia	philadelphia	PROPN
ejpam-6089	710	9	,	,	PUNCT
ejpam-6089	710	10	2001	2001	NUM
ejpam-6089	710	11	.	.	PUNCT
ejpam-6089	711	1	[	[	X
ejpam-6089	711	2	9	9	NUM
ejpam-6089	711	3	]	]	PUNCT
ejpam-6089	711	4	v.	v.	CCONJ
ejpam-6089	711	5	lakshmikantham	lakshmikantham	NOUN
ejpam-6089	711	6	and	and	CCONJ
ejpam-6089	711	7	s.	s.	PROPN
ejpam-6089	711	8	leela	leela	PROPN
ejpam-6089	711	9	.	.	PUNCT
ejpam-6089	711	10	differential	differential	PROPN
ejpam-6089	711	11	and	and	CCONJ
ejpam-6089	711	12	integral	integral	ADJ
ejpam-6089	711	13	inequalities	inequality	NOUN
ejpam-6089	711	14	,	,	PUNCT
ejpam-6089	711	15	theory	theory	NOUN
ejpam-6089	711	16	and	and	CCONJ
ejpam-6089	711	17	applications	application	NOUN
ejpam-6089	711	18	,	,	PUNCT
ejpam-6089	711	19	volume	volume	NOUN
ejpam-6089	711	20	1	1	NUM
ejpam-6089	711	21	.	.	PUNCT
ejpam-6089	711	22	academic	academic	ADJ
ejpam-6089	711	23	press	press	NOUN
ejpam-6089	711	24	,	,	PUNCT
ejpam-6089	711	25	new	new	PROPN
ejpam-6089	711	26	york	york	PROPN
ejpam-6089	711	27	,	,	PUNCT
ejpam-6089	711	28	1969	1969	NUM
ejpam-6089	711	29	.	.	PUNCT
ejpam-6089	712	1	[	[	X
ejpam-6089	712	2	10	10	NUM
ejpam-6089	712	3	]	]	X
ejpam-6089	712	4	w.	w.	PROPN
ejpam-6089	712	5	walter	walter	PROPN
ejpam-6089	712	6	.	.	PUNCT
ejpam-6089	713	1	differential	differential	PROPN
ejpam-6089	713	2	and	and	CCONJ
ejpam-6089	713	3	integral	integral	ADJ
ejpam-6089	713	4	inequalities	inequality	NOUN
ejpam-6089	713	5	,	,	PUNCT
ejpam-6089	713	6	volume	volume	NOUN
ejpam-6089	713	7	55	55	NUM
ejpam-6089	713	8	of	of	ADP
ejpam-6089	713	9	springer	springer	NOUN
ejpam-6089	713	10	tracts	tract	NOUN
ejpam-6089	713	11	in	in	ADP
ejpam-6089	713	12	natural	natural	ADJ
ejpam-6089	713	13	philosophy	philosophy	NOUN
ejpam-6089	713	14	.	.	PUNCT
ejpam-6089	714	1	springer	springer	NOUN
ejpam-6089	714	2	,	,	PUNCT
ejpam-6089	714	3	berlin	berlin	PROPN
ejpam-6089	714	4	,	,	PUNCT
ejpam-6089	714	5	2012	2012	NUM
ejpam-6089	714	6	.	.	PUNCT
ejpam-6089	715	1	original	original	ADJ
ejpam-6089	715	2	edition	edition	NOUN
ejpam-6089	715	3	in	in	ADP
ejpam-6089	715	4	german	german	NOUN
ejpam-6089	715	5	,	,	PUNCT
ejpam-6089	715	6	1964	1964	NUM
ejpam-6089	715	7	.	.	PUNCT
ejpam-6089	716	1	[	[	X
ejpam-6089	716	2	11	11	NUM
ejpam-6089	716	3	]	]	X
ejpam-6089	716	4	p.	p.	PROPN
ejpam-6089	716	5	agarwal	agarwal	PROPN
ejpam-6089	716	6	,	,	PUNCT
ejpam-6089	716	7	j.	j.	PROPN
ejpam-6089	716	8	tariboon	tariboon	PROPN
ejpam-6089	716	9	,	,	PUNCT
ejpam-6089	716	10	and	and	CCONJ
ejpam-6089	716	11	s.	s.	PROPN
ejpam-6089	716	12	k.	k.	PROPN
ejpam-6089	716	13	ntouyas	ntouyas	PROPN
ejpam-6089	716	14	.	.	PUNCT
ejpam-6089	717	1	some	some	DET
ejpam-6089	717	2	generalized	generalize	VERB
ejpam-6089	717	3	riemann	riemann	PROPN
ejpam-6089	717	4	-	-	PUNCT
ejpam-6089	717	5	liouville	liouville	VERB
ejpam-6089	717	6	k	k	ADJ
ejpam-6089	717	7	-	-	ADJ
ejpam-6089	717	8	fractional	fractional	ADJ
ejpam-6089	717	9	integral	integral	ADJ
ejpam-6089	717	10	inequalities	inequality	NOUN
ejpam-6089	717	11	.	.	PUNCT
ejpam-6089	718	1	journal	journal	PROPN
ejpam-6089	718	2	of	of	ADP
ejpam-6089	718	3	inequalities	inequality	NOUN
ejpam-6089	718	4	and	and	CCONJ
ejpam-6089	718	5	applications	application	NOUN
ejpam-6089	718	6	,	,	PUNCT
ejpam-6089	718	7	2016:122	2016:122	NUM
ejpam-6089	718	8	,	,	PUNCT
ejpam-6089	718	9	2016	2016	NUM
ejpam-6089	718	10	.	.	PUNCT
ejpam-6089	719	1	[	[	X
ejpam-6089	719	2	12	12	NUM
ejpam-6089	719	3	]	]	X
ejpam-6089	719	4	g.	g.	PROPN
ejpam-6089	719	5	a.	a.	PROPN
ejpam-6089	719	6	anastassiou	anastassiou	PROPN
ejpam-6089	719	7	.	.	PUNCT
ejpam-6089	720	1	opial	opial	ADJ
ejpam-6089	720	2	-	-	PUNCT
ejpam-6089	720	3	type	type	NOUN
ejpam-6089	720	4	inequalities	inequality	NOUN
ejpam-6089	720	5	involving	involve	VERB
ejpam-6089	720	6	riemann	riemann	PROPN
ejpam-6089	720	7	-	-	PUNCT
ejpam-6089	720	8	liouville	liouville	VERB
ejpam-6089	720	9	fractional	fractional	ADJ
ejpam-6089	720	10	derivatives	derivative	NOUN
ejpam-6089	720	11	of	of	ADP
ejpam-6089	720	12	two	two	NUM
ejpam-6089	720	13	functions	function	NOUN
ejpam-6089	720	14	with	with	ADP
ejpam-6089	720	15	applications	application	NOUN
ejpam-6089	720	16	.	.	PUNCT
ejpam-6089	721	1	mathematical	mathematical	ADJ
ejpam-6089	721	2	and	and	CCONJ
ejpam-6089	721	3	computer	computer	NOUN
ejpam-6089	721	4	modelling	modelling	NOUN
ejpam-6089	721	5	,	,	PUNCT
ejpam-6089	721	6	48(3	48(3	PROPN
ejpam-6089	721	7	-	-	SYM
ejpam-6089	721	8	4):344–374	4):344–374	NUM
ejpam-6089	721	9	,	,	PUNCT
ejpam-6089	721	10	2008	2008	NUM
ejpam-6089	721	11	.	.	PUNCT
ejpam-6089	722	1	[	[	X
ejpam-6089	722	2	13	13	NUM
ejpam-6089	722	3	]	]	X
ejpam-6089	722	4	n.	n.	PROPN
ejpam-6089	722	5	mehmood	mehmood	PROPN
ejpam-6089	722	6	,	,	PUNCT
ejpam-6089	722	7	s.	s.	PROPN
ejpam-6089	722	8	i.	i.	PROPN
ejpam-6089	722	9	butt	butt	PROPN
ejpam-6089	722	10	,	,	PUNCT
ejpam-6089	722	11	ž.	ž.	PROPN
ejpam-6089	722	12	pečarić	pečarić	PROPN
ejpam-6089	722	13	,	,	PUNCT
ejpam-6089	722	14	and	and	CCONJ
ejpam-6089	722	15	j.	j.	PROPN
ejpam-6089	722	16	pečarić.	pečarić.	PROPN
ejpam-6089	722	17	several	several	ADJ
ejpam-6089	722	18	new	new	ADJ
ejpam-6089	722	19	cyclic	cyclic	PROPN
ejpam-6089	722	20	jensen	jensen	PROPN
ejpam-6089	722	21	type	type	NOUN
ejpam-6089	722	22	inequalities	inequality	NOUN
ejpam-6089	722	23	and	and	CCONJ
ejpam-6089	722	24	their	their	PRON
ejpam-6089	722	25	applications	application	NOUN
ejpam-6089	722	26	.	.	PUNCT
ejpam-6089	723	1	journal	journal	PROPN
ejpam-6089	723	2	of	of	ADP
ejpam-6089	723	3	inequalities	inequality	NOUN
ejpam-6089	723	4	and	and	CCONJ
ejpam-6089	723	5	applications	application	NOUN
ejpam-6089	723	6	,	,	PUNCT
ejpam-6089	723	7	2019:240	2019:240	NOUN
ejpam-6089	723	8	,	,	PUNCT
ejpam-6089	723	9	2019	2019	NUM
ejpam-6089	723	10	.	.	PUNCT
ejpam-6089	724	1	[	[	X
ejpam-6089	724	2	14	14	NUM
ejpam-6089	724	3	]	]	PUNCT
ejpam-6089	724	4	x.	x.	NOUN
ejpam-6089	724	5	li	li	PROPN
ejpam-6089	724	6	,	,	PUNCT
ejpam-6089	724	7	s.	s.	PROPN
ejpam-6089	724	8	qaisar	qaisar	PROPN
ejpam-6089	724	9	,	,	PUNCT
ejpam-6089	724	10	j.	j.	PROPN
ejpam-6089	724	11	nasir	nasir	PROPN
ejpam-6089	724	12	,	,	PUNCT
ejpam-6089	724	13	s.	s.	PROPN
ejpam-6089	724	14	i.	i.	PROPN
ejpam-6089	724	15	butt	butt	PROPN
ejpam-6089	724	16	,	,	PUNCT
ejpam-6089	724	17	et	et	PROPN
ejpam-6089	724	18	al	al	PROPN
ejpam-6089	724	19	.	.	PUNCT
ejpam-6089	725	1	some	some	DET
ejpam-6089	725	2	results	result	NOUN
ejpam-6089	725	3	on	on	ADP
ejpam-6089	725	4	integral	integral	ADJ
ejpam-6089	725	5	inequalities	inequality	NOUN
ejpam-6089	725	6	via	via	ADP
ejpam-6089	725	7	riemann	riemann	PROPN
ejpam-6089	725	8	-	-	PUNCT
ejpam-6089	725	9	liouville	liouville	VERB
ejpam-6089	725	10	fractional	fractional	ADJ
ejpam-6089	725	11	integrals	integral	NOUN
ejpam-6089	725	12	.	.	PUNCT
ejpam-6089	726	1	journal	journal	PROPN
ejpam-6089	726	2	of	of	ADP
ejpam-6089	726	3	inequalities	inequality	NOUN
ejpam-6089	726	4	and	and	CCONJ
ejpam-6089	726	5	applications	application	NOUN
ejpam-6089	726	6	,	,	PUNCT
ejpam-6089	726	7	2019:214	2019:214	NUM
ejpam-6089	726	8	,	,	PUNCT
ejpam-6089	726	9	2019	2019	NUM
ejpam-6089	726	10	.	.	PUNCT
ejpam-6089	727	1	[	[	X
ejpam-6089	727	2	15	15	NUM
ejpam-6089	727	3	]	]	X
ejpam-6089	727	4	c.	c.	PROPN
ejpam-6089	727	5	zhu	zhu	PROPN
ejpam-6089	727	6	,	,	PUNCT
ejpam-6089	727	7	m.	m.	NOUN
ejpam-6089	727	8	fečkan	fečkan	PROPN
ejpam-6089	727	9	,	,	PUNCT
ejpam-6089	727	10	and	and	CCONJ
ejpam-6089	727	11	j.	j.	PROPN
ejpam-6089	727	12	wang	wang	PROPN
ejpam-6089	727	13	.	.	PUNCT
ejpam-6089	728	1	fractional	fractional	ADJ
ejpam-6089	728	2	integral	integral	ADJ
ejpam-6089	728	3	inequalities	inequality	NOUN
ejpam-6089	728	4	for	for	ADP
ejpam-6089	728	5	differential	differential	ADJ
ejpam-6089	728	6	convex	convex	NOUN
ejpam-6089	728	7	mappings	mapping	NOUN
ejpam-6089	728	8	and	and	CCONJ
ejpam-6089	728	9	applications	application	NOUN
ejpam-6089	728	10	to	to	ADP
ejpam-6089	728	11	special	special	ADJ
ejpam-6089	728	12	means	mean	NOUN
ejpam-6089	728	13	and	and	CCONJ
ejpam-6089	728	14	a	a	DET
ejpam-6089	728	15	midpoint	midpoint	NOUN
ejpam-6089	728	16	formula	formula	NOUN
ejpam-6089	728	17	.	.	PUNCT
ejpam-6089	729	1	journal	journal	NOUN
ejpam-6089	729	2	of	of	ADP
ejpam-6089	729	3	applied	apply	VERB
ejpam-6089	729	4	mathematics	mathematic	NOUN
ejpam-6089	729	5	,	,	PUNCT
ejpam-6089	729	6	statistics	statistic	NOUN
ejpam-6089	729	7	and	and	CCONJ
ejpam-6089	729	8	informatics	informatic	NOUN
ejpam-6089	729	9	,	,	PUNCT
ejpam-6089	729	10	8(2):21–28	8(2):21–28	NUM
ejpam-6089	729	11	,	,	PUNCT
ejpam-6089	729	12	2012	2012	NUM
ejpam-6089	729	13	.	.	PUNCT
ejpam-6089	730	1	[	[	X
ejpam-6089	730	2	16	16	NUM
ejpam-6089	730	3	]	]	PUNCT
ejpam-6089	730	4	s.	s.	PROPN
ejpam-6089	730	5	iqbal	iqbal	PROPN
ejpam-6089	730	6	,	,	PUNCT
ejpam-6089	730	7	m.	m.	PROPN
ejpam-6089	730	8	samraiz	samraiz	PROPN
ejpam-6089	730	9	,	,	PUNCT
ejpam-6089	730	10	g.	g.	PROPN
ejpam-6089	730	11	rahman	rahman	PROPN
ejpam-6089	730	12	,	,	PUNCT
ejpam-6089	730	13	k.	k.	PROPN
ejpam-6089	730	14	s.	s.	PROPN
ejpam-6089	730	15	nisar	nisar	PROPN
ejpam-6089	730	16	,	,	PUNCT
ejpam-6089	730	17	and	and	CCONJ
ejpam-6089	730	18	t.	t.	NOUN
ejpam-6089	730	19	abdeljawad	abdeljawad	NOUN
ejpam-6089	730	20	.	.	PUNCT
ejpam-6089	731	1	some	some	DET
ejpam-6089	731	2	new	new	ADJ
ejpam-6089	731	3	grüss	grüss	PROPN
ejpam-6089	731	4	inequalities	inequality	NOUN
ejpam-6089	731	5	associated	associate	VERB
ejpam-6089	731	6	with	with	ADP
ejpam-6089	731	7	generalized	generalized	ADJ
ejpam-6089	731	8	fractional	fractional	ADJ
ejpam-6089	731	9	derivative	derivative	NOUN
ejpam-6089	731	10	.	.	PUNCT
ejpam-6089	732	1	aims	aim	VERB
ejpam-6089	732	2	mathematics	mathematic	NOUN
ejpam-6089	732	3	,	,	PUNCT
ejpam-6089	732	4	8(1):213–227	8(1):213–227	NUM
ejpam-6089	732	5	,	,	PUNCT
ejpam-6089	732	6	2022	2022	NUM
ejpam-6089	732	7	.	.	PUNCT
ejpam-6089	733	1	[	[	X
ejpam-6089	733	2	17	17	NUM
ejpam-6089	733	3	]	]	PUNCT
ejpam-6089	733	4	a.	a.	NOUN
ejpam-6089	733	5	a.	a.	NOUN
ejpam-6089	733	6	kilbas	kilbas	PROPN
ejpam-6089	733	7	,	,	PUNCT
ejpam-6089	733	8	h.	h.	PROPN
ejpam-6089	733	9	m.	m.	PROPN
ejpam-6089	733	10	srivastava	srivastava	PROPN
ejpam-6089	733	11	,	,	PUNCT
ejpam-6089	733	12	and	and	CCONJ
ejpam-6089	733	13	j.	j.	PROPN
ejpam-6089	733	14	j.	j.	PROPN
ejpam-6089	733	15	trujillo	trujillo	PROPN
ejpam-6089	733	16	.	.	PUNCT
ejpam-6089	733	17	theory	theory	NOUN
ejpam-6089	733	18	and	and	CCONJ
ejpam-6089	733	19	applications	application	NOUN
ejpam-6089	733	20	of	of	ADP
ejpam-6089	733	21	fractional	fractional	ADJ
ejpam-6089	733	22	differential	differential	ADJ
ejpam-6089	733	23	equations	equation	NOUN
ejpam-6089	733	24	.	.	PUNCT
ejpam-6089	734	1	elsevier	elsevier	PROPN
ejpam-6089	734	2	,	,	PUNCT
ejpam-6089	734	3	amsterdam	amsterdam	PROPN
ejpam-6089	734	4	,	,	PUNCT
ejpam-6089	734	5	2006	2006	NUM
ejpam-6089	734	6	.	.	PUNCT
ejpam-6089	735	1	[	[	X
ejpam-6089	735	2	18	18	NUM
ejpam-6089	735	3	]	]	X
ejpam-6089	735	4	r.	r.	PROPN
ejpam-6089	735	5	gorenflo	gorenflo	PROPN
ejpam-6089	735	6	,	,	PUNCT
ejpam-6089	735	7	a.	a.	NOUN
ejpam-6089	735	8	a.	a.	NOUN
ejpam-6089	735	9	kilbas	kilbas	PROPN
ejpam-6089	735	10	,	,	PUNCT
ejpam-6089	735	11	f.	f.	PROPN
ejpam-6089	735	12	mainardi	mainardi	PROPN
ejpam-6089	735	13	,	,	PUNCT
ejpam-6089	735	14	and	and	CCONJ
ejpam-6089	735	15	s.	s.	PROPN
ejpam-6089	735	16	v.	v.	PROPN
ejpam-6089	735	17	rogosin	rogosin	PROPN
ejpam-6089	735	18	.	.	PUNCT
ejpam-6089	736	1	mittag	mittag	ADJ
ejpam-6089	736	2	-	-	PUNCT
ejpam-6089	736	3	leffler	leffler	NOUN
ejpam-6089	736	4	functions	function	NOUN
ejpam-6089	736	5	,	,	PUNCT
ejpam-6089	736	6	related	relate	VERB
ejpam-6089	736	7	topics	topic	NOUN
ejpam-6089	736	8	and	and	CCONJ
ejpam-6089	736	9	applications	application	NOUN
ejpam-6089	736	10	.	.	PUNCT
ejpam-6089	737	1	springer	springer	NOUN
ejpam-6089	737	2	,	,	PUNCT
ejpam-6089	737	3	berlin	berlin	PROPN
ejpam-6089	737	4	,	,	PUNCT
ejpam-6089	737	5	2014	2014	NUM
ejpam-6089	737	6	.	.	PUNCT
ejpam-6089	738	1	[	[	X
ejpam-6089	738	2	19	19	NUM
ejpam-6089	738	3	]	]	X
ejpam-6089	738	4	h.	h.	PROPN
ejpam-6089	738	5	j.	j.	PROPN
ejpam-6089	738	6	haubold	haubold	PROPN
ejpam-6089	738	7	,	,	PUNCT
ejpam-6089	738	8	a.	a.	NOUN
ejpam-6089	738	9	m.	m.	NOUN
ejpam-6089	738	10	mathai	mathai	PROPN
ejpam-6089	738	11	,	,	PUNCT
ejpam-6089	738	12	and	and	CCONJ
ejpam-6089	738	13	r.	r.	PROPN
ejpam-6089	738	14	k.	k.	PROPN
ejpam-6089	738	15	saxena	saxena	PROPN
ejpam-6089	738	16	.	.	PUNCT
ejpam-6089	739	1	mittag	mittag	ADJ
ejpam-6089	739	2	-	-	PUNCT
ejpam-6089	739	3	leffler	leffler	NOUN
ejpam-6089	739	4	functions	function	NOUN
ejpam-6089	739	5	and	and	CCONJ
ejpam-6089	739	6	their	their	PRON
ejpam-6089	739	7	applications	application	NOUN
ejpam-6089	739	8	.	.	PUNCT
ejpam-6089	740	1	journal	journal	NOUN
ejpam-6089	740	2	of	of	ADP
ejpam-6089	740	3	applied	apply	VERB
ejpam-6089	740	4	mathematics	mathematic	NOUN
ejpam-6089	740	5	,	,	PUNCT
ejpam-6089	740	6	2011:298628	2011:298628	NUM
ejpam-6089	740	7	,	,	PUNCT
ejpam-6089	740	8	2011	2011	NUM
ejpam-6089	740	9	.	.	PUNCT
ejpam-6089	741	1	[	[	X
ejpam-6089	741	2	20	20	NUM
ejpam-6089	741	3	]	]	PUNCT
ejpam-6089	741	4	a.	a.	NOUN
ejpam-6089	741	5	m.	m.	NOUN
ejpam-6089	741	6	mathai	mathai	PROPN
ejpam-6089	741	7	and	and	CCONJ
ejpam-6089	741	8	h.	h.	PROPN
ejpam-6089	741	9	j.	j.	PROPN
ejpam-6089	741	10	haubold	haubold	PROPN
ejpam-6089	741	11	.	.	PUNCT
ejpam-6089	742	1	mittag	mittag	ADJ
ejpam-6089	742	2	-	-	PUNCT
ejpam-6089	742	3	leffler	leffler	NOUN
ejpam-6089	742	4	functions	function	NOUN
ejpam-6089	742	5	and	and	CCONJ
ejpam-6089	742	6	fractional	fractional	ADJ
ejpam-6089	742	7	calculus	calculus	NOUN
ejpam-6089	742	8	.	.	PUNCT
ejpam-6089	742	9	springer	springer	NOUN
ejpam-6089	742	10	,	,	PUNCT
ejpam-6089	742	11	2008	2008	NUM
ejpam-6089	742	12	.	.	PUNCT
ejpam-6089	743	1	[	[	X
ejpam-6089	743	2	21	21	NUM
ejpam-6089	743	3	]	]	X
ejpam-6089	743	4	g.	g.	PROPN
ejpam-6089	743	5	rahman	rahman	PROPN
ejpam-6089	743	6	,	,	PUNCT
ejpam-6089	743	7	i.	i.	PROPN
ejpam-6089	743	8	suwan	suwan	PROPN
ejpam-6089	743	9	,	,	PUNCT
ejpam-6089	743	10	k.	k.	PROPN
ejpam-6089	743	11	s.	s.	PROPN
ejpam-6089	743	12	nisar	nisar	PROPN
ejpam-6089	743	13	,	,	PUNCT
ejpam-6089	743	14	t.	t.	NOUN
ejpam-6089	743	15	abdeljawad	abdeljawad	NOUN
ejpam-6089	743	16	,	,	PUNCT
ejpam-6089	743	17	m.	m.	NOUN
ejpam-6089	743	18	samraiz	samraiz	PROPN
ejpam-6089	743	19	,	,	PUNCT
ejpam-6089	743	20	and	and	CCONJ
ejpam-6089	743	21	a.	a.	PROPN
ejpam-6089	743	22	ali	ali	PROPN
ejpam-6089	743	23	.	.	PUNCT
ejpam-6089	744	1	a	a	DET
ejpam-6089	744	2	basic	basic	ADJ
ejpam-6089	744	3	study	study	NOUN
ejpam-6089	744	4	of	of	ADP
ejpam-6089	744	5	a	a	DET
ejpam-6089	744	6	fractional	fractional	ADJ
ejpam-6089	744	7	integral	integral	ADJ
ejpam-6089	744	8	operator	operator	NOUN
ejpam-6089	744	9	with	with	ADP
ejpam-6089	744	10	extended	extended	ADJ
ejpam-6089	744	11	mittag	mittag	ADJ
ejpam-6089	744	12	-	-	PUNCT
ejpam-6089	744	13	leffler	leffler	NOUN
ejpam-6089	744	14	kernel	kernel	NOUN
ejpam-6089	744	15	.	.	PUNCT
ejpam-6089	745	1	aims	aim	VERB
ejpam-6089	745	2	s.	s.	PROPN
ejpam-6089	745	3	naheed	naheed	PROPN
ejpam-6089	745	4	et	et	PROPN
ejpam-6089	745	5	al	al	PROPN
ejpam-6089	745	6	.	.	PUNCT
ejpam-6089	745	7	/	/	SYM
ejpam-6089	745	8	eur	eur	PROPN
ejpam-6089	745	9	.	.	PUNCT
ejpam-6089	746	1	j.	j.	PROPN
ejpam-6089	746	2	pure	pure	PROPN
ejpam-6089	746	3	appl	appl	PROPN
ejpam-6089	746	4	.	.	PROPN
ejpam-6089	746	5	math	math	PROPN
ejpam-6089	746	6	,	,	PUNCT
ejpam-6089	746	7	18	18	NUM
ejpam-6089	746	8	(	(	PUNCT
ejpam-6089	746	9	2	2	NUM
ejpam-6089	746	10	)	)	PUNCT
ejpam-6089	746	11	(	(	PUNCT
ejpam-6089	746	12	2025	2025	NUM
ejpam-6089	746	13	)	)	PUNCT
ejpam-6089	746	14	,	,	PUNCT
ejpam-6089	746	15	6089	6089	NUM
ejpam-6089	746	16	33	33	NUM
ejpam-6089	746	17	of	of	ADP
ejpam-6089	746	18	34	34	NUM
ejpam-6089	746	19	mathematics	mathematic	NOUN
ejpam-6089	746	20	,	,	PUNCT
ejpam-6089	746	21	6(11):12757–12770	6(11):12757–12770	NOUN
ejpam-6089	746	22	,	,	PUNCT
ejpam-6089	746	23	2021	2021	NUM
ejpam-6089	746	24	.	.	PUNCT
ejpam-6089	747	1	[	[	X
ejpam-6089	747	2	22	22	NUM
ejpam-6089	747	3	]	]	PUNCT
ejpam-6089	747	4	m.	m.	NOUN
ejpam-6089	747	5	andrić	andrić	PROPN
ejpam-6089	747	6	,	,	PUNCT
ejpam-6089	747	7	g.	g.	PROPN
ejpam-6089	747	8	farid	farid	PROPN
ejpam-6089	747	9	,	,	PUNCT
ejpam-6089	747	10	and	and	CCONJ
ejpam-6089	747	11	j.	j.	PROPN
ejpam-6089	747	12	pečarić.	pečarić.	PROPN
ejpam-6089	747	13	a	a	DET
ejpam-6089	747	14	further	further	ADJ
ejpam-6089	747	15	extension	extension	NOUN
ejpam-6089	747	16	of	of	ADP
ejpam-6089	747	17	mittag	mittag	ADJ
ejpam-6089	747	18	-	-	PUNCT
ejpam-6089	747	19	leffler	leffler	NOUN
ejpam-6089	747	20	function	function	NOUN
ejpam-6089	747	21	.	.	PUNCT
ejpam-6089	748	1	fractional	fractional	ADJ
ejpam-6089	748	2	calculus	calculus	NOUN
ejpam-6089	748	3	and	and	CCONJ
ejpam-6089	748	4	applied	apply	VERB
ejpam-6089	748	5	analysis	analysis	NOUN
ejpam-6089	748	6	,	,	PUNCT
ejpam-6089	748	7	21(5):1377–1395	21(5):1377–1395	NUM
ejpam-6089	748	8	,	,	PUNCT
ejpam-6089	748	9	2018	2018	NUM
ejpam-6089	748	10	.	.	PUNCT
ejpam-6089	749	1	[	[	X
ejpam-6089	749	2	23	23	NUM
ejpam-6089	749	3	]	]	PUNCT
ejpam-6089	749	4	a.	a.	NOUN
ejpam-6089	749	5	fernandez	fernandez	PROPN
ejpam-6089	749	6	.	.	PUNCT
ejpam-6089	750	1	a	a	DET
ejpam-6089	750	2	complex	complex	ADJ
ejpam-6089	750	3	analysis	analysis	NOUN
ejpam-6089	750	4	approach	approach	NOUN
ejpam-6089	750	5	to	to	ADP
ejpam-6089	750	6	atangana	atangana	PROPN
ejpam-6089	750	7	-	-	PUNCT
ejpam-6089	750	8	baleanu	baleanu	ADJ
ejpam-6089	750	9	fractional	fractional	ADJ
ejpam-6089	750	10	calculus	calculus	NOUN
ejpam-6089	750	11	.	.	PUNCT
ejpam-6089	751	1	mathematical	mathematical	ADJ
ejpam-6089	751	2	methods	method	NOUN
ejpam-6089	751	3	in	in	ADP
ejpam-6089	751	4	the	the	DET
ejpam-6089	751	5	applied	apply	VERB
ejpam-6089	751	6	sciences	science	NOUN
ejpam-6089	751	7	,	,	PUNCT
ejpam-6089	751	8	44(10):8070–8087	44(10):8070–8087	NOUN
ejpam-6089	751	9	,	,	PUNCT
ejpam-6089	751	10	2021	2021	NUM
ejpam-6089	751	11	.	.	PUNCT
ejpam-6089	752	1	[	[	X
ejpam-6089	752	2	24	24	NUM
ejpam-6089	752	3	]	]	PUNCT
ejpam-6089	752	4	a.	a.	NOUN
ejpam-6089	752	5	a.	a.	NOUN
ejpam-6089	752	6	kilbas	kilbas	PROPN
ejpam-6089	752	7	,	,	PUNCT
ejpam-6089	752	8	m.	m.	NOUN
ejpam-6089	752	9	saigo	saigo	PROPN
ejpam-6089	752	10	,	,	PUNCT
ejpam-6089	752	11	and	and	CCONJ
ejpam-6089	752	12	r.	r.	PROPN
ejpam-6089	752	13	k.	k.	PROPN
ejpam-6089	752	14	saxena	saxena	PROPN
ejpam-6089	752	15	.	.	PUNCT
ejpam-6089	753	1	generalized	generalize	VERB
ejpam-6089	753	2	mittag	mittag	ADJ
ejpam-6089	753	3	-	-	PUNCT
ejpam-6089	753	4	leffler	leffler	NOUN
ejpam-6089	753	5	function	function	NOUN
ejpam-6089	753	6	and	and	CCONJ
ejpam-6089	753	7	generalized	generalize	VERB
ejpam-6089	753	8	fractional	fractional	ADJ
ejpam-6089	753	9	calculus	calculus	NOUN
ejpam-6089	753	10	operators	operator	NOUN
ejpam-6089	753	11	.	.	PUNCT
ejpam-6089	754	1	integral	integral	ADJ
ejpam-6089	754	2	transforms	transform	NOUN
ejpam-6089	754	3	and	and	CCONJ
ejpam-6089	754	4	special	special	ADJ
ejpam-6089	754	5	functions	function	NOUN
ejpam-6089	754	6	,	,	PUNCT
ejpam-6089	754	7	15(1):31–49	15(1):31–49	NUM
ejpam-6089	754	8	,	,	PUNCT
ejpam-6089	754	9	2004	2004	NUM
ejpam-6089	754	10	.	.	PUNCT
ejpam-6089	755	1	[	[	X
ejpam-6089	755	2	25	25	NUM
ejpam-6089	755	3	]	]	PUNCT
ejpam-6089	755	4	t.	t.	PROPN
ejpam-6089	755	5	r.	r.	PROPN
ejpam-6089	755	6	prabhakar	prabhakar	PROPN
ejpam-6089	755	7	.	.	PUNCT
ejpam-6089	756	1	a	a	DET
ejpam-6089	756	2	singular	singular	ADJ
ejpam-6089	756	3	integral	integral	ADJ
ejpam-6089	756	4	equation	equation	NOUN
ejpam-6089	756	5	with	with	ADP
ejpam-6089	756	6	a	a	DET
ejpam-6089	756	7	generalized	generalized	ADJ
ejpam-6089	756	8	mittag	mittag	ADJ
ejpam-6089	756	9	-	-	PUNCT
ejpam-6089	756	10	leffler	leffler	NOUN
ejpam-6089	756	11	function	function	NOUN
ejpam-6089	756	12	in	in	ADP
ejpam-6089	756	13	the	the	DET
ejpam-6089	756	14	kernel	kernel	NOUN
ejpam-6089	756	15	.	.	PUNCT
ejpam-6089	757	1	yokohama	yokohama	PROPN
ejpam-6089	757	2	mathematical	mathematical	PROPN
ejpam-6089	757	3	journal	journal	PROPN
ejpam-6089	757	4	,	,	PUNCT
ejpam-6089	757	5	19(1):7–15	19(1):7–15	NUM
ejpam-6089	757	6	,	,	PUNCT
ejpam-6089	757	7	1971	1971	NUM
ejpam-6089	757	8	.	.	PUNCT
ejpam-6089	758	1	[	[	X
ejpam-6089	758	2	26	26	NUM
ejpam-6089	758	3	]	]	PUNCT
ejpam-6089	758	4	t.	t.	NOUN
ejpam-6089	758	5	abdeljawad	abdeljawad	PROPN
ejpam-6089	758	6	and	and	CCONJ
ejpam-6089	758	7	d.	d.	PROPN
ejpam-6089	758	8	baleanu	baleanu	PROPN
ejpam-6089	758	9	.	.	PUNCT
ejpam-6089	759	1	integration	integration	NOUN
ejpam-6089	759	2	by	by	ADP
ejpam-6089	759	3	parts	part	NOUN
ejpam-6089	759	4	and	and	CCONJ
ejpam-6089	759	5	its	its	PRON
ejpam-6089	759	6	applications	application	NOUN
ejpam-6089	759	7	of	of	ADP
ejpam-6089	759	8	a	a	DET
ejpam-6089	759	9	new	new	ADJ
ejpam-6089	759	10	nonlocal	nonlocal	ADJ
ejpam-6089	759	11	fractional	fractional	ADJ
ejpam-6089	759	12	derivative	derivative	NOUN
ejpam-6089	759	13	with	with	ADP
ejpam-6089	759	14	mittag	mittag	ADJ
ejpam-6089	759	15	-	-	PUNCT
ejpam-6089	759	16	leffler	leffler	NOUN
ejpam-6089	759	17	nonsingular	nonsingular	ADJ
ejpam-6089	759	18	kernel	kernel	PROPN
ejpam-6089	759	19	.	.	PUNCT
ejpam-6089	760	1	journal	journal	PROPN
ejpam-6089	760	2	of	of	ADP
ejpam-6089	760	3	nonlinear	nonlinear	PROPN
ejpam-6089	760	4	sciences	sciences	PROPN
ejpam-6089	760	5	and	and	CCONJ
ejpam-6089	760	6	applications	application	NOUN
ejpam-6089	760	7	,	,	PUNCT
ejpam-6089	760	8	10(3):1098–1107	10(3):1098–1107	NUM
ejpam-6089	760	9	,	,	PUNCT
ejpam-6089	760	10	2017	2017	NUM
ejpam-6089	760	11	.	.	PUNCT
ejpam-6089	761	1	[	[	X
ejpam-6089	761	2	27	27	NUM
ejpam-6089	761	3	]	]	X
ejpam-6089	761	4	j.-d	j.-d	PROPN
ejpam-6089	761	5	.	.	PUNCT
ejpam-6089	762	1	djida	djida	PROPN
ejpam-6089	762	2	,	,	PUNCT
ejpam-6089	762	3	a.	a.	PROPN
ejpam-6089	762	4	atangana	atangana	PROPN
ejpam-6089	762	5	,	,	PUNCT
ejpam-6089	762	6	and	and	CCONJ
ejpam-6089	762	7	i.	i.	PROPN
ejpam-6089	762	8	area	area	PROPN
ejpam-6089	762	9	.	.	PUNCT
ejpam-6089	763	1	numerical	numerical	ADJ
ejpam-6089	763	2	computation	computation	NOUN
ejpam-6089	763	3	of	of	ADP
ejpam-6089	763	4	a	a	DET
ejpam-6089	763	5	fractional	fractional	ADJ
ejpam-6089	763	6	derivative	derivative	NOUN
ejpam-6089	763	7	with	with	ADP
ejpam-6089	763	8	non	non	ADJ
ejpam-6089	763	9	-	-	ADJ
ejpam-6089	763	10	local	local	ADJ
ejpam-6089	763	11	and	and	CCONJ
ejpam-6089	763	12	non	non	ADJ
ejpam-6089	763	13	-	-	ADJ
ejpam-6089	763	14	singular	singular	ADJ
ejpam-6089	763	15	kernel	kernel	NOUN
ejpam-6089	763	16	.	.	PUNCT
ejpam-6089	764	1	mathematical	mathematical	ADJ
ejpam-6089	764	2	modelling	modelling	NOUN
ejpam-6089	764	3	of	of	ADP
ejpam-6089	764	4	natural	natural	ADJ
ejpam-6089	764	5	phenomena	phenomenon	NOUN
ejpam-6089	764	6	,	,	PUNCT
ejpam-6089	764	7	12(3):4–13	12(3):4–13	NUM
ejpam-6089	764	8	,	,	PUNCT
ejpam-6089	764	9	2017	2017	NUM
ejpam-6089	764	10	.	.	PUNCT
ejpam-6089	765	1	[	[	X
ejpam-6089	765	2	28	28	NUM
ejpam-6089	765	3	]	]	X
ejpam-6089	765	4	a.	a.	NOUN
ejpam-6089	765	5	fernandez	fernandez	PROPN
ejpam-6089	765	6	and	and	CCONJ
ejpam-6089	765	7	d.	d.	PROPN
ejpam-6089	765	8	baleanu	baleanu	PROPN
ejpam-6089	765	9	.	.	PUNCT
ejpam-6089	766	1	the	the	DET
ejpam-6089	766	2	mean	mean	ADJ
ejpam-6089	766	3	value	value	NOUN
ejpam-6089	766	4	theorem	theorem	NOUN
ejpam-6089	766	5	and	and	CCONJ
ejpam-6089	766	6	taylor	taylor	PROPN
ejpam-6089	766	7	’s	’s	PART
ejpam-6089	766	8	theorem	theorem	NOUN
ejpam-6089	766	9	for	for	ADP
ejpam-6089	766	10	fractional	fractional	ADJ
ejpam-6089	766	11	derivatives	derivative	NOUN
ejpam-6089	766	12	with	with	ADP
ejpam-6089	766	13	mittag	mittag	ADJ
ejpam-6089	766	14	-	-	PUNCT
ejpam-6089	766	15	leffler	leffler	NOUN
ejpam-6089	766	16	kernel	kernel	NOUN
ejpam-6089	766	17	.	.	PUNCT
ejpam-6089	767	1	advances	advance	NOUN
ejpam-6089	767	2	in	in	ADP
ejpam-6089	767	3	difference	difference	NOUN
ejpam-6089	767	4	equations	equation	NOUN
ejpam-6089	767	5	,	,	PUNCT
ejpam-6089	767	6	2018:86	2018:86	NUM
ejpam-6089	767	7	,	,	PUNCT
ejpam-6089	767	8	2018	2018	NUM
ejpam-6089	767	9	.	.	PUNCT
ejpam-6089	768	1	[	[	X
ejpam-6089	768	2	29	29	NUM
ejpam-6089	768	3	]	]	PUNCT
ejpam-6089	768	4	a.	a.	NOUN
ejpam-6089	768	5	fernandez	fernandez	PROPN
ejpam-6089	768	6	,	,	PUNCT
ejpam-6089	768	7	d.	d.	PROPN
ejpam-6089	768	8	baleanu	baleanu	PROPN
ejpam-6089	768	9	,	,	PUNCT
ejpam-6089	768	10	and	and	CCONJ
ejpam-6089	768	11	h.	h.	PROPN
ejpam-6089	768	12	m.	m.	PROPN
ejpam-6089	768	13	srivastava	srivastava	PROPN
ejpam-6089	768	14	.	.	PUNCT
ejpam-6089	769	1	series	series	PROPN
ejpam-6089	769	2	representations	representation	NOUN
ejpam-6089	769	3	for	for	ADP
ejpam-6089	769	4	models	model	NOUN
ejpam-6089	769	5	of	of	ADP
ejpam-6089	769	6	fractional	fractional	ADJ
ejpam-6089	769	7	calculus	calculus	NOUN
ejpam-6089	769	8	involving	involve	VERB
ejpam-6089	769	9	generalised	generalise	VERB
ejpam-6089	769	10	mittag	mittag	ADJ
ejpam-6089	769	11	-	-	PUNCT
ejpam-6089	769	12	leffler	leffler	NOUN
ejpam-6089	769	13	functions	function	NOUN
ejpam-6089	769	14	.	.	PUNCT
ejpam-6089	770	1	communications	communication	NOUN
ejpam-6089	770	2	in	in	ADP
ejpam-6089	770	3	nonlinear	nonlinear	ADJ
ejpam-6089	770	4	science	science	NOUN
ejpam-6089	770	5	and	and	CCONJ
ejpam-6089	770	6	numerical	numerical	PROPN
ejpam-6089	770	7	simulation	simulation	PROPN
ejpam-6089	770	8	,	,	PUNCT
ejpam-6089	770	9	67:517–527	67:517–527	PROPN
ejpam-6089	770	10	,	,	PUNCT
ejpam-6089	770	11	2019	2019	NUM
ejpam-6089	770	12	.	.	PUNCT
ejpam-6089	771	1	[	[	X
ejpam-6089	771	2	30	30	NUM
ejpam-6089	771	3	]	]	X
ejpam-6089	771	4	r.	r.	PROPN
ejpam-6089	771	5	garra	garra	PROPN
ejpam-6089	771	6	and	and	CCONJ
ejpam-6089	771	7	r.	r.	PROPN
ejpam-6089	771	8	garrappa	garrappa	PROPN
ejpam-6089	771	9	.	.	PUNCT
ejpam-6089	772	1	the	the	DET
ejpam-6089	772	2	prabhakar	prabhakar	NOUN
ejpam-6089	772	3	or	or	CCONJ
ejpam-6089	772	4	three	three	NUM
ejpam-6089	772	5	parameter	parameter	NOUN
ejpam-6089	772	6	mittag	mittag	ADJ
ejpam-6089	772	7	-	-	PUNCT
ejpam-6089	772	8	leffler	leffler	NOUN
ejpam-6089	772	9	function	function	NOUN
ejpam-6089	772	10	:	:	PUNCT
ejpam-6089	772	11	theory	theory	NOUN
ejpam-6089	772	12	and	and	CCONJ
ejpam-6089	772	13	application	application	NOUN
ejpam-6089	772	14	.	.	PUNCT
ejpam-6089	773	1	communications	communication	NOUN
ejpam-6089	773	2	in	in	ADP
ejpam-6089	773	3	nonlinear	nonlinear	ADJ
ejpam-6089	773	4	science	science	NOUN
ejpam-6089	773	5	and	and	CCONJ
ejpam-6089	773	6	numerical	numerical	PROPN
ejpam-6089	773	7	simulation	simulation	PROPN
ejpam-6089	773	8	,	,	PUNCT
ejpam-6089	773	9	56:314–329	56:314–329	PROPN
ejpam-6089	773	10	,	,	PUNCT
ejpam-6089	773	11	2018	2018	NUM
ejpam-6089	773	12	.	.	PUNCT
ejpam-6089	774	1	[	[	X
ejpam-6089	774	2	31	31	NUM
ejpam-6089	774	3	]	]	PUNCT
ejpam-6089	774	4	s.	s.	PROPN
ejpam-6089	774	5	uçar	uçar	PROPN
ejpam-6089	774	6	,	,	PUNCT
ejpam-6089	774	7	e.	e.	PROPN
ejpam-6089	774	8	uçar	uçar	PROPN
ejpam-6089	774	9	,	,	PUNCT
ejpam-6089	774	10	n.	n.	PROPN
ejpam-6089	774	11	özdemir	özdemir	PROPN
ejpam-6089	774	12	,	,	PUNCT
ejpam-6089	774	13	and	and	CCONJ
ejpam-6089	774	14	z.	z.	PROPN
ejpam-6089	774	15	hammouch	hammouch	PROPN
ejpam-6089	774	16	.	.	PUNCT
ejpam-6089	775	1	mathematical	mathematical	ADJ
ejpam-6089	775	2	analysis	analysis	NOUN
ejpam-6089	775	3	and	and	CCONJ
ejpam-6089	775	4	numerical	numerical	ADJ
ejpam-6089	775	5	simulation	simulation	NOUN
ejpam-6089	775	6	for	for	ADP
ejpam-6089	775	7	a	a	DET
ejpam-6089	775	8	smoking	smoking	NOUN
ejpam-6089	775	9	model	model	NOUN
ejpam-6089	775	10	with	with	ADP
ejpam-6089	775	11	atangana	atangana	PROPN
ejpam-6089	775	12	-	-	PUNCT
ejpam-6089	775	13	baleanu	baleanu	PROPN
ejpam-6089	775	14	derivative	derivative	NOUN
ejpam-6089	775	15	.	.	PUNCT
ejpam-6089	776	1	chaos	chaos	NOUN
ejpam-6089	776	2	,	,	PUNCT
ejpam-6089	776	3	solitons	soliton	NOUN
ejpam-6089	776	4	&	&	CCONJ
ejpam-6089	776	5	fractals	fractal	NOUN
ejpam-6089	776	6	,	,	PUNCT
ejpam-6089	776	7	118:300–306	118:300–306	NUM
ejpam-6089	776	8	,	,	PUNCT
ejpam-6089	776	9	2019	2019	NUM
ejpam-6089	776	10	.	.	PUNCT
ejpam-6089	777	1	[	[	X
ejpam-6089	777	2	32	32	NUM
ejpam-6089	777	3	]	]	PUNCT
ejpam-6089	777	4	m.	m.	NOUN
ejpam-6089	777	5	samraiz	samraiz	PROPN
ejpam-6089	777	6	,	,	PUNCT
ejpam-6089	777	7	z.	z.	PROPN
ejpam-6089	777	8	perveen	perveen	PROPN
ejpam-6089	777	9	,	,	PUNCT
ejpam-6089	777	10	t.	t.	PROPN
ejpam-6089	777	11	abdeljawad	abdeljawad	PROPN
ejpam-6089	777	12	,	,	PUNCT
ejpam-6089	777	13	s.	s.	PROPN
ejpam-6089	777	14	iqbal	iqbal	PROPN
ejpam-6089	777	15	,	,	PUNCT
ejpam-6089	777	16	and	and	CCONJ
ejpam-6089	777	17	s.	s.	PROPN
ejpam-6089	777	18	naheed	naheed	PROPN
ejpam-6089	777	19	.	.	PUNCT
ejpam-6089	778	1	on	on	ADP
ejpam-6089	778	2	certain	certain	ADJ
ejpam-6089	778	3	fractional	fractional	ADJ
ejpam-6089	778	4	calculus	calculus	NOUN
ejpam-6089	778	5	operators	operator	NOUN
ejpam-6089	778	6	and	and	CCONJ
ejpam-6089	778	7	applications	application	NOUN
ejpam-6089	778	8	in	in	ADP
ejpam-6089	778	9	mathematical	mathematical	ADJ
ejpam-6089	778	10	physics	physics	NOUN
ejpam-6089	778	11	.	.	PUNCT
ejpam-6089	779	1	physica	physica	PROPN
ejpam-6089	779	2	scripta	scripta	PROPN
ejpam-6089	779	3	,	,	PUNCT
ejpam-6089	779	4	95(11):115210	95(11):115210	NUM
ejpam-6089	779	5	,	,	PUNCT
ejpam-6089	779	6	2020	2020	NUM
ejpam-6089	779	7	.	.	PUNCT
ejpam-6089	780	1	[	[	X
ejpam-6089	780	2	33	33	NUM
ejpam-6089	780	3	]	]	PUNCT
ejpam-6089	780	4	s.	s.	PROPN
ejpam-6089	780	5	qaisar	qaisar	PROPN
ejpam-6089	780	6	,	,	PUNCT
ejpam-6089	780	7	j.	j.	PROPN
ejpam-6089	780	8	nasir	nasir	PROPN
ejpam-6089	780	9	,	,	PUNCT
ejpam-6089	780	10	s.	s.	PROPN
ejpam-6089	780	11	i.	i.	PROPN
ejpam-6089	780	12	butt	butt	PROPN
ejpam-6089	780	13	,	,	PUNCT
ejpam-6089	780	14	and	and	CCONJ
ejpam-6089	780	15	s.	s.	PROPN
ejpam-6089	780	16	hussain	hussain	PROPN
ejpam-6089	780	17	.	.	PUNCT
ejpam-6089	781	1	on	on	ADP
ejpam-6089	781	2	some	some	DET
ejpam-6089	781	3	fractional	fractional	ADJ
ejpam-6089	781	4	integral	integral	ADJ
ejpam-6089	781	5	inequalities	inequality	NOUN
ejpam-6089	781	6	of	of	ADP
ejpam-6089	781	7	hermite	hermite	PROPN
ejpam-6089	781	8	-	-	PUNCT
ejpam-6089	781	9	hadamard	hadamard	ADJ
ejpam-6089	781	10	type	type	NOUN
ejpam-6089	781	11	through	through	ADP
ejpam-6089	781	12	convexity	convexity	NOUN
ejpam-6089	781	13	.	.	PUNCT
ejpam-6089	781	14	symmetry	symmetry	NOUN
ejpam-6089	781	15	,	,	PUNCT
ejpam-6089	781	16	11(2):137	11(2):137	NUM
ejpam-6089	781	17	,	,	PUNCT
ejpam-6089	781	18	2019	2019	NUM
ejpam-6089	781	19	.	.	PUNCT
ejpam-6089	782	1	[	[	X
ejpam-6089	782	2	34	34	NUM
ejpam-6089	782	3	]	]	X
ejpam-6089	782	4	s.	s.	PROPN
ejpam-6089	782	5	i.	i.	PROPN
ejpam-6089	782	6	butt	butt	PROPN
ejpam-6089	782	7	,	,	PUNCT
ejpam-6089	782	8	y.	y.	PROPN
ejpam-6089	782	9	saba	saba	PROPN
ejpam-6089	782	10	,	,	PUNCT
ejpam-6089	782	11	o.	o.	PROPN
ejpam-6089	782	12	a.	a.	NOUN
ejpam-6089	782	13	ahmet	ahmet	PROPN
ejpam-6089	782	14	,	,	PUNCT
ejpam-6089	782	15	and	and	CCONJ
ejpam-6089	782	16	a.	a.	PROPN
ejpam-6089	782	17	d.	d.	PROPN
ejpam-6089	782	18	mustafa	mustafa	PROPN
ejpam-6089	782	19	.	.	PUNCT
ejpam-6089	783	1	new	new	ADJ
ejpam-6089	783	2	hadamard	hadamard	ADJ
ejpam-6089	783	3	-	-	PUNCT
ejpam-6089	783	4	type	type	NOUN
ejpam-6089	783	5	integral	integral	ADJ
ejpam-6089	783	6	inequalities	inequality	NOUN
ejpam-6089	783	7	via	via	ADP
ejpam-6089	783	8	a	a	DET
ejpam-6089	783	9	general	general	ADJ
ejpam-6089	783	10	form	form	NOUN
ejpam-6089	783	11	of	of	ADP
ejpam-6089	783	12	fractional	fractional	ADJ
ejpam-6089	783	13	integral	integral	ADJ
ejpam-6089	783	14	operators	operator	NOUN
ejpam-6089	783	15	.	.	PUNCT
ejpam-6089	784	1	chaos	chaos	NOUN
ejpam-6089	784	2	,	,	PUNCT
ejpam-6089	784	3	solitons	soliton	NOUN
ejpam-6089	784	4	&	&	CCONJ
ejpam-6089	784	5	fractals	fractal	NOUN
ejpam-6089	784	6	,	,	PUNCT
ejpam-6089	784	7	148:111025	148:111025	NUM
ejpam-6089	784	8	,	,	PUNCT
ejpam-6089	784	9	2021	2021	NUM
ejpam-6089	784	10	.	.	PUNCT
ejpam-6089	785	1	[	[	X
ejpam-6089	785	2	35	35	NUM
ejpam-6089	785	3	]	]	PUNCT
ejpam-6089	785	4	m.	m.	NOUN
ejpam-6089	785	5	z.	z.	PROPN
ejpam-6089	785	6	sarikaya	sarikaya	PROPN
ejpam-6089	785	7	,	,	PUNCT
ejpam-6089	785	8	e.	e.	PROPN
ejpam-6089	785	9	set	set	PROPN
ejpam-6089	785	10	,	,	PUNCT
ejpam-6089	785	11	h.	h.	PROPN
ejpam-6089	785	12	yaldiz	yaldiz	PROPN
ejpam-6089	785	13	,	,	PUNCT
ejpam-6089	785	14	and	and	CCONJ
ejpam-6089	785	15	n.	n.	PROPN
ejpam-6089	785	16	basak	basak	PROPN
ejpam-6089	785	17	.	.	PUNCT
ejpam-6089	786	1	hermite	hermite	PROPN
ejpam-6089	786	2	-	-	PUNCT
ejpam-6089	786	3	hadamard	hadamard	PROPN
ejpam-6089	786	4	’s	’s	PART
ejpam-6089	786	5	inequalities	inequality	NOUN
ejpam-6089	786	6	for	for	ADP
ejpam-6089	786	7	fractional	fractional	ADJ
ejpam-6089	786	8	integrals	integral	NOUN
ejpam-6089	786	9	and	and	CCONJ
ejpam-6089	786	10	related	relate	VERB
ejpam-6089	786	11	fractional	fractional	ADJ
ejpam-6089	786	12	inequalities	inequality	NOUN
ejpam-6089	786	13	.	.	PUNCT
ejpam-6089	787	1	mathematical	mathematical	ADJ
ejpam-6089	787	2	and	and	CCONJ
ejpam-6089	787	3	computer	computer	NOUN
ejpam-6089	787	4	modelling	modelling	NOUN
ejpam-6089	787	5	,	,	PUNCT
ejpam-6089	787	6	57(9	57(9	NOUN
ejpam-6089	787	7	-	-	SYM
ejpam-6089	787	8	10):2403–2407	10):2403–2407	NOUN
ejpam-6089	787	9	,	,	PUNCT
ejpam-6089	787	10	2013	2013	NUM
ejpam-6089	787	11	.	.	PUNCT
ejpam-6089	788	1	[	[	X
ejpam-6089	788	2	36	36	NUM
ejpam-6089	788	3	]	]	PUNCT
ejpam-6089	788	4	a.	a.	NOUN
ejpam-6089	788	5	fernandez	fernandez	PROPN
ejpam-6089	788	6	and	and	CCONJ
ejpam-6089	788	7	p.	p.	PROPN
ejpam-6089	788	8	mohammed	mohammed	PROPN
ejpam-6089	788	9	.	.	PUNCT
ejpam-6089	789	1	hermite	hermite	PROPN
ejpam-6089	789	2	-	-	PUNCT
ejpam-6089	789	3	hadamard	hadamard	ADJ
ejpam-6089	789	4	inequalities	inequality	NOUN
ejpam-6089	789	5	in	in	ADP
ejpam-6089	789	6	fractional	fractional	ADJ
ejpam-6089	789	7	calculus	calculus	NOUN
ejpam-6089	789	8	defined	define	VERB
ejpam-6089	789	9	using	use	VERB
ejpam-6089	789	10	mittag	mittag	ADJ
ejpam-6089	789	11	-	-	PUNCT
ejpam-6089	789	12	leffler	leffler	NOUN
ejpam-6089	789	13	kernels	kernel	NOUN
ejpam-6089	789	14	.	.	PUNCT
ejpam-6089	790	1	mathematical	mathematical	ADJ
ejpam-6089	790	2	methods	method	NOUN
ejpam-6089	790	3	in	in	ADP
ejpam-6089	790	4	the	the	DET
ejpam-6089	790	5	applied	apply	VERB
ejpam-6089	790	6	sciences	science	NOUN
ejpam-6089	790	7	,	,	PUNCT
ejpam-6089	790	8	44(10):8414–8431	44(10):8414–8431	NUM
ejpam-6089	790	9	,	,	PUNCT
ejpam-6089	790	10	2021	2021	NUM
ejpam-6089	790	11	.	.	PUNCT
ejpam-6089	791	1	[	[	X
ejpam-6089	791	2	37	37	NUM
ejpam-6089	791	3	]	]	PUNCT
ejpam-6089	791	4	m.	m.	NOUN
ejpam-6089	791	5	z.	z.	PROPN
ejpam-6089	791	6	sarikaya	sarikaya	PROPN
ejpam-6089	791	7	and	and	CCONJ
ejpam-6089	791	8	h.	h.	PROPN
ejpam-6089	791	9	yildirim	yildirim	PROPN
ejpam-6089	791	10	.	.	PUNCT
ejpam-6089	792	1	on	on	ADP
ejpam-6089	792	2	hermite	hermite	PROPN
ejpam-6089	792	3	-	-	PUNCT
ejpam-6089	792	4	hadamard	hadamard	ADJ
ejpam-6089	792	5	type	type	NOUN
ejpam-6089	792	6	inequalities	inequality	NOUN
ejpam-6089	792	7	for	for	ADP
ejpam-6089	792	8	riemanns	riemann	NOUN
ejpam-6089	792	9	.	.	PUNCT
ejpam-6089	793	1	naheed	naheed	NOUN
ejpam-6089	793	2	et	et	PROPN
ejpam-6089	793	3	al	al	PROPN
ejpam-6089	793	4	.	.	PUNCT
ejpam-6089	793	5	/	/	SYM
ejpam-6089	793	6	eur	eur	PROPN
ejpam-6089	793	7	.	.	PUNCT
ejpam-6089	794	1	j.	j.	PROPN
ejpam-6089	794	2	pure	pure	PROPN
ejpam-6089	794	3	appl	appl	PROPN
ejpam-6089	794	4	.	.	PROPN
ejpam-6089	794	5	math	math	PROPN
ejpam-6089	794	6	,	,	PUNCT
ejpam-6089	794	7	18	18	NUM
ejpam-6089	794	8	(	(	PUNCT
ejpam-6089	794	9	2	2	NUM
ejpam-6089	794	10	)	)	PUNCT
ejpam-6089	794	11	(	(	PUNCT
ejpam-6089	794	12	2025	2025	NUM
ejpam-6089	794	13	)	)	PUNCT
ejpam-6089	794	14	,	,	PUNCT
ejpam-6089	794	15	6089	6089	NUM
ejpam-6089	794	16	34	34	NUM
ejpam-6089	794	17	of	of	ADP
ejpam-6089	794	18	34	34	NUM
ejpam-6089	794	19	liouville	liouville	ADJ
ejpam-6089	794	20	fractional	fractional	ADJ
ejpam-6089	794	21	integrals	integral	NOUN
ejpam-6089	794	22	.	.	PUNCT
ejpam-6089	795	1	miskolc	miskolc	ADJ
ejpam-6089	795	2	mathematical	mathematical	ADJ
ejpam-6089	795	3	notes	note	NOUN
ejpam-6089	795	4	,	,	PUNCT
ejpam-6089	795	5	17(2):1049–1059	17(2):1049–1059	NUM
ejpam-6089	795	6	,	,	PUNCT
ejpam-6089	795	7	2017	2017	NUM
ejpam-6089	795	8	.	.	PUNCT
ejpam-6089	796	1	[	[	X
ejpam-6089	796	2	38	38	NUM
ejpam-6089	796	3	]	]	PUNCT
ejpam-6089	796	4	k.	k.	PROPN
ejpam-6089	796	5	mehrez	mehrez	PROPN
ejpam-6089	796	6	and	and	CCONJ
ejpam-6089	796	7	p.	p.	PROPN
ejpam-6089	796	8	agarwal	agarwal	PROPN
ejpam-6089	796	9	.	.	PUNCT
ejpam-6089	797	1	new	new	ADJ
ejpam-6089	797	2	hermite	hermite	PROPN
ejpam-6089	797	3	-	-	PUNCT
ejpam-6089	797	4	hadamard	hadamard	ADJ
ejpam-6089	797	5	type	type	NOUN
ejpam-6089	797	6	integral	integral	ADJ
ejpam-6089	797	7	inequalities	inequality	NOUN
ejpam-6089	797	8	for	for	ADP
ejpam-6089	797	9	convex	convex	NOUN
ejpam-6089	797	10	functions	function	NOUN
ejpam-6089	797	11	and	and	CCONJ
ejpam-6089	797	12	their	their	PRON
ejpam-6089	797	13	applications	application	NOUN
ejpam-6089	797	14	.	.	PUNCT
ejpam-6089	798	1	journal	journal	NOUN
ejpam-6089	798	2	of	of	ADP
ejpam-6089	798	3	computational	computational	ADJ
ejpam-6089	798	4	and	and	CCONJ
ejpam-6089	798	5	applied	applied	ADJ
ejpam-6089	798	6	mathematics	mathematic	NOUN
ejpam-6089	798	7	,	,	PUNCT
ejpam-6089	798	8	350:274–285	350:274–285	NUM
ejpam-6089	798	9	,	,	PUNCT
ejpam-6089	798	10	2019	2019	NUM
ejpam-6089	798	11	.	.	PUNCT