id	sid	tid	token	lemma	pos
ejpam-6745	1	1	european	european	PROPN
ejpam-6745	1	2	journal	journal	PROPN
ejpam-6745	1	3	of	of	ADP
ejpam-6745	1	4	pure	pure	ADJ
ejpam-6745	1	5	and	and	CCONJ
ejpam-6745	1	6	applied	applied	ADJ
ejpam-6745	1	7	mathematics	mathematic	NOUN
ejpam-6745	1	8	2025	2025	NUM
ejpam-6745	1	9	,	,	PUNCT
ejpam-6745	1	10	vol	vol	NOUN
ejpam-6745	1	11	.	.	PROPN
ejpam-6745	1	12	18	18	NUM
ejpam-6745	1	13	,	,	PUNCT
ejpam-6745	1	14	issue	issue	NOUN
ejpam-6745	1	15	4	4	NUM
ejpam-6745	1	16	,	,	PUNCT
ejpam-6745	1	17	article	article	NOUN
ejpam-6745	1	18	number	number	NOUN
ejpam-6745	1	19	6745	6745	NUM
ejpam-6745	1	20	issn	issn	VERB
ejpam-6745	1	21	1307	1307	NUM
ejpam-6745	1	22	-	-	SYM
ejpam-6745	1	23	5543	5543	NUM
ejpam-6745	1	24	–	–	PUNCT
ejpam-6745	1	25	ejpam.com	ejpam.com	X
ejpam-6745	1	26	published	publish	VERB
ejpam-6745	1	27	by	by	ADP
ejpam-6745	1	28	new	new	PROPN
ejpam-6745	1	29	york	york	PROPN
ejpam-6745	1	30	business	business	PROPN
ejpam-6745	1	31	global	global	ADJ
ejpam-6745	1	32	geometric	geometric	ADJ
ejpam-6745	1	33	characterizations	characterization	NOUN
ejpam-6745	1	34	of	of	ADP
ejpam-6745	1	35	imaginary	imaginary	ADJ
ejpam-6745	1	36	error	error	NOUN
ejpam-6745	1	37	functions	function	NOUN
ejpam-6745	1	38	in	in	ADP
ejpam-6745	1	39	subclasses	subclass	NOUN
ejpam-6745	1	40	of	of	ADP
ejpam-6745	1	41	spirallike	spirallike	ADJ
ejpam-6745	1	42	analytic	analytic	ADJ
ejpam-6745	1	43	functions	function	NOUN
ejpam-6745	1	44	feras	feras	PROPN
ejpam-6745	1	45	yousef1	yousef1	PROPN
ejpam-6745	1	46	,	,	PUNCT
ejpam-6745	1	47	maryam	maryam	PROPN
ejpam-6745	1	48	m.	m.	PROPN
ejpam-6745	1	49	alholi2	alholi2	PROPN
ejpam-6745	1	50	,	,	PUNCT
ejpam-6745	1	51	tariq	tariq	PROPN
ejpam-6745	1	52	al	al	PROPN
ejpam-6745	1	53	-	-	PUNCT
ejpam-6745	1	54	hawary3,∗	hawary3,∗	PROPN
ejpam-6745	1	55	1	1	NUM
ejpam-6745	1	56	department	department	NOUN
ejpam-6745	1	57	of	of	ADP
ejpam-6745	1	58	mathematics	mathematic	NOUN
ejpam-6745	1	59	,	,	PUNCT
ejpam-6745	1	60	the	the	DET
ejpam-6745	1	61	university	university	PROPN
ejpam-6745	1	62	of	of	ADP
ejpam-6745	1	63	jordan	jordan	PROPN
ejpam-6745	1	64	,	,	PUNCT
ejpam-6745	1	65	amman	amman	PROPN
ejpam-6745	1	66	11942	11942	NUM
ejpam-6745	1	67	,	,	PUNCT
ejpam-6745	1	68	jordan	jordan	PROPN
ejpam-6745	1	69	2	2	NUM
ejpam-6745	1	70	applied	apply	VERB
ejpam-6745	1	71	college	college	NOUN
ejpam-6745	1	72	,	,	PUNCT
ejpam-6745	1	73	taibah	taibah	PROPN
ejpam-6745	1	74	university	university	PROPN
ejpam-6745	1	75	,	,	PUNCT
ejpam-6745	1	76	saudi	saudi	PROPN
ejpam-6745	1	77	arabia	arabia	PROPN
ejpam-6745	1	78	3	3	NUM
ejpam-6745	1	79	department	department	NOUN
ejpam-6745	1	80	of	of	ADP
ejpam-6745	1	81	applied	apply	VERB
ejpam-6745	1	82	science	science	NOUN
ejpam-6745	1	83	,	,	PUNCT
ejpam-6745	1	84	ajloun	ajloun	PROPN
ejpam-6745	1	85	college	college	PROPN
ejpam-6745	1	86	,	,	PUNCT
ejpam-6745	1	87	al	al	PROPN
ejpam-6745	1	88	-	-	PUNCT
ejpam-6745	1	89	balqa	balqa	NOUN
ejpam-6745	1	90	applied	apply	VERB
ejpam-6745	1	91	university	university	NOUN
ejpam-6745	1	92	,	,	PUNCT
ejpam-6745	1	93	ajloun	ajloun	NOUN
ejpam-6745	1	94	26816	26816	NUM
ejpam-6745	1	95	,	,	PUNCT
ejpam-6745	1	96	jordan	jordan	PROPN
ejpam-6745	1	97	abstract	abstract	PROPN
ejpam-6745	1	98	.	.	PUNCT
ejpam-6745	2	1	in	in	ADP
ejpam-6745	2	2	this	this	DET
ejpam-6745	2	3	paper	paper	NOUN
ejpam-6745	2	4	,	,	PUNCT
ejpam-6745	2	5	we	we	PRON
ejpam-6745	2	6	investigate	investigate	VERB
ejpam-6745	2	7	the	the	DET
ejpam-6745	2	8	geometric	geometric	ADJ
ejpam-6745	2	9	behavior	behavior	NOUN
ejpam-6745	2	10	of	of	ADP
ejpam-6745	2	11	the	the	DET
ejpam-6745	2	12	generalized	generalize	VERB
ejpam-6745	2	13	normalized	normalize	VERB
ejpam-6745	2	14	imaginary	imaginary	ADJ
ejpam-6745	2	15	error	error	NOUN
ejpam-6745	2	16	function	function	NOUN
ejpam-6745	2	17	υik	υik	NOUN
ejpam-6745	2	18	(	(	PUNCT
ejpam-6745	2	19	z	z	NOUN
ejpam-6745	2	20	)	)	PUNCT
ejpam-6745	2	21	and	and	CCONJ
ejpam-6745	2	22	the	the	DET
ejpam-6745	2	23	associated	associated	ADJ
ejpam-6745	2	24	convolution	convolution	NOUN
ejpam-6745	2	25	operator	operator	NOUN
ejpam-6745	2	26	iik(z	iik(z	PRON
ejpam-6745	2	27	)	)	PUNCT
ejpam-6745	2	28	within	within	ADP
ejpam-6745	2	29	the	the	DET
ejpam-6745	2	30	framework	framework	NOUN
ejpam-6745	2	31	of	of	ADP
ejpam-6745	2	32	analytic	analytic	ADJ
ejpam-6745	2	33	function	function	NOUN
ejpam-6745	2	34	theory	theory	NOUN
ejpam-6745	2	35	.	.	PUNCT
ejpam-6745	3	1	specifically	specifically	ADV
ejpam-6745	3	2	,	,	PUNCT
ejpam-6745	3	3	we	we	PRON
ejpam-6745	3	4	establish	establish	VERB
ejpam-6745	3	5	necessary	necessary	ADJ
ejpam-6745	3	6	and	and	CCONJ
ejpam-6745	3	7	sufficient	sufficient	ADJ
ejpam-6745	3	8	conditions	condition	NOUN
ejpam-6745	3	9	under	under	ADP
ejpam-6745	3	10	which	which	PRON
ejpam-6745	3	11	these	these	DET
ejpam-6745	3	12	functions	function	NOUN
ejpam-6745	3	13	belong	belong	VERB
ejpam-6745	3	14	to	to	ADP
ejpam-6745	3	15	the	the	DET
ejpam-6745	3	16	subclasses	subclass	NOUN
ejpam-6745	3	17	spe(ϑ	spe(ϑ	PROPN
ejpam-6745	3	18	,	,	PUNCT
ejpam-6745	3	19	ζ	ζ	NOUN
ejpam-6745	3	20	)	)	PUNCT
ejpam-6745	3	21	and	and	CCONJ
ejpam-6745	3	22	cspe(ϑ	cspe(ϑ	PROPN
ejpam-6745	3	23	,	,	PUNCT
ejpam-6745	3	24	ζ	ζ	NOUN
ejpam-6745	3	25	)	)	PUNCT
ejpam-6745	3	26	of	of	ADP
ejpam-6745	3	27	spirallike	spirallike	NOUN
ejpam-6745	3	28	and	and	CCONJ
ejpam-6745	3	29	convex	convex	VERB
ejpam-6745	3	30	spirallike	spirallike	ADJ
ejpam-6745	3	31	analytic	analytic	ADJ
ejpam-6745	3	32	functions	function	NOUN
ejpam-6745	3	33	,	,	PUNCT
ejpam-6745	3	34	respectively	respectively	ADV
ejpam-6745	3	35	.	.	PUNCT
ejpam-6745	4	1	additionally	additionally	ADV
ejpam-6745	4	2	,	,	PUNCT
ejpam-6745	4	3	we	we	PRON
ejpam-6745	4	4	derive	derive	VERB
ejpam-6745	4	5	sharp	sharp	ADJ
ejpam-6745	4	6	criteria	criterion	NOUN
ejpam-6745	4	7	for	for	ADP
ejpam-6745	4	8	an	an	DET
ejpam-6745	4	9	integral	integral	ADJ
ejpam-6745	4	10	operator	operator	NOUN
ejpam-6745	4	11	involving	involve	VERB
ejpam-6745	4	12	υik	υik	NOUN
ejpam-6745	4	13	(	(	PUNCT
ejpam-6745	4	14	z	z	NOUN
ejpam-6745	4	15	)	)	PUNCT
ejpam-6745	4	16	to	to	PART
ejpam-6745	4	17	be	be	AUX
ejpam-6745	4	18	a	a	DET
ejpam-6745	4	19	member	member	NOUN
ejpam-6745	4	20	of	of	ADP
ejpam-6745	4	21	these	these	DET
ejpam-6745	4	22	subclasses	subclass	NOUN
ejpam-6745	4	23	.	.	PUNCT
ejpam-6745	5	1	these	these	DET
ejpam-6745	5	2	results	result	NOUN
ejpam-6745	5	3	extend	extend	VERB
ejpam-6745	5	4	and	and	CCONJ
ejpam-6745	5	5	generalize	generalize	VERB
ejpam-6745	5	6	several	several	ADJ
ejpam-6745	5	7	known	know	VERB
ejpam-6745	5	8	findings	finding	NOUN
ejpam-6745	5	9	and	and	CCONJ
ejpam-6745	5	10	may	may	AUX
ejpam-6745	5	11	inspire	inspire	VERB
ejpam-6745	5	12	further	further	ADJ
ejpam-6745	5	13	applications	application	NOUN
ejpam-6745	5	14	of	of	ADP
ejpam-6745	5	15	the	the	DET
ejpam-6745	5	16	imaginary	imaginary	ADJ
ejpam-6745	5	17	error	error	NOUN
ejpam-6745	5	18	function	function	NOUN
ejpam-6745	5	19	in	in	ADP
ejpam-6745	5	20	geometric	geometric	ADJ
ejpam-6745	5	21	function	function	NOUN
ejpam-6745	5	22	theory	theory	NOUN
ejpam-6745	5	23	.	.	PUNCT
ejpam-6745	6	1	2020	2020	NUM
ejpam-6745	6	2	mathematics	mathematic	NOUN
ejpam-6745	6	3	subject	subject	NOUN
ejpam-6745	6	4	classifications	classification	NOUN
ejpam-6745	6	5	:	:	PUNCT
ejpam-6745	6	6	30c45	30c45	NUM
ejpam-6745	6	7	key	key	ADJ
ejpam-6745	6	8	words	word	NOUN
ejpam-6745	6	9	and	and	CCONJ
ejpam-6745	6	10	phrases	phrase	NOUN
ejpam-6745	6	11	:	:	PUNCT
ejpam-6745	6	12	analytic	analytic	ADJ
ejpam-6745	6	13	,	,	PUNCT
ejpam-6745	6	14	univalent	univalent	ADJ
ejpam-6745	6	15	,	,	PUNCT
ejpam-6745	6	16	spirallike	spirallike	NOUN
ejpam-6745	6	17	,	,	PUNCT
ejpam-6745	6	18	convex	convex	NOUN
ejpam-6745	6	19	spirallike	spirallike	NOUN
ejpam-6745	6	20	,	,	PUNCT
ejpam-6745	6	21	error	error	NOUN
ejpam-6745	6	22	function	function	NOUN
ejpam-6745	6	23	1	1	NUM
ejpam-6745	6	24	.	.	PUNCT
ejpam-6745	7	1	introduction	introduction	NOUN
ejpam-6745	7	2	and	and	CCONJ
ejpam-6745	7	3	preliminaries	preliminary	NOUN
ejpam-6745	7	4	let	let	VERB
ejpam-6745	7	5	e	e	PRON
ejpam-6745	7	6	symbolize	symbolize	VERB
ejpam-6745	7	7	for	for	ADP
ejpam-6745	7	8	the	the	DET
ejpam-6745	7	9	class	class	NOUN
ejpam-6745	7	10	of	of	ADP
ejpam-6745	7	11	analytic	analytic	ADJ
ejpam-6745	7	12	functions	function	NOUN
ejpam-6745	7	13	of	of	ADP
ejpam-6745	7	14	the	the	DET
ejpam-6745	7	15	form	form	NOUN
ejpam-6745	7	16	:	:	PUNCT
ejpam-6745	7	17	q(z	q(z	NUM
ejpam-6745	7	18	)	)	PUNCT
ejpam-6745	7	19	=	=	SYM
ejpam-6745	8	1	z	z	NOUN
ejpam-6745	9	1	+	+	NOUN
ejpam-6745	9	2	∞∑	∞∑	NUM
ejpam-6745	9	3	ϵ=2	ϵ=2	ADJ
ejpam-6745	9	4	βϵz	βϵz	PROPN
ejpam-6745	10	1	ϵ	ϵ	INTJ
ejpam-6745	10	2	,	,	PUNCT
ejpam-6745	10	3	z	z	PROPN
ejpam-6745	10	4	∈	∈	PROPN
ejpam-6745	10	5	γ	γ	X
ejpam-6745	10	6	=	=	SYM
ejpam-6745	10	7	{	{	PUNCT
ejpam-6745	10	8	z	z	NOUN
ejpam-6745	10	9	∈	∈	PROPN
ejpam-6745	10	10	c	c	NOUN
ejpam-6745	10	11	:	:	PUNCT
ejpam-6745	10	12	|z|	|z|	NOUN
ejpam-6745	10	13	<	<	X
ejpam-6745	10	14	1	1	NUM
ejpam-6745	10	15	}	}	PUNCT
ejpam-6745	10	16	.	.	PUNCT
ejpam-6745	11	1	(	(	PUNCT
ejpam-6745	11	2	1	1	X
ejpam-6745	11	3	)	)	PUNCT
ejpam-6745	11	4	further	far	ADV
ejpam-6745	11	5	,	,	PUNCT
ejpam-6745	11	6	let	let	VERB
ejpam-6745	11	7	ne	ne	PART
ejpam-6745	11	8	be	be	AUX
ejpam-6745	11	9	a	a	DET
ejpam-6745	11	10	subclass	subclass	NOUN
ejpam-6745	11	11	of	of	ADP
ejpam-6745	11	12	e	e	NOUN
ejpam-6745	11	13	consisting	consist	VERB
ejpam-6745	11	14	of	of	ADP
ejpam-6745	11	15	functions	function	NOUN
ejpam-6745	11	16	of	of	ADP
ejpam-6745	11	17	the	the	DET
ejpam-6745	11	18	form	form	NOUN
ejpam-6745	11	19	:	:	PUNCT
ejpam-6745	11	20	q(z	q(z	NUM
ejpam-6745	11	21	)	)	PUNCT
ejpam-6745	11	22	=	=	PUNCT
ejpam-6745	12	1	z	z	NOUN
ejpam-6745	13	1	−	−	PROPN
ejpam-6745	13	2	∞∑	∞∑	NUM
ejpam-6745	13	3	ϵ=2	ϵ=2	ADJ
ejpam-6745	13	4	βϵz	βϵz	PROPN
ejpam-6745	14	1	ϵ	ϵ	INTJ
ejpam-6745	14	2	,	,	PUNCT
ejpam-6745	14	3	βϵ	βϵ	X
ejpam-6745	14	4	≥	≥	NOUN
ejpam-6745	14	5	0	0	NUM
ejpam-6745	14	6	,	,	PUNCT
ejpam-6745	14	7	z	z	PROPN
ejpam-6745	14	8	∈	∈	PROPN
ejpam-6745	14	9	γ	γ	X
ejpam-6745	14	10	.	.	PROPN
ejpam-6745	14	11	(	(	PUNCT
ejpam-6745	14	12	2	2	X
ejpam-6745	14	13	)	)	PUNCT
ejpam-6745	14	14	∗corresponding	∗corresponde	VERB
ejpam-6745	14	15	author	author	NOUN
ejpam-6745	14	16	.	.	PUNCT
ejpam-6745	15	1	doi	doi	NOUN
ejpam-6745	15	2	:	:	PUNCT
ejpam-6745	15	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6745	https://doi.org/10.29020/nybg.ejpam.v18i4.6745	PROPN
ejpam-6745	15	4	email	email	NOUN
ejpam-6745	15	5	addresses	address	NOUN
ejpam-6745	15	6	:	:	PUNCT
ejpam-6745	15	7	fyousef@ju.edu.jo	fyousef@ju.edu.jo	NOUN
ejpam-6745	15	8	(	(	PUNCT
ejpam-6745	15	9	f.	f.	PROPN
ejpam-6745	15	10	yousef	yousef	PROPN
ejpam-6745	15	11	)	)	PUNCT
ejpam-6745	15	12	,	,	PUNCT
ejpam-6745	15	13	mholi@taibahu.edu.sa	mholi@taibahu.edu.sa	NOUN
ejpam-6745	15	14	(	(	PUNCT
ejpam-6745	15	15	m.	m.	NOUN
ejpam-6745	15	16	m.	m.	NOUN
ejpam-6745	15	17	alholi	alholi	PROPN
ejpam-6745	15	18	)	)	PUNCT
ejpam-6745	15	19	,	,	PUNCT
ejpam-6745	15	20	tariq	tariq	PROPN
ejpam-6745	15	21	amh@bau.edu.jo	amh@bau.edu.jo	PROPN
ejpam-6745	15	22	(	(	PUNCT
ejpam-6745	15	23	t.	t.	PROPN
ejpam-6745	15	24	al	al	PROPN
ejpam-6745	15	25	-	-	PUNCT
ejpam-6745	15	26	hawary	hawary	PROPN
ejpam-6745	15	27	)	)	PUNCT
ejpam-6745	15	28	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6745	16	1	1	1	NUM
ejpam-6745	16	2	copyright	copyright	NOUN
ejpam-6745	16	3	:	:	PUNCT
ejpam-6745	16	4	©	©	PROPN
ejpam-6745	16	5	2025	2025	NUM
ejpam-6745	16	6	the	the	DET
ejpam-6745	16	7	author(s	author(s	NOUN
ejpam-6745	16	8	)	)	PUNCT
ejpam-6745	16	9	.	.	PUNCT
ejpam-6745	17	1	(	(	PUNCT
ejpam-6745	17	2	cc	cc	NOUN
ejpam-6745	17	3	by	by	ADP
ejpam-6745	17	4	-	-	PUNCT
ejpam-6745	17	5	nc	nc	PROPN
ejpam-6745	17	6	4.0	4.0	NUM
ejpam-6745	17	7	)	)	PUNCT
ejpam-6745	17	8	f.	f.	PROPN
ejpam-6745	17	9	yousef	yousef	PROPN
ejpam-6745	17	10	,	,	PUNCT
ejpam-6745	17	11	m.	m.	NOUN
ejpam-6745	17	12	m.	m.	PROPN
ejpam-6745	17	13	alholi	alholi	PROPN
ejpam-6745	17	14	,	,	PUNCT
ejpam-6745	17	15	t.	t.	PROPN
ejpam-6745	17	16	al	al	PROPN
ejpam-6745	17	17	-	-	PUNCT
ejpam-6745	17	18	hawary	hawary	PROPN
ejpam-6745	17	19	/	/	SYM
ejpam-6745	17	20	eur	eur	PROPN
ejpam-6745	17	21	.	.	PUNCT
ejpam-6745	18	1	j.	j.	PROPN
ejpam-6745	18	2	pure	pure	PROPN
ejpam-6745	18	3	appl	appl	PROPN
ejpam-6745	18	4	.	.	PROPN
ejpam-6745	18	5	math	math	PROPN
ejpam-6745	18	6	,	,	PUNCT
ejpam-6745	18	7	18	18	NUM
ejpam-6745	18	8	(	(	PUNCT
ejpam-6745	18	9	4	4	NUM
ejpam-6745	18	10	)	)	PUNCT
ejpam-6745	18	11	(	(	PUNCT
ejpam-6745	18	12	2025	2025	NUM
ejpam-6745	18	13	)	)	PUNCT
ejpam-6745	18	14	,	,	PUNCT
ejpam-6745	18	15	6745	6745	NUM
ejpam-6745	18	16	2	2	NUM
ejpam-6745	18	17	of	of	ADP
ejpam-6745	18	18	13	13	NUM
ejpam-6745	18	19	a	a	DET
ejpam-6745	18	20	function	function	NOUN
ejpam-6745	18	21	q	q	X
ejpam-6745	18	22	∈	∈	NOUN
ejpam-6745	18	23	e	e	NOUN
ejpam-6745	18	24	is	be	AUX
ejpam-6745	18	25	spirallike	spirallike	ADJ
ejpam-6745	18	26	if	if	SCONJ
ejpam-6745	18	27	r	r	NOUN
ejpam-6745	18	28	(	(	PUNCT
ejpam-6745	18	29	e−iϑ	e−iϑ	PROPN
ejpam-6745	18	30	zq	zq	PROPN
ejpam-6745	18	31	′(z	′(z	ADV
ejpam-6745	18	32	)	)	PUNCT
ejpam-6745	18	33	q(z	q(z	PROPN
ejpam-6745	18	34	)	)	PUNCT
ejpam-6745	18	35	)	)	PUNCT
ejpam-6745	18	36	>	>	X
ejpam-6745	19	1	0	0	NUM
ejpam-6745	19	2	,	,	PUNCT
ejpam-6745	19	3	|ϑ|	|ϑ|	ADV
ejpam-6745	19	4	<	<	X
ejpam-6745	19	5	π/2	π/2	NUM
ejpam-6745	20	1	,	,	PUNCT
ejpam-6745	20	2	z	z	PROPN
ejpam-6745	20	3	∈	∈	PROPN
ejpam-6745	20	4	γ	γ	X
ejpam-6745	20	5	.	.	PROPN
ejpam-6745	20	6	also	also	ADV
ejpam-6745	20	7	,	,	PUNCT
ejpam-6745	20	8	q(z	q(z	PROPN
ejpam-6745	20	9	)	)	PUNCT
ejpam-6745	20	10	is	be	AUX
ejpam-6745	20	11	convex	convex	ADJ
ejpam-6745	20	12	spirallike	spirallike	ADJ
ejpam-6745	20	13	if	if	SCONJ
ejpam-6745	20	14	zq′(z	zq′(z	PROPN
ejpam-6745	20	15	)	)	PUNCT
ejpam-6745	20	16	is	be	AUX
ejpam-6745	20	17	spirallike	spirallike	ADJ
ejpam-6745	20	18	.	.	PUNCT
ejpam-6745	21	1	selvaraj	selvaraj	PROPN
ejpam-6745	21	2	and	and	CCONJ
ejpam-6745	21	3	geetha	geetha	NOUN
ejpam-6745	22	1	[	[	X
ejpam-6745	22	2	1	1	X
ejpam-6745	22	3	]	]	PUNCT
ejpam-6745	22	4	introduced	introduce	VERB
ejpam-6745	22	5	the	the	DET
ejpam-6745	22	6	subclasses	subclass	NOUN
ejpam-6745	22	7	of	of	ADP
ejpam-6745	22	8	uniformly	uniformly	ADV
ejpam-6745	22	9	spirallike	spirallike	ADJ
ejpam-6745	22	10	functions	function	NOUN
ejpam-6745	22	11	sp(ϑ	sp(ϑ	NOUN
ejpam-6745	22	12	,	,	PUNCT
ejpam-6745	22	13	ζ	ζ	NOUN
ejpam-6745	22	14	)	)	PUNCT
ejpam-6745	22	15	and	and	CCONJ
ejpam-6745	22	16	csp(ϑ	csp(ϑ	PROPN
ejpam-6745	22	17	,	,	PUNCT
ejpam-6745	22	18	ζ	ζ	NOUN
ejpam-6745	22	19	)	)	PUNCT
ejpam-6745	22	20	,	,	PUNCT
ejpam-6745	22	21	as	as	SCONJ
ejpam-6745	22	22	given	give	VERB
ejpam-6745	22	23	in	in	ADP
ejpam-6745	22	24	the	the	DET
ejpam-6745	22	25	following	follow	VERB
ejpam-6745	22	26	definition	definition	NOUN
ejpam-6745	22	27	.	.	PUNCT
ejpam-6745	23	1	definition	definition	NOUN
ejpam-6745	23	2	1	1	NUM
ejpam-6745	23	3	.	.	PUNCT
ejpam-6745	24	1	a	a	DET
ejpam-6745	24	2	function	function	NOUN
ejpam-6745	24	3	q	q	NOUN
ejpam-6745	24	4	of	of	ADP
ejpam-6745	24	5	the	the	DET
ejpam-6745	24	6	form	form	NOUN
ejpam-6745	24	7	(	(	PUNCT
ejpam-6745	24	8	1	1	X
ejpam-6745	24	9	)	)	PUNCT
ejpam-6745	24	10	is	be	AUX
ejpam-6745	24	11	said	say	VERB
ejpam-6745	24	12	to	to	PART
ejpam-6745	24	13	be	be	AUX
ejpam-6745	24	14	in	in	ADP
ejpam-6745	24	15	the	the	DET
ejpam-6745	24	16	subclass	subclass	NOUN
ejpam-6745	24	17	sp(ϑ	sp(ϑ	NOUN
ejpam-6745	24	18	,	,	PUNCT
ejpam-6745	24	19	ζ	ζ	NOUN
ejpam-6745	24	20	)	)	PUNCT
ejpam-6745	24	21	,	,	PUNCT
ejpam-6745	24	22	if	if	SCONJ
ejpam-6745	24	23	it	it	PRON
ejpam-6745	24	24	satisfies	satisfy	VERB
ejpam-6745	24	25	the	the	DET
ejpam-6745	24	26	following	follow	VERB
ejpam-6745	24	27	condition	condition	NOUN
ejpam-6745	24	28	:	:	PUNCT
ejpam-6745	25	1	r	r	NOUN
ejpam-6745	25	2	{	{	PUNCT
ejpam-6745	25	3	e−iϑ	e−iϑ	X
ejpam-6745	25	4	(	(	PUNCT
ejpam-6745	25	5	zq′(z	zq′(z	NOUN
ejpam-6745	25	6	)	)	PUNCT
ejpam-6745	25	7	q(z	q(z	PROPN
ejpam-6745	25	8	)	)	PUNCT
ejpam-6745	25	9	)	)	PUNCT
ejpam-6745	25	10	}	}	PUNCT
ejpam-6745	25	11	≥	≥	NUM
ejpam-6745	25	12	∣∣∣∣zq′(z)q′(z	∣∣∣∣zq′(z)q′(z	NOUN
ejpam-6745	25	13	)	)	PUNCT
ejpam-6745	25	14	−	−	PROPN
ejpam-6745	25	15	1	1	NUM
ejpam-6745	25	16	∣∣∣∣+	∣∣∣∣+	NOUN
ejpam-6745	25	17	ζ	ζ	PROPN
ejpam-6745	25	18	(	(	PUNCT
ejpam-6745	25	19	z	z	NOUN
ejpam-6745	25	20	∈	∈	PROPN
ejpam-6745	25	21	γ	γ	X
ejpam-6745	25	22	;	;	PUNCT
ejpam-6745	25	23	|ϑ|	|ϑ|	ADV
ejpam-6745	25	24	<	<	X
ejpam-6745	25	25	π/2	π/2	NUM
ejpam-6745	25	26	;	;	PUNCT
ejpam-6745	25	27	0	0	NUM
ejpam-6745	25	28	≤	≤	NUM
ejpam-6745	25	29	ζ	ζ	X
ejpam-6745	25	30	<	<	X
ejpam-6745	25	31	1	1	NUM
ejpam-6745	25	32	)	)	PUNCT
ejpam-6745	25	33	and	and	CCONJ
ejpam-6745	25	34	q	q	PROPN
ejpam-6745	25	35	∈	∈	PROPN
ejpam-6745	25	36	csp(ϑ	csp(ϑ	PROPN
ejpam-6745	25	37	,	,	PUNCT
ejpam-6745	25	38	ζ	ζ	NOUN
ejpam-6745	25	39	)	)	PUNCT
ejpam-6745	25	40	iff	iff	PROPN
ejpam-6745	25	41	zq′(z	zq′(z	PROPN
ejpam-6745	25	42	)	)	PUNCT
ejpam-6745	25	43	∈	∈	PROPN
ejpam-6745	25	44	sp(ϑ	sp(ϑ	NOUN
ejpam-6745	25	45	,	,	PUNCT
ejpam-6745	25	46	ζ	ζ	NOUN
ejpam-6745	25	47	)	)	PUNCT
ejpam-6745	25	48	,	,	PUNCT
ejpam-6745	25	49	which	which	PRON
ejpam-6745	25	50	is	be	AUX
ejpam-6745	25	51	equivalent	equivalent	ADJ
ejpam-6745	25	52	the	the	DET
ejpam-6745	25	53	following	follow	VERB
ejpam-6745	25	54	condition	condition	NOUN
ejpam-6745	25	55	:	:	PUNCT
ejpam-6745	25	56	r	r	NOUN
ejpam-6745	25	57	{	{	PUNCT
ejpam-6745	25	58	e−iϑ	e−iϑ	X
ejpam-6745	25	59	(	(	PUNCT
ejpam-6745	25	60	1	1	NUM
ejpam-6745	25	61	+	+	NUM
ejpam-6745	25	62	zq′′(z	zq′′(z	NOUN
ejpam-6745	25	63	)	)	PUNCT
ejpam-6745	25	64	q′(z	q′(z	PROPN
ejpam-6745	25	65	)	)	PUNCT
ejpam-6745	25	66	)	)	PUNCT
ejpam-6745	25	67	}	}	PUNCT
ejpam-6745	25	68	≥	≥	NOUN
ejpam-6745	25	69	∣∣∣∣zq′′(z)q′(z	∣∣∣∣zq′′(z)q′(z	NOUN
ejpam-6745	25	70	)	)	PUNCT
ejpam-6745	25	71	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-6745	25	72	ζ	ζ	PROPN
ejpam-6745	25	73	(	(	PUNCT
ejpam-6745	25	74	z	z	NOUN
ejpam-6745	25	75	∈	∈	PROPN
ejpam-6745	25	76	γ	γ	X
ejpam-6745	25	77	;	;	PUNCT
ejpam-6745	25	78	|ϑ|	|ϑ|	ADV
ejpam-6745	25	79	<	<	X
ejpam-6745	25	80	π/2	π/2	NUM
ejpam-6745	25	81	;	;	PUNCT
ejpam-6745	25	82	0	0	NUM
ejpam-6745	25	83	≤	≤	NUM
ejpam-6745	25	84	ζ	ζ	X
ejpam-6745	25	85	<	<	X
ejpam-6745	25	86	1	1	NUM
ejpam-6745	25	87	)	)	PUNCT
ejpam-6745	25	88	.	.	PUNCT
ejpam-6745	26	1	we	we	PRON
ejpam-6745	26	2	write	write	VERB
ejpam-6745	26	3	spe(ϑ	spe(ϑ	PROPN
ejpam-6745	26	4	,	,	PUNCT
ejpam-6745	26	5	ζ	ζ	NOUN
ejpam-6745	26	6	)	)	PUNCT
ejpam-6745	26	7	=	=	SYM
ejpam-6745	26	8	sp(ϑ	sp(ϑ	NOUN
ejpam-6745	26	9	,	,	PUNCT
ejpam-6745	26	10	ζ	ζ	NOUN
ejpam-6745	26	11	)	)	PUNCT
ejpam-6745	26	12	∩ne	∩ne	NOUN
ejpam-6745	26	13	and	and	CCONJ
ejpam-6745	26	14	cspe(ϑ	cspe(ϑ	PROPN
ejpam-6745	26	15	,	,	PUNCT
ejpam-6745	26	16	ζ	ζ	NOUN
ejpam-6745	26	17	)	)	PUNCT
ejpam-6745	26	18	=	=	SYM
ejpam-6745	26	19	csp(ϑ	csp(ϑ	PROPN
ejpam-6745	26	20	,	,	PUNCT
ejpam-6745	26	21	ζ	ζ	NOUN
ejpam-6745	26	22	)	)	PUNCT
ejpam-6745	26	23	∩ne	∩ne	NOUN
ejpam-6745	26	24	.	.	PUNCT
ejpam-6745	27	1	we	we	PRON
ejpam-6745	27	2	note	note	VERB
ejpam-6745	27	3	that	that	SCONJ
ejpam-6745	27	4	,	,	PUNCT
ejpam-6745	27	5	for	for	ADP
ejpam-6745	27	6	ζ	ζ	NOUN
ejpam-6745	27	7	=	=	SYM
ejpam-6745	27	8	0	0	NUM
ejpam-6745	27	9	,	,	PUNCT
ejpam-6745	27	10	the	the	DET
ejpam-6745	27	11	subclasses	subclass	NOUN
ejpam-6745	27	12	of	of	ADP
ejpam-6745	27	13	uniformly	uniformly	ADV
ejpam-6745	27	14	spirallike	spirallike	ADJ
ejpam-6745	27	15	sp(ϑ	sp(ϑ	NOUN
ejpam-6745	27	16	,	,	PUNCT
ejpam-6745	27	17	0	0	NUM
ejpam-6745	27	18	)	)	PUNCT
ejpam-6745	27	19	=	=	SYM
ejpam-6745	27	20	sp(ϑ	sp(ϑ	NOUN
ejpam-6745	27	21	)	)	PUNCT
ejpam-6745	27	22	and	and	CCONJ
ejpam-6745	27	23	uniformly	uniformly	ADV
ejpam-6745	27	24	convex	convex	VERB
ejpam-6745	27	25	spirallike	spirallike	PROPN
ejpam-6745	27	26	csp(ϑ	csp(ϑ	PROPN
ejpam-6745	27	27	,	,	PUNCT
ejpam-6745	27	28	0	0	NUM
ejpam-6745	27	29	)	)	PUNCT
ejpam-6745	27	30	=	=	SYM
ejpam-6745	27	31	csp(ϑ	csp(ϑ	PROPN
ejpam-6745	27	32	)	)	PUNCT
ejpam-6745	27	33	introduced	introduce	VERB
ejpam-6745	27	34	by	by	ADP
ejpam-6745	27	35	ravichandran	ravichandran	PROPN
ejpam-6745	27	36	et	et	PROPN
ejpam-6745	27	37	al	al	PROPN
ejpam-6745	27	38	.	.	PUNCT
ejpam-6745	28	1	[	[	X
ejpam-6745	28	2	2	2	NUM
ejpam-6745	28	3	]	]	PUNCT
ejpam-6745	28	4	.	.	PUNCT
ejpam-6745	29	1	for	for	ADP
ejpam-6745	29	2	ϑ	ϑ	X
ejpam-6745	29	3	=	=	SYM
ejpam-6745	29	4	0	0	NUM
ejpam-6745	29	5	,	,	PUNCT
ejpam-6745	29	6	the	the	DET
ejpam-6745	29	7	subclasses	subclass	NOUN
ejpam-6745	29	8	sp(ϑ	sp(ϑ	NOUN
ejpam-6745	29	9	)	)	PUNCT
ejpam-6745	29	10	=	=	SYM
ejpam-6745	29	11	sp	sp	ADP
ejpam-6745	29	12	and	and	CCONJ
ejpam-6745	29	13	csp(ϑ	csp(ϑ	PROPN
ejpam-6745	29	14	)	)	PUNCT
ejpam-6745	29	15	=	=	SYM
ejpam-6745	29	16	csp	csp	PROPN
ejpam-6745	29	17	introduced	introduce	VERB
ejpam-6745	29	18	and	and	CCONJ
ejpam-6745	29	19	studied	study	VERB
ejpam-6745	29	20	by	by	ADP
ejpam-6745	29	21	rønning	rønne	VERB
ejpam-6745	29	22	[	[	X
ejpam-6745	29	23	3	3	NUM
ejpam-6745	29	24	]	]	PUNCT
ejpam-6745	29	25	.	.	PUNCT
ejpam-6745	30	1	for	for	ADP
ejpam-6745	30	2	more	more	ADV
ejpam-6745	30	3	intriguing	intriguing	ADJ
ejpam-6745	30	4	discoveries	discovery	NOUN
ejpam-6745	30	5	of	of	ADP
ejpam-6745	30	6	some	some	DET
ejpam-6745	30	7	related	relate	VERB
ejpam-6745	30	8	subclasses	subclass	NOUN
ejpam-6745	30	9	of	of	ADP
ejpam-6745	30	10	consistently	consistently	ADV
ejpam-6745	30	11	uniformly	uniformly	ADV
ejpam-6745	30	12	spirallike	spirallike	ADJ
ejpam-6745	30	13	and	and	CCONJ
ejpam-6745	30	14	uniformly	uniformly	ADV
ejpam-6745	30	15	convex	convex	NOUN
ejpam-6745	30	16	spirallike	spirallike	NOUN
ejpam-6745	30	17	,	,	PUNCT
ejpam-6745	30	18	see	see	VERB
ejpam-6745	30	19	the	the	DET
ejpam-6745	30	20	works	work	NOUN
ejpam-6745	30	21	of	of	ADP
ejpam-6745	30	22	al	al	PROPN
ejpam-6745	30	23	-	-	PUNCT
ejpam-6745	30	24	hawary	hawary	PROPN
ejpam-6745	30	25	et	et	PROPN
ejpam-6745	30	26	al	al	PROPN
ejpam-6745	30	27	.	.	PUNCT
ejpam-6745	31	1	[	[	X
ejpam-6745	31	2	4	4	NUM
ejpam-6745	31	3	,	,	PUNCT
ejpam-6745	31	4	5	5	NUM
ejpam-6745	31	5	]	]	PUNCT
ejpam-6745	31	6	,	,	PUNCT
ejpam-6745	31	7	bharati	bharati	PROPN
ejpam-6745	31	8	et	et	NOUN
ejpam-6745	31	9	al	al	PROPN
ejpam-6745	31	10	.	.	PUNCT
ejpam-6745	32	1	[	[	X
ejpam-6745	32	2	6	6	NUM
ejpam-6745	32	3	]	]	PUNCT
ejpam-6745	32	4	,	,	PUNCT
ejpam-6745	32	5	frasin	frasin	PROPN
ejpam-6745	32	6	et	et	PROPN
ejpam-6745	32	7	al	al	PROPN
ejpam-6745	32	8	.	.	PUNCT
ejpam-6745	33	1	[	[	X
ejpam-6745	33	2	7	7	NUM
ejpam-6745	33	3	]	]	PUNCT
ejpam-6745	33	4	,	,	PUNCT
ejpam-6745	33	5	goodman	goodman	PROPN
ejpam-6745	34	1	[	[	X
ejpam-6745	34	2	8	8	NUM
ejpam-6745	34	3	]	]	PUNCT
ejpam-6745	34	4	,	,	PUNCT
ejpam-6745	34	5	kanas	kanas	PROPN
ejpam-6745	34	6	and	and	CCONJ
ejpam-6745	34	7	wisniowska	wisniowska	NOUN
ejpam-6745	35	1	[	[	X
ejpam-6745	35	2	9	9	NUM
ejpam-6745	35	3	]	]	PUNCT
ejpam-6745	35	4	.	.	PUNCT
ejpam-6745	36	1	definition	definition	NOUN
ejpam-6745	36	2	2	2	NUM
ejpam-6745	36	3	.	.	PUNCT
ejpam-6745	37	1	[	[	X
ejpam-6745	37	2	10	10	NUM
ejpam-6745	37	3	]	]	X
ejpam-6745	37	4	a	a	DET
ejpam-6745	37	5	function	function	NOUN
ejpam-6745	37	6	h	h	NOUN
ejpam-6745	37	7	∈	∈	PROPN
ejpam-6745	37	8	e	e	NOUN
ejpam-6745	37	9	is	be	AUX
ejpam-6745	37	10	said	say	VERB
ejpam-6745	37	11	to	to	PART
ejpam-6745	37	12	be	be	AUX
ejpam-6745	37	13	in	in	ADP
ejpam-6745	37	14	the	the	DET
ejpam-6745	37	15	class	class	NOUN
ejpam-6745	37	16	gτ	gτ	NOUN
ejpam-6745	37	17	(	(	PUNCT
ejpam-6745	37	18	c1	c1	PROPN
ejpam-6745	37	19	,	,	PUNCT
ejpam-6745	37	20	c2	c2	PROPN
ejpam-6745	37	21	)	)	PUNCT
ejpam-6745	37	22	,	,	PUNCT
ejpam-6745	37	23	τ	τ	PROPN
ejpam-6745	37	24	∈	∈	PROPN
ejpam-6745	37	25	c\{0	c\{0	PROPN
ejpam-6745	37	26	}	}	PUNCT
ejpam-6745	37	27	,	,	PUNCT
ejpam-6745	37	28	−1	−1	NOUN
ejpam-6745	37	29	≤	≤	PUNCT
ejpam-6745	37	30	c2	c2	PROPN
ejpam-6745	37	31	<	<	X
ejpam-6745	37	32	c1	c1	PROPN
ejpam-6745	37	33	≤	≤	ADV
ejpam-6745	37	34	1	1	NUM
ejpam-6745	37	35	,	,	PUNCT
ejpam-6745	37	36	if	if	SCONJ
ejpam-6745	37	37	it	it	PRON
ejpam-6745	37	38	satisfies	satisfy	VERB
ejpam-6745	37	39	the	the	DET
ejpam-6745	37	40	condition∣∣∣∣	condition∣∣∣∣	PROPN
ejpam-6745	37	41	q′(z)−	q′(z)−	ADJ
ejpam-6745	37	42	1	1	NUM
ejpam-6745	37	43	(	(	PUNCT
ejpam-6745	37	44	c1	c1	PROPN
ejpam-6745	37	45	−	−	PROPN
ejpam-6745	37	46	c2)τ	c2)τ	VERB
ejpam-6745	38	1	−	−	X
ejpam-6745	38	2	c2[q′(z)−	c2[q′(z)−	PROPN
ejpam-6745	38	3	1	1	NUM
ejpam-6745	38	4	]	]	PUNCT
ejpam-6745	38	5	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6745	38	6	<	<	X
ejpam-6745	38	7	1	1	NUM
ejpam-6745	38	8	,	,	PUNCT
ejpam-6745	38	9	z	z	PROPN
ejpam-6745	38	10	∈	∈	PROPN
ejpam-6745	38	11	γ	γ	X
ejpam-6745	38	12	.	.	PUNCT
ejpam-6745	39	1	if	if	SCONJ
ejpam-6745	39	2	we	we	PRON
ejpam-6745	39	3	put	put	VERB
ejpam-6745	39	4	τ	τ	PROPN
ejpam-6745	39	5	=	=	SYM
ejpam-6745	39	6	1	1	NUM
ejpam-6745	39	7	,	,	PUNCT
ejpam-6745	39	8	c1	c1	PROPN
ejpam-6745	39	9	=	=	PUNCT
ejpam-6745	39	10	ϱ	ϱ	PROPN
ejpam-6745	39	11	and	and	CCONJ
ejpam-6745	39	12	c2	c2	PROPN
ejpam-6745	39	13	=	=	PUNCT
ejpam-6745	40	1	−ϱ(0	−ϱ(0	NOUN
ejpam-6745	40	2	<	<	X
ejpam-6745	40	3	ϱ	ϱ	ADP
ejpam-6745	40	4	≤	≤	NUM
ejpam-6745	40	5	1	1	NUM
ejpam-6745	40	6	)	)	PUNCT
ejpam-6745	40	7	,	,	PUNCT
ejpam-6745	40	8	we	we	PRON
ejpam-6745	40	9	get	get	VERB
ejpam-6745	40	10	the	the	DET
ejpam-6745	40	11	class	class	NOUN
ejpam-6745	40	12	of	of	ADP
ejpam-6745	40	13	functions	function	NOUN
ejpam-6745	40	14	q	q	PROPN
ejpam-6745	40	15	∈	∈	NOUN
ejpam-6745	40	16	e	e	NOUN
ejpam-6745	40	17	satisfying	satisfy	VERB
ejpam-6745	40	18	the	the	DET
ejpam-6745	40	19	condition	condition	NOUN
ejpam-6745	40	20	∣∣∣∣q′(z)−	∣∣∣∣q′(z)−	ADP
ejpam-6745	40	21	1	1	NUM
ejpam-6745	40	22	q′(z	q′(z	NOUN
ejpam-6745	40	23	)	)	PUNCT
ejpam-6745	41	1	+	+	CCONJ
ejpam-6745	41	2	1	1	NUM
ejpam-6745	41	3	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6745	41	4	<	<	X
ejpam-6745	41	5	ϱ	ϱ	PROPN
ejpam-6745	41	6	,	,	PUNCT
ejpam-6745	41	7	(	(	PUNCT
ejpam-6745	41	8	z	z	NOUN
ejpam-6745	41	9	∈	∈	PROPN
ejpam-6745	41	10	γ	γ	X
ejpam-6745	41	11	,	,	PUNCT
ejpam-6745	41	12	0	0	NUM
ejpam-6745	41	13	<	<	X
ejpam-6745	41	14	ϱ	ϱ	ADP
ejpam-6745	41	15	≤	≤	NUM
ejpam-6745	41	16	1	1	NUM
ejpam-6745	41	17	)	)	PUNCT
ejpam-6745	41	18	which	which	PRON
ejpam-6745	41	19	was	be	AUX
ejpam-6745	41	20	studied	study	VERB
ejpam-6745	41	21	by	by	ADP
ejpam-6745	41	22	(	(	PUNCT
ejpam-6745	41	23	among	among	ADP
ejpam-6745	41	24	others	other	NOUN
ejpam-6745	41	25	)	)	PUNCT
ejpam-6745	41	26	caplinger	caplinger	NOUN
ejpam-6745	41	27	and	and	CCONJ
ejpam-6745	41	28	causey	causey	PROPN
ejpam-6745	42	1	[	[	X
ejpam-6745	42	2	11	11	NUM
ejpam-6745	42	3	]	]	PUNCT
ejpam-6745	42	4	.	.	PUNCT
ejpam-6745	43	1	it	it	PRON
ejpam-6745	43	2	is	be	AUX
ejpam-6745	43	3	commonly	commonly	ADV
ejpam-6745	43	4	known	know	VERB
ejpam-6745	43	5	that	that	SCONJ
ejpam-6745	43	6	special	special	ADJ
ejpam-6745	43	7	functions	function	NOUN
ejpam-6745	43	8	are	be	AUX
ejpam-6745	43	9	crucial	crucial	ADJ
ejpam-6745	43	10	to	to	ADP
ejpam-6745	43	11	the	the	DET
ejpam-6745	43	12	theory	theory	NOUN
ejpam-6745	43	13	of	of	ADP
ejpam-6745	43	14	geometric	geometric	ADJ
ejpam-6745	43	15	functions	function	NOUN
ejpam-6745	43	16	,	,	PUNCT
ejpam-6745	43	17	and	and	CCONJ
ejpam-6745	43	18	that	that	SCONJ
ejpam-6745	43	19	their	their	PRON
ejpam-6745	43	20	use	use	NOUN
ejpam-6745	43	21	is	be	AUX
ejpam-6745	43	22	not	not	PART
ejpam-6745	43	23	restricted	restrict	VERB
ejpam-6745	43	24	to	to	ADP
ejpam-6745	43	25	the	the	DET
ejpam-6745	43	26	theory	theory	NOUN
ejpam-6745	43	27	of	of	ADP
ejpam-6745	43	28	geometric	geometric	ADJ
ejpam-6745	43	29	functions	function	NOUN
ejpam-6745	43	30	;	;	PUNCT
ejpam-6745	43	31	they	they	PRON
ejpam-6745	43	32	f.	f.	PROPN
ejpam-6745	43	33	yousef	yousef	PROPN
ejpam-6745	43	34	,	,	PUNCT
ejpam-6745	43	35	m.	m.	NOUN
ejpam-6745	43	36	m.	m.	PROPN
ejpam-6745	43	37	alholi	alholi	PROPN
ejpam-6745	43	38	,	,	PUNCT
ejpam-6745	43	39	t.	t.	PROPN
ejpam-6745	43	40	al	al	PROPN
ejpam-6745	43	41	-	-	PUNCT
ejpam-6745	43	42	hawary	hawary	PROPN
ejpam-6745	43	43	/	/	SYM
ejpam-6745	43	44	eur	eur	PROPN
ejpam-6745	43	45	.	.	PUNCT
ejpam-6745	44	1	j.	j.	PROPN
ejpam-6745	44	2	pure	pure	PROPN
ejpam-6745	44	3	appl	appl	PROPN
ejpam-6745	44	4	.	.	PROPN
ejpam-6745	44	5	math	math	PROPN
ejpam-6745	44	6	,	,	PUNCT
ejpam-6745	44	7	18	18	NUM
ejpam-6745	44	8	(	(	PUNCT
ejpam-6745	44	9	4	4	NUM
ejpam-6745	44	10	)	)	PUNCT
ejpam-6745	44	11	(	(	PUNCT
ejpam-6745	44	12	2025	2025	NUM
ejpam-6745	44	13	)	)	PUNCT
ejpam-6745	44	14	,	,	PUNCT
ejpam-6745	44	15	6745	6745	NUM
ejpam-6745	44	16	3	3	NUM
ejpam-6745	44	17	of	of	ADP
ejpam-6745	44	18	13	13	NUM
ejpam-6745	44	19	are	be	AUX
ejpam-6745	44	20	used	use	VERB
ejpam-6745	44	21	in	in	ADP
ejpam-6745	44	22	a	a	DET
ejpam-6745	44	23	wide	wide	ADJ
ejpam-6745	44	24	variety	variety	NOUN
ejpam-6745	44	25	of	of	ADP
ejpam-6745	44	26	problems	problem	NOUN
ejpam-6745	44	27	and	and	CCONJ
ejpam-6745	44	28	in	in	ADP
ejpam-6745	44	29	other	other	ADJ
ejpam-6745	44	30	areas	area	NOUN
ejpam-6745	44	31	of	of	ADP
ejpam-6745	44	32	mathematics	mathematic	NOUN
ejpam-6745	44	33	and	and	CCONJ
ejpam-6745	44	34	the	the	DET
ejpam-6745	44	35	applied	apply	VERB
ejpam-6745	44	36	sciences	science	NOUN
ejpam-6745	44	37	,	,	PUNCT
ejpam-6745	44	38	see	see	VERB
ejpam-6745	44	39	[	[	X
ejpam-6745	44	40	12–23	12–23	NUM
ejpam-6745	44	41	]	]	PUNCT
ejpam-6745	44	42	.	.	PUNCT
ejpam-6745	45	1	the	the	DET
ejpam-6745	45	2	error	error	NOUN
ejpam-6745	45	3	function	function	NOUN
ejpam-6745	45	4	erq	erq	NOUN
ejpam-6745	45	5	defined	define	VERB
ejpam-6745	45	6	by	by	ADP
ejpam-6745	45	7	abramowitz	abramowitz	NOUN
ejpam-6745	45	8	and	and	CCONJ
ejpam-6745	45	9	stegun	stegun	PRON
ejpam-6745	45	10	[	[	X
ejpam-6745	45	11	24	24	NUM
ejpam-6745	45	12	]	]	PUNCT
ejpam-6745	45	13	as	as	ADP
ejpam-6745	45	14	:	:	PUNCT
ejpam-6745	45	15	erq	erq	NOUN
ejpam-6745	45	16	(	(	PUNCT
ejpam-6745	45	17	z	z	NOUN
ejpam-6745	45	18	)	)	PUNCT
ejpam-6745	45	19	=	=	SYM
ejpam-6745	46	1	2√	2√	PROPN
ejpam-6745	46	2	π	π	X
ejpam-6745	46	3	∫	∫	PROPN
ejpam-6745	46	4	z	z	NOUN
ejpam-6745	46	5	0	0	NUM
ejpam-6745	46	6	e−t2dt	e−t2dt	NOUN
ejpam-6745	46	7	=	=	SYM
ejpam-6745	46	8	2√	2√	PROPN
ejpam-6745	46	9	π	π	NOUN
ejpam-6745	46	10	∞∑	∞∑	NUM
ejpam-6745	46	11	ϵ=0	ϵ=0	PUNCT
ejpam-6745	46	12	(	(	PUNCT
ejpam-6745	46	13	−1)ϵ	−1)ϵ	PROPN
ejpam-6745	46	14	z2ϵ+1	z2ϵ+1	INTJ
ejpam-6745	46	15	(	(	PUNCT
ejpam-6745	46	16	2ϵ+	2ϵ+	NUM
ejpam-6745	46	17	1	1	NUM
ejpam-6745	46	18	)	)	PUNCT
ejpam-6745	46	19	ϵ	ϵ	NOUN
ejpam-6745	46	20	!	!	PUNCT
ejpam-6745	46	21	,	,	PUNCT
ejpam-6745	46	22	(	(	PUNCT
ejpam-6745	46	23	z	z	NOUN
ejpam-6745	46	24	∈	∈	PROPN
ejpam-6745	46	25	c	c	NOUN
ejpam-6745	46	26	)	)	PUNCT
ejpam-6745	46	27	,	,	PUNCT
ejpam-6745	46	28	(	(	PUNCT
ejpam-6745	46	29	3	3	X
ejpam-6745	46	30	)	)	PUNCT
ejpam-6745	46	31	whereas	whereas	SCONJ
ejpam-6745	46	32	the	the	DET
ejpam-6745	46	33	imaginary	imaginary	ADJ
ejpam-6745	46	34	error	error	NOUN
ejpam-6745	46	35	function	function	NOUN
ejpam-6745	46	36	erqi	erqi	NOUN
ejpam-6745	46	37	(	(	PUNCT
ejpam-6745	46	38	z	z	NOUN
ejpam-6745	46	39	)	)	PUNCT
ejpam-6745	46	40	=	=	SYM
ejpam-6745	47	1	2√	2√	PROPN
ejpam-6745	47	2	π	π	X
ejpam-6745	47	3	∫	∫	PROPN
ejpam-6745	47	4	z	z	NOUN
ejpam-6745	47	5	0	0	NUM
ejpam-6745	47	6	et	et	NOUN
ejpam-6745	47	7	2	2	NUM
ejpam-6745	47	8	dt	dt	NOUN
ejpam-6745	47	9	=	=	SYM
ejpam-6745	47	10	2√	2√	PROPN
ejpam-6745	47	11	π	π	NOUN
ejpam-6745	47	12	∞∑	∞∑	NUM
ejpam-6745	47	13	ϵ=0	ϵ=0	PUNCT
ejpam-6745	47	14	z2ϵ+1	z2ϵ+1	PROPN
ejpam-6745	47	15	(	(	PUNCT
ejpam-6745	47	16	2ϵ+	2ϵ+	NUM
ejpam-6745	47	17	1	1	NUM
ejpam-6745	47	18	)	)	PUNCT
ejpam-6745	47	19	ϵ	ϵ	NOUN
ejpam-6745	47	20	!	!	PUNCT
ejpam-6745	47	21	,	,	PUNCT
ejpam-6745	47	22	(	(	PUNCT
ejpam-6745	47	23	z	z	NOUN
ejpam-6745	47	24	∈	∈	PROPN
ejpam-6745	47	25	c	c	NOUN
ejpam-6745	47	26	)	)	PUNCT
ejpam-6745	47	27	.	.	PUNCT
ejpam-6745	48	1	(	(	PUNCT
ejpam-6745	48	2	4	4	X
ejpam-6745	48	3	)	)	PUNCT
ejpam-6745	48	4	the	the	DET
ejpam-6745	48	5	error	error	NOUN
ejpam-6745	48	6	function	function	NOUN
ejpam-6745	48	7	is	be	AUX
ejpam-6745	48	8	widely	widely	ADV
ejpam-6745	48	9	used	use	VERB
ejpam-6745	48	10	in	in	ADP
ejpam-6745	48	11	statistics	statistic	NOUN
ejpam-6745	48	12	,	,	PUNCT
ejpam-6745	48	13	probability	probability	NOUN
ejpam-6745	48	14	theory	theory	NOUN
ejpam-6745	48	15	,	,	PUNCT
ejpam-6745	48	16	applied	applied	ADJ
ejpam-6745	48	17	mathematics	mathematic	NOUN
ejpam-6745	48	18	,	,	PUNCT
ejpam-6745	48	19	and	and	CCONJ
ejpam-6745	48	20	the	the	DET
ejpam-6745	48	21	physics	physics	NOUN
ejpam-6745	48	22	of	of	ADP
ejpam-6745	48	23	partial	partial	ADJ
ejpam-6745	48	24	differential	differential	NOUN
ejpam-6745	48	25	equations	equation	NOUN
ejpam-6745	48	26	.	.	PUNCT
ejpam-6745	49	1	in	in	ADP
ejpam-6745	49	2	quantum	quantum	ADJ
ejpam-6745	49	3	physics	physics	NOUN
ejpam-6745	49	4	,	,	PUNCT
ejpam-6745	49	5	the	the	DET
ejpam-6745	49	6	error	error	NOUN
ejpam-6745	49	7	function	function	NOUN
ejpam-6745	49	8	is	be	AUX
ejpam-6745	49	9	an	an	DET
ejpam-6745	49	10	essential	essential	ADJ
ejpam-6745	49	11	tool	tool	NOUN
ejpam-6745	49	12	for	for	ADP
ejpam-6745	49	13	calculating	calculate	VERB
ejpam-6745	49	14	the	the	DET
ejpam-6745	49	15	probability	probability	NOUN
ejpam-6745	49	16	of	of	ADP
ejpam-6745	49	17	observing	observe	VERB
ejpam-6745	49	18	a	a	DET
ejpam-6745	49	19	particle	particle	NOUN
ejpam-6745	49	20	in	in	ADP
ejpam-6745	49	21	a	a	DET
ejpam-6745	49	22	specific	specific	ADJ
ejpam-6745	49	23	location	location	NOUN
ejpam-6745	49	24	.	.	PUNCT
ejpam-6745	50	1	while	while	SCONJ
ejpam-6745	50	2	alzer	alzer	NOUN
ejpam-6745	50	3	[	[	X
ejpam-6745	50	4	25	25	NUM
ejpam-6745	50	5	]	]	PUNCT
ejpam-6745	50	6	and	and	CCONJ
ejpam-6745	50	7	coman	coman	PROPN
ejpam-6745	51	1	[	[	X
ejpam-6745	51	2	26	26	NUM
ejpam-6745	51	3	]	]	PUNCT
ejpam-6745	51	4	demonstrated	demonstrate	VERB
ejpam-6745	51	5	numerous	numerous	ADJ
ejpam-6745	51	6	features	feature	NOUN
ejpam-6745	51	7	and	and	CCONJ
ejpam-6745	51	8	inequalities	inequality	NOUN
ejpam-6745	51	9	of	of	ADP
ejpam-6745	51	10	the	the	DET
ejpam-6745	51	11	error	error	NOUN
ejpam-6745	51	12	function	function	NOUN
ejpam-6745	51	13	,	,	PUNCT
ejpam-6745	51	14	elbert	elbert	NOUN
ejpam-6745	51	15	et	et	PROPN
ejpam-6745	51	16	al	al	PROPN
ejpam-6745	51	17	.	.	PUNCT
ejpam-6745	52	1	[	[	X
ejpam-6745	52	2	27	27	NUM
ejpam-6745	52	3	]	]	PUNCT
ejpam-6745	52	4	examined	examine	VERB
ejpam-6745	52	5	the	the	DET
ejpam-6745	52	6	characteristics	characteristic	NOUN
ejpam-6745	52	7	of	of	ADP
ejpam-6745	52	8	the	the	DET
ejpam-6745	52	9	complementary	complementary	ADJ
ejpam-6745	52	10	error	error	NOUN
ejpam-6745	52	11	function	function	NOUN
ejpam-6745	52	12	.	.	PUNCT
ejpam-6745	53	1	figure	figure	NOUN
ejpam-6745	53	2	1	1	NUM
ejpam-6745	53	3	below	below	ADV
ejpam-6745	53	4	illustrates	illustrate	VERB
ejpam-6745	53	5	the	the	DET
ejpam-6745	53	6	behavior	behavior	NOUN
ejpam-6745	53	7	of	of	ADP
ejpam-6745	53	8	the	the	DET
ejpam-6745	53	9	real	real	ADJ
ejpam-6745	53	10	and	and	CCONJ
ejpam-6745	53	11	imaginary	imaginary	ADJ
ejpam-6745	53	12	parts	part	NOUN
ejpam-6745	53	13	of	of	ADP
ejpam-6745	53	14	erq	erq	NOUN
ejpam-6745	53	15	(	(	PUNCT
ejpam-6745	53	16	z	z	NOUN
ejpam-6745	53	17	)	)	PUNCT
ejpam-6745	53	18	in	in	ADP
ejpam-6745	53	19	the	the	DET
ejpam-6745	53	20	complex	complex	ADJ
ejpam-6745	53	21	plane	plane	NOUN
ejpam-6745	53	22	.	.	PUNCT
ejpam-6745	54	1	it	it	PRON
ejpam-6745	54	2	reveals	reveal	VERB
ejpam-6745	54	3	rich	rich	ADJ
ejpam-6745	54	4	geometric	geometric	ADJ
ejpam-6745	54	5	structure	structure	NOUN
ejpam-6745	54	6	,	,	PUNCT
ejpam-6745	54	7	including	include	VERB
ejpam-6745	54	8	symmetry	symmetry	NOUN
ejpam-6745	54	9	and	and	CCONJ
ejpam-6745	54	10	curvature	curvature	NOUN
ejpam-6745	54	11	,	,	PUNCT
ejpam-6745	54	12	which	which	PRON
ejpam-6745	54	13	motivates	motivate	VERB
ejpam-6745	54	14	its	its	PRON
ejpam-6745	54	15	role	role	NOUN
ejpam-6745	54	16	in	in	ADP
ejpam-6745	54	17	the	the	DET
ejpam-6745	54	18	geometric	geometric	ADJ
ejpam-6745	54	19	characterization	characterization	NOUN
ejpam-6745	54	20	of	of	ADP
ejpam-6745	54	21	subclasses	subclass	NOUN
ejpam-6745	54	22	of	of	ADP
ejpam-6745	54	23	analytic	analytic	ADJ
ejpam-6745	54	24	functions	function	NOUN
ejpam-6745	54	25	.	.	PUNCT
ejpam-6745	55	1	figure	figure	VERB
ejpam-6745	55	2	1	1	NUM
ejpam-6745	55	3	:	:	PUNCT
ejpam-6745	55	4	real	real	ADJ
ejpam-6745	55	5	(	(	PUNCT
ejpam-6745	55	6	left	left	ADJ
ejpam-6745	55	7	)	)	PUNCT
ejpam-6745	55	8	and	and	CCONJ
ejpam-6745	55	9	imaginary	imaginary	ADJ
ejpam-6745	55	10	(	(	PUNCT
ejpam-6745	55	11	right	right	ADJ
ejpam-6745	55	12	)	)	PUNCT
ejpam-6745	55	13	parts	part	NOUN
ejpam-6745	55	14	of	of	ADP
ejpam-6745	55	15	the	the	DET
ejpam-6745	55	16	error	error	NOUN
ejpam-6745	55	17	function	function	NOUN
ejpam-6745	55	18	erq	erq	NOUN
ejpam-6745	55	19	(	(	PUNCT
ejpam-6745	55	20	z	z	NOUN
ejpam-6745	55	21	)	)	PUNCT
ejpam-6745	55	22	over	over	ADP
ejpam-6745	55	23	the	the	DET
ejpam-6745	55	24	complex	complex	ADJ
ejpam-6745	55	25	plane	plane	NOUN
ejpam-6745	55	26	.	.	PUNCT
ejpam-6745	56	1	a	a	DET
ejpam-6745	56	2	generalization	generalization	NOUN
ejpam-6745	56	3	of	of	ADP
ejpam-6745	56	4	the	the	DET
ejpam-6745	56	5	error	error	NOUN
ejpam-6745	56	6	function	function	NOUN
ejpam-6745	56	7	given	give	VERB
ejpam-6745	56	8	by	by	ADP
ejpam-6745	56	9	(	(	PUNCT
ejpam-6745	56	10	3	3	X
ejpam-6745	56	11	)	)	PUNCT
ejpam-6745	56	12	is	be	AUX
ejpam-6745	56	13	defined	define	VERB
ejpam-6745	56	14	as	as	ADP
ejpam-6745	56	15	:	:	PUNCT
ejpam-6745	56	16	erqk	erqk	PROPN
ejpam-6745	56	17	(	(	PUNCT
ejpam-6745	56	18	z	z	NOUN
ejpam-6745	56	19	)	)	PUNCT
ejpam-6745	56	20	=	=	NOUN
ejpam-6745	57	1	k!√	k!√	NOUN
ejpam-6745	58	1	π	π	X
ejpam-6745	58	2	∫	∫	PROPN
ejpam-6745	58	3	z	z	NOUN
ejpam-6745	58	4	0	0	NUM
ejpam-6745	59	1	e−tkdt	e−tkdt	PROPN
ejpam-6745	59	2	,	,	PUNCT
ejpam-6745	59	3	k	k	PROPN
ejpam-6745	59	4	∈	∈	PROPN
ejpam-6745	59	5	n0=	n0=	PROPN
ejpam-6745	59	6	n∪{0	n∪{0	NOUN
ejpam-6745	59	7	}	}	PUNCT
ejpam-6745	59	8	=	=	PUNCT
ejpam-6745	59	9	k!√	k!√	NOUN
ejpam-6745	60	1	π	π	NOUN
ejpam-6745	60	2	∞∑	∞∑	NUM
ejpam-6745	60	3	ϵ=0	ϵ=0	PUNCT
ejpam-6745	60	4	(	(	PUNCT
ejpam-6745	60	5	−1)ϵ	−1)ϵ	NOUN
ejpam-6745	60	6	zkϵ+1	zkϵ+1	PROPN
ejpam-6745	60	7	(	(	PUNCT
ejpam-6745	60	8	kϵ+	kϵ+	NOUN
ejpam-6745	60	9	1	1	NUM
ejpam-6745	60	10	)	)	PUNCT
ejpam-6745	60	11	ϵ	ϵ	NOUN
ejpam-6745	60	12	!	!	PUNCT
ejpam-6745	60	13	,	,	PUNCT
ejpam-6745	60	14	(	(	PUNCT
ejpam-6745	60	15	z	z	NOUN
ejpam-6745	60	16	∈	∈	PROPN
ejpam-6745	60	17	c	c	NOUN
ejpam-6745	60	18	)	)	PUNCT
ejpam-6745	60	19	.	.	PUNCT
ejpam-6745	61	1	(	(	PUNCT
ejpam-6745	61	2	5	5	X
ejpam-6745	61	3	)	)	PUNCT
ejpam-6745	61	4	f.	f.	PROPN
ejpam-6745	61	5	yousef	yousef	PROPN
ejpam-6745	61	6	,	,	PUNCT
ejpam-6745	61	7	m.	m.	NOUN
ejpam-6745	61	8	m.	m.	PROPN
ejpam-6745	61	9	alholi	alholi	PROPN
ejpam-6745	61	10	,	,	PUNCT
ejpam-6745	61	11	t.	t.	PROPN
ejpam-6745	61	12	al	al	PROPN
ejpam-6745	61	13	-	-	PUNCT
ejpam-6745	61	14	hawary	hawary	PROPN
ejpam-6745	61	15	/	/	SYM
ejpam-6745	61	16	eur	eur	PROPN
ejpam-6745	61	17	.	.	PUNCT
ejpam-6745	62	1	j.	j.	PROPN
ejpam-6745	62	2	pure	pure	PROPN
ejpam-6745	62	3	appl	appl	PROPN
ejpam-6745	62	4	.	.	PROPN
ejpam-6745	62	5	math	math	PROPN
ejpam-6745	62	6	,	,	PUNCT
ejpam-6745	62	7	18	18	NUM
ejpam-6745	62	8	(	(	PUNCT
ejpam-6745	62	9	4	4	NUM
ejpam-6745	62	10	)	)	PUNCT
ejpam-6745	62	11	(	(	PUNCT
ejpam-6745	62	12	2025	2025	NUM
ejpam-6745	62	13	)	)	PUNCT
ejpam-6745	62	14	,	,	PUNCT
ejpam-6745	62	15	6745	6745	NUM
ejpam-6745	62	16	4	4	NUM
ejpam-6745	62	17	of	of	ADP
ejpam-6745	62	18	13	13	NUM
ejpam-6745	62	19	and	and	CCONJ
ejpam-6745	62	20	a	a	DET
ejpam-6745	62	21	generalization	generalization	NOUN
ejpam-6745	62	22	of	of	ADP
ejpam-6745	62	23	the	the	DET
ejpam-6745	62	24	imaginary	imaginary	ADJ
ejpam-6745	62	25	error	error	NOUN
ejpam-6745	62	26	function	function	NOUN
ejpam-6745	62	27	given	give	VERB
ejpam-6745	62	28	by	by	ADP
ejpam-6745	62	29	(	(	PUNCT
ejpam-6745	62	30	4	4	NUM
ejpam-6745	62	31	)	)	PUNCT
ejpam-6745	62	32	is	be	AUX
ejpam-6745	62	33	defined	define	VERB
ejpam-6745	62	34	by	by	ADP
ejpam-6745	62	35	erqik	erqik	NOUN
ejpam-6745	62	36	(	(	PUNCT
ejpam-6745	62	37	z	z	NOUN
ejpam-6745	62	38	)	)	PUNCT
ejpam-6745	62	39	=	=	NOUN
ejpam-6745	63	1	k!√	k!√	NOUN
ejpam-6745	64	1	π	π	X
ejpam-6745	64	2	∫	∫	PROPN
ejpam-6745	64	3	z	z	PROPN
ejpam-6745	64	4	0	0	NUM
ejpam-6745	64	5	et	et	NOUN
ejpam-6745	64	6	k	k	PROPN
ejpam-6745	64	7	dt	dt	PROPN
ejpam-6745	64	8	,	,	PUNCT
ejpam-6745	64	9	k	k	PROPN
ejpam-6745	64	10	∈	∈	PROPN
ejpam-6745	64	11	n0	n0	PROPN
ejpam-6745	64	12	=	=	PUNCT
ejpam-6745	64	13	k!√	k!√	NOUN
ejpam-6745	65	1	π	π	NOUN
ejpam-6745	66	1	∞∑	∞∑	NUM
ejpam-6745	66	2	ϵ=0	ϵ=0	X
ejpam-6745	66	3	zkϵ+1	zkϵ+1	PROPN
ejpam-6745	66	4	(	(	PUNCT
ejpam-6745	66	5	kϵ+	kϵ+	NOUN
ejpam-6745	66	6	1	1	NUM
ejpam-6745	66	7	)	)	PUNCT
ejpam-6745	66	8	ϵ	ϵ	NOUN
ejpam-6745	66	9	!	!	PUNCT
ejpam-6745	66	10	,	,	PUNCT
ejpam-6745	66	11	(	(	PUNCT
ejpam-6745	66	12	z	z	NOUN
ejpam-6745	66	13	∈	∈	PROPN
ejpam-6745	66	14	c	c	NOUN
ejpam-6745	66	15	)	)	PUNCT
ejpam-6745	66	16	.	.	PUNCT
ejpam-6745	67	1	(	(	PUNCT
ejpam-6745	67	2	6	6	NUM
ejpam-6745	67	3	)	)	PUNCT
ejpam-6745	67	4	from	from	ADP
ejpam-6745	67	5	(	(	PUNCT
ejpam-6745	67	6	5	5	NUM
ejpam-6745	67	7	)	)	PUNCT
ejpam-6745	67	8	and	and	CCONJ
ejpam-6745	67	9	(	(	PUNCT
ejpam-6745	67	10	6	6	NUM
ejpam-6745	67	11	)	)	PUNCT
ejpam-6745	67	12	,	,	PUNCT
ejpam-6745	67	13	we	we	PRON
ejpam-6745	67	14	get	get	VERB
ejpam-6745	67	15	erq0	erq0	ADJ
ejpam-6745	67	16	(	(	PUNCT
ejpam-6745	67	17	z	z	NOUN
ejpam-6745	67	18	)	)	PUNCT
ejpam-6745	67	19	=	=	PUNCT
ejpam-6745	67	20	z	z	X
ejpam-6745	67	21	e	e	NOUN
ejpam-6745	67	22	√	√	NUM
ejpam-6745	67	23	π	π	PROPN
ejpam-6745	67	24	,	,	PUNCT
ejpam-6745	67	25	erq1	erq1	PROPN
ejpam-6745	67	26	(	(	PUNCT
ejpam-6745	67	27	z	z	NOUN
ejpam-6745	67	28	)	)	PUNCT
ejpam-6745	67	29	=	=	SYM
ejpam-6745	67	30	1−	1−	NUM
ejpam-6745	67	31	ez√	ez√	PUNCT
ejpam-6745	68	1	π	π	NOUN
ejpam-6745	68	2	=	=	SYM
ejpam-6745	68	3	−erqi1	−erqi1	NUM
ejpam-6745	68	4	(	(	PUNCT
ejpam-6745	68	5	z	z	NOUN
ejpam-6745	68	6	)	)	PUNCT
ejpam-6745	68	7	,	,	PUNCT
ejpam-6745	68	8	erq2	erq2	NOUN
ejpam-6745	68	9	(	(	PUNCT
ejpam-6745	68	10	z	z	NOUN
ejpam-6745	68	11	)	)	PUNCT
ejpam-6745	68	12	=	=	SYM
ejpam-6745	68	13	erq	erq	NOUN
ejpam-6745	68	14	(	(	PUNCT
ejpam-6745	68	15	z	z	NOUN
ejpam-6745	68	16	)	)	PUNCT
ejpam-6745	68	17	and	and	CCONJ
ejpam-6745	68	18	erqi2	erqi2	NOUN
ejpam-6745	68	19	(	(	PUNCT
ejpam-6745	68	20	z	z	NOUN
ejpam-6745	68	21	)	)	PUNCT
ejpam-6745	68	22	=	=	VERB
ejpam-6745	68	23	erqi	erqi	NOUN
ejpam-6745	68	24	(	(	PUNCT
ejpam-6745	68	25	z	z	NOUN
ejpam-6745	68	26	)	)	PUNCT
ejpam-6745	68	27	.	.	PUNCT
ejpam-6745	69	1	the	the	DET
ejpam-6745	69	2	functions	function	NOUN
ejpam-6745	69	3	erqk	erqk	VERB
ejpam-6745	69	4	(	(	PUNCT
ejpam-6745	69	5	z	z	NOUN
ejpam-6745	69	6	)	)	PUNCT
ejpam-6745	69	7	and	and	CCONJ
ejpam-6745	69	8	erqik	erqik	NOUN
ejpam-6745	69	9	(	(	PUNCT
ejpam-6745	69	10	z	z	NOUN
ejpam-6745	69	11	)	)	PUNCT
ejpam-6745	69	12	are	be	AUX
ejpam-6745	69	13	not	not	PART
ejpam-6745	69	14	in	in	ADP
ejpam-6745	69	15	the	the	DET
ejpam-6745	69	16	class	class	NOUN
ejpam-6745	69	17	e	e	NOUN
ejpam-6745	69	18	.	.	PUNCT
ejpam-6745	70	1	therefore	therefore	ADV
ejpam-6745	70	2	,	,	PUNCT
ejpam-6745	70	3	we	we	PRON
ejpam-6745	70	4	will	will	AUX
ejpam-6745	70	5	consider	consider	VERB
ejpam-6745	70	6	the	the	DET
ejpam-6745	70	7	following	follow	VERB
ejpam-6745	70	8	functions	function	NOUN
ejpam-6745	70	9	given	give	VERB
ejpam-6745	70	10	by	by	ADP
ejpam-6745	70	11	al	al	PROPN
ejpam-6745	70	12	-	-	PUNCT
ejpam-6745	70	13	hawary	hawary	PROPN
ejpam-6745	70	14	et	et	PROPN
ejpam-6745	70	15	al	al	PROPN
ejpam-6745	70	16	.	.	PUNCT
ejpam-6745	71	1	[	[	X
ejpam-6745	71	2	28	28	NUM
ejpam-6745	71	3	]	]	PUNCT
ejpam-6745	71	4	.	.	PUNCT
ejpam-6745	72	1	εk	εk	PROPN
ejpam-6745	72	2	(	(	PUNCT
ejpam-6745	72	3	z	z	NOUN
ejpam-6745	72	4	)	)	PUNCT
ejpam-6745	72	5	=	=	PUNCT
ejpam-6745	73	1	√	√	PROPN
ejpam-6745	73	2	π	π	PROPN
ejpam-6745	73	3	k	k	X
ejpam-6745	73	4	!	!	PUNCT
ejpam-6745	73	5	z	z	NOUN
ejpam-6745	74	1	(	(	PUNCT
ejpam-6745	74	2	1−	1−	NUM
ejpam-6745	74	3	1	1	NUM
ejpam-6745	74	4	k	k	NOUN
ejpam-6745	74	5	)	)	PUNCT
ejpam-6745	75	1	k	k	PROPN
ejpam-6745	75	2	erqk	erqk	PROPN
ejpam-6745	75	3	(	(	PUNCT
ejpam-6745	75	4	z1	z1	PROPN
ejpam-6745	75	5	/	/	SYM
ejpam-6745	75	6	k	k	NOUN
ejpam-6745	75	7	)	)	PUNCT
ejpam-6745	76	1	=	=	PUNCT
ejpam-6745	76	2	z	z	NOUN
ejpam-6745	77	1	+	+	NOUN
ejpam-6745	77	2	∞∑	∞∑	NUM
ejpam-6745	77	3	ϵ=2	ϵ=2	PROPN
ejpam-6745	77	4	(	(	PUNCT
ejpam-6745	77	5	−1)ϵ−1	−1)ϵ−1	PROPN
ejpam-6745	77	6	(	(	PUNCT
ejpam-6745	77	7	(	(	PUNCT
ejpam-6745	77	8	ϵ−	ϵ−	NOUN
ejpam-6745	77	9	1	1	X
ejpam-6745	77	10	)	)	PUNCT
ejpam-6745	77	11	k	k	NOUN
ejpam-6745	78	1	+	+	NOUN
ejpam-6745	78	2	1	1	X
ejpam-6745	78	3	)	)	PUNCT
ejpam-6745	78	4	(	(	PUNCT
ejpam-6745	78	5	ϵ−	ϵ−	NOUN
ejpam-6745	78	6	1	1	NUM
ejpam-6745	78	7	)	)	PUNCT
ejpam-6745	78	8	!	!	PUNCT
ejpam-6745	79	1	zϵ	zϵ	PROPN
ejpam-6745	79	2	,	,	PUNCT
ejpam-6745	79	3	(	(	PUNCT
ejpam-6745	79	4	k	k	PROPN
ejpam-6745	79	5	∈	∈	PROPN
ejpam-6745	79	6	n	n	CCONJ
ejpam-6745	79	7	)	)	PUNCT
ejpam-6745	79	8	,	,	PUNCT
ejpam-6745	79	9	(	(	PUNCT
ejpam-6745	79	10	7	7	X
ejpam-6745	79	11	)	)	PUNCT
ejpam-6745	79	12	and	and	CCONJ
ejpam-6745	79	13	εik	εik	ADV
ejpam-6745	79	14	(	(	PUNCT
ejpam-6745	79	15	z	z	NOUN
ejpam-6745	79	16	)	)	PUNCT
ejpam-6745	79	17	=	=	PUNCT
ejpam-6745	80	1	√	√	PROPN
ejpam-6745	80	2	π	π	PROPN
ejpam-6745	80	3	k	k	X
ejpam-6745	80	4	!	!	PUNCT
ejpam-6745	80	5	z(1−	z(1−	PROPN
ejpam-6745	80	6	1	1	NUM
ejpam-6745	80	7	k	k	X
ejpam-6745	80	8	)	)	PUNCT
ejpam-6745	80	9	erqik	erqik	NOUN
ejpam-6745	80	10	(	(	PUNCT
ejpam-6745	80	11	z1	z1	PROPN
ejpam-6745	80	12	/	/	SYM
ejpam-6745	80	13	k	k	NOUN
ejpam-6745	80	14	)	)	PUNCT
ejpam-6745	81	1	=	=	PUNCT
ejpam-6745	81	2	z	z	NOUN
ejpam-6745	82	1	+	+	NOUN
ejpam-6745	82	2	∞∑	∞∑	NUM
ejpam-6745	82	3	ϵ=2	ϵ=2	PROPN
ejpam-6745	82	4	1	1	NUM
ejpam-6745	82	5	(	(	PUNCT
ejpam-6745	82	6	(	(	PUNCT
ejpam-6745	82	7	ϵ−	ϵ−	NOUN
ejpam-6745	82	8	1	1	X
ejpam-6745	82	9	)	)	PUNCT
ejpam-6745	82	10	k	k	NOUN
ejpam-6745	83	1	+	+	NOUN
ejpam-6745	83	2	1	1	X
ejpam-6745	83	3	)	)	PUNCT
ejpam-6745	83	4	(	(	PUNCT
ejpam-6745	83	5	ϵ−	ϵ−	NOUN
ejpam-6745	83	6	1	1	NUM
ejpam-6745	83	7	)	)	PUNCT
ejpam-6745	83	8	!	!	PUNCT
ejpam-6745	84	1	zϵ	zϵ	PROPN
ejpam-6745	84	2	,	,	PUNCT
ejpam-6745	84	3	(	(	PUNCT
ejpam-6745	84	4	k	k	PROPN
ejpam-6745	84	5	∈	∈	PROPN
ejpam-6745	84	6	n	n	CCONJ
ejpam-6745	84	7	)	)	PUNCT
ejpam-6745	84	8	.	.	PUNCT
ejpam-6745	85	1	(	(	PUNCT
ejpam-6745	85	2	8)	8)	NUM
ejpam-6745	85	3	from	from	ADP
ejpam-6745	85	4	(	(	PUNCT
ejpam-6745	85	5	7	7	NUM
ejpam-6745	85	6	)	)	PUNCT
ejpam-6745	85	7	and	and	CCONJ
ejpam-6745	85	8	(	(	PUNCT
ejpam-6745	85	9	8)	8)	NUM
ejpam-6745	85	10	,	,	PUNCT
ejpam-6745	85	11	we	we	PRON
ejpam-6745	85	12	get	get	VERB
ejpam-6745	85	13	ε1	ε1	VERB
ejpam-6745	85	14	(	(	PUNCT
ejpam-6745	85	15	z	z	NOUN
ejpam-6745	85	16	)	)	PUNCT
ejpam-6745	85	17	=	=	SYM
ejpam-6745	86	1	√	√	NUM
ejpam-6745	86	2	πerq1	πerq1	NOUN
ejpam-6745	87	1	(	(	PUNCT
ejpam-6745	87	2	z	z	X
ejpam-6745	87	3	)	)	PUNCT
ejpam-6745	87	4	=	=	SYM
ejpam-6745	87	5	1−	1−	NUM
ejpam-6745	87	6	ez	ez	PROPN
ejpam-6745	87	7	,	,	PUNCT
ejpam-6745	87	8	εi1	εi1	PROPN
ejpam-6745	87	9	(	(	PUNCT
ejpam-6745	87	10	z	z	NOUN
ejpam-6745	87	11	)	)	PUNCT
ejpam-6745	87	12	=	=	SYM
ejpam-6745	88	1	√	√	NUM
ejpam-6745	88	2	πerqi1	πerqi1	NOUN
ejpam-6745	88	3	(	(	PUNCT
ejpam-6745	88	4	z	z	NOUN
ejpam-6745	88	5	)	)	PUNCT
ejpam-6745	88	6	=	=	SYM
ejpam-6745	88	7	ez	ez	PROPN
ejpam-6745	89	1	−	−	PROPN
ejpam-6745	89	2	1	1	NUM
ejpam-6745	89	3	and	and	CCONJ
ejpam-6745	89	4	ε2	ε2	ADJ
ejpam-6745	89	5	(	(	PUNCT
ejpam-6745	89	6	z	z	NOUN
ejpam-6745	89	7	)	)	PUNCT
ejpam-6745	89	8	=	=	PUNCT
ejpam-6745	90	1	√	√	NUM
ejpam-6745	90	2	πz	πz	PRON
ejpam-6745	90	3	2	2	NUM
ejpam-6745	90	4	erq2	erq2	NOUN
ejpam-6745	90	5	(	(	PUNCT
ejpam-6745	90	6	√	√	PROPN
ejpam-6745	90	7	z	z	NOUN
ejpam-6745	90	8	)	)	PUNCT
ejpam-6745	90	9	and	and	CCONJ
ejpam-6745	90	10	εi1	εi1	NOUN
ejpam-6745	90	11	(	(	PUNCT
ejpam-6745	90	12	z	z	NOUN
ejpam-6745	90	13	)	)	PUNCT
ejpam-6745	90	14	=	=	PUNCT
ejpam-6745	91	1	√	√	NUM
ejpam-6745	91	2	πz	πz	PRON
ejpam-6745	91	3	2	2	NUM
ejpam-6745	91	4	erqi2	erqi2	NOUN
ejpam-6745	91	5	(	(	PUNCT
ejpam-6745	91	6	√	√	PROPN
ejpam-6745	91	7	z	z	NOUN
ejpam-6745	91	8	)	)	PUNCT
ejpam-6745	91	9	.	.	PUNCT
ejpam-6745	92	1	let	let	VERB
ejpam-6745	92	2	the	the	DET
ejpam-6745	92	3	function	function	NOUN
ejpam-6745	92	4	υik	υik	NOUN
ejpam-6745	92	5	(	(	PUNCT
ejpam-6745	92	6	z	z	NOUN
ejpam-6745	92	7	)	)	PUNCT
ejpam-6745	92	8	be	be	AUX
ejpam-6745	92	9	defined	define	VERB
ejpam-6745	92	10	as	as	ADP
ejpam-6745	92	11	:	:	PUNCT
ejpam-6745	92	12	υik	υik	ADJ
ejpam-6745	92	13	(	(	PUNCT
ejpam-6745	92	14	z	z	NOUN
ejpam-6745	92	15	)	)	PUNCT
ejpam-6745	92	16	=	=	SYM
ejpam-6745	93	1	2z	2z	NOUN
ejpam-6745	94	1	−	−	PUNCT
ejpam-6745	94	2	εik	εik	INTJ
ejpam-6745	94	3	(	(	PUNCT
ejpam-6745	94	4	z	z	NOUN
ejpam-6745	94	5	)	)	PUNCT
ejpam-6745	94	6	=	=	PUNCT
ejpam-6745	95	1	z	z	NOUN
ejpam-6745	96	1	−	−	ADP
ejpam-6745	96	2	∞∑	∞∑	NUM
ejpam-6745	96	3	ϵ=2	ϵ=2	PROPN
ejpam-6745	96	4	1	1	NUM
ejpam-6745	96	5	(	(	PUNCT
ejpam-6745	96	6	(	(	PUNCT
ejpam-6745	96	7	ϵ−	ϵ−	NOUN
ejpam-6745	96	8	1	1	X
ejpam-6745	96	9	)	)	PUNCT
ejpam-6745	96	10	k	k	NOUN
ejpam-6745	97	1	+	+	NOUN
ejpam-6745	97	2	1	1	X
ejpam-6745	97	3	)	)	PUNCT
ejpam-6745	97	4	(	(	PUNCT
ejpam-6745	97	5	ϵ−	ϵ−	NOUN
ejpam-6745	97	6	1	1	NUM
ejpam-6745	97	7	)	)	PUNCT
ejpam-6745	97	8	!	!	PUNCT
ejpam-6745	98	1	zϵ	zϵ	PROPN
ejpam-6745	98	2	,	,	PUNCT
ejpam-6745	98	3	z	z	PROPN
ejpam-6745	98	4	∈	∈	PROPN
ejpam-6745	98	5	γ	γ	X
ejpam-6745	98	6	,	,	PUNCT
ejpam-6745	98	7	(	(	PUNCT
ejpam-6745	98	8	9	9	NUM
ejpam-6745	98	9	)	)	PUNCT
ejpam-6745	98	10	and	and	CCONJ
ejpam-6745	98	11	the	the	DET
ejpam-6745	98	12	linear	linear	ADJ
ejpam-6745	98	13	operator	operator	NOUN
ejpam-6745	98	14	iik	iik	VERB
ejpam-6745	98	15	:	:	PUNCT
ejpam-6745	98	16	e	e	X
ejpam-6745	98	17	→	→	SYM
ejpam-6745	98	18	e	e	NOUN
ejpam-6745	98	19	defined	define	VERB
ejpam-6745	98	20	as	as	ADP
ejpam-6745	98	21	:	:	PUNCT
ejpam-6745	98	22	iik(z	iik(z	PROPN
ejpam-6745	98	23	)	)	PUNCT
ejpam-6745	98	24	=	=	PUNCT
ejpam-6745	99	1	εik	εik	INTJ
ejpam-6745	99	2	(	(	PUNCT
ejpam-6745	99	3	z	z	NOUN
ejpam-6745	99	4	)	)	PUNCT
ejpam-6745	99	5	∗	∗	NOUN
ejpam-6745	99	6	q(z	q(z	PROPN
ejpam-6745	99	7	)	)	PUNCT
ejpam-6745	99	8	=	=	SYM
ejpam-6745	99	9	z	z	NOUN
ejpam-6745	100	1	+	+	NOUN
ejpam-6745	100	2	∞∑	∞∑	NUM
ejpam-6745	100	3	ϵ=2	ϵ=2	PROPN
ejpam-6745	100	4	1	1	NUM
ejpam-6745	100	5	(	(	PUNCT
ejpam-6745	100	6	(	(	PUNCT
ejpam-6745	100	7	ϵ−	ϵ−	NOUN
ejpam-6745	100	8	1	1	X
ejpam-6745	100	9	)	)	PUNCT
ejpam-6745	100	10	k	k	NOUN
ejpam-6745	101	1	+	+	NOUN
ejpam-6745	101	2	1	1	X
ejpam-6745	101	3	)	)	PUNCT
ejpam-6745	101	4	(	(	PUNCT
ejpam-6745	101	5	ϵ−	ϵ−	NOUN
ejpam-6745	101	6	1	1	NUM
ejpam-6745	101	7	)	)	PUNCT
ejpam-6745	101	8	!	!	PUNCT
ejpam-6745	102	1	βϵz	βϵz	PROPN
ejpam-6745	102	2	ϵ.	ϵ.	NOUN
ejpam-6745	102	3	(	(	PUNCT
ejpam-6745	102	4	10	10	NUM
ejpam-6745	102	5	)	)	PUNCT
ejpam-6745	102	6	inspired	inspire	VERB
ejpam-6745	102	7	by	by	ADP
ejpam-6745	102	8	the	the	DET
ejpam-6745	102	9	works	work	NOUN
ejpam-6745	102	10	of	of	ADP
ejpam-6745	102	11	several	several	ADJ
ejpam-6745	102	12	researchers	researcher	NOUN
ejpam-6745	102	13	who	who	PRON
ejpam-6745	102	14	have	have	AUX
ejpam-6745	102	15	employed	employ	VERB
ejpam-6745	102	16	a	a	DET
ejpam-6745	102	17	variety	variety	NOUN
ejpam-6745	102	18	of	of	ADP
ejpam-6745	102	19	special	special	ADJ
ejpam-6745	102	20	functions	function	NOUN
ejpam-6745	102	21	to	to	PART
ejpam-6745	102	22	identify	identify	VERB
ejpam-6745	102	23	certain	certain	ADJ
ejpam-6745	102	24	conditions	condition	NOUN
ejpam-6745	102	25	to	to	PART
ejpam-6745	102	26	belong	belong	VERB
ejpam-6745	102	27	to	to	ADP
ejpam-6745	102	28	subclasses	subclass	NOUN
ejpam-6745	102	29	of	of	ADP
ejpam-6745	102	30	analytic	analytic	ADJ
ejpam-6745	102	31	functions	function	NOUN
ejpam-6745	102	32	(	(	PUNCT
ejpam-6745	102	33	see	see	VERB
ejpam-6745	102	34	,	,	PUNCT
ejpam-6745	102	35	[	[	X
ejpam-6745	102	36	29–36	29–36	NUM
ejpam-6745	102	37	]	]	X
ejpam-6745	102	38	)	)	PUNCT
ejpam-6745	102	39	,	,	PUNCT
ejpam-6745	102	40	we	we	PRON
ejpam-6745	102	41	will	will	AUX
ejpam-6745	102	42	determine	determine	VERB
ejpam-6745	102	43	some	some	DET
ejpam-6745	102	44	conditions	condition	NOUN
ejpam-6745	102	45	for	for	ADP
ejpam-6745	102	46	the	the	DET
ejpam-6745	102	47	error	error	NOUN
ejpam-6745	102	48	functions	function	NOUN
ejpam-6745	102	49	υik	υik	VERB
ejpam-6745	102	50	(	(	PUNCT
ejpam-6745	102	51	z	z	NOUN
ejpam-6745	102	52	)	)	PUNCT
ejpam-6745	102	53	and	and	CCONJ
ejpam-6745	102	54	iik(z	iik(z	PRON
ejpam-6745	102	55	)	)	PUNCT
ejpam-6745	102	56	,	,	PUNCT
ejpam-6745	102	57	and	and	CCONJ
ejpam-6745	102	58	an	an	DET
ejpam-6745	102	59	integral	integral	ADJ
ejpam-6745	102	60	operator	operator	NOUN
ejpam-6745	102	61	to	to	PART
ejpam-6745	102	62	belong	belong	VERB
ejpam-6745	102	63	to	to	ADP
ejpam-6745	102	64	the	the	DET
ejpam-6745	102	65	subclasses	subclass	NOUN
ejpam-6745	102	66	spe(ϑ	spe(ϑ	PROPN
ejpam-6745	102	67	,	,	PUNCT
ejpam-6745	102	68	ζ	ζ	NOUN
ejpam-6745	102	69	)	)	PUNCT
ejpam-6745	102	70	and	and	CCONJ
ejpam-6745	102	71	cspe(ϑ	cspe(ϑ	PROPN
ejpam-6745	102	72	,	,	PUNCT
ejpam-6745	102	73	ζ	ζ	NOUN
ejpam-6745	102	74	)	)	PUNCT
ejpam-6745	102	75	.	.	PUNCT
ejpam-6745	103	1	the	the	DET
ejpam-6745	103	2	lemmas	lemmas	PROPN
ejpam-6745	103	3	listed	list	VERB
ejpam-6745	103	4	below	below	ADV
ejpam-6745	103	5	will	will	AUX
ejpam-6745	103	6	be	be	AUX
ejpam-6745	103	7	useful	useful	ADJ
ejpam-6745	103	8	in	in	ADP
ejpam-6745	103	9	deriving	derive	VERB
ejpam-6745	103	10	our	our	PRON
ejpam-6745	103	11	main	main	ADJ
ejpam-6745	103	12	findings	finding	NOUN
ejpam-6745	103	13	.	.	PUNCT
ejpam-6745	104	1	f.	f.	PROPN
ejpam-6745	104	2	yousef	yousef	PROPN
ejpam-6745	104	3	,	,	PUNCT
ejpam-6745	104	4	m.	m.	NOUN
ejpam-6745	104	5	m.	m.	PROPN
ejpam-6745	104	6	alholi	alholi	PROPN
ejpam-6745	104	7	,	,	PUNCT
ejpam-6745	104	8	t.	t.	PROPN
ejpam-6745	104	9	al	al	PROPN
ejpam-6745	104	10	-	-	PUNCT
ejpam-6745	104	11	hawary	hawary	PROPN
ejpam-6745	104	12	/	/	SYM
ejpam-6745	104	13	eur	eur	PROPN
ejpam-6745	104	14	.	.	PUNCT
ejpam-6745	105	1	j.	j.	PROPN
ejpam-6745	105	2	pure	pure	PROPN
ejpam-6745	105	3	appl	appl	PROPN
ejpam-6745	105	4	.	.	PROPN
ejpam-6745	105	5	math	math	PROPN
ejpam-6745	105	6	,	,	PUNCT
ejpam-6745	105	7	18	18	NUM
ejpam-6745	105	8	(	(	PUNCT
ejpam-6745	105	9	4	4	NUM
ejpam-6745	105	10	)	)	PUNCT
ejpam-6745	105	11	(	(	PUNCT
ejpam-6745	105	12	2025	2025	NUM
ejpam-6745	105	13	)	)	PUNCT
ejpam-6745	105	14	,	,	PUNCT
ejpam-6745	105	15	6745	6745	NUM
ejpam-6745	105	16	5	5	NUM
ejpam-6745	105	17	of	of	ADP
ejpam-6745	105	18	13	13	NUM
ejpam-6745	105	19	lemma	lemma	PROPN
ejpam-6745	105	20	1	1	NUM
ejpam-6745	105	21	.	.	PUNCT
ejpam-6745	106	1	(	(	PUNCT
ejpam-6745	106	2	see	see	VERB
ejpam-6745	106	3	[	[	X
ejpam-6745	106	4	1	1	NUM
ejpam-6745	106	5	]	]	NUM
ejpam-6745	106	6	)	)	PUNCT
ejpam-6745	106	7	(	(	PUNCT
ejpam-6745	106	8	i	i	NOUN
ejpam-6745	106	9	)	)	PUNCT
ejpam-6745	106	10	a	a	DET
ejpam-6745	106	11	sufficient	sufficient	ADJ
ejpam-6745	106	12	condition	condition	NOUN
ejpam-6745	106	13	for	for	ADP
ejpam-6745	106	14	a	a	DET
ejpam-6745	106	15	function	function	NOUN
ejpam-6745	106	16	q	q	NOUN
ejpam-6745	106	17	of	of	ADP
ejpam-6745	106	18	the	the	DET
ejpam-6745	106	19	form	form	NOUN
ejpam-6745	106	20	(	(	PUNCT
ejpam-6745	106	21	1	1	X
ejpam-6745	106	22	)	)	PUNCT
ejpam-6745	106	23	to	to	PART
ejpam-6745	106	24	be	be	AUX
ejpam-6745	106	25	in	in	ADP
ejpam-6745	106	26	the	the	DET
ejpam-6745	106	27	subclass	subclass	NOUN
ejpam-6745	106	28	sp(ϑ	sp(ϑ	NOUN
ejpam-6745	106	29	,	,	PUNCT
ejpam-6745	106	30	ζ	ζ	NOUN
ejpam-6745	106	31	)	)	PUNCT
ejpam-6745	106	32	is	be	AUX
ejpam-6745	106	33	∞∑	∞∑	NUM
ejpam-6745	106	34	ϵ=2	ϵ=2	PROPN
ejpam-6745	106	35	(	(	PUNCT
ejpam-6745	106	36	2ϵ−	2ϵ−	NUM
ejpam-6745	106	37	ζ	ζ	NOUN
ejpam-6745	106	38	−	−	PUNCT
ejpam-6745	106	39	cosϑ	cosϑ	ADJ
ejpam-6745	106	40	)	)	PUNCT
ejpam-6745	106	41	|βϵ|	|βϵ|	ADJ
ejpam-6745	106	42	≤	≤	PROPN
ejpam-6745	106	43	cosϑ−	cosϑ−	NOUN
ejpam-6745	106	44	ζ	ζ	PROPN
ejpam-6745	106	45	(	(	PUNCT
ejpam-6745	106	46	|ϑ|	|ϑ|	ADV
ejpam-6745	106	47	<	<	X
ejpam-6745	106	48	π/2	π/2	NUM
ejpam-6745	106	49	;	;	PUNCT
ejpam-6745	106	50	0	0	NUM
ejpam-6745	106	51	≤	≤	NUM
ejpam-6745	106	52	ζ	ζ	X
ejpam-6745	106	53	<	<	X
ejpam-6745	106	54	1	1	NUM
ejpam-6745	106	55	)	)	PUNCT
ejpam-6745	106	56	,	,	PUNCT
ejpam-6745	106	57	(	(	PUNCT
ejpam-6745	106	58	11	11	NUM
ejpam-6745	106	59	)	)	PUNCT
ejpam-6745	106	60	and	and	CCONJ
ejpam-6745	106	61	a	a	DET
ejpam-6745	106	62	necessary	necessary	ADJ
ejpam-6745	106	63	and	and	CCONJ
ejpam-6745	106	64	sufficient	sufficient	ADJ
ejpam-6745	106	65	condition	condition	NOUN
ejpam-6745	106	66	for	for	ADP
ejpam-6745	106	67	a	a	DET
ejpam-6745	106	68	function	function	NOUN
ejpam-6745	106	69	q	q	NOUN
ejpam-6745	106	70	of	of	ADP
ejpam-6745	106	71	the	the	DET
ejpam-6745	106	72	form	form	NOUN
ejpam-6745	106	73	(	(	PUNCT
ejpam-6745	106	74	2	2	NUM
ejpam-6745	106	75	)	)	PUNCT
ejpam-6745	106	76	to	to	PART
ejpam-6745	106	77	be	be	AUX
ejpam-6745	106	78	in	in	ADP
ejpam-6745	106	79	the	the	DET
ejpam-6745	106	80	subclass	subclass	NOUN
ejpam-6745	106	81	spe(ϑ	spe(ϑ	PROPN
ejpam-6745	106	82	,	,	PUNCT
ejpam-6745	106	83	ζ	ζ	NOUN
ejpam-6745	106	84	)	)	PUNCT
ejpam-6745	106	85	is	be	AUX
ejpam-6745	106	86	that	that	SCONJ
ejpam-6745	106	87	the	the	DET
ejpam-6745	106	88	condition	condition	NOUN
ejpam-6745	106	89	(	(	PUNCT
ejpam-6745	106	90	11	11	NUM
ejpam-6745	106	91	)	)	PUNCT
ejpam-6745	106	92	is	be	AUX
ejpam-6745	106	93	satisfied	satisfied	ADJ
ejpam-6745	106	94	.	.	PUNCT
ejpam-6745	107	1	in	in	ADP
ejpam-6745	107	2	particular	particular	ADJ
ejpam-6745	107	3	,	,	PUNCT
ejpam-6745	107	4	when	when	SCONJ
ejpam-6745	107	5	ζ	ζ	NOUN
ejpam-6745	107	6	=	=	SYM
ejpam-6745	107	7	0	0	NUM
ejpam-6745	107	8	,	,	PUNCT
ejpam-6745	107	9	we	we	PRON
ejpam-6745	107	10	obtain	obtain	VERB
ejpam-6745	107	11	a	a	DET
ejpam-6745	107	12	sufficient	sufficient	ADJ
ejpam-6745	107	13	condition	condition	NOUN
ejpam-6745	107	14	for	for	ADP
ejpam-6745	107	15	a	a	DET
ejpam-6745	107	16	function	function	NOUN
ejpam-6745	107	17	q	q	NOUN
ejpam-6745	107	18	of	of	ADP
ejpam-6745	107	19	the	the	DET
ejpam-6745	107	20	form	form	NOUN
ejpam-6745	107	21	(	(	PUNCT
ejpam-6745	107	22	1	1	X
ejpam-6745	107	23	)	)	PUNCT
ejpam-6745	107	24	to	to	PART
ejpam-6745	107	25	be	be	AUX
ejpam-6745	107	26	in	in	ADP
ejpam-6745	107	27	the	the	DET
ejpam-6745	107	28	subclass	subclass	NOUN
ejpam-6745	107	29	sp(ϑ	sp(ϑ	NOUN
ejpam-6745	107	30	)	)	PUNCT
ejpam-6745	107	31	is	be	AUX
ejpam-6745	107	32	∞∑	∞∑	NUM
ejpam-6745	107	33	ϵ=2	ϵ=2	PROPN
ejpam-6745	107	34	(	(	PUNCT
ejpam-6745	107	35	2ϵ−	2ϵ−	NUM
ejpam-6745	107	36	cosϑ	cosϑ	NOUN
ejpam-6745	107	37	)	)	PUNCT
ejpam-6745	107	38	|βϵ|	|βϵ|	ADJ
ejpam-6745	107	39	≤	≤	PROPN
ejpam-6745	107	40	cosϑ	cosϑ	VERB
ejpam-6745	107	41	(	(	PUNCT
ejpam-6745	107	42	|ϑ|	|ϑ|	ADV
ejpam-6745	107	43	<	<	X
ejpam-6745	107	44	π/2	π/2	NUM
ejpam-6745	107	45	)	)	PUNCT
ejpam-6745	107	46	,	,	PUNCT
ejpam-6745	107	47	(	(	PUNCT
ejpam-6745	107	48	12	12	NUM
ejpam-6745	107	49	)	)	PUNCT
ejpam-6745	107	50	and	and	CCONJ
ejpam-6745	107	51	a	a	DET
ejpam-6745	107	52	necessary	necessary	ADJ
ejpam-6745	107	53	and	and	CCONJ
ejpam-6745	107	54	sufficient	sufficient	ADJ
ejpam-6745	107	55	condition	condition	NOUN
ejpam-6745	107	56	for	for	ADP
ejpam-6745	107	57	a	a	DET
ejpam-6745	107	58	function	function	NOUN
ejpam-6745	107	59	q	q	NOUN
ejpam-6745	107	60	of	of	ADP
ejpam-6745	107	61	the	the	DET
ejpam-6745	107	62	form	form	NOUN
ejpam-6745	107	63	(	(	PUNCT
ejpam-6745	107	64	2	2	NUM
ejpam-6745	107	65	)	)	PUNCT
ejpam-6745	107	66	to	to	PART
ejpam-6745	107	67	be	be	AUX
ejpam-6745	107	68	in	in	ADP
ejpam-6745	107	69	the	the	DET
ejpam-6745	107	70	subclass	subclass	NOUN
ejpam-6745	107	71	spe(ϑ)is	spe(ϑ)is	NUM
ejpam-6745	107	72	that	that	SCONJ
ejpam-6745	107	73	the	the	DET
ejpam-6745	107	74	condition	condition	NOUN
ejpam-6745	107	75	(	(	PUNCT
ejpam-6745	107	76	12	12	NUM
ejpam-6745	107	77	)	)	PUNCT
ejpam-6745	107	78	is	be	AUX
ejpam-6745	107	79	satisfied	satisfied	ADJ
ejpam-6745	107	80	.	.	PUNCT
ejpam-6745	108	1	(	(	PUNCT
ejpam-6745	108	2	ii	ii	NOUN
ejpam-6745	108	3	)	)	PUNCT
ejpam-6745	108	4	a	a	DET
ejpam-6745	108	5	sufficient	sufficient	ADJ
ejpam-6745	108	6	condition	condition	NOUN
ejpam-6745	108	7	for	for	ADP
ejpam-6745	108	8	a	a	DET
ejpam-6745	108	9	function	function	NOUN
ejpam-6745	108	10	q	q	NOUN
ejpam-6745	108	11	of	of	ADP
ejpam-6745	108	12	the	the	DET
ejpam-6745	108	13	form	form	NOUN
ejpam-6745	108	14	(	(	PUNCT
ejpam-6745	108	15	1	1	X
ejpam-6745	108	16	)	)	PUNCT
ejpam-6745	108	17	to	to	PART
ejpam-6745	108	18	be	be	AUX
ejpam-6745	108	19	in	in	ADP
ejpam-6745	108	20	the	the	DET
ejpam-6745	108	21	subclass	subclass	NOUN
ejpam-6745	108	22	csp(ϑ	csp(ϑ	PROPN
ejpam-6745	108	23	,	,	PUNCT
ejpam-6745	108	24	ζ)is	ζ)is	PROPN
ejpam-6745	109	1	∞∑	∞∑	NUM
ejpam-6745	109	2	ϵ=2	ϵ=2	PROPN
ejpam-6745	109	3	ϵ(2ϵ−	ϵ(2ϵ−	PRON
ejpam-6745	109	4	ζ	ζ	NOUN
ejpam-6745	109	5	−	−	PROPN
ejpam-6745	109	6	cosϑ	cosϑ	ADJ
ejpam-6745	109	7	)	)	PUNCT
ejpam-6745	109	8	|βϵ|	|βϵ|	ADJ
ejpam-6745	109	9	≤	≤	PROPN
ejpam-6745	109	10	cosϑ−	cosϑ−	NOUN
ejpam-6745	109	11	ζ	ζ	PROPN
ejpam-6745	109	12	(	(	PUNCT
ejpam-6745	109	13	|ϑ|	|ϑ|	ADV
ejpam-6745	109	14	<	<	X
ejpam-6745	109	15	π/2	π/2	NUM
ejpam-6745	109	16	;	;	PUNCT
ejpam-6745	109	17	0	0	NUM
ejpam-6745	109	18	≤	≤	NUM
ejpam-6745	109	19	ζ	ζ	X
ejpam-6745	109	20	<	<	X
ejpam-6745	109	21	1	1	NUM
ejpam-6745	109	22	)	)	PUNCT
ejpam-6745	109	23	(	(	PUNCT
ejpam-6745	109	24	13	13	NUM
ejpam-6745	109	25	)	)	PUNCT
ejpam-6745	109	26	and	and	CCONJ
ejpam-6745	109	27	a	a	DET
ejpam-6745	109	28	necessary	necessary	ADJ
ejpam-6745	109	29	and	and	CCONJ
ejpam-6745	109	30	sufficient	sufficient	ADJ
ejpam-6745	109	31	condition	condition	NOUN
ejpam-6745	109	32	for	for	ADP
ejpam-6745	109	33	a	a	DET
ejpam-6745	109	34	function	function	NOUN
ejpam-6745	109	35	q	q	NOUN
ejpam-6745	109	36	of	of	ADP
ejpam-6745	109	37	the	the	DET
ejpam-6745	109	38	form	form	NOUN
ejpam-6745	109	39	(	(	PUNCT
ejpam-6745	109	40	2	2	NUM
ejpam-6745	109	41	)	)	PUNCT
ejpam-6745	109	42	to	to	PART
ejpam-6745	109	43	be	be	AUX
ejpam-6745	109	44	in	in	ADP
ejpam-6745	109	45	the	the	DET
ejpam-6745	109	46	subclass	subclass	NOUN
ejpam-6745	109	47	cspe(ϑ	cspe(ϑ	PROPN
ejpam-6745	109	48	,	,	PUNCT
ejpam-6745	109	49	ζ	ζ	NOUN
ejpam-6745	109	50	)	)	PUNCT
ejpam-6745	109	51	is	be	AUX
ejpam-6745	109	52	that	that	SCONJ
ejpam-6745	109	53	the	the	DET
ejpam-6745	109	54	condition	condition	NOUN
ejpam-6745	109	55	(	(	PUNCT
ejpam-6745	109	56	13	13	NUM
ejpam-6745	109	57	)	)	PUNCT
ejpam-6745	109	58	is	be	AUX
ejpam-6745	109	59	satisfied	satisfied	ADJ
ejpam-6745	109	60	.	.	PUNCT
ejpam-6745	110	1	in	in	ADP
ejpam-6745	110	2	particular	particular	ADJ
ejpam-6745	110	3	,	,	PUNCT
ejpam-6745	110	4	when	when	SCONJ
ejpam-6745	110	5	ζ	ζ	NOUN
ejpam-6745	110	6	=	=	SYM
ejpam-6745	110	7	0	0	NUM
ejpam-6745	110	8	,	,	PUNCT
ejpam-6745	110	9	we	we	PRON
ejpam-6745	110	10	obtain	obtain	VERB
ejpam-6745	110	11	a	a	DET
ejpam-6745	110	12	sufficient	sufficient	ADJ
ejpam-6745	110	13	condition	condition	NOUN
ejpam-6745	110	14	for	for	ADP
ejpam-6745	110	15	a	a	DET
ejpam-6745	110	16	function	function	NOUN
ejpam-6745	110	17	q	q	NOUN
ejpam-6745	110	18	of	of	ADP
ejpam-6745	110	19	the	the	DET
ejpam-6745	110	20	form	form	NOUN
ejpam-6745	110	21	(	(	PUNCT
ejpam-6745	110	22	1	1	X
ejpam-6745	110	23	)	)	PUNCT
ejpam-6745	110	24	to	to	PART
ejpam-6745	110	25	be	be	AUX
ejpam-6745	110	26	in	in	ADP
ejpam-6745	110	27	the	the	DET
ejpam-6745	110	28	subclass	subclass	NOUN
ejpam-6745	110	29	csp(ϑ	csp(ϑ	PROPN
ejpam-6745	110	30	)	)	PUNCT
ejpam-6745	110	31	is	be	AUX
ejpam-6745	110	32	that	that	SCONJ
ejpam-6745	110	33	∞∑	∞∑	NUM
ejpam-6745	110	34	ϵ=2	ϵ=2	PROPN
ejpam-6745	110	35	ϵ(2ϵ−	ϵ(2ϵ−	PROPN
ejpam-6745	110	36	cosϑ	cosϑ	X
ejpam-6745	110	37	)	)	PUNCT
ejpam-6745	110	38	|βϵ|	|βϵ|	ADJ
ejpam-6745	110	39	≤	≤	PROPN
ejpam-6745	110	40	cosϑ	cosϑ	VERB
ejpam-6745	110	41	(	(	PUNCT
ejpam-6745	110	42	|ϑ|	|ϑ|	ADV
ejpam-6745	110	43	<	<	X
ejpam-6745	110	44	π/2	π/2	NUM
ejpam-6745	110	45	)	)	PUNCT
ejpam-6745	110	46	(	(	PUNCT
ejpam-6745	110	47	14	14	NUM
ejpam-6745	110	48	)	)	PUNCT
ejpam-6745	110	49	and	and	CCONJ
ejpam-6745	110	50	a	a	DET
ejpam-6745	110	51	necessary	necessary	ADJ
ejpam-6745	110	52	and	and	CCONJ
ejpam-6745	110	53	sufficient	sufficient	ADJ
ejpam-6745	110	54	condition	condition	NOUN
ejpam-6745	110	55	for	for	ADP
ejpam-6745	110	56	a	a	DET
ejpam-6745	110	57	function	function	NOUN
ejpam-6745	110	58	q	q	NOUN
ejpam-6745	110	59	of	of	ADP
ejpam-6745	110	60	the	the	DET
ejpam-6745	110	61	form	form	NOUN
ejpam-6745	110	62	(	(	PUNCT
ejpam-6745	110	63	2	2	NUM
ejpam-6745	110	64	)	)	PUNCT
ejpam-6745	110	65	to	to	PART
ejpam-6745	110	66	be	be	AUX
ejpam-6745	110	67	in	in	ADP
ejpam-6745	110	68	the	the	DET
ejpam-6745	110	69	subclass	subclass	ADJ
ejpam-6745	110	70	cspe(ϑ)is	cspe(ϑ)is	NOUN
ejpam-6745	110	71	that	that	SCONJ
ejpam-6745	110	72	the	the	DET
ejpam-6745	110	73	condition	condition	NOUN
ejpam-6745	110	74	(	(	PUNCT
ejpam-6745	110	75	14	14	NUM
ejpam-6745	110	76	)	)	PUNCT
ejpam-6745	110	77	is	be	AUX
ejpam-6745	110	78	satisfied	satisfied	ADJ
ejpam-6745	110	79	.	.	PUNCT
ejpam-6745	111	1	lemma	lemma	PROPN
ejpam-6745	111	2	2	2	NUM
ejpam-6745	111	3	.	.	PUNCT
ejpam-6745	112	1	[	[	X
ejpam-6745	112	2	10	10	NUM
ejpam-6745	112	3	]	]	X
ejpam-6745	112	4	if	if	SCONJ
ejpam-6745	112	5	q	q	PROPN
ejpam-6745	112	6	of	of	ADP
ejpam-6745	112	7	the	the	DET
ejpam-6745	112	8	form	form	NOUN
ejpam-6745	112	9	(	(	PUNCT
ejpam-6745	112	10	1	1	NUM
ejpam-6745	112	11	)	)	PUNCT
ejpam-6745	112	12	and	and	CCONJ
ejpam-6745	112	13	q	q	ADJ
ejpam-6745	112	14	∈	∈	PROPN
ejpam-6745	112	15	gτ	gτ	PROPN
ejpam-6745	112	16	(	(	PUNCT
ejpam-6745	112	17	c1	c1	PROPN
ejpam-6745	112	18	,	,	PUNCT
ejpam-6745	112	19	c2	c2	PROPN
ejpam-6745	112	20	)	)	PUNCT
ejpam-6745	112	21	,	,	PUNCT
ejpam-6745	112	22	then	then	ADV
ejpam-6745	112	23	|βϵ|	|βϵ|	ADJ
ejpam-6745	112	24	≤	≤	NOUN
ejpam-6745	112	25	(	(	PUNCT
ejpam-6745	112	26	c1	c1	PROPN
ejpam-6745	112	27	−	−	PROPN
ejpam-6745	112	28	c2	c2	PROPN
ejpam-6745	112	29	)	)	PUNCT
ejpam-6745	112	30	|τ	|τ	NOUN
ejpam-6745	112	31	|	|	ADV
ejpam-6745	112	32	ϵ	ϵ	X
ejpam-6745	112	33	,	,	PUNCT
ejpam-6745	112	34	ϵ	ϵ	PROPN
ejpam-6745	112	35	∈	∈	PROPN
ejpam-6745	112	36	n−	n−	NOUN
ejpam-6745	112	37	{	{	PUNCT
ejpam-6745	112	38	1	1	NUM
ejpam-6745	112	39	}	}	PUNCT
ejpam-6745	112	40	.	.	PUNCT
ejpam-6745	113	1	(	(	PUNCT
ejpam-6745	113	2	15	15	NUM
ejpam-6745	113	3	)	)	PUNCT
ejpam-6745	113	4	the	the	DET
ejpam-6745	113	5	result	result	NOUN
ejpam-6745	113	6	is	be	AUX
ejpam-6745	113	7	sharp	sharp	ADJ
ejpam-6745	113	8	for	for	ADP
ejpam-6745	113	9	the	the	DET
ejpam-6745	113	10	function	function	NOUN
ejpam-6745	113	11	q(z	q(z	PROPN
ejpam-6745	113	12	)	)	PUNCT
ejpam-6745	113	13	given	give	VERB
ejpam-6745	113	14	by	by	ADP
ejpam-6745	113	15	q(z	q(z	PROPN
ejpam-6745	113	16	)	)	PUNCT
ejpam-6745	113	17	=	=	SYM
ejpam-6745	113	18	z∫	z∫	NOUN
ejpam-6745	113	19	0	0	PUNCT
ejpam-6745	113	20	(	(	PUNCT
ejpam-6745	113	21	1	1	NUM
ejpam-6745	113	22	+	+	CCONJ
ejpam-6745	113	23	(	(	PUNCT
ejpam-6745	113	24	c1	c1	PROPN
ejpam-6745	113	25	−	−	PROPN
ejpam-6745	113	26	c2)τt	c2)τt	PROPN
ejpam-6745	113	27	ϵ−1	ϵ−1	PROPN
ejpam-6745	113	28	1	1	NUM
ejpam-6745	113	29	+	+	CCONJ
ejpam-6745	113	30	c2tϵ−1	c2tϵ−1	PROPN
ejpam-6745	113	31	)	)	PUNCT
ejpam-6745	113	32	dt	dt	PUNCT
ejpam-6745	114	1	(	(	PUNCT
ejpam-6745	114	2	z	z	NOUN
ejpam-6745	114	3	∈	∈	PROPN
ejpam-6745	114	4	γ	γ	X
ejpam-6745	114	5	,	,	PUNCT
ejpam-6745	114	6	ϵ	ϵ	PRON
ejpam-6745	114	7	≥	≥	NOUN
ejpam-6745	114	8	2	2	NUM
ejpam-6745	114	9	)	)	PUNCT
ejpam-6745	114	10	.	.	PUNCT
ejpam-6745	115	1	(	(	PUNCT
ejpam-6745	115	2	16	16	NUM
ejpam-6745	115	3	)	)	PUNCT
ejpam-6745	115	4	we	we	PRON
ejpam-6745	115	5	need	need	VERB
ejpam-6745	115	6	the	the	DET
ejpam-6745	115	7	following	follow	VERB
ejpam-6745	115	8	well	well	ADV
ejpam-6745	115	9	-	-	PUNCT
ejpam-6745	115	10	known	know	VERB
ejpam-6745	115	11	series	series	NOUN
ejpam-6745	115	12	sums	sum	VERB
ejpam-6745	115	13	to	to	PART
ejpam-6745	115	14	prove	prove	VERB
ejpam-6745	115	15	our	our	PRON
ejpam-6745	115	16	main	main	ADJ
ejpam-6745	115	17	findings	finding	NOUN
ejpam-6745	115	18	.	.	PUNCT
ejpam-6745	116	1	∞∑	∞∑	NUM
ejpam-6745	116	2	ϵ=2	ϵ=2	NUM
ejpam-6745	116	3	1	1	NUM
ejpam-6745	116	4	(	(	PUNCT
ejpam-6745	116	5	ϵ−	ϵ−	NOUN
ejpam-6745	116	6	1	1	X
ejpam-6745	116	7	)	)	PUNCT
ejpam-6745	116	8	2ϵ	2ϵ	NOUN
ejpam-6745	116	9	=	=	SYM
ejpam-6745	116	10	1	1	NUM
ejpam-6745	116	11	2	2	NUM
ejpam-6745	116	12	ln	ln	NUM
ejpam-6745	116	13	2	2	NUM
ejpam-6745	116	14	(	(	PUNCT
ejpam-6745	116	15	17	17	NUM
ejpam-6745	116	16	)	)	PUNCT
ejpam-6745	116	17	f.	f.	PROPN
ejpam-6745	116	18	yousef	yousef	PROPN
ejpam-6745	116	19	,	,	PUNCT
ejpam-6745	116	20	m.	m.	NOUN
ejpam-6745	116	21	m.	m.	PROPN
ejpam-6745	116	22	alholi	alholi	PROPN
ejpam-6745	116	23	,	,	PUNCT
ejpam-6745	116	24	t.	t.	PROPN
ejpam-6745	116	25	al	al	PROPN
ejpam-6745	116	26	-	-	PUNCT
ejpam-6745	116	27	hawary	hawary	PROPN
ejpam-6745	116	28	/	/	SYM
ejpam-6745	116	29	eur	eur	PROPN
ejpam-6745	116	30	.	.	PUNCT
ejpam-6745	117	1	j.	j.	PROPN
ejpam-6745	117	2	pure	pure	PROPN
ejpam-6745	117	3	appl	appl	PROPN
ejpam-6745	117	4	.	.	PROPN
ejpam-6745	117	5	math	math	PROPN
ejpam-6745	117	6	,	,	PUNCT
ejpam-6745	117	7	18	18	NUM
ejpam-6745	117	8	(	(	PUNCT
ejpam-6745	117	9	4	4	NUM
ejpam-6745	117	10	)	)	PUNCT
ejpam-6745	117	11	(	(	PUNCT
ejpam-6745	117	12	2025	2025	NUM
ejpam-6745	117	13	)	)	PUNCT
ejpam-6745	117	14	,	,	PUNCT
ejpam-6745	117	15	6745	6745	NUM
ejpam-6745	117	16	6	6	NUM
ejpam-6745	117	17	of	of	ADP
ejpam-6745	117	18	13	13	NUM
ejpam-6745	117	19	and	and	CCONJ
ejpam-6745	117	20	∞∑	∞∑	NUM
ejpam-6745	117	21	ϵ=3	ϵ=3	NUM
ejpam-6745	117	22	1	1	NUM
ejpam-6745	117	23	2ϵ	2ϵ	NUM
ejpam-6745	117	24	(	(	PUNCT
ejpam-6745	117	25	ϵ−	ϵ−	NOUN
ejpam-6745	117	26	1	1	X
ejpam-6745	117	27	)	)	PUNCT
ejpam-6745	117	28	=	=	SYM
ejpam-6745	117	29	1	1	NUM
ejpam-6745	117	30	2	2	NUM
ejpam-6745	117	31	ln	ln	NOUN
ejpam-6745	117	32	2−	2−	NUM
ejpam-6745	117	33	1	1	NUM
ejpam-6745	117	34	4	4	NUM
ejpam-6745	117	35	.	.	PUNCT
ejpam-6745	118	1	(	(	PUNCT
ejpam-6745	118	2	18	18	NUM
ejpam-6745	118	3	)	)	PUNCT
ejpam-6745	118	4	note	note	NOUN
ejpam-6745	118	5	that	that	SCONJ
ejpam-6745	118	6	∞∑	∞∑	NUM
ejpam-6745	118	7	ϵ=d	ϵ=d	PROPN
ejpam-6745	118	8	1	1	NUM
ejpam-6745	118	9	(	(	PUNCT
ejpam-6745	118	10	ϵ−	ϵ−	NOUN
ejpam-6745	118	11	1	1	X
ejpam-6745	118	12	)	)	PUNCT
ejpam-6745	118	13	2ϵ	2ϵ	NOUN
ejpam-6745	118	14	=	=	SYM
ejpam-6745	118	15	1	1	NUM
ejpam-6745	118	16	2	2	NUM
ejpam-6745	118	17	ln	ln	NUM
ejpam-6745	118	18	2−	2−	NUM
ejpam-6745	118	19	d−1∑	d−1∑	NOUN
ejpam-6745	118	20	ϵ=2	ϵ=2	PROPN
ejpam-6745	118	21	1	1	NUM
ejpam-6745	118	22	(	(	PUNCT
ejpam-6745	118	23	ϵ−	ϵ−	NOUN
ejpam-6745	118	24	1	1	X
ejpam-6745	118	25	)	)	PUNCT
ejpam-6745	118	26	2ϵ	2ϵ	NOUN
ejpam-6745	118	27	,	,	PUNCT
ejpam-6745	119	1	d	d	X
ejpam-6745	119	2	=	=	SYM
ejpam-6745	119	3	3	3	NUM
ejpam-6745	119	4	,	,	PUNCT
ejpam-6745	119	5	4	4	NUM
ejpam-6745	119	6	,	,	PUNCT
ejpam-6745	119	7	·	·	PUNCT
ejpam-6745	119	8	·	·	PUNCT
ejpam-6745	119	9	·	·	PUNCT
ejpam-6745	119	10	.	.	PUNCT
ejpam-6745	120	1	(	(	PUNCT
ejpam-6745	120	2	19	19	NUM
ejpam-6745	120	3	)	)	PUNCT
ejpam-6745	120	4	the	the	DET
ejpam-6745	120	5	following	follow	VERB
ejpam-6745	120	6	inequalities	inequality	NOUN
ejpam-6745	120	7	are	be	AUX
ejpam-6745	120	8	also	also	ADV
ejpam-6745	120	9	required	require	VERB
ejpam-6745	120	10	(	(	PUNCT
ejpam-6745	120	11	ϵ−	ϵ−	PROPN
ejpam-6745	120	12	1)k	1)k	NUM
ejpam-6745	120	13	+	+	CCONJ
ejpam-6745	120	14	1	1	NUM
ejpam-6745	120	15	>	>	X
ejpam-6745	120	16	(	(	PUNCT
ejpam-6745	120	17	ϵ−	ϵ−	PROPN
ejpam-6745	120	18	1)k	1)k	NUM
ejpam-6745	120	19	(	(	PUNCT
ejpam-6745	120	20	ϵ	ϵ	X
ejpam-6745	120	21	,	,	PUNCT
ejpam-6745	120	22	k	k	PROPN
ejpam-6745	120	23	∈	∈	PROPN
ejpam-6745	120	24	n	n	CCONJ
ejpam-6745	120	25	)	)	PUNCT
ejpam-6745	120	26	(	(	PUNCT
ejpam-6745	120	27	20	20	NUM
ejpam-6745	120	28	)	)	PUNCT
ejpam-6745	120	29	and	and	CCONJ
ejpam-6745	120	30	ϵ	ϵ	X
ejpam-6745	120	31	!	!	PROPN
ejpam-6745	120	32	≥	≥	PROPN
ejpam-6745	121	1	2ϵ−1	2ϵ−1	NUM
ejpam-6745	121	2	(	(	PUNCT
ejpam-6745	121	3	ϵ	ϵ	PROPN
ejpam-6745	121	4	∈	∈	PROPN
ejpam-6745	121	5	n	n	CCONJ
ejpam-6745	121	6	)	)	PUNCT
ejpam-6745	121	7	.	.	PUNCT
ejpam-6745	122	1	(	(	PUNCT
ejpam-6745	122	2	21	21	NUM
ejpam-6745	122	3	)	)	PUNCT
ejpam-6745	122	4	2	2	NUM
ejpam-6745	122	5	.	.	NOUN
ejpam-6745	122	6	necessary	necessary	ADJ
ejpam-6745	122	7	and	and	CCONJ
ejpam-6745	122	8	sufficient	sufficient	ADJ
ejpam-6745	122	9	conditions	condition	NOUN
ejpam-6745	122	10	for	for	ADP
ejpam-6745	122	11	the	the	DET
ejpam-6745	122	12	function	function	NOUN
ejpam-6745	122	13	υik	υik	VERB
ejpam-6745	122	14	in	in	ADP
ejpam-6745	122	15	this	this	DET
ejpam-6745	122	16	section	section	NOUN
ejpam-6745	122	17	,	,	PUNCT
ejpam-6745	122	18	we	we	PRON
ejpam-6745	122	19	find	find	VERB
ejpam-6745	122	20	some	some	DET
ejpam-6745	122	21	necessary	necessary	ADJ
ejpam-6745	122	22	and	and	CCONJ
ejpam-6745	122	23	sufficient	sufficient	ADJ
ejpam-6745	122	24	conditions	condition	NOUN
ejpam-6745	122	25	for	for	ADP
ejpam-6745	122	26	the	the	DET
ejpam-6745	122	27	function	function	NOUN
ejpam-6745	122	28	υik	υik	VERB
ejpam-6745	122	29	to	to	PART
ejpam-6745	122	30	be	be	AUX
ejpam-6745	122	31	in	in	ADP
ejpam-6745	122	32	the	the	DET
ejpam-6745	122	33	subclasses	subclass	NOUN
ejpam-6745	122	34	spe(ϑ	spe(ϑ	PROPN
ejpam-6745	122	35	,	,	PUNCT
ejpam-6745	122	36	ζ	ζ	NOUN
ejpam-6745	122	37	)	)	PUNCT
ejpam-6745	122	38	and	and	CCONJ
ejpam-6745	122	39	cspe(ϑ	cspe(ϑ	PROPN
ejpam-6745	122	40	,	,	PUNCT
ejpam-6745	122	41	ζ	ζ	NOUN
ejpam-6745	122	42	)	)	PUNCT
ejpam-6745	122	43	.	.	PUNCT
ejpam-6745	123	1	theorem	theorem	NOUN
ejpam-6745	123	2	1	1	NUM
ejpam-6745	123	3	.	.	PUNCT
ejpam-6745	124	1	if	if	SCONJ
ejpam-6745	124	2	k	k	PROPN
ejpam-6745	124	3	∈	∈	PROPN
ejpam-6745	124	4	n	n	CCONJ
ejpam-6745	124	5	,	,	PUNCT
ejpam-6745	124	6	then	then	ADV
ejpam-6745	124	7	υik	υik	ADJ
ejpam-6745	124	8	(	(	PUNCT
ejpam-6745	124	9	z	z	NOUN
ejpam-6745	124	10	)	)	PUNCT
ejpam-6745	124	11	is	be	AUX
ejpam-6745	124	12	in	in	ADP
ejpam-6745	124	13	the	the	DET
ejpam-6745	124	14	subclass	subclass	NOUN
ejpam-6745	124	15	spe(ϑ	spe(ϑ	PROPN
ejpam-6745	124	16	,	,	PUNCT
ejpam-6745	124	17	ζ	ζ	NOUN
ejpam-6745	124	18	)	)	PUNCT
ejpam-6745	124	19	if	if	SCONJ
ejpam-6745	124	20	and	and	CCONJ
ejpam-6745	124	21	only	only	ADV
ejpam-6745	124	22	if	if	SCONJ
ejpam-6745	124	23	2(6−	2(6−	NUM
ejpam-6745	124	24	ζ	ζ	NOUN
ejpam-6745	124	25	−	−	PUNCT
ejpam-6745	124	26	cosϑ	cosϑ	ADJ
ejpam-6745	124	27	)	)	PUNCT
ejpam-6745	124	28	ln	ln	PROPN
ejpam-6745	124	29	2	2	NUM
ejpam-6745	124	30	≤	≤	NOUN
ejpam-6745	124	31	k	k	PROPN
ejpam-6745	124	32	(	(	PUNCT
ejpam-6745	124	33	cosϑ−	cosϑ−	PROPN
ejpam-6745	124	34	ζ	ζ	PROPN
ejpam-6745	124	35	)	)	PUNCT
ejpam-6745	124	36	.	.	PUNCT
ejpam-6745	125	1	(	(	PUNCT
ejpam-6745	125	2	22	22	NUM
ejpam-6745	125	3	)	)	PUNCT
ejpam-6745	125	4	proof	proof	NOUN
ejpam-6745	125	5	.	.	PUNCT
ejpam-6745	126	1	since	since	SCONJ
ejpam-6745	126	2	υik	υik	ADJ
ejpam-6745	126	3	(	(	PUNCT
ejpam-6745	126	4	z	z	NOUN
ejpam-6745	126	5	)	)	PUNCT
ejpam-6745	126	6	=	=	PUNCT
ejpam-6745	126	7	z	z	NOUN
ejpam-6745	126	8	−	−	ADP
ejpam-6745	126	9	∞∑	∞∑	NUM
ejpam-6745	126	10	ϵ=2	ϵ=2	PROPN
ejpam-6745	126	11	1	1	NUM
ejpam-6745	126	12	(	(	PUNCT
ejpam-6745	126	13	(	(	PUNCT
ejpam-6745	126	14	ϵ−	ϵ−	NOUN
ejpam-6745	126	15	1	1	X
ejpam-6745	126	16	)	)	PUNCT
ejpam-6745	126	17	k	k	NOUN
ejpam-6745	127	1	+	+	NOUN
ejpam-6745	127	2	1	1	X
ejpam-6745	127	3	)	)	PUNCT
ejpam-6745	127	4	(	(	PUNCT
ejpam-6745	127	5	ϵ−	ϵ−	NOUN
ejpam-6745	127	6	1	1	NUM
ejpam-6745	127	7	)	)	PUNCT
ejpam-6745	127	8	!	!	PUNCT
ejpam-6745	128	1	zϵ	zϵ	PROPN
ejpam-6745	128	2	,	,	PUNCT
ejpam-6745	128	3	(	(	PUNCT
ejpam-6745	128	4	23	23	NUM
ejpam-6745	128	5	)	)	PUNCT
ejpam-6745	128	6	by	by	ADP
ejpam-6745	128	7	virtue	virtue	NOUN
ejpam-6745	128	8	of	of	ADP
ejpam-6745	128	9	(	(	PUNCT
ejpam-6745	128	10	11	11	NUM
ejpam-6745	128	11	)	)	PUNCT
ejpam-6745	128	12	it	it	PRON
ejpam-6745	128	13	suffices	suffice	VERB
ejpam-6745	128	14	to	to	PART
ejpam-6745	128	15	show	show	VERB
ejpam-6745	128	16	that	that	SCONJ
ejpam-6745	128	17	l1(ϑ	l1(ϑ	PROPN
ejpam-6745	128	18	,	,	PUNCT
ejpam-6745	128	19	ζ	ζ	NOUN
ejpam-6745	128	20	)	)	PUNCT
ejpam-6745	128	21	≤	≤	PROPN
ejpam-6745	128	22	cosϑ−	cosϑ−	PROPN
ejpam-6745	128	23	ζ	ζ	PROPN
ejpam-6745	128	24	,	,	PUNCT
ejpam-6745	128	25	where	where	SCONJ
ejpam-6745	128	26	l1(ϑ	l1(ϑ	PROPN
ejpam-6745	128	27	,	,	PUNCT
ejpam-6745	128	28	ζ	ζ	NOUN
ejpam-6745	128	29	)	)	PUNCT
ejpam-6745	128	30	=	=	NOUN
ejpam-6745	129	1	∞∑	∞∑	NUM
ejpam-6745	129	2	ϵ=2	ϵ=2	NOUN
ejpam-6745	130	1	[	[	X
ejpam-6745	130	2	2ϵ−	2ϵ−	NUM
ejpam-6745	130	3	ζ	ζ	NOUN
ejpam-6745	130	4	−	−	NOUN
ejpam-6745	130	5	cosϑ	cosϑ	VERB
ejpam-6745	130	6	]	]	X
ejpam-6745	130	7	1	1	NUM
ejpam-6745	130	8	(	(	PUNCT
ejpam-6745	130	9	(	(	PUNCT
ejpam-6745	130	10	ϵ−	ϵ−	NOUN
ejpam-6745	130	11	1	1	X
ejpam-6745	130	12	)	)	PUNCT
ejpam-6745	130	13	k	k	NOUN
ejpam-6745	131	1	+	+	NOUN
ejpam-6745	131	2	1	1	X
ejpam-6745	131	3	)	)	PUNCT
ejpam-6745	131	4	(	(	PUNCT
ejpam-6745	131	5	ϵ−	ϵ−	NOUN
ejpam-6745	131	6	1	1	NUM
ejpam-6745	131	7	)	)	PUNCT
ejpam-6745	131	8	!	!	PUNCT
ejpam-6745	131	9	.	.	PUNCT
ejpam-6745	132	1	writing	write	VERB
ejpam-6745	132	2	ϵ	ϵ	X
ejpam-6745	132	3	=	=	SYM
ejpam-6745	132	4	(	(	PUNCT
ejpam-6745	132	5	ϵ−	ϵ−	NOUN
ejpam-6745	132	6	1	1	NUM
ejpam-6745	132	7	)	)	PUNCT
ejpam-6745	132	8	+	+	NUM
ejpam-6745	132	9	1	1	NUM
ejpam-6745	132	10	,	,	PUNCT
ejpam-6745	132	11	we	we	PRON
ejpam-6745	132	12	get	get	VERB
ejpam-6745	132	13	l1(ϑ	l1(ϑ	PROPN
ejpam-6745	132	14	,	,	PUNCT
ejpam-6745	132	15	ζ	ζ	NOUN
ejpam-6745	132	16	)	)	PUNCT
ejpam-6745	132	17	=	=	NOUN
ejpam-6745	133	1	∞∑	∞∑	NUM
ejpam-6745	133	2	ϵ=2	ϵ=2	PROPN
ejpam-6745	133	3	2(ϵ−	2(ϵ−	PROPN
ejpam-6745	133	4	1	1	NUM
ejpam-6745	133	5	)	)	PUNCT
ejpam-6745	133	6	(	(	PUNCT
ejpam-6745	133	7	(	(	PUNCT
ejpam-6745	133	8	ϵ−	ϵ−	NOUN
ejpam-6745	133	9	1	1	X
ejpam-6745	133	10	)	)	PUNCT
ejpam-6745	133	11	k	k	NOUN
ejpam-6745	134	1	+	+	NOUN
ejpam-6745	134	2	1	1	X
ejpam-6745	134	3	)	)	PUNCT
ejpam-6745	134	4	(	(	PUNCT
ejpam-6745	134	5	ϵ−	ϵ−	NOUN
ejpam-6745	134	6	1	1	NUM
ejpam-6745	134	7	)	)	PUNCT
ejpam-6745	134	8	!	!	PUNCT
ejpam-6745	135	1	+	+	CCONJ
ejpam-6745	135	2	∞∑	∞∑	NUM
ejpam-6745	135	3	ϵ=2	ϵ=2	NUM
ejpam-6745	135	4	2−	2−	NUM
ejpam-6745	135	5	ζ	ζ	NOUN
ejpam-6745	135	6	−	−	NOUN
ejpam-6745	135	7	cosϑ	cosϑ	NOUN
ejpam-6745	135	8	(	(	PUNCT
ejpam-6745	135	9	(	(	PUNCT
ejpam-6745	135	10	ϵ−	ϵ−	NOUN
ejpam-6745	135	11	1	1	X
ejpam-6745	135	12	)	)	PUNCT
ejpam-6745	135	13	k	k	NOUN
ejpam-6745	136	1	+	+	NOUN
ejpam-6745	136	2	1	1	X
ejpam-6745	136	3	)	)	PUNCT
ejpam-6745	136	4	(	(	PUNCT
ejpam-6745	136	5	ϵ−	ϵ−	NOUN
ejpam-6745	136	6	1	1	NUM
ejpam-6745	136	7	)	)	PUNCT
ejpam-6745	136	8	!	!	PUNCT
ejpam-6745	137	1	=	=	PUNCT
ejpam-6745	138	1	∞∑	∞∑	NUM
ejpam-6745	138	2	ϵ=2	ϵ=2	PROPN
ejpam-6745	138	3	2	2	NUM
ejpam-6745	138	4	(	(	PUNCT
ejpam-6745	138	5	(	(	PUNCT
ejpam-6745	138	6	ϵ−	ϵ−	NOUN
ejpam-6745	138	7	1	1	X
ejpam-6745	138	8	)	)	PUNCT
ejpam-6745	138	9	k	k	NOUN
ejpam-6745	139	1	+	+	NOUN
ejpam-6745	139	2	1	1	X
ejpam-6745	139	3	)	)	PUNCT
ejpam-6745	139	4	(	(	PUNCT
ejpam-6745	139	5	ϵ−	ϵ−	NOUN
ejpam-6745	139	6	2	2	NUM
ejpam-6745	139	7	)	)	PUNCT
ejpam-6745	139	8	!	!	PUNCT
ejpam-6745	140	1	+	+	CCONJ
ejpam-6745	140	2	∞∑	∞∑	NUM
ejpam-6745	140	3	ϵ=2	ϵ=2	NUM
ejpam-6745	140	4	2−	2−	NUM
ejpam-6745	140	5	ζ	ζ	NOUN
ejpam-6745	140	6	−	−	NOUN
ejpam-6745	140	7	cosϑ	cosϑ	NOUN
ejpam-6745	140	8	(	(	PUNCT
ejpam-6745	140	9	(	(	PUNCT
ejpam-6745	140	10	ϵ−	ϵ−	NOUN
ejpam-6745	140	11	1	1	X
ejpam-6745	140	12	)	)	PUNCT
ejpam-6745	140	13	k	k	NOUN
ejpam-6745	141	1	+	+	NOUN
ejpam-6745	141	2	1	1	X
ejpam-6745	141	3	)	)	PUNCT
ejpam-6745	141	4	(	(	PUNCT
ejpam-6745	141	5	ϵ−	ϵ−	NOUN
ejpam-6745	141	6	1	1	NUM
ejpam-6745	141	7	)	)	PUNCT
ejpam-6745	141	8	!	!	PUNCT
ejpam-6745	141	9	.	.	PUNCT
ejpam-6745	142	1	by	by	ADP
ejpam-6745	142	2	(	(	PUNCT
ejpam-6745	142	3	20	20	NUM
ejpam-6745	142	4	)	)	PUNCT
ejpam-6745	142	5	,	,	PUNCT
ejpam-6745	142	6	we	we	PRON
ejpam-6745	142	7	get	get	VERB
ejpam-6745	142	8	l1(ϑ	l1(ϑ	PROPN
ejpam-6745	142	9	,	,	PUNCT
ejpam-6745	142	10	ζ	ζ	NOUN
ejpam-6745	142	11	)	)	PUNCT
ejpam-6745	142	12	≤	≤	NOUN
ejpam-6745	142	13	2	2	NUM
ejpam-6745	142	14	k	k	NOUN
ejpam-6745	142	15	∞∑	∞∑	NUM
ejpam-6745	142	16	ϵ=2	ϵ=2	PROPN
ejpam-6745	142	17	1	1	NUM
ejpam-6745	142	18	(	(	PUNCT
ejpam-6745	142	19	ϵ−	ϵ−	NOUN
ejpam-6745	142	20	1	1	NUM
ejpam-6745	142	21	)	)	PUNCT
ejpam-6745	142	22	(	(	PUNCT
ejpam-6745	142	23	ϵ−	ϵ−	NOUN
ejpam-6745	142	24	2	2	NUM
ejpam-6745	142	25	)	)	PUNCT
ejpam-6745	142	26	!	!	PUNCT
ejpam-6745	143	1	+	+	CCONJ
ejpam-6745	143	2	2−	2−	NUM
ejpam-6745	143	3	ζ	ζ	NOUN
ejpam-6745	143	4	−	−	NOUN
ejpam-6745	143	5	cosϑ	cosϑ	VERB
ejpam-6745	143	6	k	k	NOUN
ejpam-6745	143	7	∞∑	∞∑	ADJ
ejpam-6745	143	8	ϵ=2	ϵ=2	PROPN
ejpam-6745	143	9	1	1	NUM
ejpam-6745	143	10	(	(	PUNCT
ejpam-6745	143	11	ϵ−	ϵ−	NOUN
ejpam-6745	143	12	1	1	NUM
ejpam-6745	143	13	)	)	PUNCT
ejpam-6745	143	14	(	(	PUNCT
ejpam-6745	143	15	ϵ−	ϵ−	NOUN
ejpam-6745	143	16	1	1	NUM
ejpam-6745	143	17	)	)	PUNCT
ejpam-6745	143	18	!	!	PUNCT
ejpam-6745	143	19	.	.	PUNCT
ejpam-6745	144	1	f.	f.	PROPN
ejpam-6745	144	2	yousef	yousef	PROPN
ejpam-6745	144	3	,	,	PUNCT
ejpam-6745	144	4	m.	m.	NOUN
ejpam-6745	144	5	m.	m.	PROPN
ejpam-6745	144	6	alholi	alholi	PROPN
ejpam-6745	144	7	,	,	PUNCT
ejpam-6745	144	8	t.	t.	PROPN
ejpam-6745	144	9	al	al	PROPN
ejpam-6745	144	10	-	-	PUNCT
ejpam-6745	144	11	hawary	hawary	PROPN
ejpam-6745	144	12	/	/	SYM
ejpam-6745	144	13	eur	eur	PROPN
ejpam-6745	144	14	.	.	PUNCT
ejpam-6745	145	1	j.	j.	PROPN
ejpam-6745	145	2	pure	pure	PROPN
ejpam-6745	145	3	appl	appl	PROPN
ejpam-6745	145	4	.	.	PROPN
ejpam-6745	145	5	math	math	PROPN
ejpam-6745	145	6	,	,	PUNCT
ejpam-6745	145	7	18	18	NUM
ejpam-6745	145	8	(	(	PUNCT
ejpam-6745	145	9	4	4	NUM
ejpam-6745	145	10	)	)	PUNCT
ejpam-6745	145	11	(	(	PUNCT
ejpam-6745	145	12	2025	2025	NUM
ejpam-6745	145	13	)	)	PUNCT
ejpam-6745	145	14	,	,	PUNCT
ejpam-6745	145	15	6745	6745	NUM
ejpam-6745	145	16	7	7	NUM
ejpam-6745	145	17	of	of	ADP
ejpam-6745	145	18	13	13	NUM
ejpam-6745	145	19	by	by	ADP
ejpam-6745	145	20	(	(	PUNCT
ejpam-6745	145	21	21	21	NUM
ejpam-6745	145	22	)	)	PUNCT
ejpam-6745	145	23	,	,	PUNCT
ejpam-6745	145	24	we	we	PRON
ejpam-6745	145	25	get	get	VERB
ejpam-6745	145	26	l1(ϑ	l1(ϑ	PROPN
ejpam-6745	145	27	,	,	PUNCT
ejpam-6745	145	28	ζ	ζ	NOUN
ejpam-6745	145	29	)	)	PUNCT
ejpam-6745	145	30	≤	≤	NOUN
ejpam-6745	146	1	16	16	NUM
ejpam-6745	147	1	k	k	X
ejpam-6745	147	2	∞∑	∞∑	NUM
ejpam-6745	147	3	ϵ=3	ϵ=3	NUM
ejpam-6745	147	4	1	1	NUM
ejpam-6745	147	5	(	(	PUNCT
ejpam-6745	147	6	ϵ−	ϵ−	NOUN
ejpam-6745	147	7	1	1	X
ejpam-6745	147	8	)	)	PUNCT
ejpam-6745	147	9	2ϵ	2ϵ	NOUN
ejpam-6745	147	10	+	+	CCONJ
ejpam-6745	147	11	4	4	NUM
ejpam-6745	147	12	(	(	PUNCT
ejpam-6745	147	13	2−	2−	NUM
ejpam-6745	147	14	ζ	ζ	NOUN
ejpam-6745	147	15	−	−	NOUN
ejpam-6745	147	16	cosϑ	cosϑ	ADJ
ejpam-6745	147	17	)	)	PUNCT
ejpam-6745	148	1	k	k	NOUN
ejpam-6745	149	1	∞∑	∞∑	ADJ
ejpam-6745	149	2	ϵ=2	ϵ=2	PROPN
ejpam-6745	149	3	1	1	NUM
ejpam-6745	149	4	(	(	PUNCT
ejpam-6745	149	5	ϵ−	ϵ−	NOUN
ejpam-6745	149	6	1	1	X
ejpam-6745	149	7	)	)	PUNCT
ejpam-6745	149	8	2ϵ	2ϵ	NOUN
ejpam-6745	149	9	.	.	PUNCT
ejpam-6745	150	1	using	use	VERB
ejpam-6745	150	2	the	the	DET
ejpam-6745	150	3	series	series	NOUN
ejpam-6745	150	4	sums	sum	NOUN
ejpam-6745	150	5	(	(	PUNCT
ejpam-6745	150	6	17	17	NUM
ejpam-6745	150	7	)	)	PUNCT
ejpam-6745	150	8	,	,	PUNCT
ejpam-6745	150	9	we	we	PRON
ejpam-6745	150	10	get	get	VERB
ejpam-6745	150	11	l1(ϑ	l1(ϑ	PROPN
ejpam-6745	150	12	,	,	PUNCT
ejpam-6745	150	13	ζ	ζ	NOUN
ejpam-6745	150	14	)	)	PUNCT
ejpam-6745	150	15	≤	≤	NOUN
ejpam-6745	150	16	8	8	NUM
ejpam-6745	150	17	k	k	NOUN
ejpam-6745	150	18	(	(	PUNCT
ejpam-6745	150	19	ln	ln	NOUN
ejpam-6745	150	20	2	2	NUM
ejpam-6745	150	21	)	)	PUNCT
ejpam-6745	150	22	+	+	CCONJ
ejpam-6745	150	23	2	2	NUM
ejpam-6745	150	24	(	(	PUNCT
ejpam-6745	150	25	2−	2−	NUM
ejpam-6745	150	26	ζ	ζ	NOUN
ejpam-6745	150	27	−	−	PROPN
ejpam-6745	150	28	cosϑ	cosϑ	ADJ
ejpam-6745	150	29	)	)	PUNCT
ejpam-6745	151	1	k	k	NOUN
ejpam-6745	151	2	(	(	PUNCT
ejpam-6745	151	3	ln	ln	NOUN
ejpam-6745	151	4	2	2	NUM
ejpam-6745	151	5	)	)	PUNCT
ejpam-6745	151	6	=	=	SYM
ejpam-6745	152	1	2(6−	2(6−	NUM
ejpam-6745	152	2	ζ	ζ	NOUN
ejpam-6745	152	3	−	−	PROPN
ejpam-6745	152	4	cosϑ	cosϑ	ADJ
ejpam-6745	152	5	)	)	PUNCT
ejpam-6745	153	1	k	k	PROPN
ejpam-6745	153	2	ln	ln	ADJ
ejpam-6745	154	1	2	2	X
ejpam-6745	154	2	.	.	PUNCT
ejpam-6745	155	1	however	however	ADV
ejpam-6745	155	2	,	,	PUNCT
ejpam-6745	155	3	if	if	SCONJ
ejpam-6745	155	4	and	and	CCONJ
ejpam-6745	155	5	only	only	ADV
ejpam-6745	155	6	if	if	SCONJ
ejpam-6745	155	7	(	(	PUNCT
ejpam-6745	155	8	22	22	NUM
ejpam-6745	155	9	)	)	PUNCT
ejpam-6745	155	10	holds	hold	VERB
ejpam-6745	155	11	,	,	PUNCT
ejpam-6745	155	12	the	the	DET
ejpam-6745	155	13	last	last	ADJ
ejpam-6745	155	14	expression	expression	NOUN
ejpam-6745	155	15	is	be	AUX
ejpam-6745	155	16	bounded	bound	VERB
ejpam-6745	155	17	above	above	ADV
ejpam-6745	155	18	by	by	ADP
ejpam-6745	155	19	cosϑ−	cosϑ−	PROPN
ejpam-6745	155	20	ζ	ζ	PROPN
ejpam-6745	155	21	.	.	PUNCT
ejpam-6745	156	1	theorem	theorem	NOUN
ejpam-6745	156	2	2	2	NUM
ejpam-6745	156	3	.	.	PUNCT
ejpam-6745	157	1	if	if	SCONJ
ejpam-6745	157	2	k	k	PROPN
ejpam-6745	157	3	∈	∈	PROPN
ejpam-6745	157	4	n	n	CCONJ
ejpam-6745	157	5	,	,	PUNCT
ejpam-6745	157	6	then	then	ADV
ejpam-6745	157	7	υik	υik	ADJ
ejpam-6745	157	8	(	(	PUNCT
ejpam-6745	157	9	z	z	NOUN
ejpam-6745	157	10	)	)	PUNCT
ejpam-6745	157	11	is	be	AUX
ejpam-6745	157	12	in	in	ADP
ejpam-6745	157	13	the	the	DET
ejpam-6745	157	14	subclass	subclass	NOUN
ejpam-6745	157	15	cspe(ϑ	cspe(ϑ	PROPN
ejpam-6745	157	16	,	,	PUNCT
ejpam-6745	157	17	ζ	ζ	NOUN
ejpam-6745	157	18	)	)	PUNCT
ejpam-6745	157	19	if	if	SCONJ
ejpam-6745	158	1	and	and	CCONJ
ejpam-6745	158	2	only	only	ADV
ejpam-6745	158	3	if	if	SCONJ
ejpam-6745	158	4	2(22−	2(22−	NUM
ejpam-6745	158	5	3ζ	3ζ	NOUN
ejpam-6745	158	6	−	−	PROPN
ejpam-6745	158	7	3	3	NUM
ejpam-6745	158	8	cosϑ	cosϑ	NOUN
ejpam-6745	158	9	)	)	PUNCT
ejpam-6745	159	1	ln	ln	ADV
ejpam-6745	159	2	2	2	NUM
ejpam-6745	159	3	≤	≤	NUM
ejpam-6745	159	4	8	8	NUM
ejpam-6745	159	5	+	+	CCONJ
ejpam-6745	159	6	k(cosϑ−	k(cosϑ−	PROPN
ejpam-6745	159	7	ζ	ζ	PROPN
ejpam-6745	159	8	)	)	PUNCT
ejpam-6745	159	9	.	.	PUNCT
ejpam-6745	160	1	(	(	PUNCT
ejpam-6745	160	2	24	24	NUM
ejpam-6745	160	3	)	)	PUNCT
ejpam-6745	160	4	proof	proof	NOUN
ejpam-6745	160	5	.	.	PUNCT
ejpam-6745	161	1	since	since	SCONJ
ejpam-6745	161	2	υik	υik	ADJ
ejpam-6745	161	3	(	(	PUNCT
ejpam-6745	161	4	z	z	NOUN
ejpam-6745	161	5	)	)	PUNCT
ejpam-6745	161	6	is	be	AUX
ejpam-6745	161	7	given	give	VERB
ejpam-6745	161	8	by	by	ADP
ejpam-6745	161	9	(	(	PUNCT
ejpam-6745	161	10	23	23	NUM
ejpam-6745	161	11	)	)	PUNCT
ejpam-6745	161	12	and	and	CCONJ
ejpam-6745	161	13	by	by	ADP
ejpam-6745	161	14	virtue	virtue	NOUN
ejpam-6745	161	15	(	(	PUNCT
ejpam-6745	161	16	13	13	NUM
ejpam-6745	161	17	)	)	PUNCT
ejpam-6745	161	18	,	,	PUNCT
ejpam-6745	161	19	it	it	PRON
ejpam-6745	161	20	suffices	suffice	VERB
ejpam-6745	161	21	to	to	PART
ejpam-6745	161	22	show	show	VERB
ejpam-6745	161	23	that	that	SCONJ
ejpam-6745	161	24	l2(λ1	l2(λ1	NOUN
ejpam-6745	161	25	,	,	PUNCT
ejpam-6745	161	26	λ2	λ2	NOUN
ejpam-6745	161	27	)	)	PUNCT
ejpam-6745	161	28	≤	≤	NUM
ejpam-6745	161	29	cosϑ−	cosϑ−	PROPN
ejpam-6745	161	30	ζ	ζ	PROPN
ejpam-6745	161	31	,	,	PUNCT
ejpam-6745	161	32	where	where	SCONJ
ejpam-6745	161	33	l2(ϑ	l2(ϑ	NOUN
ejpam-6745	161	34	,	,	PUNCT
ejpam-6745	161	35	ζ	ζ	NOUN
ejpam-6745	161	36	)	)	PUNCT
ejpam-6745	161	37	=	=	NOUN
ejpam-6745	162	1	∞∑	∞∑	NUM
ejpam-6745	162	2	ϵ=2	ϵ=2	PROPN
ejpam-6745	162	3	ϵ	ϵ	X
ejpam-6745	162	4	[	[	X
ejpam-6745	162	5	2ϵ−	2ϵ−	NUM
ejpam-6745	162	6	ζ	ζ	NOUN
ejpam-6745	162	7	−	−	NOUN
ejpam-6745	162	8	cosϑ	cosϑ	VERB
ejpam-6745	162	9	]	]	X
ejpam-6745	162	10	1	1	NUM
ejpam-6745	162	11	(	(	PUNCT
ejpam-6745	162	12	(	(	PUNCT
ejpam-6745	162	13	ϵ−	ϵ−	NOUN
ejpam-6745	162	14	1	1	X
ejpam-6745	162	15	)	)	PUNCT
ejpam-6745	162	16	k	k	NOUN
ejpam-6745	163	1	+	+	NOUN
ejpam-6745	163	2	1	1	X
ejpam-6745	163	3	)	)	PUNCT
ejpam-6745	163	4	(	(	PUNCT
ejpam-6745	163	5	ϵ−	ϵ−	NOUN
ejpam-6745	163	6	1	1	NUM
ejpam-6745	163	7	)	)	PUNCT
ejpam-6745	163	8	!	!	PUNCT
ejpam-6745	164	1	=	=	PUNCT
ejpam-6745	165	1	∞∑	∞∑	NUM
ejpam-6745	165	2	ϵ=2	ϵ=2	PROPN
ejpam-6745	165	3	[	[	PUNCT
ejpam-6745	165	4	2ϵ2	2ϵ2	NUM
ejpam-6745	165	5	−	−	PROPN
ejpam-6745	165	6	(	(	PUNCT
ejpam-6745	165	7	ζ	ζ	NOUN
ejpam-6745	165	8	+	+	CCONJ
ejpam-6745	165	9	cosϑ	cosϑ	ADJ
ejpam-6745	165	10	)	)	PUNCT
ejpam-6745	165	11	ϵ	ϵ	X
ejpam-6745	165	12	]	]	PUNCT
ejpam-6745	165	13	1	1	NUM
ejpam-6745	165	14	(	(	PUNCT
ejpam-6745	165	15	(	(	PUNCT
ejpam-6745	165	16	ϵ−	ϵ−	NOUN
ejpam-6745	165	17	1	1	X
ejpam-6745	165	18	)	)	PUNCT
ejpam-6745	165	19	k	k	NOUN
ejpam-6745	166	1	+	+	NOUN
ejpam-6745	166	2	1	1	X
ejpam-6745	166	3	)	)	PUNCT
ejpam-6745	166	4	(	(	PUNCT
ejpam-6745	166	5	ϵ−	ϵ−	NOUN
ejpam-6745	166	6	1	1	NUM
ejpam-6745	166	7	)	)	PUNCT
ejpam-6745	166	8	!	!	PUNCT
ejpam-6745	166	9	.	.	PUNCT
ejpam-6745	167	1	writing	write	VERB
ejpam-6745	167	2	ϵ	ϵ	X
ejpam-6745	167	3	=	=	SYM
ejpam-6745	167	4	(	(	PUNCT
ejpam-6745	167	5	ϵ−	ϵ−	NOUN
ejpam-6745	167	6	1	1	NUM
ejpam-6745	167	7	)	)	PUNCT
ejpam-6745	167	8	+	+	NUM
ejpam-6745	167	9	1	1	NUM
ejpam-6745	167	10	,	,	PUNCT
ejpam-6745	167	11	(	(	PUNCT
ejpam-6745	167	12	25	25	NUM
ejpam-6745	167	13	)	)	PUNCT
ejpam-6745	167	14	and	and	CCONJ
ejpam-6745	167	15	ϵ2	ϵ2	NOUN
ejpam-6745	167	16	=	=	PUNCT
ejpam-6745	167	17	(	(	PUNCT
ejpam-6745	167	18	ϵ−	ϵ−	NOUN
ejpam-6745	167	19	1)(ϵ−	1)(ϵ−	NUM
ejpam-6745	167	20	2	2	NUM
ejpam-6745	167	21	)	)	PUNCT
ejpam-6745	167	22	+	+	CCONJ
ejpam-6745	167	23	3(ϵ−	3(ϵ−	NUM
ejpam-6745	167	24	1	1	NUM
ejpam-6745	167	25	)	)	PUNCT
ejpam-6745	168	1	+	+	NUM
ejpam-6745	168	2	1	1	NUM
ejpam-6745	168	3	,	,	PUNCT
ejpam-6745	168	4	(	(	PUNCT
ejpam-6745	168	5	26	26	NUM
ejpam-6745	168	6	)	)	PUNCT
ejpam-6745	168	7	we	we	PRON
ejpam-6745	168	8	get	get	VERB
ejpam-6745	168	9	l2(ϑ	l2(ϑ	NOUN
ejpam-6745	168	10	,	,	PUNCT
ejpam-6745	168	11	ζ	ζ	NOUN
ejpam-6745	168	12	)	)	PUNCT
ejpam-6745	168	13	=	=	SYM
ejpam-6745	169	1	2	2	NUM
ejpam-6745	169	2	∞∑	∞∑	NUM
ejpam-6745	169	3	ϵ=2	ϵ=2	NOUN
ejpam-6745	169	4	(	(	PUNCT
ejpam-6745	169	5	ϵ−	ϵ−	NOUN
ejpam-6745	169	6	1)(ϵ−	1)(ϵ−	PROPN
ejpam-6745	169	7	2	2	NUM
ejpam-6745	169	8	)	)	PUNCT
ejpam-6745	169	9	(	(	PUNCT
ejpam-6745	169	10	(	(	PUNCT
ejpam-6745	169	11	ϵ−	ϵ−	NOUN
ejpam-6745	169	12	1	1	X
ejpam-6745	169	13	)	)	PUNCT
ejpam-6745	169	14	k	k	NOUN
ejpam-6745	170	1	+	+	NOUN
ejpam-6745	170	2	1	1	X
ejpam-6745	170	3	)	)	PUNCT
ejpam-6745	170	4	(	(	PUNCT
ejpam-6745	170	5	ϵ−	ϵ−	NOUN
ejpam-6745	170	6	1	1	NUM
ejpam-6745	170	7	)	)	PUNCT
ejpam-6745	170	8	!	!	PUNCT
ejpam-6745	171	1	+	+	CCONJ
ejpam-6745	171	2	(	(	PUNCT
ejpam-6745	171	3	6−	6−	NUM
ejpam-6745	171	4	ζ	ζ	NOUN
ejpam-6745	171	5	−	−	NOUN
ejpam-6745	171	6	cosϑ	cosϑ	NOUN
ejpam-6745	171	7	)	)	PUNCT
ejpam-6745	172	1	∞∑	∞∑	NUM
ejpam-6745	172	2	ϵ=2	ϵ=2	NOUN
ejpam-6745	172	3	ϵ−	ϵ−	NOUN
ejpam-6745	172	4	1	1	NUM
ejpam-6745	172	5	(	(	PUNCT
ejpam-6745	172	6	(	(	PUNCT
ejpam-6745	172	7	ϵ−	ϵ−	NOUN
ejpam-6745	172	8	1	1	X
ejpam-6745	172	9	)	)	PUNCT
ejpam-6745	172	10	k	k	NOUN
ejpam-6745	173	1	+	+	NOUN
ejpam-6745	173	2	1	1	X
ejpam-6745	173	3	)	)	PUNCT
ejpam-6745	173	4	(	(	PUNCT
ejpam-6745	173	5	ϵ−	ϵ−	NOUN
ejpam-6745	173	6	1	1	NUM
ejpam-6745	173	7	)	)	PUNCT
ejpam-6745	173	8	!	!	PUNCT
ejpam-6745	174	1	+	+	CCONJ
ejpam-6745	174	2	(	(	PUNCT
ejpam-6745	174	3	2−	2−	NUM
ejpam-6745	174	4	ζ	ζ	NOUN
ejpam-6745	174	5	−	−	NOUN
ejpam-6745	174	6	cosϑ	cosϑ	NOUN
ejpam-6745	174	7	)	)	PUNCT
ejpam-6745	175	1	∞∑	∞∑	NUM
ejpam-6745	175	2	ϵ=2	ϵ=2	NUM
ejpam-6745	175	3	1	1	NUM
ejpam-6745	175	4	(	(	PUNCT
ejpam-6745	175	5	(	(	PUNCT
ejpam-6745	175	6	ϵ−	ϵ−	NOUN
ejpam-6745	175	7	1	1	X
ejpam-6745	175	8	)	)	PUNCT
ejpam-6745	175	9	k	k	NOUN
ejpam-6745	176	1	+	+	NOUN
ejpam-6745	176	2	1	1	X
ejpam-6745	176	3	)	)	PUNCT
ejpam-6745	176	4	(	(	PUNCT
ejpam-6745	176	5	ϵ−	ϵ−	NOUN
ejpam-6745	176	6	1	1	NUM
ejpam-6745	176	7	)	)	PUNCT
ejpam-6745	176	8	!	!	PUNCT
ejpam-6745	177	1	=	=	SYM
ejpam-6745	178	1	2	2	NUM
ejpam-6745	178	2	∞∑	∞∑	NUM
ejpam-6745	178	3	ϵ=3	ϵ=3	NUM
ejpam-6745	178	4	1	1	NUM
ejpam-6745	178	5	(	(	PUNCT
ejpam-6745	178	6	(	(	PUNCT
ejpam-6745	178	7	ϵ−	ϵ−	NOUN
ejpam-6745	178	8	1	1	X
ejpam-6745	178	9	)	)	PUNCT
ejpam-6745	178	10	k	k	NOUN
ejpam-6745	179	1	+	+	NOUN
ejpam-6745	179	2	1	1	X
ejpam-6745	179	3	)	)	PUNCT
ejpam-6745	179	4	(	(	PUNCT
ejpam-6745	179	5	ϵ−	ϵ−	NOUN
ejpam-6745	179	6	3	3	NUM
ejpam-6745	179	7	)	)	PUNCT
ejpam-6745	179	8	!	!	PUNCT
ejpam-6745	180	1	+	+	CCONJ
ejpam-6745	180	2	(	(	PUNCT
ejpam-6745	180	3	6−	6−	NUM
ejpam-6745	180	4	ζ	ζ	NOUN
ejpam-6745	180	5	−	−	NOUN
ejpam-6745	180	6	cosϑ	cosϑ	NOUN
ejpam-6745	180	7	)	)	PUNCT
ejpam-6745	181	1	∞∑	∞∑	NUM
ejpam-6745	181	2	ϵ=2	ϵ=2	NUM
ejpam-6745	181	3	1	1	NUM
ejpam-6745	181	4	(	(	PUNCT
ejpam-6745	181	5	(	(	PUNCT
ejpam-6745	181	6	ϵ−	ϵ−	NOUN
ejpam-6745	181	7	1	1	X
ejpam-6745	181	8	)	)	PUNCT
ejpam-6745	181	9	k	k	NOUN
ejpam-6745	182	1	+	+	NOUN
ejpam-6745	182	2	1	1	X
ejpam-6745	182	3	)	)	PUNCT
ejpam-6745	182	4	(	(	PUNCT
ejpam-6745	182	5	ϵ−	ϵ−	NOUN
ejpam-6745	182	6	2	2	NUM
ejpam-6745	182	7	)	)	PUNCT
ejpam-6745	182	8	!	!	PUNCT
ejpam-6745	183	1	+	+	CCONJ
ejpam-6745	183	2	(	(	PUNCT
ejpam-6745	183	3	2−	2−	NUM
ejpam-6745	183	4	ζ	ζ	NOUN
ejpam-6745	183	5	−	−	NOUN
ejpam-6745	183	6	cosϑ	cosϑ	NOUN
ejpam-6745	183	7	)	)	PUNCT
ejpam-6745	184	1	∞∑	∞∑	NUM
ejpam-6745	184	2	ϵ=2	ϵ=2	NUM
ejpam-6745	184	3	1	1	NUM
ejpam-6745	184	4	(	(	PUNCT
ejpam-6745	184	5	(	(	PUNCT
ejpam-6745	184	6	ϵ−	ϵ−	NOUN
ejpam-6745	184	7	1	1	X
ejpam-6745	184	8	)	)	PUNCT
ejpam-6745	184	9	k	k	NOUN
ejpam-6745	185	1	+	+	NOUN
ejpam-6745	185	2	1	1	X
ejpam-6745	185	3	)	)	PUNCT
ejpam-6745	185	4	(	(	PUNCT
ejpam-6745	185	5	ϵ−	ϵ−	NOUN
ejpam-6745	185	6	1	1	NUM
ejpam-6745	185	7	)	)	PUNCT
ejpam-6745	185	8	!	!	PUNCT
ejpam-6745	185	9	.	.	PUNCT
ejpam-6745	186	1	f.	f.	PROPN
ejpam-6745	186	2	yousef	yousef	PROPN
ejpam-6745	186	3	,	,	PUNCT
ejpam-6745	186	4	m.	m.	NOUN
ejpam-6745	186	5	m.	m.	PROPN
ejpam-6745	186	6	alholi	alholi	PROPN
ejpam-6745	186	7	,	,	PUNCT
ejpam-6745	186	8	t.	t.	PROPN
ejpam-6745	186	9	al	al	PROPN
ejpam-6745	186	10	-	-	PUNCT
ejpam-6745	186	11	hawary	hawary	PROPN
ejpam-6745	186	12	/	/	SYM
ejpam-6745	186	13	eur	eur	PROPN
ejpam-6745	186	14	.	.	PUNCT
ejpam-6745	187	1	j.	j.	PROPN
ejpam-6745	187	2	pure	pure	PROPN
ejpam-6745	187	3	appl	appl	PROPN
ejpam-6745	187	4	.	.	PROPN
ejpam-6745	187	5	math	math	PROPN
ejpam-6745	187	6	,	,	PUNCT
ejpam-6745	187	7	18	18	NUM
ejpam-6745	187	8	(	(	PUNCT
ejpam-6745	187	9	4	4	NUM
ejpam-6745	187	10	)	)	PUNCT
ejpam-6745	187	11	(	(	PUNCT
ejpam-6745	187	12	2025	2025	NUM
ejpam-6745	187	13	)	)	PUNCT
ejpam-6745	187	14	,	,	PUNCT
ejpam-6745	187	15	6745	6745	NUM
ejpam-6745	187	16	8	8	NUM
ejpam-6745	187	17	of	of	ADP
ejpam-6745	187	18	13	13	NUM
ejpam-6745	187	19	by	by	ADP
ejpam-6745	187	20	(	(	PUNCT
ejpam-6745	187	21	20	20	NUM
ejpam-6745	187	22	)	)	PUNCT
ejpam-6745	187	23	,	,	PUNCT
ejpam-6745	187	24	we	we	PRON
ejpam-6745	187	25	get	get	VERB
ejpam-6745	187	26	l2(ϑ	l2(ϑ	NOUN
ejpam-6745	187	27	,	,	PUNCT
ejpam-6745	187	28	ζ	ζ	NOUN
ejpam-6745	187	29	)	)	PUNCT
ejpam-6745	187	30	≤	≤	NOUN
ejpam-6745	187	31	2	2	NUM
ejpam-6745	187	32	k	k	NOUN
ejpam-6745	187	33	∞∑	∞∑	NUM
ejpam-6745	187	34	ϵ=3	ϵ=3	NUM
ejpam-6745	187	35	1	1	NUM
ejpam-6745	187	36	(	(	PUNCT
ejpam-6745	187	37	ϵ−	ϵ−	NOUN
ejpam-6745	187	38	1	1	NUM
ejpam-6745	187	39	)	)	PUNCT
ejpam-6745	187	40	(	(	PUNCT
ejpam-6745	187	41	ϵ−	ϵ−	NOUN
ejpam-6745	187	42	3	3	NUM
ejpam-6745	187	43	)	)	PUNCT
ejpam-6745	187	44	!	!	PUNCT
ejpam-6745	188	1	+	+	CCONJ
ejpam-6745	188	2	(	(	PUNCT
ejpam-6745	188	3	6−	6−	NUM
ejpam-6745	188	4	ζ	ζ	NOUN
ejpam-6745	188	5	−	−	NOUN
ejpam-6745	188	6	cosϑ	cosϑ	ADJ
ejpam-6745	188	7	)	)	PUNCT
ejpam-6745	189	1	k	k	NOUN
ejpam-6745	190	1	∞∑	∞∑	ADJ
ejpam-6745	190	2	ϵ=2	ϵ=2	PROPN
ejpam-6745	190	3	1	1	NUM
ejpam-6745	190	4	(	(	PUNCT
ejpam-6745	190	5	ϵ−	ϵ−	NOUN
ejpam-6745	190	6	1	1	NUM
ejpam-6745	190	7	)	)	PUNCT
ejpam-6745	190	8	(	(	PUNCT
ejpam-6745	190	9	ϵ−	ϵ−	NOUN
ejpam-6745	190	10	2	2	NUM
ejpam-6745	190	11	)	)	PUNCT
ejpam-6745	190	12	!	!	PUNCT
ejpam-6745	191	1	+	+	CCONJ
ejpam-6745	191	2	(	(	PUNCT
ejpam-6745	191	3	2−	2−	NUM
ejpam-6745	191	4	ζ	ζ	NOUN
ejpam-6745	191	5	−	−	NOUN
ejpam-6745	191	6	cosϑ	cosϑ	ADJ
ejpam-6745	191	7	)	)	PUNCT
ejpam-6745	192	1	k	k	NOUN
ejpam-6745	193	1	∞∑	∞∑	ADJ
ejpam-6745	193	2	ϵ=2	ϵ=2	PROPN
ejpam-6745	193	3	1	1	NUM
ejpam-6745	193	4	(	(	PUNCT
ejpam-6745	193	5	ϵ−	ϵ−	NOUN
ejpam-6745	193	6	1	1	NUM
ejpam-6745	193	7	)	)	PUNCT
ejpam-6745	193	8	(	(	PUNCT
ejpam-6745	193	9	ϵ−	ϵ−	NOUN
ejpam-6745	193	10	1	1	NUM
ejpam-6745	193	11	)	)	PUNCT
ejpam-6745	193	12	!	!	PUNCT
ejpam-6745	193	13	.	.	PUNCT
ejpam-6745	194	1	by	by	ADP
ejpam-6745	194	2	(	(	PUNCT
ejpam-6745	194	3	21	21	NUM
ejpam-6745	194	4	)	)	PUNCT
ejpam-6745	194	5	,	,	PUNCT
ejpam-6745	194	6	we	we	PRON
ejpam-6745	194	7	get	get	VERB
ejpam-6745	194	8	l2(ϑ	l2(ϑ	NOUN
ejpam-6745	194	9	,	,	PUNCT
ejpam-6745	194	10	ζ	ζ	NOUN
ejpam-6745	194	11	)	)	PUNCT
ejpam-6745	194	12	≤	≤	NOUN
ejpam-6745	194	13	32	32	NUM
ejpam-6745	195	1	k	k	NOUN
ejpam-6745	196	1	∞∑	∞∑	NUM
ejpam-6745	196	2	ϵ=3	ϵ=3	NUM
ejpam-6745	196	3	1	1	NUM
ejpam-6745	196	4	(	(	PUNCT
ejpam-6745	196	5	ϵ−	ϵ−	NOUN
ejpam-6745	196	6	1	1	X
ejpam-6745	196	7	)	)	PUNCT
ejpam-6745	196	8	2ϵ	2ϵ	NOUN
ejpam-6745	196	9	+	+	CCONJ
ejpam-6745	196	10	8(6−	8(6−	NUM
ejpam-6745	196	11	ζ	ζ	NOUN
ejpam-6745	196	12	−	−	NOUN
ejpam-6745	196	13	cosϑ	cosϑ	ADJ
ejpam-6745	196	14	)	)	PUNCT
ejpam-6745	197	1	k	k	NOUN
ejpam-6745	198	1	∞∑	∞∑	ADJ
ejpam-6745	198	2	ϵ=2	ϵ=2	PROPN
ejpam-6745	198	3	1	1	NUM
ejpam-6745	198	4	(	(	PUNCT
ejpam-6745	198	5	ϵ−	ϵ−	NOUN
ejpam-6745	198	6	1	1	X
ejpam-6745	198	7	)	)	PUNCT
ejpam-6745	198	8	2ϵ	2ϵ	NOUN
ejpam-6745	199	1	+	+	CCONJ
ejpam-6745	199	2	4(2−	4(2−	NUM
ejpam-6745	199	3	ζ	ζ	NOUN
ejpam-6745	199	4	−	−	NOUN
ejpam-6745	199	5	cosϑ	cosϑ	ADJ
ejpam-6745	199	6	)	)	PUNCT
ejpam-6745	200	1	k	k	NOUN
ejpam-6745	201	1	∞∑	∞∑	ADJ
ejpam-6745	201	2	ϵ=2	ϵ=2	PROPN
ejpam-6745	201	3	1	1	NUM
ejpam-6745	201	4	(	(	PUNCT
ejpam-6745	201	5	ϵ−	ϵ−	NOUN
ejpam-6745	201	6	1	1	X
ejpam-6745	201	7	)	)	PUNCT
ejpam-6745	201	8	2ϵ	2ϵ	NOUN
ejpam-6745	201	9	.	.	PUNCT
ejpam-6745	202	1	using	use	VERB
ejpam-6745	202	2	the	the	DET
ejpam-6745	202	3	series	series	NOUN
ejpam-6745	202	4	sums	sum	NOUN
ejpam-6745	202	5	(	(	PUNCT
ejpam-6745	202	6	17	17	NUM
ejpam-6745	202	7	)	)	PUNCT
ejpam-6745	202	8	and	and	CCONJ
ejpam-6745	202	9	(	(	PUNCT
ejpam-6745	202	10	18	18	NUM
ejpam-6745	202	11	)	)	PUNCT
ejpam-6745	202	12	,	,	PUNCT
ejpam-6745	202	13	we	we	PRON
ejpam-6745	202	14	get	get	VERB
ejpam-6745	202	15	l2(ϑ	l2(ϑ	NOUN
ejpam-6745	202	16	,	,	PUNCT
ejpam-6745	202	17	ζ	ζ	NOUN
ejpam-6745	202	18	)	)	PUNCT
ejpam-6745	202	19	≤	≤	NOUN
ejpam-6745	202	20	1	1	NUM
ejpam-6745	202	21	k	k	NOUN
ejpam-6745	202	22	(	(	PUNCT
ejpam-6745	202	23	16	16	NUM
ejpam-6745	202	24	ln	ln	ADJ
ejpam-6745	202	25	2−	2−	NUM
ejpam-6745	202	26	8)	8)	NUM
ejpam-6745	202	27	+	+	CCONJ
ejpam-6745	202	28	6−	6−	NUM
ejpam-6745	202	29	ζ	ζ	NOUN
ejpam-6745	202	30	−	−	NOUN
ejpam-6745	202	31	cosϑ	cosϑ	ADJ
ejpam-6745	202	32	k	k	X
ejpam-6745	202	33	(	(	PUNCT
ejpam-6745	202	34	4	4	NUM
ejpam-6745	202	35	ln	ln	NOUN
ejpam-6745	202	36	2	2	NUM
ejpam-6745	202	37	)	)	PUNCT
ejpam-6745	202	38	+	+	CCONJ
ejpam-6745	202	39	2−	2−	NUM
ejpam-6745	202	40	ζ	ζ	NOUN
ejpam-6745	202	41	−	−	NOUN
ejpam-6745	202	42	cosϑ	cosϑ	ADJ
ejpam-6745	202	43	k	k	X
ejpam-6745	202	44	(	(	PUNCT
ejpam-6745	202	45	2	2	NUM
ejpam-6745	202	46	ln	ln	NOUN
ejpam-6745	202	47	2	2	NUM
ejpam-6745	202	48	)	)	PUNCT
ejpam-6745	202	49	=	=	SYM
ejpam-6745	202	50	2(22−	2(22−	NUM
ejpam-6745	202	51	3ζ	3ζ	NOUN
ejpam-6745	202	52	−	−	PROPN
ejpam-6745	202	53	3	3	NUM
ejpam-6745	202	54	cosϑ	cosϑ	X
ejpam-6745	202	55	)	)	PUNCT
ejpam-6745	203	1	k	k	PROPN
ejpam-6745	203	2	ln	ln	ADJ
ejpam-6745	203	3	2−	2−	NUM
ejpam-6745	203	4	8	8	NUM
ejpam-6745	203	5	k	k	NOUN
ejpam-6745	203	6	.	.	PUNCT
ejpam-6745	204	1	however	however	ADV
ejpam-6745	204	2	,	,	PUNCT
ejpam-6745	204	3	if	if	SCONJ
ejpam-6745	204	4	and	and	CCONJ
ejpam-6745	204	5	only	only	ADV
ejpam-6745	204	6	if	if	SCONJ
ejpam-6745	204	7	(	(	PUNCT
ejpam-6745	204	8	24	24	NUM
ejpam-6745	204	9	)	)	PUNCT
ejpam-6745	204	10	holds	hold	VERB
ejpam-6745	204	11	,	,	PUNCT
ejpam-6745	204	12	the	the	DET
ejpam-6745	204	13	last	last	ADJ
ejpam-6745	204	14	expression	expression	NOUN
ejpam-6745	204	15	is	be	AUX
ejpam-6745	204	16	bounded	bound	VERB
ejpam-6745	204	17	above	above	ADV
ejpam-6745	204	18	by	by	ADP
ejpam-6745	204	19	cosϑ−	cosϑ−	PROPN
ejpam-6745	204	20	ζ	ζ	PROPN
ejpam-6745	204	21	.	.	PROPN
ejpam-6745	205	1	3	3	X
ejpam-6745	205	2	.	.	NOUN
ejpam-6745	205	3	necessary	necessary	ADJ
ejpam-6745	205	4	and	and	CCONJ
ejpam-6745	205	5	sufficient	sufficient	ADJ
ejpam-6745	205	6	conditions	condition	NOUN
ejpam-6745	205	7	for	for	ADP
ejpam-6745	205	8	the	the	DET
ejpam-6745	205	9	convolution	convolution	NOUN
ejpam-6745	205	10	operator	operator	NOUN
ejpam-6745	205	11	iik(z	iik(z	PRON
ejpam-6745	205	12	)	)	PUNCT
ejpam-6745	205	13	in	in	ADP
ejpam-6745	205	14	this	this	DET
ejpam-6745	205	15	section	section	NOUN
ejpam-6745	205	16	,	,	PUNCT
ejpam-6745	205	17	we	we	PRON
ejpam-6745	205	18	find	find	VERB
ejpam-6745	205	19	sufficient	sufficient	ADJ
ejpam-6745	205	20	conditions	condition	NOUN
ejpam-6745	205	21	for	for	SCONJ
ejpam-6745	205	22	the	the	DET
ejpam-6745	205	23	convolution	convolution	NOUN
ejpam-6745	205	24	operator	operator	NOUN
ejpam-6745	205	25	iik(z	iik(z	PRON
ejpam-6745	205	26	)	)	PUNCT
ejpam-6745	205	27	to	to	PART
ejpam-6745	205	28	be	be	AUX
ejpam-6745	205	29	in	in	ADP
ejpam-6745	205	30	the	the	DET
ejpam-6745	205	31	subclasses	subclass	NOUN
ejpam-6745	205	32	spe(ϑ	spe(ϑ	PROPN
ejpam-6745	205	33	,	,	PUNCT
ejpam-6745	205	34	ζ	ζ	NOUN
ejpam-6745	205	35	)	)	PUNCT
ejpam-6745	205	36	and	and	CCONJ
ejpam-6745	205	37	cspe(ϑ	cspe(ϑ	PROPN
ejpam-6745	205	38	,	,	PUNCT
ejpam-6745	205	39	ζ	ζ	NOUN
ejpam-6745	205	40	)	)	PUNCT
ejpam-6745	205	41	.	.	PUNCT
ejpam-6745	206	1	theorem	theorem	NOUN
ejpam-6745	206	2	3	3	X
ejpam-6745	206	3	.	.	PUNCT
ejpam-6745	207	1	let	let	VERB
ejpam-6745	207	2	k	k	PROPN
ejpam-6745	207	3	∈	∈	PROPN
ejpam-6745	207	4	n.	n.	NOUN
ejpam-6745	207	5	if	if	SCONJ
ejpam-6745	207	6	q	q	X
ejpam-6745	207	7	∈	∈	PROPN
ejpam-6745	207	8	gτ	gτ	PROPN
ejpam-6745	207	9	(	(	PUNCT
ejpam-6745	207	10	c1	c1	PROPN
ejpam-6745	207	11	,	,	PUNCT
ejpam-6745	207	12	c2	c2	PROPN
ejpam-6745	207	13	)	)	PUNCT
ejpam-6745	207	14	,	,	PUNCT
ejpam-6745	207	15	then	then	ADV
ejpam-6745	207	16	iik(z	iik(z	PROPN
ejpam-6745	207	17	)	)	PUNCT
ejpam-6745	207	18	is	be	AUX
ejpam-6745	207	19	in	in	ADP
ejpam-6745	207	20	the	the	DET
ejpam-6745	207	21	subclass	subclass	NOUN
ejpam-6745	207	22	spe(ϑ	spe(ϑ	PROPN
ejpam-6745	207	23	,	,	PUNCT
ejpam-6745	207	24	ζ	ζ	NOUN
ejpam-6745	207	25	)	)	PUNCT
ejpam-6745	207	26	if	if	SCONJ
ejpam-6745	207	27	(	(	PUNCT
ejpam-6745	207	28	c1	c1	PROPN
ejpam-6745	207	29	−	−	PROPN
ejpam-6745	207	30	c2)|τ	c2)|τ	PROPN
ejpam-6745	207	31	|(4−	|(4−	ADP
ejpam-6745	207	32	ζ	ζ	NOUN
ejpam-6745	207	33	−	−	PROPN
ejpam-6745	207	34	cosϑ	cosϑ	NOUN
ejpam-6745	207	35	)	)	PUNCT
ejpam-6745	208	1	ln	ln	PROPN
ejpam-6745	208	2	2	2	NUM
ejpam-6745	208	3	≤	≤	NOUN
ejpam-6745	209	1	k	k	PROPN
ejpam-6745	209	2	(	(	PUNCT
ejpam-6745	209	3	cosϑ−	cosϑ−	PROPN
ejpam-6745	209	4	ζ	ζ	PROPN
ejpam-6745	209	5	)	)	PUNCT
ejpam-6745	209	6	.	.	PUNCT
ejpam-6745	210	1	(	(	PUNCT
ejpam-6745	210	2	27	27	NUM
ejpam-6745	210	3	)	)	PUNCT
ejpam-6745	210	4	proof	proof	NOUN
ejpam-6745	210	5	.	.	PUNCT
ejpam-6745	211	1	in	in	ADP
ejpam-6745	211	2	view	view	NOUN
ejpam-6745	211	3	of	of	ADP
ejpam-6745	211	4	(	(	PUNCT
ejpam-6745	211	5	11	11	NUM
ejpam-6745	211	6	)	)	PUNCT
ejpam-6745	211	7	,	,	PUNCT
ejpam-6745	211	8	it	it	PRON
ejpam-6745	211	9	suffices	suffice	VERB
ejpam-6745	211	10	to	to	PART
ejpam-6745	211	11	show	show	VERB
ejpam-6745	211	12	that	that	SCONJ
ejpam-6745	211	13	m1(ϑ	m1(ϑ	NOUN
ejpam-6745	211	14	,	,	PUNCT
ejpam-6745	211	15	ζ	ζ	NOUN
ejpam-6745	211	16	)	)	PUNCT
ejpam-6745	211	17	=	=	NOUN
ejpam-6745	212	1	∞∑	∞∑	NUM
ejpam-6745	212	2	ϵ=2	ϵ=2	NOUN
ejpam-6745	213	1	[	[	X
ejpam-6745	213	2	2ϵ−	2ϵ−	NUM
ejpam-6745	213	3	ζ	ζ	NOUN
ejpam-6745	213	4	−	−	NOUN
ejpam-6745	213	5	cosϑ	cosϑ	VERB
ejpam-6745	213	6	]	]	X
ejpam-6745	213	7	1	1	NUM
ejpam-6745	213	8	(	(	PUNCT
ejpam-6745	213	9	(	(	PUNCT
ejpam-6745	213	10	ϵ−	ϵ−	NOUN
ejpam-6745	213	11	1	1	X
ejpam-6745	213	12	)	)	PUNCT
ejpam-6745	213	13	k	k	NOUN
ejpam-6745	214	1	+	+	NOUN
ejpam-6745	214	2	1	1	X
ejpam-6745	214	3	)	)	PUNCT
ejpam-6745	214	4	(	(	PUNCT
ejpam-6745	214	5	ϵ−	ϵ−	NOUN
ejpam-6745	214	6	1	1	NUM
ejpam-6745	214	7	)	)	PUNCT
ejpam-6745	214	8	!	!	PUNCT
ejpam-6745	215	1	|βϵ|	|βϵ|	ADJ
ejpam-6745	215	2	≤	≤	PROPN
ejpam-6745	215	3	cosϑ−	cosϑ−	NOUN
ejpam-6745	215	4	ζ	ζ	PROPN
ejpam-6745	215	5	.	.	PUNCT
ejpam-6745	216	1	since	since	SCONJ
ejpam-6745	216	2	q	q	PROPN
ejpam-6745	216	3	∈	∈	PROPN
ejpam-6745	216	4	gτ	gτ	PROPN
ejpam-6745	216	5	(	(	PUNCT
ejpam-6745	216	6	c1	c1	PROPN
ejpam-6745	216	7	,	,	PUNCT
ejpam-6745	216	8	c2	c2	PROPN
ejpam-6745	216	9	)	)	PUNCT
ejpam-6745	216	10	,	,	PUNCT
ejpam-6745	216	11	then	then	ADV
ejpam-6745	216	12	by	by	ADP
ejpam-6745	216	13	virtue	virtue	NOUN
ejpam-6745	216	14	(	(	PUNCT
ejpam-6745	216	15	15	15	NUM
ejpam-6745	216	16	)	)	PUNCT
ejpam-6745	216	17	,	,	PUNCT
ejpam-6745	216	18	we	we	PRON
ejpam-6745	216	19	have	have	VERB
ejpam-6745	216	20	m1(ϑ	m1(ϑ	NOUN
ejpam-6745	216	21	,	,	PUNCT
ejpam-6745	216	22	ζ	ζ	NOUN
ejpam-6745	216	23	)	)	PUNCT
ejpam-6745	216	24	≤	≤	NOUN
ejpam-6745	216	25	(	(	PUNCT
ejpam-6745	216	26	c1	c1	PROPN
ejpam-6745	216	27	−	−	PROPN
ejpam-6745	216	28	c2)|τ	c2)|τ	PROPN
ejpam-6745	216	29	|	|	ADV
ejpam-6745	216	30	(	(	PUNCT
ejpam-6745	216	31	∞∑	∞∑	ADJ
ejpam-6745	216	32	ϵ=2	ϵ=2	PROPN
ejpam-6745	216	33	2	2	NUM
ejpam-6745	216	34	(	(	PUNCT
ejpam-6745	216	35	(	(	PUNCT
ejpam-6745	216	36	ϵ−	ϵ−	NOUN
ejpam-6745	216	37	1	1	X
ejpam-6745	216	38	)	)	PUNCT
ejpam-6745	216	39	k	k	NOUN
ejpam-6745	217	1	+	+	NOUN
ejpam-6745	217	2	1	1	X
ejpam-6745	217	3	)	)	PUNCT
ejpam-6745	217	4	(	(	PUNCT
ejpam-6745	217	5	ϵ−	ϵ−	NOUN
ejpam-6745	217	6	1	1	NUM
ejpam-6745	217	7	)	)	PUNCT
ejpam-6745	217	8	!	!	PUNCT
ejpam-6745	218	1	−	−	NOUN
ejpam-6745	219	1	∞∑	∞∑	NUM
ejpam-6745	219	2	ϵ=2	ϵ=2	ADJ
ejpam-6745	219	3	ζ	ζ	NOUN
ejpam-6745	219	4	+	+	CCONJ
ejpam-6745	219	5	cosϑ	cosϑ	VERB
ejpam-6745	219	6	(	(	PUNCT
ejpam-6745	219	7	(	(	PUNCT
ejpam-6745	219	8	ϵ−	ϵ−	NOUN
ejpam-6745	219	9	1	1	X
ejpam-6745	219	10	)	)	PUNCT
ejpam-6745	219	11	k	k	NOUN
ejpam-6745	219	12	+	+	PUNCT
ejpam-6745	219	13	1)ϵ	1)ϵ	NUM
ejpam-6745	219	14	!	!	PUNCT
ejpam-6745	219	15	)	)	PUNCT
ejpam-6745	219	16	.	.	PUNCT
ejpam-6745	220	1	by	by	ADP
ejpam-6745	220	2	(	(	PUNCT
ejpam-6745	220	3	20	20	NUM
ejpam-6745	220	4	)	)	PUNCT
ejpam-6745	220	5	and	and	CCONJ
ejpam-6745	220	6	(	(	PUNCT
ejpam-6745	220	7	21	21	NUM
ejpam-6745	220	8	)	)	PUNCT
ejpam-6745	220	9	,	,	PUNCT
ejpam-6745	220	10	we	we	PRON
ejpam-6745	220	11	get	get	VERB
ejpam-6745	220	12	m1(ϑ	m1(ϑ	NOUN
ejpam-6745	220	13	,	,	PUNCT
ejpam-6745	220	14	ζ	ζ	NOUN
ejpam-6745	220	15	)	)	PUNCT
ejpam-6745	220	16	≤	≤	NOUN
ejpam-6745	220	17	(	(	PUNCT
ejpam-6745	220	18	c1	c1	PROPN
ejpam-6745	220	19	−	−	PROPN
ejpam-6745	220	20	c2)|τ	c2)|τ	PROPN
ejpam-6745	221	1	|	|	ADV
ejpam-6745	221	2	k	k	PROPN
ejpam-6745	221	3	(	(	PUNCT
ejpam-6745	221	4	8	8	NUM
ejpam-6745	221	5	∞∑	∞∑	NUM
ejpam-6745	221	6	ϵ=2	ϵ=2	NUM
ejpam-6745	221	7	1	1	NUM
ejpam-6745	221	8	(	(	PUNCT
ejpam-6745	221	9	ϵ−	ϵ−	NOUN
ejpam-6745	221	10	1	1	X
ejpam-6745	221	11	)	)	PUNCT
ejpam-6745	221	12	2ϵ	2ϵ	NOUN
ejpam-6745	221	13	−	−	NOUN
ejpam-6745	221	14	2	2	NUM
ejpam-6745	221	15	∞∑	∞∑	NUM
ejpam-6745	221	16	ϵ=2	ϵ=2	ADJ
ejpam-6745	221	17	ζ	ζ	NOUN
ejpam-6745	221	18	+	+	CCONJ
ejpam-6745	221	19	cosϑ	cosϑ	ADJ
ejpam-6745	221	20	(	(	PUNCT
ejpam-6745	221	21	ϵ−	ϵ−	NOUN
ejpam-6745	221	22	1	1	X
ejpam-6745	221	23	)	)	PUNCT
ejpam-6745	221	24	2ϵ	2ϵ	NUM
ejpam-6745	221	25	)	)	PUNCT
ejpam-6745	221	26	.	.	PUNCT
ejpam-6745	222	1	f.	f.	PROPN
ejpam-6745	222	2	yousef	yousef	PROPN
ejpam-6745	222	3	,	,	PUNCT
ejpam-6745	222	4	m.	m.	NOUN
ejpam-6745	222	5	m.	m.	PROPN
ejpam-6745	222	6	alholi	alholi	PROPN
ejpam-6745	222	7	,	,	PUNCT
ejpam-6745	222	8	t.	t.	PROPN
ejpam-6745	222	9	al	al	PROPN
ejpam-6745	222	10	-	-	PUNCT
ejpam-6745	222	11	hawary	hawary	PROPN
ejpam-6745	222	12	/	/	SYM
ejpam-6745	222	13	eur	eur	PROPN
ejpam-6745	222	14	.	.	PUNCT
ejpam-6745	223	1	j.	j.	PROPN
ejpam-6745	223	2	pure	pure	PROPN
ejpam-6745	223	3	appl	appl	PROPN
ejpam-6745	223	4	.	.	PROPN
ejpam-6745	223	5	math	math	PROPN
ejpam-6745	223	6	,	,	PUNCT
ejpam-6745	223	7	18	18	NUM
ejpam-6745	223	8	(	(	PUNCT
ejpam-6745	223	9	4	4	NUM
ejpam-6745	223	10	)	)	PUNCT
ejpam-6745	223	11	(	(	PUNCT
ejpam-6745	223	12	2025	2025	NUM
ejpam-6745	223	13	)	)	PUNCT
ejpam-6745	223	14	,	,	PUNCT
ejpam-6745	223	15	6745	6745	NUM
ejpam-6745	223	16	9	9	NUM
ejpam-6745	223	17	of	of	ADP
ejpam-6745	223	18	13	13	NUM
ejpam-6745	223	19	by	by	ADP
ejpam-6745	223	20	(	(	PUNCT
ejpam-6745	223	21	17	17	NUM
ejpam-6745	223	22	)	)	PUNCT
ejpam-6745	223	23	,	,	PUNCT
ejpam-6745	223	24	we	we	PRON
ejpam-6745	223	25	get	get	VERB
ejpam-6745	223	26	m1(ϑ	m1(ϑ	NOUN
ejpam-6745	223	27	,	,	PUNCT
ejpam-6745	223	28	ζ	ζ	NOUN
ejpam-6745	223	29	)	)	PUNCT
ejpam-6745	223	30	≤	≤	NOUN
ejpam-6745	223	31	(	(	PUNCT
ejpam-6745	223	32	c1	c1	PROPN
ejpam-6745	223	33	−	−	PROPN
ejpam-6745	224	1	c2)|τ	c2)|τ	PROPN
ejpam-6745	225	1	|	|	ADV
ejpam-6745	225	2	k	k	PROPN
ejpam-6745	225	3	(	(	PUNCT
ejpam-6745	225	4	4−	4−	NOUN
ejpam-6745	225	5	ζ	ζ	NOUN
ejpam-6745	225	6	−	−	PROPN
ejpam-6745	225	7	cosϑ	cosϑ	X
ejpam-6745	225	8	)	)	PUNCT
ejpam-6745	225	9	ln	ln	ADP
ejpam-6745	225	10	2	2	NUM
ejpam-6745	225	11	.	.	PUNCT
ejpam-6745	226	1	however	however	ADV
ejpam-6745	226	2	,	,	PUNCT
ejpam-6745	226	3	the	the	DET
ejpam-6745	226	4	last	last	ADJ
ejpam-6745	226	5	expression	expression	NOUN
ejpam-6745	226	6	is	be	AUX
ejpam-6745	226	7	bounded	bound	VERB
ejpam-6745	226	8	above	above	ADV
ejpam-6745	226	9	by	by	ADP
ejpam-6745	226	10	cosϑ−	cosϑ−	PROPN
ejpam-6745	226	11	ζ	ζ	PROPN
ejpam-6745	226	12	if	if	SCONJ
ejpam-6745	226	13	(	(	PUNCT
ejpam-6745	226	14	27	27	NUM
ejpam-6745	226	15	)	)	PUNCT
ejpam-6745	226	16	holds	hold	VERB
ejpam-6745	226	17	.	.	PUNCT
ejpam-6745	227	1	theorem	theorem	NOUN
ejpam-6745	227	2	4	4	NUM
ejpam-6745	227	3	.	.	PUNCT
ejpam-6745	228	1	let	let	VERB
ejpam-6745	228	2	k	k	PROPN
ejpam-6745	228	3	∈	∈	PROPN
ejpam-6745	228	4	n.	n.	NOUN
ejpam-6745	228	5	if	if	SCONJ
ejpam-6745	228	6	q	q	X
ejpam-6745	228	7	∈	∈	PROPN
ejpam-6745	228	8	gτ	gτ	PROPN
ejpam-6745	228	9	(	(	PUNCT
ejpam-6745	228	10	c1	c1	PROPN
ejpam-6745	228	11	,	,	PUNCT
ejpam-6745	228	12	c2	c2	PROPN
ejpam-6745	228	13	)	)	PUNCT
ejpam-6745	228	14	,	,	PUNCT
ejpam-6745	228	15	then	then	ADV
ejpam-6745	228	16	iik(z	iik(z	PROPN
ejpam-6745	228	17	)	)	PUNCT
ejpam-6745	228	18	is	be	AUX
ejpam-6745	228	19	in	in	ADP
ejpam-6745	228	20	the	the	DET
ejpam-6745	228	21	subclass	subclass	NOUN
ejpam-6745	228	22	cspe(ϑ	cspe(ϑ	PROPN
ejpam-6745	228	23	,	,	PUNCT
ejpam-6745	228	24	ζ	ζ	NOUN
ejpam-6745	228	25	)	)	PUNCT
ejpam-6745	228	26	if	if	SCONJ
ejpam-6745	228	27	2(c1	2(c1	NUM
ejpam-6745	228	28	−	−	PROPN
ejpam-6745	228	29	c2)|τ	c2)|τ	PROPN
ejpam-6745	228	30	|	|	ADV
ejpam-6745	228	31	(	(	PUNCT
ejpam-6745	228	32	6−	6−	NUM
ejpam-6745	228	33	ζ	ζ	NOUN
ejpam-6745	228	34	−	−	NOUN
ejpam-6745	228	35	cosϑ	cosϑ	ADJ
ejpam-6745	228	36	)	)	PUNCT
ejpam-6745	229	1	ln	ln	PROPN
ejpam-6745	229	2	2	2	NUM
ejpam-6745	229	3	≤	≤	NOUN
ejpam-6745	230	1	k	k	PROPN
ejpam-6745	230	2	(	(	PUNCT
ejpam-6745	230	3	cosϑ−	cosϑ−	PROPN
ejpam-6745	230	4	ζ	ζ	PROPN
ejpam-6745	230	5	)	)	PUNCT
ejpam-6745	230	6	.	.	PUNCT
ejpam-6745	231	1	(	(	PUNCT
ejpam-6745	231	2	28	28	NUM
ejpam-6745	231	3	)	)	PUNCT
ejpam-6745	231	4	proof	proof	NOUN
ejpam-6745	231	5	.	.	PUNCT
ejpam-6745	232	1	by	by	ADP
ejpam-6745	232	2	view	view	NOUN
ejpam-6745	232	3	of	of	ADP
ejpam-6745	232	4	(	(	PUNCT
ejpam-6745	232	5	13	13	NUM
ejpam-6745	232	6	)	)	PUNCT
ejpam-6745	232	7	,	,	PUNCT
ejpam-6745	232	8	it	it	PRON
ejpam-6745	232	9	suffices	suffice	VERB
ejpam-6745	232	10	to	to	PART
ejpam-6745	232	11	show	show	VERB
ejpam-6745	232	12	that	that	SCONJ
ejpam-6745	232	13	m2(ϑ	m2(ϑ	NOUN
ejpam-6745	232	14	,	,	PUNCT
ejpam-6745	232	15	ζ	ζ	NOUN
ejpam-6745	232	16	)	)	PUNCT
ejpam-6745	232	17	=	=	NOUN
ejpam-6745	233	1	∞∑	∞∑	NUM
ejpam-6745	233	2	ϵ=2	ϵ=2	PROPN
ejpam-6745	233	3	ϵ	ϵ	X
ejpam-6745	233	4	[	[	X
ejpam-6745	233	5	2ϵ−	2ϵ−	NUM
ejpam-6745	233	6	ζ	ζ	NOUN
ejpam-6745	233	7	−	−	NOUN
ejpam-6745	233	8	cosϑ	cosϑ	VERB
ejpam-6745	233	9	]	]	X
ejpam-6745	233	10	1	1	NUM
ejpam-6745	233	11	(	(	PUNCT
ejpam-6745	233	12	(	(	PUNCT
ejpam-6745	233	13	ϵ−	ϵ−	NOUN
ejpam-6745	233	14	1	1	X
ejpam-6745	233	15	)	)	PUNCT
ejpam-6745	233	16	k	k	NOUN
ejpam-6745	234	1	+	+	NOUN
ejpam-6745	234	2	1	1	X
ejpam-6745	234	3	)	)	PUNCT
ejpam-6745	234	4	(	(	PUNCT
ejpam-6745	234	5	ϵ−	ϵ−	NOUN
ejpam-6745	234	6	1	1	NUM
ejpam-6745	234	7	)	)	PUNCT
ejpam-6745	234	8	!	!	PUNCT
ejpam-6745	235	1	|βϵ|	|βϵ|	ADJ
ejpam-6745	235	2	≤	≤	PROPN
ejpam-6745	235	3	cosϑ−	cosϑ−	NOUN
ejpam-6745	235	4	ζ	ζ	PROPN
ejpam-6745	235	5	.	.	PUNCT
ejpam-6745	236	1	since	since	SCONJ
ejpam-6745	236	2	q	q	PROPN
ejpam-6745	236	3	∈	∈	PROPN
ejpam-6745	236	4	gτ	gτ	PROPN
ejpam-6745	236	5	(	(	PUNCT
ejpam-6745	236	6	c1	c1	PROPN
ejpam-6745	236	7	,	,	PUNCT
ejpam-6745	236	8	c2	c2	PROPN
ejpam-6745	236	9	)	)	PUNCT
ejpam-6745	236	10	,	,	PUNCT
ejpam-6745	236	11	then	then	ADV
ejpam-6745	236	12	by	by	ADP
ejpam-6745	236	13	virtue	virtue	NOUN
ejpam-6745	236	14	(	(	PUNCT
ejpam-6745	236	15	15	15	NUM
ejpam-6745	236	16	)	)	PUNCT
ejpam-6745	236	17	,	,	PUNCT
ejpam-6745	236	18	we	we	PRON
ejpam-6745	236	19	have	have	VERB
ejpam-6745	236	20	m2(ϑ	m2(ϑ	NOUN
ejpam-6745	236	21	,	,	PUNCT
ejpam-6745	236	22	ζ	ζ	NOUN
ejpam-6745	236	23	)	)	PUNCT
ejpam-6745	236	24	≤	≤	NOUN
ejpam-6745	236	25	(	(	PUNCT
ejpam-6745	236	26	c1	c1	PROPN
ejpam-6745	236	27	−	−	PROPN
ejpam-6745	236	28	c2)|τ	c2)|τ	PROPN
ejpam-6745	236	29	|	|	ADV
ejpam-6745	236	30	(	(	PUNCT
ejpam-6745	236	31	∞∑	∞∑	NUM
ejpam-6745	236	32	ϵ=2	ϵ=2	PROPN
ejpam-6745	236	33	2ϵ	2ϵ	NOUN
ejpam-6745	236	34	(	(	PUNCT
ejpam-6745	236	35	(	(	PUNCT
ejpam-6745	236	36	ϵ−	ϵ−	NOUN
ejpam-6745	236	37	1	1	X
ejpam-6745	236	38	)	)	PUNCT
ejpam-6745	236	39	k	k	NOUN
ejpam-6745	237	1	+	+	NOUN
ejpam-6745	237	2	1	1	X
ejpam-6745	237	3	)	)	PUNCT
ejpam-6745	237	4	(	(	PUNCT
ejpam-6745	237	5	ϵ−	ϵ−	NOUN
ejpam-6745	237	6	1	1	NUM
ejpam-6745	237	7	)	)	PUNCT
ejpam-6745	237	8	!	!	PUNCT
ejpam-6745	238	1	−	−	NOUN
ejpam-6745	239	1	∞∑	∞∑	NUM
ejpam-6745	239	2	ϵ=2	ϵ=2	ADJ
ejpam-6745	239	3	ζ	ζ	NOUN
ejpam-6745	239	4	+	+	CCONJ
ejpam-6745	239	5	cosϑ	cosϑ	VERB
ejpam-6745	239	6	(	(	PUNCT
ejpam-6745	239	7	(	(	PUNCT
ejpam-6745	239	8	ϵ−	ϵ−	NOUN
ejpam-6745	239	9	1	1	X
ejpam-6745	239	10	)	)	PUNCT
ejpam-6745	239	11	k	k	NOUN
ejpam-6745	240	1	+	+	NOUN
ejpam-6745	240	2	1	1	X
ejpam-6745	240	3	)	)	PUNCT
ejpam-6745	240	4	(	(	PUNCT
ejpam-6745	240	5	ϵ−	ϵ−	NOUN
ejpam-6745	240	6	1	1	NUM
ejpam-6745	240	7	)	)	PUNCT
ejpam-6745	240	8	!	!	PUNCT
ejpam-6745	240	9	)	)	PUNCT
ejpam-6745	240	10	.	.	PUNCT
ejpam-6745	241	1	by	by	ADP
ejpam-6745	241	2	(	(	PUNCT
ejpam-6745	241	3	25	25	NUM
ejpam-6745	241	4	)	)	PUNCT
ejpam-6745	241	5	,	,	PUNCT
ejpam-6745	241	6	we	we	PRON
ejpam-6745	241	7	get	get	VERB
ejpam-6745	241	8	m2(ϑ	m2(ϑ	NOUN
ejpam-6745	241	9	,	,	PUNCT
ejpam-6745	241	10	ζ	ζ	NOUN
ejpam-6745	241	11	)	)	PUNCT
ejpam-6745	241	12	≤	≤	NOUN
ejpam-6745	241	13	(	(	PUNCT
ejpam-6745	241	14	c1	c1	PROPN
ejpam-6745	241	15	−	−	PROPN
ejpam-6745	241	16	c2)|τ	c2)|τ	PROPN
ejpam-6745	241	17	|	|	ADV
ejpam-6745	241	18	(	(	PUNCT
ejpam-6745	241	19	∞∑	∞∑	NUM
ejpam-6745	241	20	ϵ=2	ϵ=2	PROPN
ejpam-6745	241	21	2(ϵ−	2(ϵ−	PROPN
ejpam-6745	241	22	1	1	NUM
ejpam-6745	241	23	)	)	PUNCT
ejpam-6745	241	24	(	(	PUNCT
ejpam-6745	241	25	(	(	PUNCT
ejpam-6745	241	26	ϵ−	ϵ−	NOUN
ejpam-6745	241	27	1	1	X
ejpam-6745	241	28	)	)	PUNCT
ejpam-6745	241	29	k	k	NOUN
ejpam-6745	242	1	+	+	NOUN
ejpam-6745	242	2	1	1	X
ejpam-6745	242	3	)	)	PUNCT
ejpam-6745	242	4	(	(	PUNCT
ejpam-6745	242	5	ϵ−	ϵ−	NOUN
ejpam-6745	242	6	1	1	NUM
ejpam-6745	242	7	)	)	PUNCT
ejpam-6745	242	8	!	!	PUNCT
ejpam-6745	243	1	+	+	CCONJ
ejpam-6745	243	2	∞∑	∞∑	NUM
ejpam-6745	243	3	ϵ=2	ϵ=2	NUM
ejpam-6745	243	4	2−	2−	NUM
ejpam-6745	243	5	ζ	ζ	NOUN
ejpam-6745	243	6	−	−	NOUN
ejpam-6745	243	7	cosϑ	cosϑ	NOUN
ejpam-6745	243	8	(	(	PUNCT
ejpam-6745	243	9	(	(	PUNCT
ejpam-6745	243	10	ϵ−	ϵ−	NOUN
ejpam-6745	243	11	1	1	X
ejpam-6745	243	12	)	)	PUNCT
ejpam-6745	243	13	k	k	NOUN
ejpam-6745	244	1	+	+	NOUN
ejpam-6745	244	2	1	1	X
ejpam-6745	244	3	)	)	PUNCT
ejpam-6745	244	4	(	(	PUNCT
ejpam-6745	244	5	ϵ−	ϵ−	NOUN
ejpam-6745	244	6	1	1	NUM
ejpam-6745	244	7	)	)	PUNCT
ejpam-6745	244	8	!	!	PUNCT
ejpam-6745	244	9	)	)	PUNCT
ejpam-6745	245	1	=	=	PUNCT
ejpam-6745	245	2	(	(	PUNCT
ejpam-6745	245	3	c1	c1	PROPN
ejpam-6745	245	4	−	−	PROPN
ejpam-6745	246	1	c2)|τ	c2)|τ	PROPN
ejpam-6745	247	1	|	|	ADV
ejpam-6745	247	2	(	(	PUNCT
ejpam-6745	247	3	∞∑	∞∑	ADJ
ejpam-6745	247	4	ϵ=2	ϵ=2	PROPN
ejpam-6745	247	5	2	2	NUM
ejpam-6745	247	6	(	(	PUNCT
ejpam-6745	247	7	(	(	PUNCT
ejpam-6745	247	8	ϵ−	ϵ−	NOUN
ejpam-6745	247	9	1	1	X
ejpam-6745	247	10	)	)	PUNCT
ejpam-6745	247	11	k	k	NOUN
ejpam-6745	248	1	+	+	NOUN
ejpam-6745	248	2	1	1	X
ejpam-6745	248	3	)	)	PUNCT
ejpam-6745	248	4	(	(	PUNCT
ejpam-6745	248	5	ϵ−	ϵ−	NOUN
ejpam-6745	248	6	2	2	NUM
ejpam-6745	248	7	)	)	PUNCT
ejpam-6745	248	8	!	!	PUNCT
ejpam-6745	249	1	+	+	CCONJ
ejpam-6745	249	2	∞∑	∞∑	NUM
ejpam-6745	249	3	ϵ=2	ϵ=2	NUM
ejpam-6745	249	4	2−	2−	NUM
ejpam-6745	249	5	ζ	ζ	NOUN
ejpam-6745	249	6	−	−	NOUN
ejpam-6745	249	7	cosϑ	cosϑ	NOUN
ejpam-6745	249	8	(	(	PUNCT
ejpam-6745	249	9	(	(	PUNCT
ejpam-6745	249	10	ϵ−	ϵ−	NOUN
ejpam-6745	249	11	1	1	X
ejpam-6745	249	12	)	)	PUNCT
ejpam-6745	249	13	k	k	NOUN
ejpam-6745	250	1	+	+	NOUN
ejpam-6745	250	2	1	1	X
ejpam-6745	250	3	)	)	PUNCT
ejpam-6745	250	4	(	(	PUNCT
ejpam-6745	250	5	ϵ−	ϵ−	NOUN
ejpam-6745	250	6	1	1	NUM
ejpam-6745	250	7	)	)	PUNCT
ejpam-6745	250	8	!	!	PUNCT
ejpam-6745	250	9	)	)	PUNCT
ejpam-6745	250	10	.	.	PUNCT
ejpam-6745	251	1	by	by	ADP
ejpam-6745	251	2	(	(	PUNCT
ejpam-6745	251	3	20	20	NUM
ejpam-6745	251	4	)	)	PUNCT
ejpam-6745	251	5	and	and	CCONJ
ejpam-6745	251	6	(	(	PUNCT
ejpam-6745	251	7	21	21	NUM
ejpam-6745	251	8	)	)	PUNCT
ejpam-6745	251	9	,	,	PUNCT
ejpam-6745	251	10	we	we	PRON
ejpam-6745	251	11	get	get	VERB
ejpam-6745	251	12	m2(ϑ	m2(ϑ	NOUN
ejpam-6745	251	13	,	,	PUNCT
ejpam-6745	251	14	ζ	ζ	NOUN
ejpam-6745	251	15	)	)	PUNCT
ejpam-6745	251	16	≤	≤	NOUN
ejpam-6745	251	17	(	(	PUNCT
ejpam-6745	251	18	c1	c1	PROPN
ejpam-6745	251	19	−	−	PROPN
ejpam-6745	252	1	c2)|τ	c2)|τ	PROPN
ejpam-6745	253	1	|	|	ADV
ejpam-6745	253	2	k	k	PROPN
ejpam-6745	253	3	(	(	PUNCT
ejpam-6745	253	4	16	16	NUM
ejpam-6745	253	5	∞∑	∞∑	NUM
ejpam-6745	253	6	ϵ=2	ϵ=2	NUM
ejpam-6745	253	7	1	1	NUM
ejpam-6745	253	8	(	(	PUNCT
ejpam-6745	253	9	ϵ−	ϵ−	NOUN
ejpam-6745	253	10	1	1	X
ejpam-6745	253	11	)	)	PUNCT
ejpam-6745	253	12	2ϵ	2ϵ	NOUN
ejpam-6745	254	1	+	+	CCONJ
ejpam-6745	254	2	4	4	NUM
ejpam-6745	254	3	∞∑	∞∑	NUM
ejpam-6745	254	4	ϵ=2	ϵ=2	NUM
ejpam-6745	254	5	2−	2−	NUM
ejpam-6745	254	6	ζ	ζ	NOUN
ejpam-6745	254	7	−	−	NOUN
ejpam-6745	254	8	cosϑ	cosϑ	ADJ
ejpam-6745	254	9	(	(	PUNCT
ejpam-6745	254	10	ϵ−	ϵ−	NOUN
ejpam-6745	254	11	1	1	X
ejpam-6745	254	12	)	)	PUNCT
ejpam-6745	254	13	2ϵ	2ϵ	NUM
ejpam-6745	254	14	)	)	PUNCT
ejpam-6745	254	15	.	.	PUNCT
ejpam-6745	255	1	by	by	ADP
ejpam-6745	255	2	(	(	PUNCT
ejpam-6745	255	3	17	17	NUM
ejpam-6745	255	4	)	)	PUNCT
ejpam-6745	255	5	,	,	PUNCT
ejpam-6745	255	6	we	we	PRON
ejpam-6745	255	7	get	get	VERB
ejpam-6745	255	8	m2(ϑ	m2(ϑ	NOUN
ejpam-6745	255	9	,	,	PUNCT
ejpam-6745	255	10	ζ	ζ	NOUN
ejpam-6745	255	11	)	)	PUNCT
ejpam-6745	255	12	≤	≤	NUM
ejpam-6745	256	1	2(c1	2(c1	NUM
ejpam-6745	256	2	−	−	NOUN
ejpam-6745	256	3	c2)|τ	c2)|τ	PROPN
ejpam-6745	256	4	|	|	ADV
ejpam-6745	256	5	k	k	X
ejpam-6745	257	1	(	(	PUNCT
ejpam-6745	257	2	6−	6−	NUM
ejpam-6745	257	3	ζ	ζ	NOUN
ejpam-6745	257	4	−	−	NOUN
ejpam-6745	257	5	cosϑ	cosϑ	NOUN
ejpam-6745	257	6	)	)	PUNCT
ejpam-6745	258	1	ln	ln	ADP
ejpam-6745	258	2	2	2	NUM
ejpam-6745	258	3	.	.	PUNCT
ejpam-6745	259	1	however	however	ADV
ejpam-6745	259	2	,	,	PUNCT
ejpam-6745	259	3	the	the	DET
ejpam-6745	259	4	last	last	ADJ
ejpam-6745	259	5	expression	expression	NOUN
ejpam-6745	259	6	is	be	AUX
ejpam-6745	259	7	bounded	bound	VERB
ejpam-6745	259	8	above	above	ADV
ejpam-6745	259	9	by	by	ADP
ejpam-6745	259	10	cosϑ−	cosϑ−	PROPN
ejpam-6745	259	11	ζ	ζ	PROPN
ejpam-6745	259	12	if	if	SCONJ
ejpam-6745	259	13	(	(	PUNCT
ejpam-6745	259	14	28	28	NUM
ejpam-6745	259	15	)	)	PUNCT
ejpam-6745	259	16	holds	hold	VERB
ejpam-6745	259	17	.	.	PUNCT
ejpam-6745	260	1	f.	f.	PROPN
ejpam-6745	260	2	yousef	yousef	PROPN
ejpam-6745	260	3	,	,	PUNCT
ejpam-6745	260	4	m.	m.	NOUN
ejpam-6745	260	5	m.	m.	PROPN
ejpam-6745	260	6	alholi	alholi	PROPN
ejpam-6745	260	7	,	,	PUNCT
ejpam-6745	260	8	t.	t.	PROPN
ejpam-6745	260	9	al	al	PROPN
ejpam-6745	260	10	-	-	PUNCT
ejpam-6745	260	11	hawary	hawary	PROPN
ejpam-6745	260	12	/	/	SYM
ejpam-6745	260	13	eur	eur	PROPN
ejpam-6745	260	14	.	.	PUNCT
ejpam-6745	261	1	j.	j.	PROPN
ejpam-6745	261	2	pure	pure	PROPN
ejpam-6745	261	3	appl	appl	PROPN
ejpam-6745	261	4	.	.	PROPN
ejpam-6745	261	5	math	math	PROPN
ejpam-6745	261	6	,	,	PUNCT
ejpam-6745	261	7	18	18	NUM
ejpam-6745	261	8	(	(	PUNCT
ejpam-6745	261	9	4	4	NUM
ejpam-6745	261	10	)	)	PUNCT
ejpam-6745	261	11	(	(	PUNCT
ejpam-6745	261	12	2025	2025	NUM
ejpam-6745	261	13	)	)	PUNCT
ejpam-6745	261	14	,	,	PUNCT
ejpam-6745	261	15	6745	6745	NUM
ejpam-6745	261	16	10	10	NUM
ejpam-6745	261	17	of	of	ADP
ejpam-6745	261	18	13	13	NUM
ejpam-6745	261	19	4	4	NUM
ejpam-6745	261	20	.	.	NOUN
ejpam-6745	261	21	necessary	necessary	ADJ
ejpam-6745	261	22	and	and	CCONJ
ejpam-6745	261	23	sufficient	sufficient	ADJ
ejpam-6745	261	24	conditions	condition	NOUN
ejpam-6745	261	25	for	for	ADP
ejpam-6745	261	26	the	the	DET
ejpam-6745	261	27	integral	integral	ADJ
ejpam-6745	261	28	operator	operator	NOUN
ejpam-6745	261	29	lik(z	lik(z	PROPN
ejpam-6745	261	30	)	)	PUNCT
ejpam-6745	261	31	in	in	ADP
ejpam-6745	261	32	this	this	DET
ejpam-6745	261	33	section	section	NOUN
ejpam-6745	261	34	,	,	PUNCT
ejpam-6745	261	35	we	we	PRON
ejpam-6745	261	36	find	find	VERB
ejpam-6745	261	37	necessary	necessary	ADJ
ejpam-6745	261	38	and	and	CCONJ
ejpam-6745	261	39	sufficient	sufficient	ADJ
ejpam-6745	261	40	conditions	condition	NOUN
ejpam-6745	261	41	of	of	ADP
ejpam-6745	261	42	the	the	DET
ejpam-6745	261	43	integral	integral	ADJ
ejpam-6745	261	44	operator	operator	NOUN
ejpam-6745	261	45	lik(z	lik(z	PROPN
ejpam-6745	261	46	)	)	PUNCT
ejpam-6745	261	47	:	:	PUNCT
ejpam-6745	262	1	=	=	PUNCT
ejpam-6745	262	2	∫	∫	PROPN
ejpam-6745	262	3	z	z	NOUN
ejpam-6745	262	4	0	0	NUM
ejpam-6745	262	5	υik(t	υik(t	PROPN
ejpam-6745	262	6	)	)	PUNCT
ejpam-6745	262	7	t	t	NOUN
ejpam-6745	262	8	dt	dt	PROPN
ejpam-6745	262	9	,	,	PUNCT
ejpam-6745	262	10	z	z	PROPN
ejpam-6745	262	11	∈	∈	PROPN
ejpam-6745	262	12	γ	γ	X
ejpam-6745	262	13	,	,	PUNCT
ejpam-6745	262	14	(	(	PUNCT
ejpam-6745	262	15	29	29	NUM
ejpam-6745	262	16	)	)	PUNCT
ejpam-6745	262	17	to	to	PART
ejpam-6745	262	18	be	be	AUX
ejpam-6745	262	19	in	in	ADP
ejpam-6745	262	20	the	the	DET
ejpam-6745	262	21	subclasses	subclass	NOUN
ejpam-6745	262	22	spe(ϑ	spe(ϑ	PROPN
ejpam-6745	262	23	,	,	PUNCT
ejpam-6745	262	24	ζ	ζ	NOUN
ejpam-6745	262	25	)	)	PUNCT
ejpam-6745	262	26	and	and	CCONJ
ejpam-6745	262	27	cspe(ϑ	cspe(ϑ	PROPN
ejpam-6745	262	28	,	,	PUNCT
ejpam-6745	262	29	ζ	ζ	NOUN
ejpam-6745	262	30	)	)	PUNCT
ejpam-6745	262	31	.	.	PUNCT
ejpam-6745	263	1	theorem	theorem	NOUN
ejpam-6745	263	2	5	5	NUM
ejpam-6745	263	3	.	.	PUNCT
ejpam-6745	264	1	let	let	VERB
ejpam-6745	264	2	k	k	PROPN
ejpam-6745	264	3	∈	∈	PROPN
ejpam-6745	264	4	n.	n.	NOUN
ejpam-6745	264	5	the	the	DET
ejpam-6745	264	6	integral	integral	ADJ
ejpam-6745	264	7	operator	operator	NOUN
ejpam-6745	264	8	lik(z	lik(z	PROPN
ejpam-6745	264	9	)	)	PUNCT
ejpam-6745	264	10	is	be	AUX
ejpam-6745	264	11	in	in	ADP
ejpam-6745	264	12	the	the	DET
ejpam-6745	264	13	subclass	subclass	NOUN
ejpam-6745	264	14	spe(ϑ	spe(ϑ	PROPN
ejpam-6745	264	15	,	,	PUNCT
ejpam-6745	264	16	ζ	ζ	NOUN
ejpam-6745	264	17	)	)	PUNCT
ejpam-6745	265	1	if	if	SCONJ
ejpam-6745	266	1	and	and	CCONJ
ejpam-6745	266	2	only	only	ADV
ejpam-6745	266	3	if	if	SCONJ
ejpam-6745	266	4	the	the	DET
ejpam-6745	266	5	inequality	inequality	NOUN
ejpam-6745	266	6	(	(	PUNCT
ejpam-6745	266	7	4−	4−	NOUN
ejpam-6745	266	8	ζ	ζ	NOUN
ejpam-6745	266	9	−	−	PROPN
ejpam-6745	266	10	cosϑ	cosϑ	ADJ
ejpam-6745	266	11	)	)	PUNCT
ejpam-6745	266	12	ln	ln	NOUN
ejpam-6745	266	13	2	2	NUM
ejpam-6745	266	14	≤	≤	NUM
ejpam-6745	266	15	k(cosϑ−	k(cosϑ−	PROPN
ejpam-6745	266	16	ζ	ζ	NOUN
ejpam-6745	266	17	)	)	PUNCT
ejpam-6745	266	18	(	(	PUNCT
ejpam-6745	266	19	30	30	NUM
ejpam-6745	266	20	)	)	PUNCT
ejpam-6745	266	21	holds	hold	VERB
ejpam-6745	266	22	.	.	PUNCT
ejpam-6745	267	1	proof	proof	NOUN
ejpam-6745	267	2	.	.	PUNCT
ejpam-6745	268	1	according	accord	VERB
ejpam-6745	268	2	to	to	ADP
ejpam-6745	268	3	(	(	PUNCT
ejpam-6745	268	4	9	9	X
ejpam-6745	268	5	)	)	PUNCT
ejpam-6745	268	6	it	it	PRON
ejpam-6745	268	7	follows	follow	VERB
ejpam-6745	268	8	that	that	SCONJ
ejpam-6745	268	9	lik(z	lik(z	NOUN
ejpam-6745	268	10	)	)	PUNCT
ejpam-6745	269	1	=	=	PUNCT
ejpam-6745	269	2	z	z	NOUN
ejpam-6745	270	1	−	−	ADP
ejpam-6745	270	2	∞∑	∞∑	NUM
ejpam-6745	270	3	ϵ=2	ϵ=2	PROPN
ejpam-6745	270	4	1	1	NUM
ejpam-6745	270	5	(	(	PUNCT
ejpam-6745	270	6	(	(	PUNCT
ejpam-6745	270	7	ϵ−	ϵ−	NOUN
ejpam-6745	270	8	1	1	X
ejpam-6745	270	9	)	)	PUNCT
ejpam-6745	270	10	k	k	NOUN
ejpam-6745	271	1	+	+	NOUN
ejpam-6745	271	2	1	1	X
ejpam-6745	271	3	)	)	PUNCT
ejpam-6745	271	4	(	(	PUNCT
ejpam-6745	271	5	ϵ−	ϵ−	NOUN
ejpam-6745	271	6	1	1	NUM
ejpam-6745	271	7	)	)	PUNCT
ejpam-6745	271	8	!	!	PUNCT
ejpam-6745	272	1	zϵ	zϵ	NOUN
ejpam-6745	273	1	ϵ	ϵ	INTJ
ejpam-6745	273	2	,	,	PUNCT
ejpam-6745	273	3	z	z	PROPN
ejpam-6745	273	4	∈	∈	PROPN
ejpam-6745	273	5	γ	γ	X
ejpam-6745	273	6	.	.	PROPN
ejpam-6745	274	1	(	(	PUNCT
ejpam-6745	274	2	31	31	NUM
ejpam-6745	274	3	)	)	PUNCT
ejpam-6745	274	4	from	from	ADP
ejpam-6745	274	5	(	(	PUNCT
ejpam-6745	274	6	11	11	NUM
ejpam-6745	274	7	)	)	PUNCT
ejpam-6745	274	8	,	,	PUNCT
ejpam-6745	274	9	the	the	DET
ejpam-6745	274	10	integral	integral	ADJ
ejpam-6745	274	11	operator	operator	NOUN
ejpam-6745	274	12	lik(z	lik(z	PROPN
ejpam-6745	274	13	)	)	PUNCT
ejpam-6745	274	14	belongs	belong	VERB
ejpam-6745	274	15	to	to	ADP
ejpam-6745	274	16	spe(ϑ	spe(ϑ	PROPN
ejpam-6745	274	17	,	,	PUNCT
ejpam-6745	274	18	ζ	ζ	NOUN
ejpam-6745	274	19	)	)	PUNCT
ejpam-6745	274	20	if	if	SCONJ
ejpam-6745	275	1	and	and	CCONJ
ejpam-6745	275	2	only	only	ADV
ejpam-6745	275	3	if	if	SCONJ
ejpam-6745	275	4	∞∑	∞∑	PRON
ejpam-6745	275	5	ϵ=2	ϵ=2	NOUN
ejpam-6745	276	1	[	[	X
ejpam-6745	276	2	2ϵ−	2ϵ−	NUM
ejpam-6745	276	3	ζ	ζ	NOUN
ejpam-6745	276	4	−	−	NOUN
ejpam-6745	276	5	cosϑ	cosϑ	VERB
ejpam-6745	276	6	]	]	PUNCT
ejpam-6745	276	7	1	1	NUM
ejpam-6745	276	8	ϵ((ϵ−	ϵ((ϵ−	PROPN
ejpam-6745	276	9	1	1	NUM
ejpam-6745	276	10	)	)	PUNCT
ejpam-6745	276	11	k	k	NOUN
ejpam-6745	277	1	+	+	NOUN
ejpam-6745	277	2	1	1	X
ejpam-6745	277	3	)	)	PUNCT
ejpam-6745	277	4	(	(	PUNCT
ejpam-6745	277	5	ϵ−	ϵ−	NOUN
ejpam-6745	277	6	1	1	NUM
ejpam-6745	277	7	)	)	PUNCT
ejpam-6745	277	8	!	!	PUNCT
ejpam-6745	278	1	=	=	PUNCT
ejpam-6745	279	1	∞∑	∞∑	NUM
ejpam-6745	279	2	ϵ=2	ϵ=2	PROPN
ejpam-6745	279	3	2	2	NUM
ejpam-6745	279	4	(	(	PUNCT
ejpam-6745	279	5	(	(	PUNCT
ejpam-6745	279	6	ϵ−	ϵ−	NOUN
ejpam-6745	279	7	1	1	X
ejpam-6745	279	8	)	)	PUNCT
ejpam-6745	279	9	k	k	NOUN
ejpam-6745	280	1	+	+	NOUN
ejpam-6745	280	2	1	1	X
ejpam-6745	280	3	)	)	PUNCT
ejpam-6745	280	4	(	(	PUNCT
ejpam-6745	280	5	ϵ−	ϵ−	NOUN
ejpam-6745	280	6	1	1	NUM
ejpam-6745	280	7	)	)	PUNCT
ejpam-6745	280	8	!	!	PUNCT
ejpam-6745	281	1	−	−	NOUN
ejpam-6745	282	1	∞∑	∞∑	NUM
ejpam-6745	282	2	ϵ=2	ϵ=2	ADJ
ejpam-6745	282	3	ζ	ζ	NOUN
ejpam-6745	282	4	+	+	CCONJ
ejpam-6745	282	5	cosϑ	cosϑ	VERB
ejpam-6745	282	6	(	(	PUNCT
ejpam-6745	282	7	(	(	PUNCT
ejpam-6745	282	8	ϵ−	ϵ−	NOUN
ejpam-6745	282	9	1	1	X
ejpam-6745	282	10	)	)	PUNCT
ejpam-6745	282	11	k	k	NOUN
ejpam-6745	282	12	+	+	PUNCT
ejpam-6745	282	13	1)ϵ	1)ϵ	NUM
ejpam-6745	282	14	!	!	PUNCT
ejpam-6745	282	15	≤	≤	PROPN
ejpam-6745	282	16	cosϑ−	cosϑ−	PROPN
ejpam-6745	282	17	ζ	ζ	PROPN
ejpam-6745	282	18	.	.	PUNCT
ejpam-6745	282	19	by	by	ADP
ejpam-6745	282	20	a	a	DET
ejpam-6745	282	21	similar	similar	ADJ
ejpam-6745	282	22	proof	proof	NOUN
ejpam-6745	282	23	of	of	ADP
ejpam-6745	282	24	theorem	theorem	NOUN
ejpam-6745	282	25	3	3	NUM
ejpam-6745	282	26	,	,	PUNCT
ejpam-6745	282	27	we	we	PRON
ejpam-6745	282	28	get	get	VERB
ejpam-6745	282	29	that	that	DET
ejpam-6745	282	30	lik(z	lik(z	PROPN
ejpam-6745	282	31	)	)	PUNCT
ejpam-6745	282	32	∈	∈	PROPN
ejpam-6745	282	33	spe(ϑ	spe(ϑ	PROPN
ejpam-6745	282	34	,	,	PUNCT
ejpam-6745	282	35	ζ	ζ	NOUN
ejpam-6745	282	36	)	)	PUNCT
ejpam-6745	282	37	if	if	SCONJ
ejpam-6745	282	38	and	and	CCONJ
ejpam-6745	282	39	only	only	ADV
ejpam-6745	282	40	if	if	SCONJ
ejpam-6745	282	41	(	(	PUNCT
ejpam-6745	282	42	30	30	NUM
ejpam-6745	282	43	)	)	PUNCT
ejpam-6745	282	44	holds	hold	VERB
ejpam-6745	282	45	.	.	PUNCT
ejpam-6745	283	1	theorem	theorem	NOUN
ejpam-6745	283	2	6	6	NUM
ejpam-6745	283	3	.	.	PUNCT
ejpam-6745	284	1	let	let	VERB
ejpam-6745	284	2	k	k	PROPN
ejpam-6745	284	3	∈	∈	PROPN
ejpam-6745	284	4	n.	n.	NOUN
ejpam-6745	284	5	the	the	DET
ejpam-6745	284	6	integral	integral	ADJ
ejpam-6745	284	7	operator	operator	NOUN
ejpam-6745	284	8	lik(z	lik(z	PROPN
ejpam-6745	284	9	)	)	PUNCT
ejpam-6745	284	10	is	be	AUX
ejpam-6745	284	11	in	in	ADP
ejpam-6745	284	12	the	the	DET
ejpam-6745	284	13	subclass	subclass	NOUN
ejpam-6745	284	14	cspe(ϑ	cspe(ϑ	PROPN
ejpam-6745	284	15	,	,	PUNCT
ejpam-6745	284	16	ζ	ζ	NOUN
ejpam-6745	284	17	)	)	PUNCT
ejpam-6745	285	1	if	if	SCONJ
ejpam-6745	286	1	and	and	CCONJ
ejpam-6745	286	2	only	only	ADV
ejpam-6745	286	3	if	if	SCONJ
ejpam-6745	286	4	the	the	DET
ejpam-6745	286	5	inequality	inequality	NOUN
ejpam-6745	286	6	(	(	PUNCT
ejpam-6745	286	7	22	22	NUM
ejpam-6745	286	8	)	)	PUNCT
ejpam-6745	286	9	holds	hold	VERB
ejpam-6745	286	10	.	.	PUNCT
ejpam-6745	287	1	proof	proof	NOUN
ejpam-6745	287	2	.	.	PUNCT
ejpam-6745	288	1	since	since	SCONJ
ejpam-6745	288	2	lik(z	lik(z	PROPN
ejpam-6745	288	3	)	)	PUNCT
ejpam-6745	288	4	is	be	AUX
ejpam-6745	288	5	given	give	VERB
ejpam-6745	288	6	by	by	ADP
ejpam-6745	288	7	(	(	PUNCT
ejpam-6745	288	8	31	31	NUM
ejpam-6745	288	9	)	)	PUNCT
ejpam-6745	288	10	and	and	CCONJ
ejpam-6745	288	11	in	in	ADP
ejpam-6745	288	12	view	view	NOUN
ejpam-6745	288	13	(	(	PUNCT
ejpam-6745	288	14	13	13	NUM
ejpam-6745	288	15	)	)	PUNCT
ejpam-6745	288	16	,	,	PUNCT
ejpam-6745	288	17	the	the	DET
ejpam-6745	288	18	integral	integral	ADJ
ejpam-6745	288	19	operator	operator	NOUN
ejpam-6745	288	20	lik(z	lik(z	PROPN
ejpam-6745	288	21	)	)	PUNCT
ejpam-6745	288	22	belongs	belong	VERB
ejpam-6745	288	23	to	to	ADP
ejpam-6745	288	24	cspe(ϑ	cspe(ϑ	PROPN
ejpam-6745	288	25	,	,	PUNCT
ejpam-6745	288	26	ζ	ζ	NOUN
ejpam-6745	288	27	)	)	PUNCT
ejpam-6745	288	28	if	if	SCONJ
ejpam-6745	289	1	and	and	CCONJ
ejpam-6745	289	2	only	only	ADV
ejpam-6745	289	3	if	if	SCONJ
ejpam-6745	289	4	∞∑	∞∑	PRON
ejpam-6745	289	5	ϵ=2	ϵ=2	PROPN
ejpam-6745	290	1	ϵ	ϵ	X
ejpam-6745	290	2	[	[	X
ejpam-6745	290	3	2ϵ−	2ϵ−	NUM
ejpam-6745	290	4	ζ	ζ	NOUN
ejpam-6745	290	5	−	−	NOUN
ejpam-6745	290	6	cosϑ	cosϑ	VERB
ejpam-6745	290	7	]	]	PUNCT
ejpam-6745	290	8	1	1	NUM
ejpam-6745	290	9	ϵ((ϵ−	ϵ((ϵ−	PROPN
ejpam-6745	290	10	1	1	NUM
ejpam-6745	290	11	)	)	PUNCT
ejpam-6745	290	12	k	k	NOUN
ejpam-6745	291	1	+	+	NOUN
ejpam-6745	291	2	1	1	X
ejpam-6745	291	3	)	)	PUNCT
ejpam-6745	291	4	(	(	PUNCT
ejpam-6745	291	5	ϵ−	ϵ−	NOUN
ejpam-6745	291	6	1	1	NUM
ejpam-6745	291	7	)	)	PUNCT
ejpam-6745	291	8	!	!	PUNCT
ejpam-6745	292	1	=	=	PUNCT
ejpam-6745	293	1	∞∑	∞∑	NUM
ejpam-6745	293	2	ϵ=2	ϵ=2	PROPN
ejpam-6745	293	3	2ϵ	2ϵ	NOUN
ejpam-6745	293	4	(	(	PUNCT
ejpam-6745	293	5	(	(	PUNCT
ejpam-6745	293	6	ϵ−	ϵ−	NOUN
ejpam-6745	293	7	1	1	X
ejpam-6745	293	8	)	)	PUNCT
ejpam-6745	293	9	k	k	NOUN
ejpam-6745	294	1	+	+	NOUN
ejpam-6745	294	2	1	1	X
ejpam-6745	294	3	)	)	PUNCT
ejpam-6745	294	4	(	(	PUNCT
ejpam-6745	294	5	ϵ−	ϵ−	NOUN
ejpam-6745	294	6	1	1	NUM
ejpam-6745	294	7	)	)	PUNCT
ejpam-6745	294	8	!	!	PUNCT
ejpam-6745	295	1	−	−	NOUN
ejpam-6745	296	1	∞∑	∞∑	NUM
ejpam-6745	296	2	ϵ=2	ϵ=2	ADJ
ejpam-6745	296	3	ζ	ζ	NOUN
ejpam-6745	296	4	+	+	CCONJ
ejpam-6745	296	5	cosϑ	cosϑ	VERB
ejpam-6745	296	6	(	(	PUNCT
ejpam-6745	296	7	(	(	PUNCT
ejpam-6745	296	8	ϵ−	ϵ−	NOUN
ejpam-6745	296	9	1	1	X
ejpam-6745	296	10	)	)	PUNCT
ejpam-6745	296	11	k	k	NOUN
ejpam-6745	297	1	+	+	NOUN
ejpam-6745	297	2	1	1	X
ejpam-6745	297	3	)	)	PUNCT
ejpam-6745	297	4	(	(	PUNCT
ejpam-6745	297	5	ϵ−	ϵ−	NOUN
ejpam-6745	297	6	1	1	NUM
ejpam-6745	297	7	)	)	PUNCT
ejpam-6745	297	8	!	!	PUNCT
ejpam-6745	298	1	≤	≤	NUM
ejpam-6745	298	2	cosϑ−	cosϑ−	PROPN
ejpam-6745	298	3	ζ	ζ	PROPN
ejpam-6745	298	4	.	.	PUNCT
ejpam-6745	299	1	by	by	ADP
ejpam-6745	299	2	a	a	DET
ejpam-6745	299	3	similar	similar	ADJ
ejpam-6745	299	4	proof	proof	NOUN
ejpam-6745	299	5	of	of	ADP
ejpam-6745	299	6	theorem	theorem	NOUN
ejpam-6745	299	7	4	4	NUM
ejpam-6745	299	8	,	,	PUNCT
ejpam-6745	299	9	we	we	PRON
ejpam-6745	299	10	get	get	VERB
ejpam-6745	299	11	that	that	DET
ejpam-6745	299	12	lik(z	lik(z	PROPN
ejpam-6745	299	13	)	)	PUNCT
ejpam-6745	299	14	∈	∈	PROPN
ejpam-6745	299	15	cspe(ϑ	cspe(ϑ	PROPN
ejpam-6745	299	16	,	,	PUNCT
ejpam-6745	299	17	ζ	ζ	NOUN
ejpam-6745	299	18	)	)	PUNCT
ejpam-6745	300	1	if	if	SCONJ
ejpam-6745	300	2	and	and	CCONJ
ejpam-6745	300	3	only	only	ADV
ejpam-6745	300	4	if	if	SCONJ
ejpam-6745	300	5	(	(	PUNCT
ejpam-6745	300	6	22	22	NUM
ejpam-6745	300	7	)	)	PUNCT
ejpam-6745	300	8	holds	hold	VERB
ejpam-6745	300	9	.	.	PUNCT
ejpam-6745	301	1	remark	remark	PROPN
ejpam-6745	301	2	1	1	NUM
ejpam-6745	301	3	.	.	PUNCT
ejpam-6745	302	1	particularization	particularization	NOUN
ejpam-6745	302	2	of	of	ADP
ejpam-6745	302	3	the	the	DET
ejpam-6745	302	4	parameters	parameter	NOUN
ejpam-6745	302	5	ϑ	ϑ	X
ejpam-6745	302	6	and	and	CCONJ
ejpam-6745	302	7	ζ	ζ	NOUN
ejpam-6745	302	8	in	in	ADP
ejpam-6745	302	9	our	our	PRON
ejpam-6745	302	10	theorems	theorem	NOUN
ejpam-6745	302	11	,	,	PUNCT
ejpam-6745	302	12	we	we	PRON
ejpam-6745	302	13	get	get	VERB
ejpam-6745	302	14	several	several	ADJ
ejpam-6745	302	15	subresults	subresult	NOUN
ejpam-6745	302	16	related	relate	VERB
ejpam-6745	302	17	to	to	ADP
ejpam-6745	302	18	the	the	DET
ejpam-6745	302	19	subclasses	subclass	NOUN
ejpam-6745	302	20	spe(ϑ	spe(ϑ	PROPN
ejpam-6745	302	21	,	,	PUNCT
ejpam-6745	302	22	ζ	ζ	NOUN
ejpam-6745	302	23	)	)	PUNCT
ejpam-6745	302	24	and	and	CCONJ
ejpam-6745	302	25	cspe(ϑ	cspe(ϑ	PROPN
ejpam-6745	302	26	,	,	PUNCT
ejpam-6745	302	27	ζ	ζ	NOUN
ejpam-6745	302	28	)	)	PUNCT
ejpam-6745	302	29	.	.	PUNCT
ejpam-6745	303	1	for	for	ADP
ejpam-6745	303	2	example	example	NOUN
ejpam-6745	303	3	,	,	PUNCT
ejpam-6745	303	4	if	if	SCONJ
ejpam-6745	303	5	ζ	ζ	NOUN
ejpam-6745	303	6	=	=	SYM
ejpam-6745	303	7	0	0	NUM
ejpam-6745	303	8	or	or	CCONJ
ejpam-6745	303	9	ϑ	ϑ	X
ejpam-6745	303	10	=	=	SYM
ejpam-6745	303	11	0	0	NUM
ejpam-6745	303	12	,	,	PUNCT
ejpam-6745	303	13	we	we	PRON
ejpam-6745	303	14	get	get	VERB
ejpam-6745	303	15	many	many	ADJ
ejpam-6745	303	16	subresults	subresult	NOUN
ejpam-6745	303	17	for	for	ADP
ejpam-6745	303	18	the	the	DET
ejpam-6745	303	19	subclasses	subclass	NOUN
ejpam-6745	303	20	spe(ϑ	spe(ϑ	PROPN
ejpam-6745	303	21	)	)	PUNCT
ejpam-6745	303	22	,	,	PUNCT
ejpam-6745	303	23	cspe(ϑ	cspe(ϑ	PROPN
ejpam-6745	303	24	)	)	PUNCT
ejpam-6745	303	25	,	,	PUNCT
ejpam-6745	303	26	spe(ζ	spe(ζ	NOUN
ejpam-6745	303	27	)	)	PUNCT
ejpam-6745	303	28	and	and	CCONJ
ejpam-6745	303	29	cspe(ϑ	cspe(ϑ	PROPN
ejpam-6745	303	30	)	)	PUNCT
ejpam-6745	303	31	.	.	PUNCT
ejpam-6745	304	1	f.	f.	PROPN
ejpam-6745	304	2	yousef	yousef	PROPN
ejpam-6745	304	3	,	,	PUNCT
ejpam-6745	304	4	m.	m.	NOUN
ejpam-6745	304	5	m.	m.	PROPN
ejpam-6745	304	6	alholi	alholi	PROPN
ejpam-6745	304	7	,	,	PUNCT
ejpam-6745	304	8	t.	t.	PROPN
ejpam-6745	304	9	al	al	PROPN
ejpam-6745	304	10	-	-	PUNCT
ejpam-6745	304	11	hawary	hawary	PROPN
ejpam-6745	304	12	/	/	SYM
ejpam-6745	304	13	eur	eur	PROPN
ejpam-6745	304	14	.	.	PUNCT
ejpam-6745	305	1	j.	j.	PROPN
ejpam-6745	305	2	pure	pure	PROPN
ejpam-6745	305	3	appl	appl	PROPN
ejpam-6745	305	4	.	.	PROPN
ejpam-6745	305	5	math	math	PROPN
ejpam-6745	305	6	,	,	PUNCT
ejpam-6745	305	7	18	18	NUM
ejpam-6745	305	8	(	(	PUNCT
ejpam-6745	305	9	4	4	NUM
ejpam-6745	305	10	)	)	PUNCT
ejpam-6745	305	11	(	(	PUNCT
ejpam-6745	305	12	2025	2025	NUM
ejpam-6745	305	13	)	)	PUNCT
ejpam-6745	305	14	,	,	PUNCT
ejpam-6745	305	15	6745	6745	NUM
ejpam-6745	305	16	11	11	NUM
ejpam-6745	305	17	of	of	ADP
ejpam-6745	305	18	13	13	NUM
ejpam-6745	305	19	5	5	NUM
ejpam-6745	305	20	.	.	PUNCT
ejpam-6745	306	1	conclusion	conclusion	NOUN
ejpam-6745	306	2	in	in	ADP
ejpam-6745	306	3	this	this	DET
ejpam-6745	306	4	paper	paper	NOUN
ejpam-6745	306	5	,	,	PUNCT
ejpam-6745	306	6	we	we	PRON
ejpam-6745	306	7	have	have	AUX
ejpam-6745	306	8	established	establish	VERB
ejpam-6745	306	9	several	several	ADJ
ejpam-6745	306	10	geometric	geometric	ADJ
ejpam-6745	306	11	criteria	criterion	NOUN
ejpam-6745	306	12	for	for	ADP
ejpam-6745	306	13	the	the	DET
ejpam-6745	306	14	generalized	generalize	VERB
ejpam-6745	306	15	normalized	normalize	VERB
ejpam-6745	306	16	imaginary	imaginary	ADJ
ejpam-6745	306	17	error	error	NOUN
ejpam-6745	306	18	function	function	NOUN
ejpam-6745	306	19	υik	υik	ADJ
ejpam-6745	306	20	,	,	PUNCT
ejpam-6745	306	21	its	its	PRON
ejpam-6745	306	22	associated	associated	ADJ
ejpam-6745	306	23	convolution	convolution	NOUN
ejpam-6745	306	24	operator	operator	NOUN
ejpam-6745	306	25	iik(z	iik(z	PRON
ejpam-6745	306	26	)	)	PUNCT
ejpam-6745	306	27	,	,	PUNCT
ejpam-6745	306	28	and	and	CCONJ
ejpam-6745	306	29	an	an	DET
ejpam-6745	306	30	integral	integral	ADJ
ejpam-6745	306	31	operator	operator	NOUN
ejpam-6745	306	32	involving	involve	VERB
ejpam-6745	306	33	υik	υik	NOUN
ejpam-6745	306	34	to	to	PART
ejpam-6745	306	35	belong	belong	VERB
ejpam-6745	306	36	to	to	ADP
ejpam-6745	306	37	the	the	DET
ejpam-6745	306	38	subclasses	subclass	NOUN
ejpam-6745	306	39	spe(ϑ	spe(ϑ	PROPN
ejpam-6745	306	40	,	,	PUNCT
ejpam-6745	306	41	ζ	ζ	NOUN
ejpam-6745	306	42	)	)	PUNCT
ejpam-6745	306	43	and	and	CCONJ
ejpam-6745	306	44	cspe(ϑ	cspe(ϑ	PROPN
ejpam-6745	306	45	,	,	PUNCT
ejpam-6745	306	46	ζ	ζ	NOUN
ejpam-6745	306	47	)	)	PUNCT
ejpam-6745	306	48	of	of	ADP
ejpam-6745	306	49	spirallike	spirallike	NOUN
ejpam-6745	306	50	and	and	CCONJ
ejpam-6745	306	51	convex	convex	VERB
ejpam-6745	306	52	spirallike	spirallike	ADJ
ejpam-6745	306	53	analytic	analytic	ADJ
ejpam-6745	306	54	functions	function	NOUN
ejpam-6745	306	55	defined	define	VERB
ejpam-6745	306	56	in	in	ADP
ejpam-6745	306	57	the	the	DET
ejpam-6745	306	58	open	open	ADJ
ejpam-6745	306	59	unit	unit	NOUN
ejpam-6745	306	60	disk	disk	NOUN
ejpam-6745	306	61	γ	γ	PROPN
ejpam-6745	306	62	.	.	PUNCT
ejpam-6745	306	63	by	by	ADP
ejpam-6745	306	64	employing	employ	VERB
ejpam-6745	306	65	a	a	DET
ejpam-6745	306	66	combination	combination	NOUN
ejpam-6745	306	67	of	of	ADP
ejpam-6745	306	68	analytic	analytic	ADJ
ejpam-6745	306	69	techniques	technique	NOUN
ejpam-6745	306	70	and	and	CCONJ
ejpam-6745	306	71	coefficient	coefficient	NOUN
ejpam-6745	306	72	-	-	PUNCT
ejpam-6745	306	73	based	base	VERB
ejpam-6745	306	74	inequalities	inequality	NOUN
ejpam-6745	306	75	,	,	PUNCT
ejpam-6745	306	76	we	we	PRON
ejpam-6745	306	77	derived	derive	VERB
ejpam-6745	306	78	sharp	sharp	ADV
ejpam-6745	306	79	necessary	necessary	ADJ
ejpam-6745	306	80	and	and	CCONJ
ejpam-6745	306	81	sufficient	sufficient	ADJ
ejpam-6745	306	82	conditions	condition	NOUN
ejpam-6745	306	83	in	in	ADP
ejpam-6745	306	84	terms	term	NOUN
ejpam-6745	306	85	of	of	ADP
ejpam-6745	306	86	the	the	DET
ejpam-6745	306	87	parameters	parameter	NOUN
ejpam-6745	306	88	k	k	X
ejpam-6745	306	89	,	,	PUNCT
ejpam-6745	306	90	ϑ	ϑ	NOUN
ejpam-6745	306	91	,	,	PUNCT
ejpam-6745	306	92	and	and	CCONJ
ejpam-6745	306	93	ζ	ζ	NOUN
ejpam-6745	306	94	,	,	PUNCT
ejpam-6745	306	95	thereby	thereby	ADV
ejpam-6745	306	96	extending	extend	VERB
ejpam-6745	306	97	known	know	VERB
ejpam-6745	306	98	results	result	NOUN
ejpam-6745	306	99	in	in	ADP
ejpam-6745	306	100	the	the	DET
ejpam-6745	306	101	theory	theory	NOUN
ejpam-6745	306	102	of	of	ADP
ejpam-6745	306	103	geometric	geometric	ADJ
ejpam-6745	306	104	function	function	NOUN
ejpam-6745	306	105	classes	class	NOUN
ejpam-6745	306	106	.	.	PUNCT
ejpam-6745	307	1	our	our	PRON
ejpam-6745	307	2	findings	finding	NOUN
ejpam-6745	307	3	highlight	highlight	VERB
ejpam-6745	307	4	the	the	DET
ejpam-6745	307	5	analytical	analytical	ADJ
ejpam-6745	307	6	richness	richness	NOUN
ejpam-6745	307	7	of	of	ADP
ejpam-6745	307	8	the	the	DET
ejpam-6745	307	9	imaginary	imaginary	ADJ
ejpam-6745	307	10	error	error	NOUN
ejpam-6745	307	11	function	function	NOUN
ejpam-6745	307	12	and	and	CCONJ
ejpam-6745	307	13	its	its	PRON
ejpam-6745	307	14	potential	potential	NOUN
ejpam-6745	307	15	for	for	ADP
ejpam-6745	307	16	characterizing	characterize	VERB
ejpam-6745	307	17	function	function	NOUN
ejpam-6745	307	18	spaces	space	NOUN
ejpam-6745	307	19	through	through	ADP
ejpam-6745	307	20	generalized	generalized	ADJ
ejpam-6745	307	21	transformations	transformation	NOUN
ejpam-6745	307	22	.	.	PUNCT
ejpam-6745	308	1	this	this	DET
ejpam-6745	308	2	study	study	NOUN
ejpam-6745	308	3	may	may	AUX
ejpam-6745	308	4	encourage	encourage	VERB
ejpam-6745	308	5	researchers	researcher	NOUN
ejpam-6745	308	6	to	to	PART
ejpam-6745	308	7	include	include	VERB
ejpam-6745	308	8	the	the	DET
ejpam-6745	308	9	generalized	generalize	VERB
ejpam-6745	308	10	normalized	normalize	VERB
ejpam-6745	308	11	imaginary	imaginary	ADJ
ejpam-6745	308	12	error	error	NOUN
ejpam-6745	308	13	function	function	NOUN
ejpam-6745	308	14	in	in	ADP
ejpam-6745	308	15	other	other	ADJ
ejpam-6745	308	16	classes	class	NOUN
ejpam-6745	308	17	of	of	ADP
ejpam-6745	308	18	analytic	analytic	ADJ
ejpam-6745	308	19	functions	function	NOUN
ejpam-6745	308	20	defined	define	VERB
ejpam-6745	308	21	on	on	ADP
ejpam-6745	308	22	γ	γ	NOUN
ejpam-6745	308	23	and	and	CCONJ
ejpam-6745	308	24	creating	create	VERB
ejpam-6745	308	25	new	new	ADJ
ejpam-6745	308	26	necessary	necessary	ADJ
ejpam-6745	308	27	and	and	CCONJ
ejpam-6745	308	28	sufficient	sufficient	ADJ
ejpam-6745	308	29	conditions	condition	NOUN
ejpam-6745	308	30	.	.	PUNCT
ejpam-6745	309	1	references	reference	NOUN
ejpam-6745	309	2	[	[	X
ejpam-6745	309	3	1	1	NUM
ejpam-6745	309	4	]	]	PUNCT
ejpam-6745	309	5	c.	c.	PROPN
ejpam-6745	309	6	selvaraj	selvaraj	PROPN
ejpam-6745	309	7	and	and	CCONJ
ejpam-6745	309	8	r.	r.	PROPN
ejpam-6745	309	9	geetha	geetha	PROPN
ejpam-6745	309	10	.	.	PUNCT
ejpam-6745	310	1	on	on	ADP
ejpam-6745	310	2	subclasses	subclass	NOUN
ejpam-6745	310	3	of	of	ADP
ejpam-6745	310	4	uniformly	uniformly	ADV
ejpam-6745	310	5	convex	convex	NOUN
ejpam-6745	310	6	spirallike	spirallike	ADJ
ejpam-6745	310	7	functions	function	NOUN
ejpam-6745	310	8	and	and	CCONJ
ejpam-6745	310	9	corresponding	correspond	VERB
ejpam-6745	310	10	class	class	NOUN
ejpam-6745	310	11	of	of	ADP
ejpam-6745	310	12	spirallike	spirallike	ADJ
ejpam-6745	310	13	functions	function	NOUN
ejpam-6745	310	14	.	.	PUNCT
ejpam-6745	311	1	int	int	NOUN
ejpam-6745	311	2	.	.	PUNCT
ejpam-6745	312	1	j.	j.	PROPN
ejpam-6745	312	2	contemp	contemp	PROPN
ejpam-6745	312	3	.	.	PUNCT
ejpam-6745	313	1	math	math	NOUN
ejpam-6745	313	2	.	.	PUNCT
ejpam-6745	314	1	sci	sci	PROPN
ejpam-6745	314	2	,	,	PUNCT
ejpam-6745	314	3	5(3740):1845–1854	5(3740):1845–1854	NUM
ejpam-6745	314	4	,	,	PUNCT
ejpam-6745	314	5	2010	2010	NUM
ejpam-6745	314	6	.	.	PUNCT
ejpam-6745	315	1	[	[	X
ejpam-6745	315	2	2	2	X
ejpam-6745	315	3	]	]	PUNCT
ejpam-6745	315	4	v.	v.	ADP
ejpam-6745	315	5	ravichandran	ravichandran	NOUN
ejpam-6745	315	6	,	,	PUNCT
ejpam-6745	315	7	c.	c.	PROPN
ejpam-6745	315	8	selvaraj	selvaraj	NOUN
ejpam-6745	315	9	and	and	CCONJ
ejpam-6745	315	10	rajalakshmi	rajalakshmi	VERB
ejpam-6745	315	11	rajagopal	rajagopal	NOUN
ejpam-6745	315	12	.	.	PUNCT
ejpam-6745	316	1	on	on	ADP
ejpam-6745	316	2	uniformly	uniformly	ADV
ejpam-6745	316	3	convex	convex	VERB
ejpam-6745	316	4	spiral	spiral	ADJ
ejpam-6745	316	5	functions	function	NOUN
ejpam-6745	316	6	and	and	CCONJ
ejpam-6745	316	7	uniformly	uniformly	ADV
ejpam-6745	316	8	spirallike	spirallike	ADJ
ejpam-6745	316	9	function	function	NOUN
ejpam-6745	316	10	.	.	PUNCT
ejpam-6745	317	1	soochow	soochow	PROPN
ejpam-6745	317	2	journal	journal	PROPN
ejpam-6745	317	3	of	of	ADP
ejpam-6745	317	4	mathematics	mathematic	NOUN
ejpam-6745	317	5	,	,	PUNCT
ejpam-6745	317	6	29(4):392–405	29(4):392–405	PROPN
ejpam-6745	317	7	,	,	PUNCT
ejpam-6745	317	8	2003	2003	NUM
ejpam-6745	317	9	.	.	PUNCT
ejpam-6745	318	1	[	[	X
ejpam-6745	318	2	3	3	X
ejpam-6745	318	3	]	]	X
ejpam-6745	318	4	f.	f.	NOUN
ejpam-6745	318	5	rønning	rønning	PROPN
ejpam-6745	318	6	.	.	PUNCT
ejpam-6745	319	1	uniformly	uniformly	ADV
ejpam-6745	319	2	convex	convex	NOUN
ejpam-6745	319	3	functions	function	NOUN
ejpam-6745	319	4	and	and	CCONJ
ejpam-6745	319	5	a	a	DET
ejpam-6745	319	6	corresponding	corresponding	ADJ
ejpam-6745	319	7	class	class	NOUN
ejpam-6745	319	8	of	of	ADP
ejpam-6745	319	9	starlike	starlike	NOUN
ejpam-6745	319	10	functions	function	NOUN
ejpam-6745	319	11	.	.	PUNCT
ejpam-6745	320	1	proceedings	proceeding	NOUN
ejpam-6745	320	2	of	of	ADP
ejpam-6745	320	3	the	the	DET
ejpam-6745	320	4	american	american	PROPN
ejpam-6745	320	5	mathematical	mathematical	PROPN
ejpam-6745	320	6	society	society	NOUN
ejpam-6745	320	7	,	,	PUNCT
ejpam-6745	320	8	18(1):189–196	18(1):189–196	NUM
ejpam-6745	320	9	,	,	PUNCT
ejpam-6745	320	10	1993	1993	NUM
ejpam-6745	320	11	.	.	PUNCT
ejpam-6745	321	1	[	[	X
ejpam-6745	321	2	4	4	X
ejpam-6745	321	3	]	]	PUNCT
ejpam-6745	321	4	t.	t.	PROPN
ejpam-6745	321	5	al	al	PROPN
ejpam-6745	321	6	-	-	PUNCT
ejpam-6745	321	7	hawary	hawary	PROPN
ejpam-6745	321	8	,	,	PUNCT
ejpam-6745	321	9	a.	a.	PROPN
ejpam-6745	321	10	amourah	amourah	PROPN
ejpam-6745	321	11	,	,	PUNCT
ejpam-6745	321	12	j.	j.	PROPN
ejpam-6745	321	13	salah	salah	PROPN
ejpam-6745	321	14	,	,	PUNCT
ejpam-6745	321	15	and	and	CCONJ
ejpam-6745	321	16	f.	f.	PROPN
ejpam-6745	321	17	yousef	yousef	PROPN
ejpam-6745	321	18	.	.	PUNCT
ejpam-6745	322	1	two	two	NUM
ejpam-6745	322	2	inclusive	inclusive	ADJ
ejpam-6745	322	3	subfamilies	subfamily	NOUN
ejpam-6745	322	4	of	of	ADP
ejpam-6745	322	5	bi	bi	ADJ
ejpam-6745	322	6	-	-	ADJ
ejpam-6745	322	7	univalent	univalent	ADJ
ejpam-6745	322	8	functions	function	NOUN
ejpam-6745	322	9	.	.	PUNCT
ejpam-6745	323	1	int	int	NOUN
ejpam-6745	323	2	.	.	PUNCT
ejpam-6745	324	1	journal	journal	PROPN
ejpam-6745	324	2	of	of	ADP
ejpam-6745	324	3	neutrosophic	neutrosophic	ADJ
ejpam-6745	324	4	science	science	NOUN
ejpam-6745	324	5	,	,	PUNCT
ejpam-6745	324	6	24(4):315–323	24(4):315–323	NUM
ejpam-6745	324	7	,	,	PUNCT
ejpam-6745	324	8	2024	2024	NUM
ejpam-6745	324	9	.	.	PUNCT
ejpam-6745	325	1	[	[	X
ejpam-6745	325	2	5	5	X
ejpam-6745	325	3	]	]	PUNCT
ejpam-6745	325	4	t.	t.	PROPN
ejpam-6745	325	5	al	al	PROPN
ejpam-6745	325	6	-	-	PUNCT
ejpam-6745	325	7	hawary	hawary	PROPN
ejpam-6745	325	8	,	,	PUNCT
ejpam-6745	325	9	b.	b.	PROPN
ejpam-6745	325	10	a.	a.	PROPN
ejpam-6745	325	11	frasin	frasin	PROPN
ejpam-6745	325	12	,	,	PUNCT
ejpam-6745	325	13	and	and	CCONJ
ejpam-6745	325	14	f.	f.	PROPN
ejpam-6745	325	15	yousef	yousef	PROPN
ejpam-6745	325	16	.	.	PUNCT
ejpam-6745	326	1	coefficients	coefficient	NOUN
ejpam-6745	326	2	estimates	estimate	NOUN
ejpam-6745	326	3	for	for	ADP
ejpam-6745	326	4	certain	certain	ADJ
ejpam-6745	326	5	classes	class	NOUN
ejpam-6745	326	6	of	of	ADP
ejpam-6745	326	7	analytic	analytic	ADJ
ejpam-6745	326	8	functions	function	NOUN
ejpam-6745	326	9	of	of	ADP
ejpam-6745	326	10	complex	complex	ADJ
ejpam-6745	326	11	order	order	NOUN
ejpam-6745	326	12	.	.	PUNCT
ejpam-6745	327	1	afrika	afrika	ADJ
ejpam-6745	327	2	matematika	matematika	PROPN
ejpam-6745	327	3	,	,	PUNCT
ejpam-6745	327	4	29(7):1265–1271	29(7):1265–1271	NUM
ejpam-6745	327	5	,	,	PUNCT
ejpam-6745	327	6	2018	2018	NUM
ejpam-6745	327	7	.	.	PUNCT
ejpam-6745	328	1	[	[	X
ejpam-6745	328	2	6	6	NUM
ejpam-6745	328	3	]	]	PUNCT
ejpam-6745	328	4	r.	r.	PROPN
ejpam-6745	328	5	bharati	bharati	PROPN
ejpam-6745	328	6	,	,	PUNCT
ejpam-6745	328	7	r.	r.	PROPN
ejpam-6745	328	8	parvatham	parvatham	PROPN
ejpam-6745	328	9	,	,	PUNCT
ejpam-6745	328	10	and	and	CCONJ
ejpam-6745	328	11	a.	a.	NOUN
ejpam-6745	328	12	swaminathan	swaminathan	ADV
ejpam-6745	328	13	.	.	PUNCT
ejpam-6745	329	1	on	on	ADP
ejpam-6745	329	2	subclasses	subclass	NOUN
ejpam-6745	329	3	of	of	ADP
ejpam-6745	329	4	uniformly	uniformly	ADJ
ejpam-6745	329	5	convex	convex	NOUN
ejpam-6745	329	6	functions	function	NOUN
ejpam-6745	329	7	and	and	CCONJ
ejpam-6745	329	8	corresponding	correspond	VERB
ejpam-6745	329	9	class	class	NOUN
ejpam-6745	329	10	of	of	ADP
ejpam-6745	329	11	starlike	starlike	NOUN
ejpam-6745	329	12	functions	function	NOUN
ejpam-6745	329	13	.	.	PUNCT
ejpam-6745	330	1	tamkang	tamkang	PROPN
ejpam-6745	330	2	journal	journal	PROPN
ejpam-6745	330	3	of	of	ADP
ejpam-6745	330	4	mathematics	mathematic	NOUN
ejpam-6745	330	5	,	,	PUNCT
ejpam-6745	330	6	28(1):17–32	28(1):17–32	NUM
ejpam-6745	330	7	,	,	PUNCT
ejpam-6745	330	8	1997	1997	NUM
ejpam-6745	330	9	.	.	PUNCT
ejpam-6745	331	1	[	[	X
ejpam-6745	331	2	7	7	NUM
ejpam-6745	331	3	]	]	X
ejpam-6745	331	4	b.a	b.a	PROPN
ejpam-6745	331	5	.	.	PROPN
ejpam-6745	331	6	frasin	frasin	PROPN
ejpam-6745	331	7	,	,	PUNCT
ejpam-6745	331	8	t.	t.	PROPN
ejpam-6745	331	9	al	al	PROPN
ejpam-6745	331	10	-	-	PUNCT
ejpam-6745	331	11	hawary	hawary	PROPN
ejpam-6745	331	12	,	,	PUNCT
ejpam-6745	331	13	and	and	CCONJ
ejpam-6745	331	14	f.	f.	PROPN
ejpam-6745	331	15	yousef	yousef	PROPN
ejpam-6745	331	16	.	.	PUNCT
ejpam-6745	331	17	necessary	necessary	ADJ
ejpam-6745	331	18	and	and	CCONJ
ejpam-6745	331	19	sufficient	sufficient	ADJ
ejpam-6745	331	20	conditions	condition	NOUN
ejpam-6745	331	21	for	for	ADP
ejpam-6745	331	22	hypergeometric	hypergeometric	ADJ
ejpam-6745	331	23	functions	function	NOUN
ejpam-6745	331	24	to	to	PART
ejpam-6745	331	25	be	be	AUX
ejpam-6745	331	26	in	in	ADP
ejpam-6745	331	27	a	a	DET
ejpam-6745	331	28	subclass	subclass	NOUN
ejpam-6745	331	29	of	of	ADP
ejpam-6745	331	30	analytic	analytic	ADJ
ejpam-6745	331	31	functions	function	NOUN
ejpam-6745	331	32	.	.	PUNCT
ejpam-6745	332	1	afrika	afrika	PROPN
ejpam-6745	332	2	matematika	matematika	PROPN
ejpam-6745	332	3	,	,	PUNCT
ejpam-6745	332	4	30(1):223–230	30(1):223–230	PROPN
ejpam-6745	332	5	,	,	PUNCT
ejpam-6745	332	6	2019	2019	NUM
ejpam-6745	332	7	.	.	PUNCT
ejpam-6745	333	1	[	[	X
ejpam-6745	333	2	8	8	NUM
ejpam-6745	333	3	]	]	PUNCT
ejpam-6745	333	4	a.	a.	PROPN
ejpam-6745	333	5	w.	w.	PROPN
ejpam-6745	333	6	goodman	goodman	PROPN
ejpam-6745	333	7	.	.	PUNCT
ejpam-6745	334	1	on	on	ADP
ejpam-6745	334	2	uniformly	uniformly	ADV
ejpam-6745	334	3	convex	convex	NOUN
ejpam-6745	334	4	functions	function	NOUN
ejpam-6745	334	5	.	.	PUNCT
ejpam-6745	335	1	annales	annale	VERB
ejpam-6745	335	2	polonici	polonici	PROPN
ejpam-6745	335	3	mathematici	mathematici	NOUN
ejpam-6745	335	4	,	,	PUNCT
ejpam-6745	335	5	56(1):87–92	56(1):87–92	NUM
ejpam-6745	335	6	,	,	PUNCT
ejpam-6745	335	7	1991	1991	NUM
ejpam-6745	335	8	.	.	PUNCT
ejpam-6745	336	1	[	[	X
ejpam-6745	336	2	9	9	NUM
ejpam-6745	336	3	]	]	PUNCT
ejpam-6745	336	4	s.	s.	PROPN
ejpam-6745	336	5	kanas	kanas	PROPN
ejpam-6745	336	6	and	and	CCONJ
ejpam-6745	336	7	a.	a.	PROPN
ejpam-6745	336	8	wisniowska	wisniowska	PROPN
ejpam-6745	336	9	.	.	PUNCT
ejpam-6745	337	1	conic	conic	ADJ
ejpam-6745	337	2	regions	region	NOUN
ejpam-6745	337	3	and	and	CCONJ
ejpam-6745	337	4	k	k	ADJ
ejpam-6745	337	5	-	-	PUNCT
ejpam-6745	337	6	uniform	uniform	ADJ
ejpam-6745	337	7	convexity	convexity	NOUN
ejpam-6745	337	8	.	.	PUNCT
ejpam-6745	338	1	journal	journal	PROPN
ejpam-6745	338	2	of	of	ADP
ejpam-6745	338	3	computational	computational	ADJ
ejpam-6745	338	4	and	and	CCONJ
ejpam-6745	338	5	applied	applied	ADJ
ejpam-6745	338	6	mathematics	mathematic	NOUN
ejpam-6745	338	7	,	,	PUNCT
ejpam-6745	338	8	105(1	105(1	PROPN
ejpam-6745	338	9	-	-	SYM
ejpam-6745	338	10	2):327–336	2):327–336	NUM
ejpam-6745	338	11	,	,	PUNCT
ejpam-6745	338	12	1999	1999	NUM
ejpam-6745	338	13	.	.	PUNCT
ejpam-6745	339	1	[	[	X
ejpam-6745	339	2	10	10	NUM
ejpam-6745	339	3	]	]	PUNCT
ejpam-6745	339	4	k.	k.	PROPN
ejpam-6745	339	5	k.	k.	PROPN
ejpam-6745	340	1	dixit	dixit	PROPN
ejpam-6745	340	2	and	and	CCONJ
ejpam-6745	340	3	s.	s.	PROPN
ejpam-6745	340	4	k.	k.	PROPN
ejpam-6745	340	5	pal	pal	PROPN
ejpam-6745	340	6	.	.	PUNCT
ejpam-6745	341	1	on	on	ADP
ejpam-6745	341	2	a	a	DET
ejpam-6745	341	3	class	class	NOUN
ejpam-6745	341	4	of	of	ADP
ejpam-6745	341	5	univalent	univalent	ADJ
ejpam-6745	341	6	functions	function	NOUN
ejpam-6745	341	7	related	relate	VERB
ejpam-6745	341	8	to	to	ADP
ejpam-6745	341	9	complex	complex	ADJ
ejpam-6745	341	10	order	order	NOUN
ejpam-6745	341	11	.	.	PUNCT
ejpam-6745	342	1	indian	indian	ADJ
ejpam-6745	342	2	journal	journal	PROPN
ejpam-6745	342	3	of	of	ADP
ejpam-6745	342	4	pure	pure	ADJ
ejpam-6745	342	5	and	and	CCONJ
ejpam-6745	342	6	applied	applied	ADJ
ejpam-6745	342	7	mathematics	mathematic	NOUN
ejpam-6745	342	8	,	,	PUNCT
ejpam-6745	342	9	26(9):889–896	26(9):889–896	PROPN
ejpam-6745	342	10	,	,	PUNCT
ejpam-6745	342	11	1995	1995	NUM
ejpam-6745	342	12	.	.	PUNCT
ejpam-6745	343	1	[	[	X
ejpam-6745	343	2	11	11	NUM
ejpam-6745	343	3	]	]	PUNCT
ejpam-6745	343	4	t.	t.	PROPN
ejpam-6745	343	5	r.	r.	PROPN
ejpam-6745	343	6	caplinger	caplinger	PROPN
ejpam-6745	343	7	and	and	CCONJ
ejpam-6745	343	8	w.	w.	PROPN
ejpam-6745	343	9	m.	m.	PROPN
ejpam-6745	343	10	causey	causey	PROPN
ejpam-6745	343	11	.	.	PUNCT
ejpam-6745	344	1	a	a	DET
ejpam-6745	344	2	class	class	NOUN
ejpam-6745	344	3	of	of	ADP
ejpam-6745	344	4	univalent	univalent	ADJ
ejpam-6745	344	5	functions	function	NOUN
ejpam-6745	344	6	.	.	PUNCT
ejpam-6745	345	1	proceedings	proceeding	NOUN
ejpam-6745	345	2	of	of	ADP
ejpam-6745	345	3	the	the	DET
ejpam-6745	345	4	american	american	PROPN
ejpam-6745	345	5	mathematical	mathematical	PROPN
ejpam-6745	345	6	society	society	NOUN
ejpam-6745	345	7	,	,	PUNCT
ejpam-6745	345	8	39(2):357–361	39(2):357–361	NOUN
ejpam-6745	345	9	,	,	PUNCT
ejpam-6745	345	10	1973	1973	NUM
ejpam-6745	345	11	.	.	PUNCT
ejpam-6745	346	1	f.	f.	PROPN
ejpam-6745	346	2	yousef	yousef	PROPN
ejpam-6745	346	3	,	,	PUNCT
ejpam-6745	346	4	m.	m.	NOUN
ejpam-6745	346	5	m.	m.	PROPN
ejpam-6745	346	6	alholi	alholi	PROPN
ejpam-6745	346	7	,	,	PUNCT
ejpam-6745	346	8	t.	t.	PROPN
ejpam-6745	346	9	al	al	PROPN
ejpam-6745	346	10	-	-	PUNCT
ejpam-6745	346	11	hawary	hawary	PROPN
ejpam-6745	346	12	/	/	SYM
ejpam-6745	346	13	eur	eur	PROPN
ejpam-6745	346	14	.	.	PUNCT
ejpam-6745	347	1	j.	j.	PROPN
ejpam-6745	347	2	pure	pure	PROPN
ejpam-6745	347	3	appl	appl	PROPN
ejpam-6745	347	4	.	.	PROPN
ejpam-6745	347	5	math	math	PROPN
ejpam-6745	347	6	,	,	PUNCT
ejpam-6745	347	7	18	18	NUM
ejpam-6745	347	8	(	(	PUNCT
ejpam-6745	347	9	4	4	NUM
ejpam-6745	347	10	)	)	PUNCT
ejpam-6745	347	11	(	(	PUNCT
ejpam-6745	347	12	2025	2025	NUM
ejpam-6745	347	13	)	)	PUNCT
ejpam-6745	347	14	,	,	PUNCT
ejpam-6745	347	15	6745	6745	NUM
ejpam-6745	347	16	12	12	NUM
ejpam-6745	347	17	of	of	ADP
ejpam-6745	347	18	13	13	NUM
ejpam-6745	347	19	[	[	X
ejpam-6745	347	20	12	12	NUM
ejpam-6745	347	21	]	]	PUNCT
ejpam-6745	347	22	a.	a.	NOUN
ejpam-6745	347	23	a.	a.	NOUN
ejpam-6745	347	24	attiya	attiya	PROPN
ejpam-6745	347	25	.	.	PUNCT
ejpam-6745	348	1	some	some	DET
ejpam-6745	348	2	applications	application	NOUN
ejpam-6745	348	3	of	of	ADP
ejpam-6745	348	4	mittag	mittag	ADJ
ejpam-6745	348	5	-	-	PUNCT
ejpam-6745	348	6	leffler	leffler	NOUN
ejpam-6745	348	7	function	function	NOUN
ejpam-6745	348	8	in	in	ADP
ejpam-6745	348	9	the	the	DET
ejpam-6745	348	10	unit	unit	NOUN
ejpam-6745	348	11	disk	disk	NOUN
ejpam-6745	348	12	.	.	PUNCT
ejpam-6745	349	1	filomat	filomat	PROPN
ejpam-6745	349	2	,	,	PUNCT
ejpam-6745	349	3	30(7):2075–2081	30(7):2075–2081	NUM
ejpam-6745	349	4	,	,	PUNCT
ejpam-6745	349	5	2016	2016	NUM
ejpam-6745	349	6	.	.	PUNCT
ejpam-6745	350	1	[	[	X
ejpam-6745	350	2	13	13	NUM
ejpam-6745	350	3	]	]	PUNCT
ejpam-6745	350	4	a.	a.	NOUN
ejpam-6745	350	5	amourah	amourah	PROPN
ejpam-6745	350	6	,	,	PUNCT
ejpam-6745	350	7	t.	t.	PROPN
ejpam-6745	350	8	al	al	PROPN
ejpam-6745	350	9	-	-	PUNCT
ejpam-6745	350	10	hawary	hawary	PROPN
ejpam-6745	350	11	,	,	PUNCT
ejpam-6745	350	12	f.	f.	PROPN
ejpam-6745	350	13	yousef	yousef	PROPN
ejpam-6745	350	14	,	,	PUNCT
ejpam-6745	350	15	and	and	CCONJ
ejpam-6745	350	16	j.	j.	PROPN
ejpam-6745	350	17	salah	salah	PROPN
ejpam-6745	350	18	.	.	PUNCT
ejpam-6745	351	1	collection	collection	NOUN
ejpam-6745	351	2	of	of	ADP
ejpam-6745	351	3	bi	bi	ADJ
ejpam-6745	351	4	-	-	ADJ
ejpam-6745	351	5	univalent	univalent	ADJ
ejpam-6745	351	6	functions	function	NOUN
ejpam-6745	351	7	using	use	VERB
ejpam-6745	351	8	bell	bell	NOUN
ejpam-6745	351	9	distribution	distribution	NOUN
ejpam-6745	351	10	associated	associate	VERB
ejpam-6745	351	11	with	with	ADP
ejpam-6745	351	12	jacobi	jacobi	PROPN
ejpam-6745	351	13	polynomials	polynomials	PROPN
ejpam-6745	351	14	.	.	PUNCT
ejpam-6745	352	1	international	international	ADJ
ejpam-6745	352	2	journal	journal	PROPN
ejpam-6745	352	3	of	of	ADP
ejpam-6745	352	4	neutrosophic	neutrosophic	ADJ
ejpam-6745	352	5	science	science	NOUN
ejpam-6745	352	6	,	,	PUNCT
ejpam-6745	352	7	25(1):228–238	25(1):228–238	PROPN
ejpam-6745	352	8	,	,	PUNCT
ejpam-6745	352	9	2025	2025	NUM
ejpam-6745	352	10	.	.	PUNCT
ejpam-6745	353	1	[	[	X
ejpam-6745	353	2	14	14	NUM
ejpam-6745	353	3	]	]	PUNCT
ejpam-6745	353	4	a.	a.	NOUN
ejpam-6745	353	5	fallatah	fallatah	PROPN
ejpam-6745	353	6	,	,	PUNCT
ejpam-6745	353	7	t.	t.	PROPN
ejpam-6745	353	8	al	al	PROPN
ejpam-6745	353	9	-	-	PUNCT
ejpam-6745	353	10	hawary	hawary	PROPN
ejpam-6745	353	11	,	,	PUNCT
ejpam-6745	353	12	m.	m.	NOUN
ejpam-6745	353	13	o.	o.	PROPN
ejpam-6745	353	14	massa’deh	massa’deh	PROPN
ejpam-6745	353	15	,	,	PUNCT
ejpam-6745	353	16	and	and	CCONJ
ejpam-6745	353	17	f.	f.	PROPN
ejpam-6745	353	18	yousef	yousef	PROPN
ejpam-6745	353	19	.	.	PUNCT
ejpam-6745	354	1	subfamilies	subfamily	NOUN
ejpam-6745	354	2	of	of	ADP
ejpam-6745	354	3	analytic	analytic	ADJ
ejpam-6745	354	4	functions	function	NOUN
ejpam-6745	354	5	associated	associate	VERB
ejpam-6745	354	6	with	with	ADP
ejpam-6745	354	7	rabotnov	rabotnov	NOUN
ejpam-6745	354	8	function	function	NOUN
ejpam-6745	354	9	.	.	PUNCT
ejpam-6745	355	1	international	international	ADJ
ejpam-6745	355	2	journal	journal	PROPN
ejpam-6745	355	3	of	of	ADP
ejpam-6745	355	4	neutrosophic	neutrosophic	ADJ
ejpam-6745	355	5	science	science	NOUN
ejpam-6745	355	6	,	,	PUNCT
ejpam-6745	355	7	26(1):33–39	26(1):33–39	NUM
ejpam-6745	355	8	,	,	PUNCT
ejpam-6745	355	9	2025	2025	NUM
ejpam-6745	355	10	.	.	PUNCT
ejpam-6745	356	1	[	[	X
ejpam-6745	356	2	15	15	NUM
ejpam-6745	356	3	]	]	X
ejpam-6745	356	4	a.	a.	NOUN
ejpam-6745	356	5	o.	o.	PROPN
ejpam-6745	356	6	mostafa	mostafa	PROPN
ejpam-6745	356	7	.	.	PUNCT
ejpam-6745	357	1	a	a	DET
ejpam-6745	357	2	study	study	NOUN
ejpam-6745	357	3	on	on	ADP
ejpam-6745	357	4	starlike	starlike	NOUN
ejpam-6745	357	5	and	and	CCONJ
ejpam-6745	357	6	convex	convex	NOUN
ejpam-6745	357	7	properties	property	NOUN
ejpam-6745	357	8	for	for	ADP
ejpam-6745	357	9	hypergeometric	hypergeometric	ADJ
ejpam-6745	357	10	functions	function	NOUN
ejpam-6745	357	11	.	.	PUNCT
ejpam-6745	358	1	j.	j.	PROPN
ejpam-6745	358	2	inequal	inequal	PROPN
ejpam-6745	358	3	.	.	PUNCT
ejpam-6745	359	1	pure	pure	ADJ
ejpam-6745	359	2	appl	appl	PROPN
ejpam-6745	359	3	.	.	PUNCT
ejpam-6745	359	4	math	math	PROPN
ejpam-6745	359	5	.	.	PUNCT
ejpam-6745	359	6	,	,	PUNCT
ejpam-6745	360	1	10(3):1–16	10(3):1–16	NUM
ejpam-6745	360	2	,	,	PUNCT
ejpam-6745	360	3	2009	2009	NUM
ejpam-6745	360	4	.	.	PUNCT
ejpam-6745	361	1	[	[	X
ejpam-6745	361	2	16	16	NUM
ejpam-6745	361	3	]	]	X
ejpam-6745	361	4	b.	b.	PROPN
ejpam-6745	361	5	a.	a.	PROPN
ejpam-6745	361	6	frasin	frasin	PROPN
ejpam-6745	361	7	,	,	PUNCT
ejpam-6745	361	8	t.	t.	PROPN
ejpam-6745	361	9	al	al	PROPN
ejpam-6745	361	10	-	-	PUNCT
ejpam-6745	361	11	hawary	hawary	PROPN
ejpam-6745	361	12	,	,	PUNCT
ejpam-6745	361	13	f.	f.	PROPN
ejpam-6745	361	14	yousef	yousef	PROPN
ejpam-6745	361	15	,	,	PUNCT
ejpam-6745	361	16	and	and	CCONJ
ejpam-6745	361	17	i.	i.	PROPN
ejpam-6745	361	18	aldawish	aldawish	PROPN
ejpam-6745	361	19	.	.	PUNCT
ejpam-6745	362	1	on	on	ADP
ejpam-6745	362	2	subclasses	subclass	NOUN
ejpam-6745	362	3	of	of	ADP
ejpam-6745	362	4	analytic	analytic	ADJ
ejpam-6745	362	5	functions	function	NOUN
ejpam-6745	362	6	associated	associate	VERB
ejpam-6745	362	7	with	with	ADP
ejpam-6745	362	8	struve	struve	PROPN
ejpam-6745	362	9	functions	function	NOUN
ejpam-6745	362	10	.	.	PUNCT
ejpam-6745	363	1	nonlinear	nonlinear	ADJ
ejpam-6745	363	2	functional	functional	ADJ
ejpam-6745	363	3	analysis	analysis	NOUN
ejpam-6745	363	4	and	and	CCONJ
ejpam-6745	363	5	applications	application	NOUN
ejpam-6745	363	6	,	,	PUNCT
ejpam-6745	363	7	27(1):99–110	27(1):99–110	NUM
ejpam-6745	363	8	,	,	PUNCT
ejpam-6745	363	9	2022	2022	NUM
ejpam-6745	363	10	.	.	PUNCT
ejpam-6745	364	1	[	[	X
ejpam-6745	364	2	17	17	NUM
ejpam-6745	364	3	]	]	X
ejpam-6745	364	4	e.	e.	PROPN
ejpam-6745	364	5	merkes	merkes	PROPN
ejpam-6745	364	6	and	and	CCONJ
ejpam-6745	364	7	b.	b.	PROPN
ejpam-6745	364	8	t.	t.	PROPN
ejpam-6745	364	9	scott	scott	PROPN
ejpam-6745	364	10	.	.	PUNCT
ejpam-6745	365	1	starlike	starlike	ADJ
ejpam-6745	365	2	hypergeometric	hypergeometric	ADJ
ejpam-6745	365	3	functions	function	NOUN
ejpam-6745	365	4	.	.	PUNCT
ejpam-6745	366	1	proceedings	proceeding	NOUN
ejpam-6745	366	2	of	of	ADP
ejpam-6745	366	3	the	the	DET
ejpam-6745	366	4	american	american	PROPN
ejpam-6745	366	5	mathematical	mathematical	PROPN
ejpam-6745	366	6	society	society	NOUN
ejpam-6745	366	7	,	,	PUNCT
ejpam-6745	366	8	12(6):885–888	12(6):885–888	PROPN
ejpam-6745	366	9	,	,	PUNCT
ejpam-6745	366	10	1961	1961	NUM
ejpam-6745	366	11	.	.	PUNCT
ejpam-6745	367	1	[	[	X
ejpam-6745	367	2	18	18	NUM
ejpam-6745	367	3	]	]	PUNCT
ejpam-6745	367	4	m.	m.	NOUN
ejpam-6745	367	5	illafe	illafe	NOUN
ejpam-6745	367	6	,	,	PUNCT
ejpam-6745	367	7	m.	m.	NOUN
ejpam-6745	367	8	h.	h.	PROPN
ejpam-6745	367	9	mohd	mohd	PROPN
ejpam-6745	367	10	,	,	PUNCT
ejpam-6745	367	11	f.	f.	PROPN
ejpam-6745	367	12	yousef	yousef	PROPN
ejpam-6745	367	13	,	,	PUNCT
ejpam-6745	367	14	and	and	CCONJ
ejpam-6745	367	15	s.	s.	PROPN
ejpam-6745	367	16	supramaniam	supramaniam	PROPN
ejpam-6745	367	17	.	.	PUNCT
ejpam-6745	368	1	a	a	DET
ejpam-6745	368	2	subclass	subclass	NOUN
ejpam-6745	368	3	of	of	ADP
ejpam-6745	368	4	bi	bi	ADJ
ejpam-6745	368	5	-	-	ADJ
ejpam-6745	368	6	univalent	univalent	ADJ
ejpam-6745	368	7	functions	function	NOUN
ejpam-6745	368	8	defined	define	VERB
ejpam-6745	368	9	by	by	ADP
ejpam-6745	368	10	asymmetric	asymmetric	ADJ
ejpam-6745	368	11	q	q	ADJ
ejpam-6745	368	12	-	-	ADJ
ejpam-6745	368	13	derivative	derivative	ADJ
ejpam-6745	368	14	operator	operator	NOUN
ejpam-6745	368	15	and	and	CCONJ
ejpam-6745	368	16	gegenbauer	gegenbauer	NOUN
ejpam-6745	368	17	polynomials	polynomial	NOUN
ejpam-6745	368	18	.	.	PUNCT
ejpam-6745	369	1	european	european	PROPN
ejpam-6745	369	2	journal	journal	PROPN
ejpam-6745	369	3	of	of	ADP
ejpam-6745	369	4	pure	pure	ADJ
ejpam-6745	369	5	and	and	CCONJ
ejpam-6745	369	6	applied	applied	ADJ
ejpam-6745	369	7	mathematics	mathematic	NOUN
ejpam-6745	369	8	,	,	PUNCT
ejpam-6745	369	9	17(4):2467–2480	17(4):2467–2480	NUM
ejpam-6745	369	10	,	,	PUNCT
ejpam-6745	369	11	2024	2024	NUM
ejpam-6745	369	12	.	.	PUNCT
ejpam-6745	370	1	[	[	X
ejpam-6745	370	2	19	19	NUM
ejpam-6745	370	3	]	]	PUNCT
ejpam-6745	370	4	m.	m.	NOUN
ejpam-6745	370	5	illafe	illafe	NOUN
ejpam-6745	370	6	,	,	PUNCT
ejpam-6745	370	7	m.	m.	NOUN
ejpam-6745	370	8	haji	haji	PROPN
ejpam-6745	370	9	mohd	mohd	PROPN
ejpam-6745	370	10	,	,	PUNCT
ejpam-6745	370	11	f.	f.	PROPN
ejpam-6745	370	12	yousef	yousef	PROPN
ejpam-6745	370	13	,	,	PUNCT
ejpam-6745	370	14	and	and	CCONJ
ejpam-6745	370	15	s.	s.	PROPN
ejpam-6745	370	16	supramaniam	supramaniam	PROPN
ejpam-6745	370	17	.	.	PUNCT
ejpam-6745	371	1	bounds	bound	VERB
ejpam-6745	371	2	for	for	ADP
ejpam-6745	371	3	the	the	DET
ejpam-6745	371	4	second	second	ADJ
ejpam-6745	371	5	hankel	hankel	NOUN
ejpam-6745	371	6	determinant	determinant	ADJ
ejpam-6745	371	7	of	of	ADP
ejpam-6745	371	8	a	a	DET
ejpam-6745	371	9	general	general	ADJ
ejpam-6745	371	10	subclass	subclass	NOUN
ejpam-6745	371	11	of	of	ADP
ejpam-6745	371	12	bi	bi	ADJ
ejpam-6745	371	13	-	-	ADJ
ejpam-6745	371	14	univalent	univalent	ADJ
ejpam-6745	371	15	functions	function	NOUN
ejpam-6745	371	16	.	.	PUNCT
ejpam-6745	372	1	international	international	ADJ
ejpam-6745	372	2	journal	journal	PROPN
ejpam-6745	372	3	of	of	ADP
ejpam-6745	372	4	mathematics	mathematic	NOUN
ejpam-6745	372	5	,	,	PUNCT
ejpam-6745	372	6	engineering	engineering	NOUN
ejpam-6745	372	7	,	,	PUNCT
ejpam-6745	372	8	and	and	CCONJ
ejpam-6745	372	9	management	management	NOUN
ejpam-6745	372	10	sciences	science	NOUN
ejpam-6745	372	11	,	,	PUNCT
ejpam-6745	372	12	9(5):1226–1239	9(5):1226–1239	NUM
ejpam-6745	372	13	,	,	PUNCT
ejpam-6745	372	14	2024	2024	NUM
ejpam-6745	372	15	.	.	PUNCT
ejpam-6745	373	1	[	[	X
ejpam-6745	373	2	20	20	NUM
ejpam-6745	373	3	]	]	X
ejpam-6745	373	4	n.	n.	PROPN
ejpam-6745	373	5	e.	e.	PROPN
ejpam-6745	373	6	cho	cho	PROPN
ejpam-6745	373	7	,	,	PUNCT
ejpam-6745	373	8	s.	s.	PROPN
ejpam-6745	373	9	y.	y.	PROPN
ejpam-6745	373	10	woo	woo	PROPN
ejpam-6745	373	11	,	,	PUNCT
ejpam-6745	373	12	and	and	CCONJ
ejpam-6745	373	13	s.	s.	PROPN
ejpam-6745	373	14	owa	owa	PROPN
ejpam-6745	373	15	.	.	PROPN
ejpam-6745	373	16	uniform	uniform	PROPN
ejpam-6745	373	17	convexity	convexity	NOUN
ejpam-6745	373	18	properties	property	NOUN
ejpam-6745	373	19	for	for	ADP
ejpam-6745	373	20	hypergeometric	hypergeometric	ADJ
ejpam-6745	373	21	functions	function	NOUN
ejpam-6745	373	22	.	.	PUNCT
ejpam-6745	374	1	fractional	fractional	ADJ
ejpam-6745	374	2	calculus	calculus	NOUN
ejpam-6745	374	3	and	and	CCONJ
ejpam-6745	374	4	applied	apply	VERB
ejpam-6745	374	5	analysis	analysis	NOUN
ejpam-6745	374	6	,	,	PUNCT
ejpam-6745	374	7	5(3):303–314	5(3):303–314	NUM
ejpam-6745	374	8	,	,	PUNCT
ejpam-6745	374	9	2002	2002	NUM
ejpam-6745	374	10	.	.	PUNCT
ejpam-6745	375	1	[	[	X
ejpam-6745	375	2	21	21	NUM
ejpam-6745	375	3	]	]	X
ejpam-6745	375	4	s.	s.	PROPN
ejpam-6745	375	5	r.	r.	PROPN
ejpam-6745	375	6	mondal	mondal	PROPN
ejpam-6745	375	7	and	and	CCONJ
ejpam-6745	375	8	a.	a.	NOUN
ejpam-6745	375	9	swaminathan	swaminathan	ADV
ejpam-6745	375	10	.	.	PUNCT
ejpam-6745	376	1	geometric	geometric	ADJ
ejpam-6745	376	2	properties	property	NOUN
ejpam-6745	376	3	of	of	ADP
ejpam-6745	376	4	generalized	generalized	ADJ
ejpam-6745	376	5	bessel	bessel	NOUN
ejpam-6745	376	6	functions	function	NOUN
ejpam-6745	376	7	.	.	PUNCT
ejpam-6745	377	1	bull	bull	NOUN
ejpam-6745	377	2	.	.	PUNCT
ejpam-6745	378	1	malays	malays	PROPN
ejpam-6745	378	2	.	.	PUNCT
ejpam-6745	379	1	math	math	NOUN
ejpam-6745	379	2	.	.	PUNCT
ejpam-6745	380	1	sci	sci	PROPN
ejpam-6745	380	2	.	.	PROPN
ejpam-6745	380	3	soc	soc	PROPN
ejpam-6745	380	4	.	.	PUNCT
ejpam-6745	380	5	,	,	PUNCT
ejpam-6745	380	6	35(1):179–194	35(1):179–194	PROPN
ejpam-6745	380	7	,	,	PUNCT
ejpam-6745	380	8	2012	2012	NUM
ejpam-6745	380	9	.	.	PUNCT
ejpam-6745	381	1	[	[	X
ejpam-6745	381	2	22	22	NUM
ejpam-6745	381	3	]	]	PUNCT
ejpam-6745	381	4	t.	t.	PROPN
ejpam-6745	381	5	al	al	PROPN
ejpam-6745	381	6	-	-	PUNCT
ejpam-6745	381	7	hawary	hawary	PROPN
ejpam-6745	381	8	,	,	PUNCT
ejpam-6745	381	9	i.	i.	PROPN
ejpam-6745	381	10	aldawish	aldawish	PROPN
ejpam-6745	381	11	,	,	PUNCT
ejpam-6745	381	12	b.	b.	PROPN
ejpam-6745	381	13	a.	a.	PROPN
ejpam-6745	381	14	frasin	frasin	PROPN
ejpam-6745	381	15	,	,	PUNCT
ejpam-6745	381	16	o.	o.	PROPN
ejpam-6745	381	17	alkam	alkam	PROPN
ejpam-6745	381	18	,	,	PUNCT
ejpam-6745	381	19	and	and	CCONJ
ejpam-6745	381	20	f.	f.	PROPN
ejpam-6745	381	21	yousef	yousef	PROPN
ejpam-6745	381	22	.	.	PUNCT
ejpam-6745	382	1	necessary	necessary	ADJ
ejpam-6745	382	2	and	and	CCONJ
ejpam-6745	382	3	sufficient	sufficient	ADJ
ejpam-6745	382	4	conditions	condition	NOUN
ejpam-6745	382	5	for	for	SCONJ
ejpam-6745	382	6	normalized	normalize	VERB
ejpam-6745	382	7	wright	wright	PROPN
ejpam-6745	382	8	functions	function	NOUN
ejpam-6745	382	9	to	to	PART
ejpam-6745	382	10	be	be	AUX
ejpam-6745	382	11	in	in	ADP
ejpam-6745	382	12	certain	certain	ADJ
ejpam-6745	382	13	classes	class	NOUN
ejpam-6745	382	14	of	of	ADP
ejpam-6745	382	15	analytic	analytic	ADJ
ejpam-6745	382	16	functions	function	NOUN
ejpam-6745	382	17	.	.	PUNCT
ejpam-6745	383	1	mathematics	mathematic	NOUN
ejpam-6745	383	2	,	,	PUNCT
ejpam-6745	383	3	10(24):4693	10(24):4693	NUM
ejpam-6745	383	4	,	,	PUNCT
ejpam-6745	383	5	2022	2022	NUM
ejpam-6745	383	6	.	.	PUNCT
ejpam-6745	384	1	[	[	X
ejpam-6745	384	2	23	23	NUM
ejpam-6745	384	3	]	]	PUNCT
ejpam-6745	384	4	t.	t.	PROPN
ejpam-6745	384	5	al	al	PROPN
ejpam-6745	384	6	-	-	PUNCT
ejpam-6745	384	7	hawary	hawary	PROPN
ejpam-6745	384	8	,	,	PUNCT
ejpam-6745	384	9	m.	m.	NOUN
ejpam-6745	384	10	illafe	illafe	NOUN
ejpam-6745	384	11	,	,	PUNCT
ejpam-6745	384	12	and	and	CCONJ
ejpam-6745	384	13	f.	f.	PROPN
ejpam-6745	384	14	yousef	yousef	PROPN
ejpam-6745	384	15	.	.	PUNCT
ejpam-6745	385	1	certain	certain	ADJ
ejpam-6745	385	2	constraints	constraint	NOUN
ejpam-6745	385	3	for	for	ADP
ejpam-6745	385	4	functions	function	NOUN
ejpam-6745	385	5	provided	provide	VERB
ejpam-6745	385	6	by	by	ADP
ejpam-6745	385	7	touchard	touchard	NOUN
ejpam-6745	385	8	polynomials	polynomial	NOUN
ejpam-6745	385	9	.	.	PUNCT
ejpam-6745	386	1	international	international	ADJ
ejpam-6745	386	2	journal	journal	PROPN
ejpam-6745	386	3	of	of	ADP
ejpam-6745	386	4	mathematics	mathematics	PROPN
ejpam-6745	386	5	and	and	CCONJ
ejpam-6745	386	6	mathematical	mathematical	ADJ
ejpam-6745	386	7	sciences	science	NOUN
ejpam-6745	386	8	,	,	PUNCT
ejpam-6745	386	9	2025(1):2581058	2025(1):2581058	NUM
ejpam-6745	386	10	,	,	PUNCT
ejpam-6745	386	11	2025	2025	NUM
ejpam-6745	386	12	.	.	PUNCT
ejpam-6745	387	1	[	[	X
ejpam-6745	387	2	24	24	NUM
ejpam-6745	387	3	]	]	PUNCT
ejpam-6745	387	4	m.	m.	NOUN
ejpam-6745	387	5	abramowitz	abramowitz	PROPN
ejpam-6745	387	6	and	and	CCONJ
ejpam-6745	387	7	i.	i.	PROPN
ejpam-6745	387	8	a.	a.	PROPN
ejpam-6745	387	9	stegun	stegun	PROPN
ejpam-6745	387	10	.	.	PUNCT
ejpam-6745	388	1	handbook	handbook	NOUN
ejpam-6745	388	2	of	of	ADP
ejpam-6745	388	3	mathematical	mathematical	ADJ
ejpam-6745	388	4	functions	function	NOUN
ejpam-6745	388	5	with	with	ADP
ejpam-6745	388	6	formulas	formula	NOUN
ejpam-6745	388	7	,	,	PUNCT
ejpam-6745	388	8	graphs	graph	NOUN
ejpam-6745	388	9	and	and	CCONJ
ejpam-6745	388	10	matematical	matematical	ADJ
ejpam-6745	388	11	tables	table	NOUN
ejpam-6745	388	12	.	.	PUNCT
ejpam-6745	389	1	dorer	dorer	PROPN
ejpam-6745	389	2	publications	publications	PROPN
ejpam-6745	389	3	inc	inc	PROPN
ejpam-6745	389	4	.	.	PROPN
ejpam-6745	389	5	,	,	PUNCT
ejpam-6745	389	6	new	new	PROPN
ejpam-6745	389	7	york	york	PROPN
ejpam-6745	389	8	,	,	PUNCT
ejpam-6745	389	9	1965	1965	NUM
ejpam-6745	390	1	.	.	PUNCT
ejpam-6745	391	1	[	[	X
ejpam-6745	391	2	25	25	NUM
ejpam-6745	391	3	]	]	PUNCT
ejpam-6745	391	4	h.	h.	PROPN
ejpam-6745	391	5	alzer	alzer	PROPN
ejpam-6745	391	6	.	.	PUNCT
ejpam-6745	392	1	error	error	NOUN
ejpam-6745	392	2	functions	function	NOUN
ejpam-6745	392	3	inequalities	inequality	NOUN
ejpam-6745	392	4	.	.	PUNCT
ejpam-6745	393	1	advances	advance	NOUN
ejpam-6745	393	2	in	in	ADP
ejpam-6745	393	3	computational	computational	ADJ
ejpam-6745	393	4	mathematics	mathematic	NOUN
ejpam-6745	393	5	,	,	PUNCT
ejpam-6745	393	6	33(3):349–379	33(3):349–379	PROPN
ejpam-6745	393	7	,	,	PUNCT
ejpam-6745	393	8	2010	2010	NUM
ejpam-6745	393	9	.	.	PUNCT
ejpam-6745	394	1	[	[	X
ejpam-6745	394	2	26	26	NUM
ejpam-6745	394	3	]	]	X
ejpam-6745	394	4	d.	d.	PROPN
ejpam-6745	394	5	coman	coman	PROPN
ejpam-6745	394	6	.	.	PUNCT
ejpam-6745	395	1	the	the	DET
ejpam-6745	395	2	radius	radius	NOUN
ejpam-6745	395	3	of	of	ADP
ejpam-6745	395	4	starlikeness	starlikeness	NOUN
ejpam-6745	395	5	for	for	ADP
ejpam-6745	395	6	error	error	NOUN
ejpam-6745	395	7	function	function	NOUN
ejpam-6745	395	8	.	.	PUNCT
ejpam-6745	396	1	stud	stud	PROPN
ejpam-6745	396	2	.	.	PUNCT
ejpam-6745	397	1	univ	univ	PROPN
ejpam-6745	397	2	.	.	PUNCT
ejpam-6745	398	1	babes	babe	NOUN
ejpam-6745	398	2	-	-	PUNCT
ejpam-6745	398	3	bolyai	bolyai	NOUN
ejpam-6745	398	4	math	math	NOUN
ejpam-6745	398	5	,	,	PUNCT
ejpam-6745	398	6	36(2):13–16	36(2):13–16	NUM
ejpam-6745	398	7	,	,	PUNCT
ejpam-6745	398	8	1991	1991	NUM
ejpam-6745	398	9	.	.	PUNCT
ejpam-6745	399	1	[	[	X
ejpam-6745	399	2	27	27	NUM
ejpam-6745	399	3	]	]	PUNCT
ejpam-6745	399	4	a.	a.	NOUN
ejpam-6745	399	5	elbert	elbert	NOUN
ejpam-6745	399	6	and	and	CCONJ
ejpam-6745	399	7	a.	a.	NOUN
ejpam-6745	399	8	laforgia	laforgia	NOUN
ejpam-6745	399	9	.	.	PUNCT
ejpam-6745	400	1	the	the	DET
ejpam-6745	400	2	zeros	zero	NOUN
ejpam-6745	400	3	of	of	ADP
ejpam-6745	400	4	the	the	DET
ejpam-6745	400	5	complementary	complementary	ADJ
ejpam-6745	400	6	error	error	NOUN
ejpam-6745	400	7	function	function	NOUN
ejpam-6745	400	8	.	.	PUNCT
ejpam-6745	401	1	numerical	numerical	ADJ
ejpam-6745	401	2	algorithms	algorithms	PROPN
ejpam-6745	401	3	,	,	PUNCT
ejpam-6745	401	4	49(1):153–157	49(1):153–157	NOUN
ejpam-6745	401	5	,	,	PUNCT
ejpam-6745	401	6	2008	2008	NUM
ejpam-6745	401	7	.	.	PUNCT
ejpam-6745	402	1	[	[	X
ejpam-6745	402	2	28	28	NUM
ejpam-6745	402	3	]	]	PUNCT
ejpam-6745	402	4	t.	t.	PROPN
ejpam-6745	402	5	al	al	PROPN
ejpam-6745	402	6	-	-	PUNCT
ejpam-6745	402	7	hawary	hawary	PROPN
ejpam-6745	402	8	,	,	PUNCT
ejpam-6745	402	9	b.a	b.a	PROPN
ejpam-6745	402	10	.	.	PROPN
ejpam-6745	402	11	frasin	frasin	PROPN
ejpam-6745	402	12	and	and	CCONJ
ejpam-6745	402	13	j.	j.	PROPN
ejpam-6745	402	14	salah	salah	PROPN
ejpam-6745	402	15	.	.	PUNCT
ejpam-6745	403	1	comprehensive	comprehensive	ADJ
ejpam-6745	403	2	subfamilies	subfamily	NOUN
ejpam-6745	403	3	of	of	ADP
ejpam-6745	403	4	bi	bi	ADJ
ejpam-6745	403	5	-	-	ADJ
ejpam-6745	403	6	univalent	univalent	ADJ
ejpam-6745	403	7	functions	function	NOUN
ejpam-6745	403	8	defined	define	VERB
ejpam-6745	403	9	by	by	ADP
ejpam-6745	403	10	error	error	NOUN
ejpam-6745	403	11	function	function	NOUN
ejpam-6745	403	12	subordinate	subordinate	NOUN
ejpam-6745	403	13	to	to	PART
ejpam-6745	403	14	euler	euler	VERB
ejpam-6745	403	15	polynomials	polynomial	NOUN
ejpam-6745	403	16	.	.	PUNCT
ejpam-6745	404	1	symmetry	symmetry	PROPN
ejpam-6745	404	2	,	,	PUNCT
ejpam-6745	404	3	17(2):256	17(2):256	NUM
ejpam-6745	404	4	,	,	PUNCT
ejpam-6745	404	5	2025	2025	NUM
ejpam-6745	404	6	.	.	PUNCT
ejpam-6745	405	1	f.	f.	PROPN
ejpam-6745	405	2	yousef	yousef	PROPN
ejpam-6745	405	3	,	,	PUNCT
ejpam-6745	405	4	m.	m.	NOUN
ejpam-6745	405	5	m.	m.	PROPN
ejpam-6745	405	6	alholi	alholi	PROPN
ejpam-6745	405	7	,	,	PUNCT
ejpam-6745	405	8	t.	t.	PROPN
ejpam-6745	405	9	al	al	PROPN
ejpam-6745	405	10	-	-	PUNCT
ejpam-6745	405	11	hawary	hawary	PROPN
ejpam-6745	405	12	/	/	SYM
ejpam-6745	405	13	eur	eur	PROPN
ejpam-6745	405	14	.	.	PUNCT
ejpam-6745	406	1	j.	j.	PROPN
ejpam-6745	406	2	pure	pure	PROPN
ejpam-6745	406	3	appl	appl	PROPN
ejpam-6745	406	4	.	.	PROPN
ejpam-6745	406	5	math	math	PROPN
ejpam-6745	406	6	,	,	PUNCT
ejpam-6745	406	7	18	18	NUM
ejpam-6745	406	8	(	(	PUNCT
ejpam-6745	406	9	4	4	NUM
ejpam-6745	406	10	)	)	PUNCT
ejpam-6745	406	11	(	(	PUNCT
ejpam-6745	406	12	2025	2025	NUM
ejpam-6745	406	13	)	)	PUNCT
ejpam-6745	406	14	,	,	PUNCT
ejpam-6745	406	15	6745	6745	NUM
ejpam-6745	406	16	13	13	NUM
ejpam-6745	406	17	of	of	ADP
ejpam-6745	406	18	13	13	NUM
ejpam-6745	406	19	[	[	SYM
ejpam-6745	406	20	29	29	NUM
ejpam-6745	406	21	]	]	PUNCT
ejpam-6745	406	22	a.	a.	NOUN
ejpam-6745	406	23	amourah	amourah	PROPN
ejpam-6745	406	24	,	,	PUNCT
ejpam-6745	406	25	f.	f.	PROPN
ejpam-6745	406	26	yousef	yousef	PROPN
ejpam-6745	406	27	,	,	PUNCT
ejpam-6745	406	28	t.	t.	PROPN
ejpam-6745	406	29	al	al	PROPN
ejpam-6745	406	30	-	-	PUNCT
ejpam-6745	406	31	hawary	hawary	PROPN
ejpam-6745	406	32	,	,	PUNCT
ejpam-6745	406	33	and	and	CCONJ
ejpam-6745	406	34	m.	m.	NOUN
ejpam-6745	406	35	darus	darus	NOUN
ejpam-6745	406	36	.	.	PUNCT
ejpam-6745	407	1	on	on	ADP
ejpam-6745	407	2	h3(p	h3(p	NOUN
ejpam-6745	407	3	)	)	PUNCT
ejpam-6745	407	4	hankel	hankel	NOUN
ejpam-6745	407	5	determinant	determinant	ADJ
ejpam-6745	407	6	for	for	ADP
ejpam-6745	407	7	certain	certain	ADJ
ejpam-6745	407	8	subclass	subclass	NOUN
ejpam-6745	407	9	of	of	ADP
ejpam-6745	407	10	p	p	NOUN
ejpam-6745	407	11	-	-	PUNCT
ejpam-6745	407	12	valent	valent	NOUN
ejpam-6745	407	13	functions	function	NOUN
ejpam-6745	407	14	.	.	PUNCT
ejpam-6745	408	1	italian	italian	ADJ
ejpam-6745	408	2	journal	journal	NOUN
ejpam-6745	408	3	of	of	ADP
ejpam-6745	408	4	pure	pure	ADJ
ejpam-6745	408	5	and	and	CCONJ
ejpam-6745	408	6	applied	applied	ADJ
ejpam-6745	408	7	mathematics	mathematic	NOUN
ejpam-6745	408	8	,	,	PUNCT
ejpam-6745	408	9	37:611–618	37:611–618	NUM
ejpam-6745	408	10	,	,	PUNCT
ejpam-6745	408	11	2017	2017	NUM
ejpam-6745	408	12	.	.	PUNCT
ejpam-6745	409	1	[	[	X
ejpam-6745	409	2	30	30	NUM
ejpam-6745	409	3	]	]	X
ejpam-6745	409	4	b.	b.	PROPN
ejpam-6745	409	5	a.	a.	PROPN
ejpam-6745	409	6	frasin	frasin	PROPN
ejpam-6745	409	7	,	,	PUNCT
ejpam-6745	409	8	f.	f.	PROPN
ejpam-6745	409	9	yousef	yousef	PROPN
ejpam-6745	409	10	,	,	PUNCT
ejpam-6745	409	11	t.	t.	PROPN
ejpam-6745	409	12	al	al	PROPN
ejpam-6745	409	13	-	-	PUNCT
ejpam-6745	409	14	hawary	hawary	PROPN
ejpam-6745	409	15	,	,	PUNCT
ejpam-6745	409	16	and	and	CCONJ
ejpam-6745	409	17	i.	i.	PROPN
ejpam-6745	409	18	aldawish	aldawish	PROPN
ejpam-6745	409	19	.	.	PUNCT
ejpam-6745	410	1	application	application	NOUN
ejpam-6745	410	2	of	of	ADP
ejpam-6745	410	3	generalized	generalized	ADJ
ejpam-6745	410	4	bessel	bessel	NOUN
ejpam-6745	410	5	functions	function	NOUN
ejpam-6745	410	6	to	to	ADP
ejpam-6745	410	7	classes	class	NOUN
ejpam-6745	410	8	of	of	ADP
ejpam-6745	410	9	analytic	analytic	ADJ
ejpam-6745	410	10	functions	function	NOUN
ejpam-6745	410	11	.	.	PUNCT
ejpam-6745	411	1	afrika	afrika	ADJ
ejpam-6745	411	2	matematika	matematika	PROPN
ejpam-6745	411	3	,	,	PUNCT
ejpam-6745	411	4	32(3):431–439	32(3):431–439	NOUN
ejpam-6745	411	5	,	,	PUNCT
ejpam-6745	411	6	2021	2021	NUM
ejpam-6745	411	7	.	.	PUNCT
ejpam-6745	412	1	[	[	X
ejpam-6745	412	2	31	31	NUM
ejpam-6745	412	3	]	]	PUNCT
ejpam-6745	412	4	f.	f.	PROPN
ejpam-6745	412	5	yousef	yousef	PROPN
ejpam-6745	412	6	,	,	PUNCT
ejpam-6745	412	7	b.	b.	PROPN
ejpam-6745	412	8	a.	a.	PROPN
ejpam-6745	412	9	frasin	frasin	PROPN
ejpam-6745	412	10	,	,	PUNCT
ejpam-6745	412	11	and	and	CCONJ
ejpam-6745	412	12	t.	t.	PROPN
ejpam-6745	412	13	al	al	PROPN
ejpam-6745	412	14	-	-	PUNCT
ejpam-6745	412	15	hawary	hawary	PROPN
ejpam-6745	412	16	.	.	PUNCT
ejpam-6745	413	1	fekete	fekete	PROPN
ejpam-6745	413	2	-	-	PUNCT
ejpam-6745	413	3	szegö	szegö	PROPN
ejpam-6745	413	4	inequality	inequality	NOUN
ejpam-6745	413	5	for	for	ADP
ejpam-6745	413	6	analytic	analytic	ADJ
ejpam-6745	413	7	and	and	CCONJ
ejpam-6745	413	8	bi	bi	ADJ
ejpam-6745	413	9	-	-	ADJ
ejpam-6745	413	10	univalent	univalent	ADJ
ejpam-6745	413	11	functions	function	NOUN
ejpam-6745	413	12	subordinate	subordinate	VERB
ejpam-6745	413	13	to	to	ADP
ejpam-6745	413	14	chebyshev	chebyshev	NOUN
ejpam-6745	413	15	polynomials	polynomial	NOUN
ejpam-6745	413	16	.	.	PUNCT
ejpam-6745	414	1	filomat	filomat	NOUN
ejpam-6745	414	2	,	,	PUNCT
ejpam-6745	414	3	32(9):3229	32(9):3229	NUM
ejpam-6745	414	4	–	–	PUNCT
ejpam-6745	414	5	3236	3236	NUM
ejpam-6745	414	6	,	,	PUNCT
ejpam-6745	414	7	2018	2018	NUM
ejpam-6745	414	8	.	.	PUNCT
ejpam-6745	415	1	[	[	X
ejpam-6745	415	2	32	32	NUM
ejpam-6745	415	3	]	]	X
ejpam-6745	415	4	g.	g.	PROPN
ejpam-6745	415	5	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-6745	415	6	,	,	PUNCT
ejpam-6745	415	7	b.	b.	PROPN
ejpam-6745	415	8	a.	a.	PROPN
ejpam-6745	415	9	frasin	frasin	PROPN
ejpam-6745	415	10	,	,	PUNCT
ejpam-6745	415	11	and	and	CCONJ
ejpam-6745	415	12	t.	t.	PROPN
ejpam-6745	415	13	al	al	PROPN
ejpam-6745	415	14	-	-	PUNCT
ejpam-6745	415	15	hawary	hawary	PROPN
ejpam-6745	415	16	.	.	PUNCT
ejpam-6745	416	1	uniformly	uniformly	ADV
ejpam-6745	416	2	convex	convex	VERB
ejpam-6745	416	3	spiral	spiral	ADJ
ejpam-6745	416	4	functions	function	NOUN
ejpam-6745	416	5	and	and	CCONJ
ejpam-6745	416	6	uniformly	uniformly	ADV
ejpam-6745	416	7	spirallike	spirallike	ADJ
ejpam-6745	416	8	function	function	NOUN
ejpam-6745	416	9	associated	associate	VERB
ejpam-6745	416	10	with	with	ADP
ejpam-6745	416	11	pascal	pascal	ADJ
ejpam-6745	416	12	distribution	distribution	NOUN
ejpam-6745	416	13	series	series	NOUN
ejpam-6745	416	14	.	.	PUNCT
ejpam-6745	417	1	mat	mat	PROPN
ejpam-6745	417	2	.	.	PROPN
ejpam-6745	417	3	bohem	bohem	PROPN
ejpam-6745	417	4	.	.	PROPN
ejpam-6745	417	5	,	,	PUNCT
ejpam-6745	417	6	23:1–11	23:1–11	PROPN
ejpam-6745	417	7	,	,	PUNCT
ejpam-6745	417	8	2021	2021	NUM
ejpam-6745	417	9	.	.	PUNCT
ejpam-6745	418	1	[	[	X
ejpam-6745	418	2	33	33	NUM
ejpam-6745	418	3	]	]	PUNCT
ejpam-6745	418	4	r.	r.	PROPN
ejpam-6745	418	5	m.	m.	PROPN
ejpam-6745	418	6	el	el	PROPN
ejpam-6745	418	7	-	-	NOUN
ejpam-6745	418	8	ashwah	ashwah	NOUN
ejpam-6745	418	9	and	and	CCONJ
ejpam-6745	418	10	w.	w.	PROPN
ejpam-6745	418	11	y	y	PROPN
ejpam-6745	418	12	kota	kota	PROPN
ejpam-6745	418	13	.	.	PUNCT
ejpam-6745	419	1	some	some	DET
ejpam-6745	419	2	condition	condition	NOUN
ejpam-6745	419	3	on	on	ADP
ejpam-6745	419	4	a	a	DET
ejpam-6745	419	5	poisson	poisson	NOUN
ejpam-6745	419	6	distribution	distribution	NOUN
ejpam-6745	419	7	series	series	NOUN
ejpam-6745	419	8	to	to	PART
ejpam-6745	419	9	be	be	AUX
ejpam-6745	419	10	in	in	ADP
ejpam-6745	419	11	subclasses	subclass	NOUN
ejpam-6745	419	12	of	of	ADP
ejpam-6745	419	13	univalent	univalent	ADJ
ejpam-6745	419	14	functions	function	NOUN
ejpam-6745	419	15	.	.	PUNCT
ejpam-6745	420	1	acta	acta	PROPN
ejpam-6745	420	2	univ	univ	PROPN
ejpam-6745	420	3	.	.	PUNCT
ejpam-6745	421	1	apulensis	apulensis	NOUN
ejpam-6745	421	2	,	,	PUNCT
ejpam-6745	421	3	51:89–103	51:89–103	NUM
ejpam-6745	421	4	,	,	PUNCT
ejpam-6745	421	5	2017	2017	NUM
ejpam-6745	421	6	.	.	PUNCT
ejpam-6745	422	1	[	[	X
ejpam-6745	422	2	34	34	NUM
ejpam-6745	422	3	]	]	X
ejpam-6745	422	4	s.	s.	PROPN
ejpam-6745	422	5	m.	m.	PROPN
ejpam-6745	422	6	el	el	PROPN
ejpam-6745	422	7	-	-	PUNCT
ejpam-6745	422	8	deeb	deeb	PROPN
ejpam-6745	422	9	,	,	PUNCT
ejpam-6745	422	10	t.	t.	PROPN
ejpam-6745	422	11	bulboacă	bulboacă	PROPN
ejpam-6745	422	12	and	and	CCONJ
ejpam-6745	422	13	j.	j.	PROPN
ejpam-6745	422	14	dziok	dziok	PROPN
ejpam-6745	422	15	.	.	PUNCT
ejpam-6745	423	1	pascal	pascal	ADJ
ejpam-6745	423	2	distribution	distribution	NOUN
ejpam-6745	423	3	series	series	NOUN
ejpam-6745	423	4	connected	connect	VERB
ejpam-6745	423	5	with	with	ADP
ejpam-6745	423	6	certain	certain	ADJ
ejpam-6745	423	7	subclasses	subclass	NOUN
ejpam-6745	423	8	of	of	ADP
ejpam-6745	423	9	univalent	univalent	ADJ
ejpam-6745	423	10	functions	function	NOUN
ejpam-6745	423	11	.	.	PUNCT
ejpam-6745	424	1	kyungpook	kyungpook	PROPN
ejpam-6745	424	2	mathematical	mathematical	PROPN
ejpam-6745	424	3	journal	journal	PROPN
ejpam-6745	424	4	,	,	PUNCT
ejpam-6745	424	5	59(2):301–314	59(2):301–314	PROPN
ejpam-6745	424	6	,	,	PUNCT
ejpam-6745	424	7	2019	2019	NUM
ejpam-6745	424	8	.	.	PUNCT
ejpam-6745	425	1	[	[	X
ejpam-6745	425	2	35	35	NUM
ejpam-6745	425	3	]	]	PUNCT
ejpam-6745	425	4	t.	t.	PROPN
ejpam-6745	425	5	al	al	PROPN
ejpam-6745	425	6	-	-	PUNCT
ejpam-6745	425	7	hawary	hawary	PROPN
ejpam-6745	425	8	,	,	PUNCT
ejpam-6745	425	9	a.	a.	PROPN
ejpam-6745	425	10	amourah	amourah	PROPN
ejpam-6745	425	11	,	,	PUNCT
ejpam-6745	425	12	f.	f.	PROPN
ejpam-6745	425	13	yousef	yousef	PROPN
ejpam-6745	425	14	,	,	PUNCT
ejpam-6745	425	15	and	and	CCONJ
ejpam-6745	425	16	j.	j.	PROPN
ejpam-6745	425	17	salah	salah	PROPN
ejpam-6745	425	18	.	.	PUNCT
ejpam-6745	426	1	investigating	investigate	VERB
ejpam-6745	426	2	new	new	ADJ
ejpam-6745	426	3	inclusive	inclusive	ADJ
ejpam-6745	426	4	subclasses	subclass	NOUN
ejpam-6745	426	5	of	of	ADP
ejpam-6745	426	6	bi	bi	ADJ
ejpam-6745	426	7	-	-	ADJ
ejpam-6745	426	8	univalent	univalent	ADJ
ejpam-6745	426	9	functions	function	NOUN
ejpam-6745	426	10	linked	link	VERB
ejpam-6745	426	11	to	to	ADP
ejpam-6745	426	12	gregory	gregory	PROPN
ejpam-6745	426	13	numbers	numbers	PROPN
ejpam-6745	426	14	.	.	PUNCT
ejpam-6745	427	1	wseas	wseas	NOUN
ejpam-6745	427	2	transactions	transaction	NOUN
ejpam-6745	427	3	on	on	ADP
ejpam-6745	427	4	mathematics	mathematic	NOUN
ejpam-6745	427	5	,	,	PUNCT
ejpam-6745	427	6	24:231–239	24:231–239	NUM
ejpam-6745	427	7	,	,	PUNCT
ejpam-6745	427	8	2025	2025	NUM
ejpam-6745	427	9	.	.	PUNCT
ejpam-6745	428	1	[	[	X
ejpam-6745	428	2	36	36	NUM
ejpam-6745	428	3	]	]	PUNCT
ejpam-6745	428	4	t.	t.	PROPN
ejpam-6745	428	5	janani	janani	PROPN
ejpam-6745	428	6	and	and	CCONJ
ejpam-6745	428	7	g.	g.	PROPN
ejpam-6745	428	8	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-6745	428	9	.	.	PUNCT
ejpam-6745	429	1	inclusion	inclusion	NOUN
ejpam-6745	429	2	results	result	NOUN
ejpam-6745	429	3	on	on	ADP
ejpam-6745	429	4	subclasses	subclass	NOUN
ejpam-6745	429	5	of	of	ADP
ejpam-6745	429	6	starlike	starlike	NOUN
ejpam-6745	429	7	and	and	CCONJ
ejpam-6745	429	8	convex	convex	NOUN
ejpam-6745	429	9	functions	function	NOUN
ejpam-6745	429	10	associated	associate	VERB
ejpam-6745	429	11	with	with	ADP
ejpam-6745	429	12	struve	struve	PROPN
ejpam-6745	429	13	functions	function	NOUN
ejpam-6745	429	14	.	.	PUNCT
ejpam-6745	430	1	italian	italian	ADJ
ejpam-6745	430	2	journal	journal	NOUN
ejpam-6745	430	3	of	of	ADP
ejpam-6745	430	4	pure	pure	ADJ
ejpam-6745	430	5	and	and	CCONJ
ejpam-6745	430	6	applied	applied	ADJ
ejpam-6745	430	7	mathematics	mathematic	NOUN
ejpam-6745	430	8	,	,	PUNCT
ejpam-6745	430	9	32:467–476	32:467–476	PROPN
ejpam-6745	430	10	,	,	PUNCT
ejpam-6745	430	11	2014	2014	NUM
ejpam-6745	430	12	.	.	PUNCT