id	sid	tid	token	lemma	pos
ejpam-7071	1	1	european	european	PROPN
ejpam-7071	1	2	journal	journal	PROPN
ejpam-7071	1	3	of	of	ADP
ejpam-7071	1	4	pure	pure	ADJ
ejpam-7071	1	5	and	and	CCONJ
ejpam-7071	1	6	applied	applied	ADJ
ejpam-7071	1	7	mathematics	mathematic	NOUN
ejpam-7071	1	8	2025	2025	NUM
ejpam-7071	1	9	,	,	PUNCT
ejpam-7071	1	10	vol	vol	NOUN
ejpam-7071	1	11	.	.	PROPN
ejpam-7071	1	12	18	18	NUM
ejpam-7071	1	13	,	,	PUNCT
ejpam-7071	1	14	issue	issue	NOUN
ejpam-7071	1	15	4	4	NUM
ejpam-7071	1	16	,	,	PUNCT
ejpam-7071	1	17	article	article	NOUN
ejpam-7071	1	18	number	number	NOUN
ejpam-7071	1	19	7071	7071	NUM
ejpam-7071	1	20	issn	issn	PROPN
ejpam-7071	1	21	1307	1307	NUM
ejpam-7071	1	22	-	-	SYM
ejpam-7071	1	23	5543	5543	NUM
ejpam-7071	1	24	–	–	PUNCT
ejpam-7071	1	25	ejpam.com	ejpam.com	X
ejpam-7071	1	26	published	publish	VERB
ejpam-7071	1	27	by	by	ADP
ejpam-7071	1	28	new	new	PROPN
ejpam-7071	1	29	york	york	PROPN
ejpam-7071	1	30	business	business	PROPN
ejpam-7071	1	31	global	global	ADJ
ejpam-7071	1	32	analytic	analytic	ADJ
ejpam-7071	1	33	subclass	subclass	NOUN
ejpam-7071	1	34	conditions	condition	NOUN
ejpam-7071	1	35	for	for	ADP
ejpam-7071	1	36	operators	operator	NOUN
ejpam-7071	1	37	involving	involve	VERB
ejpam-7071	1	38	the	the	DET
ejpam-7071	1	39	generalized	generalized	ADJ
ejpam-7071	1	40	imaginary	imaginary	ADJ
ejpam-7071	1	41	error	error	NOUN
ejpam-7071	1	42	function	function	NOUN
ejpam-7071	1	43	a.	a.	NOUN
ejpam-7071	1	44	alameer1,∗	alameer1,∗	PROPN
ejpam-7071	1	45	,	,	PUNCT
ejpam-7071	1	46	tariq	tariq	PROPN
ejpam-7071	1	47	al	al	PROPN
ejpam-7071	1	48	-	-	PUNCT
ejpam-7071	1	49	hawary2,∗	hawary2,∗	PROPN
ejpam-7071	1	50	,	,	PUNCT
ejpam-7071	1	51	basem	basem	PROPN
ejpam-7071	1	52	aref	aref	PROPN
ejpam-7071	1	53	frasin3	frasin3	PROPN
ejpam-7071	1	54	,	,	PUNCT
ejpam-7071	1	55	feras	feras	PROPN
ejpam-7071	1	56	yousef4	yousef4	NOUN
ejpam-7071	2	1	1	1	NUM
ejpam-7071	2	2	department	department	NOUN
ejpam-7071	2	3	of	of	ADP
ejpam-7071	2	4	mathematics	mathematic	NOUN
ejpam-7071	2	5	,	,	PUNCT
ejpam-7071	2	6	university	university	NOUN
ejpam-7071	2	7	of	of	ADP
ejpam-7071	2	8	hafr	hafr	PROPN
ejpam-7071	2	9	al	al	PROPN
ejpam-7071	2	10	-	-	PUNCT
ejpam-7071	2	11	batin	batin	PROPN
ejpam-7071	2	12	,	,	PUNCT
ejpam-7071	2	13	hafr	hafr	NOUN
ejpam-7071	2	14	al	al	PROPN
ejpam-7071	2	15	batin	batin	PROPN
ejpam-7071	2	16	31991	31991	NUM
ejpam-7071	2	17	,	,	PUNCT
ejpam-7071	2	18	saudi	saudi	PROPN
ejpam-7071	2	19	arabia	arabia	PROPN
ejpam-7071	2	20	2	2	NUM
ejpam-7071	2	21	department	department	NOUN
ejpam-7071	2	22	of	of	ADP
ejpam-7071	2	23	applied	apply	VERB
ejpam-7071	2	24	science	science	NOUN
ejpam-7071	2	25	,	,	PUNCT
ejpam-7071	2	26	ajloun	ajloun	PROPN
ejpam-7071	2	27	college	college	PROPN
ejpam-7071	2	28	,	,	PUNCT
ejpam-7071	2	29	al	al	PROPN
ejpam-7071	2	30	-	-	PUNCT
ejpam-7071	2	31	balqa	balqa	NOUN
ejpam-7071	2	32	applied	apply	VERB
ejpam-7071	2	33	university	university	NOUN
ejpam-7071	2	34	,	,	PUNCT
ejpam-7071	2	35	ajloun	ajloun	NOUN
ejpam-7071	2	36	26816	26816	NUM
ejpam-7071	2	37	,	,	PUNCT
ejpam-7071	2	38	jordan	jordan	PROPN
ejpam-7071	2	39	3	3	NUM
ejpam-7071	2	40	faculty	faculty	NOUN
ejpam-7071	2	41	of	of	ADP
ejpam-7071	2	42	science	science	NOUN
ejpam-7071	2	43	,	,	PUNCT
ejpam-7071	2	44	department	department	NOUN
ejpam-7071	2	45	of	of	ADP
ejpam-7071	2	46	mathematics	mathematics	PROPN
ejpam-7071	2	47	,	,	PUNCT
ejpam-7071	2	48	al	al	PROPN
ejpam-7071	2	49	al	al	PROPN
ejpam-7071	2	50	-	-	PUNCT
ejpam-7071	2	51	bayt	bayt	ADJ
ejpam-7071	2	52	university	university	NOUN
ejpam-7071	2	53	,	,	PUNCT
ejpam-7071	2	54	mafraq	mafraq	PROPN
ejpam-7071	2	55	,	,	PUNCT
ejpam-7071	2	56	jordan	jordan	PROPN
ejpam-7071	2	57	4	4	NUM
ejpam-7071	2	58	department	department	NOUN
ejpam-7071	2	59	of	of	ADP
ejpam-7071	2	60	mathematics	mathematic	NOUN
ejpam-7071	2	61	,	,	PUNCT
ejpam-7071	2	62	the	the	DET
ejpam-7071	2	63	university	university	PROPN
ejpam-7071	2	64	of	of	ADP
ejpam-7071	2	65	jordan	jordan	PROPN
ejpam-7071	2	66	,	,	PUNCT
ejpam-7071	2	67	amman	amman	PROPN
ejpam-7071	2	68	11942	11942	NUM
ejpam-7071	2	69	,	,	PUNCT
ejpam-7071	2	70	jordan	jordan	PROPN
ejpam-7071	2	71	abstract	abstract	PROPN
ejpam-7071	2	72	.	.	PUNCT
ejpam-7071	3	1	in	in	ADP
ejpam-7071	3	2	this	this	DET
ejpam-7071	3	3	paper	paper	NOUN
ejpam-7071	3	4	,	,	PUNCT
ejpam-7071	3	5	we	we	PRON
ejpam-7071	3	6	establish	establish	VERB
ejpam-7071	3	7	necessary	necessary	ADJ
ejpam-7071	3	8	and	and	CCONJ
ejpam-7071	3	9	sufficient	sufficient	ADJ
ejpam-7071	3	10	criteria	criterion	NOUN
ejpam-7071	3	11	for	for	ADP
ejpam-7071	3	12	the	the	DET
ejpam-7071	3	13	generalized	generalized	ADJ
ejpam-7071	3	14	imaginary	imaginary	ADJ
ejpam-7071	3	15	error	error	NOUN
ejpam-7071	3	16	function	function	NOUN
ejpam-7071	3	17	ϖin	ϖin	PROPN
ejpam-7071	3	18	(	(	PUNCT
ejpam-7071	3	19	z	z	NOUN
ejpam-7071	3	20	)	)	PUNCT
ejpam-7071	3	21	to	to	PART
ejpam-7071	3	22	belong	belong	VERB
ejpam-7071	3	23	to	to	ADP
ejpam-7071	3	24	the	the	DET
ejpam-7071	3	25	class	class	NOUN
ejpam-7071	3	26	f(ℏ1	f(ℏ1	NOUN
ejpam-7071	3	27	,	,	PUNCT
ejpam-7071	3	28	ℏ2	ℏ2	NOUN
ejpam-7071	3	29	)	)	PUNCT
ejpam-7071	3	30	.	.	PUNCT
ejpam-7071	4	1	we	we	PRON
ejpam-7071	4	2	also	also	ADV
ejpam-7071	4	3	derive	derive	VERB
ejpam-7071	4	4	an	an	DET
ejpam-7071	4	5	inclusion	inclusion	NOUN
ejpam-7071	4	6	relation	relation	NOUN
ejpam-7071	4	7	between	between	ADP
ejpam-7071	4	8	the	the	DET
ejpam-7071	4	9	classes	class	NOUN
ejpam-7071	4	10	gτ	gτ	NOUN
ejpam-7071	4	11	(	(	PUNCT
ejpam-7071	4	12	a1	a1	PROPN
ejpam-7071	4	13	,	,	PUNCT
ejpam-7071	4	14	a2	a2	NOUN
ejpam-7071	4	15	)	)	PUNCT
ejpam-7071	4	16	and	and	CCONJ
ejpam-7071	4	17	f(ℏ1	f(ℏ1	NOUN
ejpam-7071	4	18	,	,	PUNCT
ejpam-7071	4	19	ℏ2	ℏ2	NOUN
ejpam-7071	4	20	)	)	PUNCT
ejpam-7071	4	21	.	.	PUNCT
ejpam-7071	5	1	furthermore	furthermore	ADV
ejpam-7071	5	2	,	,	PUNCT
ejpam-7071	5	3	we	we	PRON
ejpam-7071	5	4	provide	provide	VERB
ejpam-7071	5	5	a	a	DET
ejpam-7071	5	6	necessary	necessary	ADJ
ejpam-7071	5	7	and	and	CCONJ
ejpam-7071	5	8	sufficient	sufficient	ADJ
ejpam-7071	5	9	condition	condition	NOUN
ejpam-7071	5	10	for	for	ADP
ejpam-7071	5	11	the	the	DET
ejpam-7071	5	12	integral	integral	ADJ
ejpam-7071	5	13	operator	operator	NOUN
ejpam-7071	5	14	gim(z	gim(z	PROPN
ejpam-7071	5	15	)	)	PUNCT
ejpam-7071	5	16	:	:	PUNCT
ejpam-7071	6	1	=	=	PUNCT
ejpam-7071	6	2	∫	∫	PROPN
ejpam-7071	6	3	z	z	NOUN
ejpam-7071	6	4	0	0	NUM
ejpam-7071	6	5	ϖin(z	ϖin(z	PROPN
ejpam-7071	6	6	)	)	PUNCT
ejpam-7071	6	7	t	t	NOUN
ejpam-7071	6	8	dt	dt	NOUN
ejpam-7071	6	9	to	to	PART
ejpam-7071	6	10	lie	lie	VERB
ejpam-7071	6	11	in	in	ADP
ejpam-7071	6	12	the	the	DET
ejpam-7071	6	13	class	class	NOUN
ejpam-7071	6	14	f(ℏ1	f(ℏ1	NOUN
ejpam-7071	6	15	,	,	PUNCT
ejpam-7071	6	16	ℏ2	ℏ2	NOUN
ejpam-7071	6	17	)	)	PUNCT
ejpam-7071	6	18	.	.	PUNCT
ejpam-7071	7	1	2020	2020	NUM
ejpam-7071	7	2	mathematics	mathematic	NOUN
ejpam-7071	7	3	subject	subject	NOUN
ejpam-7071	7	4	classifications	classification	NOUN
ejpam-7071	7	5	:	:	PUNCT
ejpam-7071	7	6	30c45	30c45	NUM
ejpam-7071	7	7	key	key	ADJ
ejpam-7071	7	8	words	word	NOUN
ejpam-7071	7	9	and	and	CCONJ
ejpam-7071	7	10	phrases	phrase	NOUN
ejpam-7071	7	11	:	:	PUNCT
ejpam-7071	7	12	analytic	analytic	ADJ
ejpam-7071	7	13	,	,	PUNCT
ejpam-7071	7	14	univalent	univalent	ADJ
ejpam-7071	7	15	,	,	PUNCT
ejpam-7071	7	16	error	error	NOUN
ejpam-7071	7	17	function	function	NOUN
ejpam-7071	7	18	1	1	NUM
ejpam-7071	7	19	.	.	PUNCT
ejpam-7071	8	1	introduction	introduction	NOUN
ejpam-7071	8	2	and	and	CCONJ
ejpam-7071	8	3	preliminaries	preliminary	NOUN
ejpam-7071	8	4	let	let	VERB
ejpam-7071	8	5	an	an	PRON
ejpam-7071	8	6	indicate	indicate	VERB
ejpam-7071	8	7	the	the	DET
ejpam-7071	8	8	class	class	NOUN
ejpam-7071	8	9	of	of	ADP
ejpam-7071	8	10	analytic	analytic	ADJ
ejpam-7071	8	11	functions	function	NOUN
ejpam-7071	8	12	of	of	ADP
ejpam-7071	8	13	the	the	DET
ejpam-7071	8	14	form	form	NOUN
ejpam-7071	8	15	g(z	g(z	ADJ
ejpam-7071	8	16	)	)	PUNCT
ejpam-7071	8	17	=	=	SYM
ejpam-7071	9	1	z	z	NOUN
ejpam-7071	10	1	+	+	PUNCT
ejpam-7071	10	2	∞∑	∞∑	NUM
ejpam-7071	10	3	ρ=2	ρ=2	PUNCT
ejpam-7071	10	4	aρz	aρz	NOUN
ejpam-7071	10	5	ρ	ρ	NOUN
ejpam-7071	10	6	;	;	PUNCT
ejpam-7071	10	7	z	z	PROPN
ejpam-7071	10	8	∈	∈	NOUN
ejpam-7071	10	9	∆	∆	X
ejpam-7071	10	10	=	=	PRON
ejpam-7071	10	11	{	{	PUNCT
ejpam-7071	10	12	z	z	PROPN
ejpam-7071	10	13	∈	∈	PROPN
ejpam-7071	10	14	c	c	NOUN
ejpam-7071	10	15	:	:	PUNCT
ejpam-7071	10	16	|z|	|z|	NOUN
ejpam-7071	10	17	<	<	X
ejpam-7071	10	18	1	1	NUM
ejpam-7071	10	19	}	}	PUNCT
ejpam-7071	10	20	.	.	PUNCT
ejpam-7071	11	1	(	(	PUNCT
ejpam-7071	11	2	1	1	X
ejpam-7071	11	3	)	)	PUNCT
ejpam-7071	11	4	also	also	ADV
ejpam-7071	11	5	,	,	PUNCT
ejpam-7071	11	6	consider	consider	VERB
ejpam-7071	11	7	s	s	PRON
ejpam-7071	11	8	to	to	PART
ejpam-7071	11	9	be	be	AUX
ejpam-7071	11	10	the	the	DET
ejpam-7071	11	11	subclass	subclass	NOUN
ejpam-7071	11	12	of	of	ADP
ejpam-7071	11	13	an	an	DET
ejpam-7071	11	14	consisting	consisting	NOUN
ejpam-7071	11	15	of	of	ADP
ejpam-7071	11	16	functions	function	NOUN
ejpam-7071	11	17	which	which	PRON
ejpam-7071	11	18	are	be	AUX
ejpam-7071	11	19	univalent	univalent	ADJ
ejpam-7071	11	20	in	in	ADP
ejpam-7071	11	21	∆.	∆.	NOUN
ejpam-7071	11	22	according	accord	VERB
ejpam-7071	11	23	to	to	ADP
ejpam-7071	11	24	kamali	kamali	PROPN
ejpam-7071	11	25	et	et	PROPN
ejpam-7071	11	26	al	al	PROPN
ejpam-7071	11	27	.	.	PUNCT
ejpam-7071	12	1	[	[	X
ejpam-7071	12	2	1	1	NUM
ejpam-7071	12	3	]	]	PUNCT
ejpam-7071	12	4	,	,	PUNCT
ejpam-7071	12	5	let	let	VERB
ejpam-7071	12	6	f(ℏ1	f(ℏ1	ADJ
ejpam-7071	12	7	,	,	PUNCT
ejpam-7071	12	8	ℏ2	ℏ2	NOUN
ejpam-7071	12	9	)	)	PUNCT
ejpam-7071	12	10	be	be	AUX
ejpam-7071	12	11	a	a	DET
ejpam-7071	12	12	subclass	subclass	NOUN
ejpam-7071	12	13	of	of	ADP
ejpam-7071	12	14	an	an	PRON
ejpam-7071	12	15	,	,	PUNCT
ejpam-7071	12	16	containing	contain	VERB
ejpam-7071	12	17	the	the	DET
ejpam-7071	12	18	functions	function	NOUN
ejpam-7071	12	19	of	of	ADP
ejpam-7071	12	20	the	the	DET
ejpam-7071	12	21	form	form	NOUN
ejpam-7071	12	22	(	(	PUNCT
ejpam-7071	12	23	1	1	X
ejpam-7071	12	24	)	)	PUNCT
ejpam-7071	12	25	that	that	PRON
ejpam-7071	12	26	satisfy	satisfy	VERB
ejpam-7071	12	27	the	the	DET
ejpam-7071	12	28	following	follow	VERB
ejpam-7071	12	29	analytical	analytical	ADJ
ejpam-7071	12	30	requirement	requirement	NOUN
ejpam-7071	12	31	:	:	PUNCT
ejpam-7071	12	32	re	re	X
ejpam-7071	12	33	(	(	PUNCT
ejpam-7071	12	34	ℏ2z3g′′′(z	ℏ2z3g′′′(z	NOUN
ejpam-7071	12	35	)	)	PUNCT
ejpam-7071	13	1	+	+	CCONJ
ejpam-7071	13	2	(	(	PUNCT
ejpam-7071	13	3	2ℏ2	2ℏ2	NUM
ejpam-7071	13	4	+	+	CCONJ
ejpam-7071	13	5	1)z2g′′(z	1)z2g′′(z	NUM
ejpam-7071	13	6	)	)	PUNCT
ejpam-7071	13	7	+	+	CCONJ
ejpam-7071	13	8	zg′(z	zg′(z	NOUN
ejpam-7071	13	9	)	)	PUNCT
ejpam-7071	13	10	ℏ2z2g′′(z	ℏ2z2g′′(z	NOUN
ejpam-7071	13	11	)	)	PUNCT
ejpam-7071	14	1	+	+	CCONJ
ejpam-7071	14	2	zg′(z	zg′(z	NOUN
ejpam-7071	14	3	)	)	PUNCT
ejpam-7071	14	4	)	)	PUNCT
ejpam-7071	15	1	>	>	X
ejpam-7071	15	2	ℏ1	ℏ1	PROPN
ejpam-7071	15	3	;	;	PUNCT
ejpam-7071	15	4	(	(	PUNCT
ejpam-7071	15	5	ℏ1	ℏ1	ADJ
ejpam-7071	15	6	,	,	PUNCT
ejpam-7071	15	7	ℏ2	ℏ2	NOUN
ejpam-7071	15	8	∈	∈	PROPN
ejpam-7071	16	1	[	[	X
ejpam-7071	16	2	0	0	NUM
ejpam-7071	16	3	,	,	PUNCT
ejpam-7071	16	4	1	1	NUM
ejpam-7071	16	5	)	)	PUNCT
ejpam-7071	16	6	,	,	PUNCT
ejpam-7071	16	7	|z|	|z|	VERB
ejpam-7071	16	8	<	<	X
ejpam-7071	16	9	1	1	NUM
ejpam-7071	16	10	)	)	PUNCT
ejpam-7071	16	11	.	.	PUNCT
ejpam-7071	17	1	∗corresponding	∗corresponde	VERB
ejpam-7071	17	2	author	author	NOUN
ejpam-7071	17	3	.	.	PUNCT
ejpam-7071	18	1	∗corresponding	∗corresponde	VERB
ejpam-7071	18	2	author	author	NOUN
ejpam-7071	18	3	.	.	PUNCT
ejpam-7071	19	1	doi	doi	NOUN
ejpam-7071	19	2	:	:	PUNCT
ejpam-7071	19	3	https://doi.org/10.29020/nybg.ejpam.v18i4.7071	https://doi.org/10.29020/nybg.ejpam.v18i4.7071	ADJ
ejpam-7071	19	4	email	email	NOUN
ejpam-7071	19	5	addresses	address	NOUN
ejpam-7071	19	6	:	:	PUNCT
ejpam-7071	19	7	aamalameer@uhb.edu.sa	aamalameer@uhb.edu.sa	PROPN
ejpam-7071	19	8	(	(	PUNCT
ejpam-7071	19	9	a.	a.	NOUN
ejpam-7071	19	10	alameer	alameer	PROPN
ejpam-7071	19	11	)	)	PUNCT
ejpam-7071	19	12	,	,	PUNCT
ejpam-7071	19	13	tariq	tariq	NOUN
ejpam-7071	19	14	amh@bau.edu.jo	amh@bau.edu.jo	PROPN
ejpam-7071	19	15	(	(	PUNCT
ejpam-7071	19	16	t.	t.	PROPN
ejpam-7071	19	17	al	al	PROPN
ejpam-7071	19	18	-	-	PUNCT
ejpam-7071	19	19	hawary	hawary	PROPN
ejpam-7071	19	20	)	)	PUNCT
ejpam-7071	19	21	,	,	PUNCT
ejpam-7071	19	22	bafrasin@yahoo.com	bafrasin@yahoo.com	X
ejpam-7071	20	1	(	(	PUNCT
ejpam-7071	20	2	b.	b.	PROPN
ejpam-7071	20	3	a.	a.	PROPN
ejpam-7071	20	4	frasin	frasin	PROPN
ejpam-7071	20	5	)	)	PUNCT
ejpam-7071	20	6	,	,	PUNCT
ejpam-7071	20	7	fyousef@ju.edu.jo	fyousef@ju.edu.jo	NOUN
ejpam-7071	20	8	(	(	PUNCT
ejpam-7071	20	9	f.	f.	PROPN
ejpam-7071	20	10	yousef	yousef	PROPN
ejpam-7071	20	11	)	)	PUNCT
ejpam-7071	20	12	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-7071	21	1	1	1	NUM
ejpam-7071	21	2	copyright	copyright	NOUN
ejpam-7071	21	3	:	:	PUNCT
ejpam-7071	21	4	©	©	PROPN
ejpam-7071	21	5	2025	2025	NUM
ejpam-7071	21	6	the	the	DET
ejpam-7071	21	7	author(s	author(s	NOUN
ejpam-7071	21	8	)	)	PUNCT
ejpam-7071	21	9	.	.	PUNCT
ejpam-7071	22	1	(	(	PUNCT
ejpam-7071	22	2	cc	cc	NOUN
ejpam-7071	22	3	by	by	ADP
ejpam-7071	22	4	-	-	PUNCT
ejpam-7071	22	5	nc	nc	PROPN
ejpam-7071	22	6	4.0	4.0	NUM
ejpam-7071	22	7	)	)	PUNCT
ejpam-7071	22	8	a.	a.	NOUN
ejpam-7071	22	9	alameer	alameer	NOUN
ejpam-7071	22	10	et	et	PROPN
ejpam-7071	22	11	al	al	PROPN
ejpam-7071	22	12	.	.	PUNCT
ejpam-7071	22	13	/	/	SYM
ejpam-7071	22	14	eur	eur	PROPN
ejpam-7071	22	15	.	.	PUNCT
ejpam-7071	23	1	j.	j.	PROPN
ejpam-7071	23	2	pure	pure	PROPN
ejpam-7071	23	3	appl	appl	PROPN
ejpam-7071	23	4	.	.	PROPN
ejpam-7071	23	5	math	math	PROPN
ejpam-7071	23	6	,	,	PUNCT
ejpam-7071	23	7	18	18	NUM
ejpam-7071	23	8	(	(	PUNCT
ejpam-7071	23	9	4	4	NUM
ejpam-7071	23	10	)	)	PUNCT
ejpam-7071	23	11	(	(	PUNCT
ejpam-7071	23	12	2025	2025	NUM
ejpam-7071	23	13	)	)	PUNCT
ejpam-7071	23	14	,	,	PUNCT
ejpam-7071	23	15	7071	7071	NUM
ejpam-7071	23	16	2	2	NUM
ejpam-7071	23	17	of	of	ADP
ejpam-7071	23	18	11	11	NUM
ejpam-7071	23	19	example	example	NOUN
ejpam-7071	23	20	1	1	NUM
ejpam-7071	23	21	.	.	PUNCT
ejpam-7071	24	1	[	[	X
ejpam-7071	24	2	2	2	X
ejpam-7071	24	3	]	]	PUNCT
ejpam-7071	24	4	for	for	ADP
ejpam-7071	24	5	some	some	DET
ejpam-7071	24	6	ℏ1	ℏ1	PROPN
ejpam-7071	24	7	∈	∈	PROPN
ejpam-7071	24	8	[	[	X
ejpam-7071	24	9	0	0	NUM
ejpam-7071	24	10	,	,	PUNCT
ejpam-7071	24	11	1	1	NUM
ejpam-7071	24	12	)	)	PUNCT
ejpam-7071	24	13	,	,	PUNCT
ejpam-7071	24	14	by	by	ADP
ejpam-7071	24	15	choosing	choose	VERB
ejpam-7071	24	16	ℏ2	ℏ2	NOUN
ejpam-7071	24	17	=	=	SYM
ejpam-7071	24	18	0	0	PUNCT
ejpam-7071	24	19	and	and	CCONJ
ejpam-7071	24	20	taking	take	VERB
ejpam-7071	24	21	g(z	g(z	PROPN
ejpam-7071	24	22	)	)	PUNCT
ejpam-7071	24	23	of	of	ADP
ejpam-7071	24	24	the	the	DET
ejpam-7071	24	25	form	form	NOUN
ejpam-7071	24	26	(	(	PUNCT
ejpam-7071	24	27	1	1	NUM
ejpam-7071	24	28	)	)	PUNCT
ejpam-7071	24	29	,	,	PUNCT
ejpam-7071	24	30	let	let	VERB
ejpam-7071	24	31	the	the	DET
ejpam-7071	24	32	subclass	subclass	NOUN
ejpam-7071	24	33	f(ℏ1	f(ℏ1	NOUN
ejpam-7071	24	34	,	,	PUNCT
ejpam-7071	24	35	0	0	NUM
ejpam-7071	24	36	)	)	PUNCT
ejpam-7071	24	37	≡	≡	PROPN
ejpam-7071	24	38	k(ℏ1	k(ℏ1	PROPN
ejpam-7071	24	39	)	)	PUNCT
ejpam-7071	24	40	consists	consist	VERB
ejpam-7071	24	41	of	of	ADP
ejpam-7071	24	42	functions	function	NOUN
ejpam-7071	24	43	in	in	ADP
ejpam-7071	24	44	an	an	DET
ejpam-7071	24	45	that	that	DET
ejpam-7071	24	46	satisfy	satisfy	NOUN
ejpam-7071	24	47	the	the	DET
ejpam-7071	24	48	inequality	inequality	NOUN
ejpam-7071	24	49	:	:	PUNCT
ejpam-7071	24	50	re	re	X
ejpam-7071	24	51	(	(	PUNCT
ejpam-7071	24	52	zg′′(z	zg′′(z	NOUN
ejpam-7071	24	53	)	)	PUNCT
ejpam-7071	24	54	g′(z	g′(z	VERB
ejpam-7071	24	55	)	)	PUNCT
ejpam-7071	25	1	+	+	CCONJ
ejpam-7071	25	2	1	1	X
ejpam-7071	25	3	)	)	PUNCT
ejpam-7071	25	4	>	>	X
ejpam-7071	25	5	ℏ1	ℏ1	PROPN
ejpam-7071	25	6	;	;	PUNCT
ejpam-7071	25	7	|z|	|z|	VERB
ejpam-7071	25	8	<	<	X
ejpam-7071	25	9	1	1	NUM
ejpam-7071	25	10	.	.	PUNCT
ejpam-7071	26	1	also	also	ADV
ejpam-7071	26	2	,	,	PUNCT
ejpam-7071	26	3	if	if	SCONJ
ejpam-7071	26	4	ℏ1	ℏ1	ADJ
ejpam-7071	26	5	=	=	ADJ
ejpam-7071	26	6	ℏ2	ℏ2	NOUN
ejpam-7071	26	7	=	=	SYM
ejpam-7071	26	8	0	0	NUM
ejpam-7071	26	9	,	,	PUNCT
ejpam-7071	26	10	the	the	DET
ejpam-7071	26	11	subclass	subclass	NOUN
ejpam-7071	26	12	f(0	f(0	NOUN
ejpam-7071	26	13	,	,	PUNCT
ejpam-7071	26	14	0	0	NUM
ejpam-7071	26	15	)	)	PUNCT
ejpam-7071	26	16	≡	≡	PROPN
ejpam-7071	26	17	k(0	k(0	PROPN
ejpam-7071	26	18	)	)	PUNCT
ejpam-7071	26	19	≡	≡	PROPN
ejpam-7071	26	20	k	k	PROPN
ejpam-7071	26	21	consists	consist	VERB
ejpam-7071	26	22	of	of	ADP
ejpam-7071	26	23	functions	function	NOUN
ejpam-7071	26	24	in	in	ADP
ejpam-7071	26	25	an	an	DET
ejpam-7071	26	26	satisfying	satisfying	NOUN
ejpam-7071	26	27	the	the	DET
ejpam-7071	26	28	inequality	inequality	NOUN
ejpam-7071	26	29	:	:	PUNCT
ejpam-7071	26	30	re	re	X
ejpam-7071	26	31	(	(	PUNCT
ejpam-7071	26	32	zg′′(z	zg′′(z	NOUN
ejpam-7071	26	33	)	)	PUNCT
ejpam-7071	26	34	g′(z	g′(z	VERB
ejpam-7071	26	35	)	)	PUNCT
ejpam-7071	27	1	+	+	CCONJ
ejpam-7071	27	2	1	1	X
ejpam-7071	27	3	)	)	PUNCT
ejpam-7071	27	4	>	>	X
ejpam-7071	27	5	0	0	NUM
ejpam-7071	27	6	;	;	PUNCT
ejpam-7071	27	7	|z|	|z|	VERB
ejpam-7071	27	8	<	<	X
ejpam-7071	27	9	1	1	NUM
ejpam-7071	27	10	.	.	PUNCT
ejpam-7071	28	1	both	both	DET
ejpam-7071	28	2	subclasses	subclass	NOUN
ejpam-7071	28	3	k(ℏ1	k(ℏ1	PROPN
ejpam-7071	28	4	)	)	PUNCT
ejpam-7071	28	5	and	and	CCONJ
ejpam-7071	28	6	k	k	PROPN
ejpam-7071	28	7	are	be	AUX
ejpam-7071	28	8	well	well	ADV
ejpam-7071	28	9	known	know	VERB
ejpam-7071	28	10	subclasses	subclass	NOUN
ejpam-7071	28	11	of	of	ADP
ejpam-7071	28	12	convex	convex	NOUN
ejpam-7071	28	13	functions	function	NOUN
ejpam-7071	28	14	of	of	ADP
ejpam-7071	28	15	order	order	NOUN
ejpam-7071	28	16	ℏ1	ℏ1	ADJ
ejpam-7071	28	17	and	and	CCONJ
ejpam-7071	28	18	convex	convex	NOUN
ejpam-7071	28	19	functions	function	NOUN
ejpam-7071	28	20	(	(	PUNCT
ejpam-7071	28	21	convex	convex	NOUN
ejpam-7071	28	22	functions	function	NOUN
ejpam-7071	28	23	of	of	ADP
ejpam-7071	28	24	order	order	NOUN
ejpam-7071	28	25	zero	zero	NUM
ejpam-7071	28	26	)	)	PUNCT
ejpam-7071	28	27	,	,	PUNCT
ejpam-7071	28	28	respectively	respectively	ADV
ejpam-7071	28	29	(	(	PUNCT
ejpam-7071	28	30	see	see	VERB
ejpam-7071	28	31	[	[	X
ejpam-7071	28	32	2	2	NUM
ejpam-7071	28	33	]	]	NUM
ejpam-7071	28	34	)	)	PUNCT
ejpam-7071	28	35	.	.	PUNCT
ejpam-7071	29	1	for	for	ADP
ejpam-7071	29	2	functions	function	NOUN
ejpam-7071	29	3	of	of	ADP
ejpam-7071	29	4	the	the	DET
ejpam-7071	29	5	previously	previously	ADV
ejpam-7071	29	6	described	describe	VERB
ejpam-7071	29	7	subclass	subclass	NOUN
ejpam-7071	29	8	,	,	PUNCT
ejpam-7071	29	9	we	we	PRON
ejpam-7071	29	10	require	require	VERB
ejpam-7071	29	11	the	the	DET
ejpam-7071	29	12	following	follow	VERB
ejpam-7071	29	13	sufficient	sufficient	ADJ
ejpam-7071	29	14	and	and	CCONJ
ejpam-7071	29	15	necessary	necessary	ADJ
ejpam-7071	29	16	conditions	condition	NOUN
ejpam-7071	29	17	.	.	PUNCT
ejpam-7071	30	1	lemma	lemma	PROPN
ejpam-7071	30	2	1	1	NUM
ejpam-7071	30	3	.	.	PUNCT
ejpam-7071	31	1	[	[	X
ejpam-7071	31	2	1	1	X
ejpam-7071	31	3	]	]	PUNCT
ejpam-7071	31	4	a	a	DET
ejpam-7071	31	5	function	function	NOUN
ejpam-7071	31	6	g	g	PROPN
ejpam-7071	31	7	∈	∈	PROPN
ejpam-7071	31	8	f(ℏ1	f(ℏ1	NOUN
ejpam-7071	31	9	,	,	PUNCT
ejpam-7071	31	10	ℏ2	ℏ2	NOUN
ejpam-7071	31	11	)	)	PUNCT
ejpam-7071	31	12	if	if	SCONJ
ejpam-7071	31	13	and	and	CCONJ
ejpam-7071	31	14	only	only	ADV
ejpam-7071	31	15	if	if	SCONJ
ejpam-7071	31	16	∞∑	∞∑	NUM
ejpam-7071	31	17	ρ=2	ρ=2	NUM
ejpam-7071	31	18	ρ(ρ−	ρ(ρ−	ADJ
ejpam-7071	31	19	ℏ1	ℏ1	PROPN
ejpam-7071	31	20	)	)	PUNCT
ejpam-7071	31	21	(	(	PUNCT
ejpam-7071	31	22	ℏ2(ρ−	ℏ2(ρ−	ADJ
ejpam-7071	31	23	1	1	X
ejpam-7071	31	24	)	)	PUNCT
ejpam-7071	31	25	+	+	CCONJ
ejpam-7071	31	26	1	1	X
ejpam-7071	31	27	)	)	PUNCT
ejpam-7071	31	28	|aρ|	|aρ|	ADJ
ejpam-7071	31	29	≤	≤	NOUN
ejpam-7071	31	30	1−	1−	NUM
ejpam-7071	31	31	ℏ1	ℏ1	PROPN
ejpam-7071	31	32	.	.	PUNCT
ejpam-7071	32	1	(	(	PUNCT
ejpam-7071	32	2	2	2	X
ejpam-7071	32	3	)	)	PUNCT
ejpam-7071	32	4	definition	definition	NOUN
ejpam-7071	32	5	1	1	NUM
ejpam-7071	32	6	.	.	PUNCT
ejpam-7071	33	1	[	[	X
ejpam-7071	33	2	3	3	X
ejpam-7071	33	3	]	]	X
ejpam-7071	33	4	a	a	DET
ejpam-7071	33	5	function	function	NOUN
ejpam-7071	33	6	g	g	PROPN
ejpam-7071	33	7	∈	∈	PROPN
ejpam-7071	33	8	an	an	PRON
ejpam-7071	33	9	is	be	AUX
ejpam-7071	33	10	said	say	VERB
ejpam-7071	33	11	to	to	PART
ejpam-7071	33	12	be	be	AUX
ejpam-7071	33	13	in	in	ADP
ejpam-7071	33	14	the	the	DET
ejpam-7071	33	15	class	class	NOUN
ejpam-7071	33	16	gτ	gτ	PROPN
ejpam-7071	33	17	(	(	PUNCT
ejpam-7071	33	18	a1	a1	PROPN
ejpam-7071	33	19	,	,	PUNCT
ejpam-7071	33	20	a2	a2	PROPN
ejpam-7071	33	21	)	)	PUNCT
ejpam-7071	33	22	,	,	PUNCT
ejpam-7071	33	23	τ	τ	PROPN
ejpam-7071	33	24	∈	∈	PROPN
ejpam-7071	33	25	c\{0	c\{0	PROPN
ejpam-7071	33	26	}	}	PUNCT
ejpam-7071	33	27	,	,	PUNCT
ejpam-7071	33	28	−1	−1	NOUN
ejpam-7071	33	29	≤	≤	PROPN
ejpam-7071	33	30	a2	a2	PROPN
ejpam-7071	33	31	<	<	X
ejpam-7071	33	32	a1	a1	NOUN
ejpam-7071	33	33	≤	≤	ADV
ejpam-7071	33	34	1	1	NUM
ejpam-7071	33	35	,	,	PUNCT
ejpam-7071	33	36	if	if	SCONJ
ejpam-7071	33	37	it	it	PRON
ejpam-7071	33	38	satisfies	satisfy	VERB
ejpam-7071	33	39	the	the	DET
ejpam-7071	33	40	inequality:∣∣∣∣	inequality:∣∣∣∣	PROPN
ejpam-7071	33	41	g′(z)−	g′(z)−	PROPN
ejpam-7071	33	42	1	1	NUM
ejpam-7071	33	43	(	(	PUNCT
ejpam-7071	33	44	a1	a1	PROPN
ejpam-7071	33	45	−a2)τ	−a2)τ	PROPN
ejpam-7071	33	46	−a2[g′(z)−	−a2[g′(z)−	PROPN
ejpam-7071	33	47	1	1	NUM
ejpam-7071	33	48	]	]	PUNCT
ejpam-7071	33	49	∣∣∣∣	∣∣∣∣	NOUN
ejpam-7071	33	50	<	<	X
ejpam-7071	33	51	1	1	NUM
ejpam-7071	33	52	;	;	PUNCT
ejpam-7071	33	53	z	z	PROPN
ejpam-7071	33	54	∈	∈	PROPN
ejpam-7071	34	1	∆.	∆.	PRON
ejpam-7071	34	2	special	special	ADJ
ejpam-7071	34	3	functions	function	NOUN
ejpam-7071	34	4	are	be	AUX
ejpam-7071	34	5	widely	widely	ADV
ejpam-7071	34	6	acknowledged	acknowledge	VERB
ejpam-7071	34	7	as	as	ADP
ejpam-7071	34	8	being	be	AUX
ejpam-7071	34	9	crucial	crucial	ADJ
ejpam-7071	34	10	to	to	ADP
ejpam-7071	34	11	geometric	geometric	ADJ
ejpam-7071	34	12	function	function	NOUN
ejpam-7071	34	13	theory	theory	NOUN
ejpam-7071	34	14	and	and	CCONJ
ejpam-7071	34	15	are	be	AUX
ejpam-7071	34	16	employed	employ	VERB
ejpam-7071	34	17	in	in	ADP
ejpam-7071	34	18	numerous	numerous	ADJ
ejpam-7071	34	19	applications	application	NOUN
ejpam-7071	34	20	in	in	ADP
ejpam-7071	34	21	applied	applied	ADJ
ejpam-7071	34	22	mathematics	mathematic	NOUN
ejpam-7071	34	23	,	,	PUNCT
ejpam-7071	34	24	statistics	statistic	NOUN
ejpam-7071	34	25	,	,	PUNCT
ejpam-7071	34	26	engineering	engineering	NOUN
ejpam-7071	34	27	,	,	PUNCT
ejpam-7071	34	28	and	and	CCONJ
ejpam-7071	34	29	physics	physics	NOUN
ejpam-7071	35	1	[	[	X
ejpam-7071	35	2	4–8	4–8	NOUN
ejpam-7071	35	3	]	]	X
ejpam-7071	35	4	.	.	PUNCT
ejpam-7071	36	1	because	because	SCONJ
ejpam-7071	36	2	these	these	DET
ejpam-7071	36	3	functions	function	NOUN
ejpam-7071	36	4	are	be	AUX
ejpam-7071	36	5	widely	widely	ADV
ejpam-7071	36	6	used	use	VERB
ejpam-7071	36	7	,	,	PUNCT
ejpam-7071	36	8	many	many	ADJ
ejpam-7071	36	9	academics	academic	NOUN
ejpam-7071	36	10	are	be	AUX
ejpam-7071	36	11	interested	interested	ADJ
ejpam-7071	36	12	in	in	ADP
ejpam-7071	36	13	obtaining	obtain	VERB
ejpam-7071	36	14	the	the	DET
ejpam-7071	36	15	geometric	geometric	ADJ
ejpam-7071	36	16	features	feature	NOUN
ejpam-7071	36	17	of	of	ADP
ejpam-7071	36	18	special	special	ADJ
ejpam-7071	36	19	functions	function	NOUN
ejpam-7071	36	20	;	;	PUNCT
ejpam-7071	36	21	see	see	VERB
ejpam-7071	36	22	[	[	X
ejpam-7071	36	23	9–15	9–15	PROPN
ejpam-7071	36	24	]	]	X
ejpam-7071	36	25	.	.	PUNCT
ejpam-7071	37	1	abramowitz	abramowitz	PROPN
ejpam-7071	37	2	and	and	CCONJ
ejpam-7071	37	3	stegun	stegun	PRON
ejpam-7071	37	4	[	[	X
ejpam-7071	37	5	16	16	NUM
ejpam-7071	37	6	]	]	PUNCT
ejpam-7071	37	7	defined	define	VERB
ejpam-7071	37	8	the	the	DET
ejpam-7071	37	9	following	follow	VERB
ejpam-7071	37	10	error	error	NOUN
ejpam-7071	37	11	function	function	NOUN
ejpam-7071	37	12	erg	erg	PROPN
ejpam-7071	37	13	(	(	PUNCT
ejpam-7071	37	14	z	z	NOUN
ejpam-7071	37	15	)	)	PUNCT
ejpam-7071	37	16	=	=	SYM
ejpam-7071	38	1	2√	2√	PROPN
ejpam-7071	38	2	π	π	X
ejpam-7071	38	3	∫	∫	PROPN
ejpam-7071	38	4	z	z	NOUN
ejpam-7071	38	5	0	0	NUM
ejpam-7071	38	6	e−t2dt	e−t2dt	NOUN
ejpam-7071	38	7	=	=	SYM
ejpam-7071	38	8	2√	2√	PROPN
ejpam-7071	38	9	π	π	PROPN
ejpam-7071	38	10	∞∑	∞∑	NOUN
ejpam-7071	38	11	ρ=0	ρ=0	NUM
ejpam-7071	38	12	(	(	PUNCT
ejpam-7071	38	13	−1)ρ	−1)ρ	NOUN
ejpam-7071	38	14	z2ρ+1	z2ρ+1	X
ejpam-7071	38	15	(	(	PUNCT
ejpam-7071	38	16	2ρ+	2ρ+	NOUN
ejpam-7071	38	17	1	1	NUM
ejpam-7071	38	18	)	)	PUNCT
ejpam-7071	38	19	ρ	ρ	PROPN
ejpam-7071	38	20	!	!	PROPN
ejpam-7071	38	21	,	,	PUNCT
ejpam-7071	38	22	(	(	PUNCT
ejpam-7071	38	23	z	z	NOUN
ejpam-7071	38	24	∈	∈	PROPN
ejpam-7071	38	25	c	c	NOUN
ejpam-7071	38	26	)	)	PUNCT
ejpam-7071	38	27	,	,	PUNCT
ejpam-7071	38	28	(	(	PUNCT
ejpam-7071	38	29	3	3	X
ejpam-7071	38	30	)	)	PUNCT
ejpam-7071	38	31	whereas	whereas	SCONJ
ejpam-7071	38	32	the	the	DET
ejpam-7071	38	33	imaginary	imaginary	ADJ
ejpam-7071	38	34	error	error	NOUN
ejpam-7071	38	35	function	function	NOUN
ejpam-7071	38	36	ergi	ergi	NOUN
ejpam-7071	38	37	(	(	PUNCT
ejpam-7071	38	38	z	z	NOUN
ejpam-7071	38	39	)	)	PUNCT
ejpam-7071	38	40	=	=	SYM
ejpam-7071	39	1	2√	2√	PROPN
ejpam-7071	39	2	π	π	X
ejpam-7071	39	3	∫	∫	PROPN
ejpam-7071	39	4	z	z	NOUN
ejpam-7071	39	5	0	0	NUM
ejpam-7071	39	6	et	et	NOUN
ejpam-7071	39	7	2	2	NUM
ejpam-7071	39	8	dt	dt	NOUN
ejpam-7071	39	9	=	=	SYM
ejpam-7071	39	10	2√	2√	PROPN
ejpam-7071	39	11	π	π	PROPN
ejpam-7071	39	12	∞∑	∞∑	NUM
ejpam-7071	39	13	ρ=0	ρ=0	PROPN
ejpam-7071	39	14	z2ρ+1	z2ρ+1	NOUN
ejpam-7071	39	15	(	(	PUNCT
ejpam-7071	39	16	2ρ+	2ρ+	NOUN
ejpam-7071	39	17	1	1	NUM
ejpam-7071	39	18	)	)	PUNCT
ejpam-7071	39	19	ρ	ρ	PROPN
ejpam-7071	39	20	!	!	PROPN
ejpam-7071	39	21	,	,	PUNCT
ejpam-7071	39	22	(	(	PUNCT
ejpam-7071	39	23	z	z	NOUN
ejpam-7071	39	24	∈	∈	PROPN
ejpam-7071	39	25	c	c	NOUN
ejpam-7071	39	26	)	)	PUNCT
ejpam-7071	39	27	.	.	PUNCT
ejpam-7071	40	1	(	(	PUNCT
ejpam-7071	40	2	4	4	X
ejpam-7071	40	3	)	)	PUNCT
ejpam-7071	40	4	the	the	DET
ejpam-7071	40	5	physics	physics	NOUN
ejpam-7071	40	6	of	of	ADP
ejpam-7071	40	7	partial	partial	ADJ
ejpam-7071	40	8	differential	differential	NOUN
ejpam-7071	40	9	equations	equation	NOUN
ejpam-7071	40	10	,	,	PUNCT
ejpam-7071	40	11	probability	probability	NOUN
ejpam-7071	40	12	theory	theory	NOUN
ejpam-7071	40	13	,	,	PUNCT
ejpam-7071	40	14	statistics	statistic	NOUN
ejpam-7071	40	15	,	,	PUNCT
ejpam-7071	40	16	and	and	CCONJ
ejpam-7071	40	17	applied	apply	VERB
ejpam-7071	40	18	mathematics	mathematic	NOUN
ejpam-7071	40	19	make	make	VERB
ejpam-7071	40	20	extensive	extensive	ADJ
ejpam-7071	40	21	use	use	NOUN
ejpam-7071	40	22	of	of	ADP
ejpam-7071	40	23	the	the	DET
ejpam-7071	40	24	error	error	NOUN
ejpam-7071	40	25	function	function	NOUN
ejpam-7071	40	26	.	.	PUNCT
ejpam-7071	41	1	the	the	DET
ejpam-7071	41	2	error	error	NOUN
ejpam-7071	41	3	function	function	NOUN
ejpam-7071	41	4	is	be	AUX
ejpam-7071	41	5	crucial	crucial	ADJ
ejpam-7071	41	6	to	to	ADP
ejpam-7071	41	7	estimating	estimate	VERB
ejpam-7071	41	8	the	the	DET
ejpam-7071	41	9	likelihood	likelihood	NOUN
ejpam-7071	41	10	of	of	ADP
ejpam-7071	41	11	seeing	see	VERB
ejpam-7071	41	12	a	a	DET
ejpam-7071	41	13	particle	particle	NOUN
ejpam-7071	41	14	in	in	ADP
ejpam-7071	41	15	a	a	DET
ejpam-7071	41	16	given	give	VERB
ejpam-7071	41	17	area	area	NOUN
ejpam-7071	41	18	in	in	ADP
ejpam-7071	41	19	quantum	quantum	ADJ
ejpam-7071	41	20	mechanics	mechanic	NOUN
ejpam-7071	41	21	.	.	PUNCT
ejpam-7071	42	1	alzer	alzer	NOUN
ejpam-7071	42	2	[	[	X
ejpam-7071	42	3	17	17	NUM
ejpam-7071	42	4	]	]	PUNCT
ejpam-7071	42	5	and	and	CCONJ
ejpam-7071	42	6	coman	coman	PROPN
ejpam-7071	43	1	[	[	X
ejpam-7071	43	2	18	18	NUM
ejpam-7071	43	3	]	]	PUNCT
ejpam-7071	43	4	demonstrated	demonstrate	VERB
ejpam-7071	43	5	several	several	ADJ
ejpam-7071	43	6	characteristics	characteristic	NOUN
ejpam-7071	43	7	and	and	CCONJ
ejpam-7071	43	8	inequalities	inequality	NOUN
ejpam-7071	43	9	of	of	ADP
ejpam-7071	43	10	the	the	DET
ejpam-7071	43	11	error	error	NOUN
ejpam-7071	43	12	function	function	NOUN
ejpam-7071	43	13	,	,	PUNCT
ejpam-7071	43	14	whereas	whereas	SCONJ
ejpam-7071	43	15	elbert	elbert	NOUN
ejpam-7071	43	16	et	et	PROPN
ejpam-7071	43	17	.	.	PUNCT
ejpam-7071	44	1	al	al	PROPN
ejpam-7071	45	1	[	[	X
ejpam-7071	45	2	19	19	NUM
ejpam-7071	45	3	]	]	PUNCT
ejpam-7071	45	4	studied	study	VERB
ejpam-7071	45	5	the	the	DET
ejpam-7071	45	6	properties	property	NOUN
ejpam-7071	45	7	of	of	ADP
ejpam-7071	45	8	complementary	complementary	ADJ
ejpam-7071	45	9	error	error	NOUN
ejpam-7071	45	10	function	function	NOUN
ejpam-7071	45	11	.	.	PUNCT
ejpam-7071	46	1	a.	a.	NOUN
ejpam-7071	46	2	alameer	alameer	PROPN
ejpam-7071	46	3	et	et	PROPN
ejpam-7071	46	4	al	al	PROPN
ejpam-7071	46	5	.	.	PUNCT
ejpam-7071	46	6	/	/	SYM
ejpam-7071	46	7	eur	eur	PROPN
ejpam-7071	46	8	.	.	PUNCT
ejpam-7071	47	1	j.	j.	PROPN
ejpam-7071	47	2	pure	pure	PROPN
ejpam-7071	47	3	appl	appl	PROPN
ejpam-7071	47	4	.	.	PROPN
ejpam-7071	47	5	math	math	PROPN
ejpam-7071	47	6	,	,	PUNCT
ejpam-7071	47	7	18	18	NUM
ejpam-7071	47	8	(	(	PUNCT
ejpam-7071	47	9	4	4	NUM
ejpam-7071	47	10	)	)	PUNCT
ejpam-7071	47	11	(	(	PUNCT
ejpam-7071	47	12	2025	2025	NUM
ejpam-7071	47	13	)	)	PUNCT
ejpam-7071	47	14	,	,	PUNCT
ejpam-7071	47	15	7071	7071	NUM
ejpam-7071	47	16	3	3	NUM
ejpam-7071	47	17	of	of	ADP
ejpam-7071	47	18	11	11	NUM
ejpam-7071	47	19	figure	figure	NOUN
ejpam-7071	47	20	1	1	NUM
ejpam-7071	47	21	:	:	PUNCT
ejpam-7071	47	22	real	real	ADJ
ejpam-7071	47	23	(	(	PUNCT
ejpam-7071	47	24	left	left	ADJ
ejpam-7071	47	25	)	)	PUNCT
ejpam-7071	47	26	and	and	CCONJ
ejpam-7071	47	27	imaginary	imaginary	ADJ
ejpam-7071	47	28	(	(	PUNCT
ejpam-7071	47	29	right	right	ADJ
ejpam-7071	47	30	)	)	PUNCT
ejpam-7071	47	31	parts	part	NOUN
ejpam-7071	47	32	of	of	ADP
ejpam-7071	47	33	the	the	DET
ejpam-7071	47	34	error	error	NOUN
ejpam-7071	47	35	function	function	NOUN
ejpam-7071	47	36	erq	erq	NOUN
ejpam-7071	47	37	(	(	PUNCT
ejpam-7071	47	38	z	z	NOUN
ejpam-7071	47	39	)	)	PUNCT
ejpam-7071	47	40	over	over	ADP
ejpam-7071	47	41	the	the	DET
ejpam-7071	47	42	complex	complex	ADJ
ejpam-7071	47	43	plane	plane	NOUN
ejpam-7071	47	44	.	.	PUNCT
ejpam-7071	48	1	the	the	DET
ejpam-7071	48	2	behavior	behavior	NOUN
ejpam-7071	48	3	of	of	ADP
ejpam-7071	48	4	the	the	DET
ejpam-7071	48	5	real	real	ADJ
ejpam-7071	48	6	and	and	CCONJ
ejpam-7071	48	7	imaginary	imaginary	ADJ
ejpam-7071	48	8	components	component	NOUN
ejpam-7071	48	9	of	of	ADP
ejpam-7071	48	10	erg	erg	PROPN
ejpam-7071	48	11	(	(	PUNCT
ejpam-7071	48	12	z	z	NOUN
ejpam-7071	48	13	)	)	PUNCT
ejpam-7071	48	14	in	in	ADP
ejpam-7071	48	15	the	the	DET
ejpam-7071	48	16	complex	complex	ADJ
ejpam-7071	48	17	plane	plane	NOUN
ejpam-7071	48	18	is	be	AUX
ejpam-7071	48	19	depicted	depict	VERB
ejpam-7071	48	20	in	in	ADP
ejpam-7071	48	21	figure	figure	NOUN
ejpam-7071	48	22	1	1	NUM
ejpam-7071	48	23	below	below	ADV
ejpam-7071	48	24	.	.	PUNCT
ejpam-7071	49	1	its	its	PRON
ejpam-7071	49	2	relevance	relevance	NOUN
ejpam-7071	49	3	in	in	ADP
ejpam-7071	49	4	the	the	DET
ejpam-7071	49	5	geometric	geometric	ADJ
ejpam-7071	49	6	characterization	characterization	NOUN
ejpam-7071	49	7	of	of	ADP
ejpam-7071	49	8	subclasses	subclass	NOUN
ejpam-7071	49	9	of	of	ADP
ejpam-7071	49	10	analytic	analytic	ADJ
ejpam-7071	49	11	functions	function	NOUN
ejpam-7071	49	12	is	be	AUX
ejpam-7071	49	13	motivated	motivate	VERB
ejpam-7071	49	14	by	by	ADP
ejpam-7071	49	15	the	the	DET
ejpam-7071	49	16	rich	rich	ADJ
ejpam-7071	49	17	geometric	geometric	ADJ
ejpam-7071	49	18	structure	structure	NOUN
ejpam-7071	49	19	it	it	PRON
ejpam-7071	49	20	displays	display	VERB
ejpam-7071	49	21	,	,	PUNCT
ejpam-7071	49	22	including	include	VERB
ejpam-7071	49	23	symmetry	symmetry	NOUN
ejpam-7071	49	24	and	and	CCONJ
ejpam-7071	49	25	curvature	curvature	NOUN
ejpam-7071	49	26	.	.	PUNCT
ejpam-7071	50	1	a	a	DET
ejpam-7071	50	2	generalization	generalization	NOUN
ejpam-7071	50	3	of	of	ADP
ejpam-7071	50	4	the	the	DET
ejpam-7071	50	5	error	error	NOUN
ejpam-7071	50	6	function	function	NOUN
ejpam-7071	50	7	(	(	PUNCT
ejpam-7071	50	8	3	3	X
ejpam-7071	50	9	)	)	PUNCT
ejpam-7071	50	10	is	be	AUX
ejpam-7071	50	11	given	give	VERB
ejpam-7071	50	12	by	by	ADP
ejpam-7071	50	13	ergn	ergn	NOUN
ejpam-7071	50	14	(	(	PUNCT
ejpam-7071	50	15	z	z	NOUN
ejpam-7071	50	16	)	)	PUNCT
ejpam-7071	50	17	=	=	SYM
ejpam-7071	51	1	n!√	n!√	PROPN
ejpam-7071	51	2	π	π	X
ejpam-7071	51	3	∫	∫	PROPN
ejpam-7071	51	4	z	z	PROPN
ejpam-7071	51	5	0	0	NUM
ejpam-7071	51	6	e−tndt	e−tndt	NOUN
ejpam-7071	51	7	,	,	PUNCT
ejpam-7071	51	8	n	n	PROPN
ejpam-7071	51	9	∈	∈	PROPN
ejpam-7071	51	10	n0=	n0=	PROPN
ejpam-7071	51	11	n∪{0	n∪{0	NOUN
ejpam-7071	51	12	}	}	PUNCT
ejpam-7071	51	13	=	=	PUNCT
ejpam-7071	51	14	n!√	n!√	PROPN
ejpam-7071	51	15	π	π	PROPN
ejpam-7071	51	16	∞∑	∞∑	NUM
ejpam-7071	51	17	ρ=0	ρ=0	PUNCT
ejpam-7071	51	18	(	(	PUNCT
ejpam-7071	51	19	−1)ρ	−1)ρ	NOUN
ejpam-7071	51	20	znρ+1	znρ+1	NOUN
ejpam-7071	51	21	(	(	PUNCT
ejpam-7071	51	22	nρ+	nρ+	PROPN
ejpam-7071	51	23	1	1	NUM
ejpam-7071	51	24	)	)	PUNCT
ejpam-7071	51	25	ρ	ρ	PROPN
ejpam-7071	51	26	!	!	PROPN
ejpam-7071	51	27	,	,	PUNCT
ejpam-7071	51	28	(	(	PUNCT
ejpam-7071	51	29	z	z	NOUN
ejpam-7071	51	30	∈	∈	PROPN
ejpam-7071	51	31	c	c	NOUN
ejpam-7071	51	32	)	)	PUNCT
ejpam-7071	51	33	.	.	PUNCT
ejpam-7071	52	1	(	(	PUNCT
ejpam-7071	52	2	5	5	X
ejpam-7071	52	3	)	)	PUNCT
ejpam-7071	52	4	in	in	ADP
ejpam-7071	52	5	addition	addition	NOUN
ejpam-7071	52	6	,	,	PUNCT
ejpam-7071	52	7	a	a	DET
ejpam-7071	52	8	generalization	generalization	NOUN
ejpam-7071	52	9	of	of	ADP
ejpam-7071	52	10	the	the	DET
ejpam-7071	52	11	imaginary	imaginary	ADJ
ejpam-7071	52	12	error	error	NOUN
ejpam-7071	52	13	function	function	NOUN
ejpam-7071	52	14	(	(	PUNCT
ejpam-7071	52	15	4	4	NUM
ejpam-7071	52	16	)	)	PUNCT
ejpam-7071	52	17	is	be	AUX
ejpam-7071	52	18	given	give	VERB
ejpam-7071	52	19	by	by	ADP
ejpam-7071	52	20	ergin	ergin	NOUN
ejpam-7071	52	21	(	(	PUNCT
ejpam-7071	52	22	z	z	NOUN
ejpam-7071	52	23	)	)	PUNCT
ejpam-7071	52	24	=	=	SYM
ejpam-7071	53	1	n!√	n!√	PROPN
ejpam-7071	53	2	π	π	X
ejpam-7071	53	3	∫	∫	PROPN
ejpam-7071	53	4	z	z	PROPN
ejpam-7071	53	5	0	0	NUM
ejpam-7071	53	6	et	et	PROPN
ejpam-7071	53	7	n	n	PRON
ejpam-7071	53	8	dt	dt	PROPN
ejpam-7071	53	9	,	,	PUNCT
ejpam-7071	53	10	n	n	PROPN
ejpam-7071	53	11	∈	∈	PROPN
ejpam-7071	53	12	n0	n0	NOUN
ejpam-7071	53	13	=	=	SYM
ejpam-7071	53	14	n!√	n!√	PROPN
ejpam-7071	53	15	π	π	PROPN
ejpam-7071	53	16	∞∑	∞∑	NUM
ejpam-7071	53	17	ρ=0	ρ=0	PROPN
ejpam-7071	53	18	znρ+1	znρ+1	NOUN
ejpam-7071	53	19	(	(	PUNCT
ejpam-7071	53	20	nρ+	nρ+	PROPN
ejpam-7071	53	21	1	1	NUM
ejpam-7071	53	22	)	)	PUNCT
ejpam-7071	53	23	ρ	ρ	PROPN
ejpam-7071	53	24	!	!	PROPN
ejpam-7071	53	25	,	,	PUNCT
ejpam-7071	53	26	(	(	PUNCT
ejpam-7071	53	27	z	z	NOUN
ejpam-7071	53	28	∈	∈	PROPN
ejpam-7071	53	29	c	c	NOUN
ejpam-7071	53	30	)	)	PUNCT
ejpam-7071	53	31	.	.	PUNCT
ejpam-7071	54	1	(	(	PUNCT
ejpam-7071	54	2	6	6	NUM
ejpam-7071	54	3	)	)	PUNCT
ejpam-7071	54	4	from	from	ADP
ejpam-7071	54	5	(	(	PUNCT
ejpam-7071	54	6	5	5	NUM
ejpam-7071	54	7	)	)	PUNCT
ejpam-7071	54	8	and	and	CCONJ
ejpam-7071	54	9	(	(	PUNCT
ejpam-7071	54	10	6	6	NUM
ejpam-7071	54	11	)	)	PUNCT
ejpam-7071	54	12	,	,	PUNCT
ejpam-7071	54	13	we	we	PRON
ejpam-7071	54	14	get	get	VERB
ejpam-7071	54	15	erg0	erg0	NOUN
ejpam-7071	54	16	(	(	PUNCT
ejpam-7071	54	17	z	z	X
ejpam-7071	54	18	)	)	PUNCT
ejpam-7071	54	19	=	=	PUNCT
ejpam-7071	54	20	z	z	X
ejpam-7071	54	21	e	e	NOUN
ejpam-7071	54	22	√	√	PROPN
ejpam-7071	54	23	π	π	PROPN
ejpam-7071	54	24	,	,	PUNCT
ejpam-7071	54	25	erg1	erg1	PROPN
ejpam-7071	54	26	(	(	PUNCT
ejpam-7071	54	27	z	z	NOUN
ejpam-7071	54	28	)	)	PUNCT
ejpam-7071	54	29	=	=	SYM
ejpam-7071	54	30	1−	1−	NUM
ejpam-7071	54	31	ez√	ez√	PUNCT
ejpam-7071	55	1	π	π	PROPN
ejpam-7071	55	2	=	=	SYM
ejpam-7071	55	3	−ergi1	−ergi1	X
ejpam-7071	55	4	(	(	PUNCT
ejpam-7071	55	5	z	z	NOUN
ejpam-7071	55	6	)	)	PUNCT
ejpam-7071	55	7	,	,	PUNCT
ejpam-7071	55	8	erg2	erg2	NOUN
ejpam-7071	55	9	(	(	PUNCT
ejpam-7071	55	10	z	z	NOUN
ejpam-7071	55	11	)	)	PUNCT
ejpam-7071	55	12	=	=	SYM
ejpam-7071	55	13	erg	erg	X
ejpam-7071	55	14	(	(	PUNCT
ejpam-7071	55	15	z	z	NOUN
ejpam-7071	55	16	)	)	PUNCT
ejpam-7071	55	17	and	and	CCONJ
ejpam-7071	55	18	ergi2	ergi2	NOUN
ejpam-7071	55	19	(	(	PUNCT
ejpam-7071	55	20	z	z	X
ejpam-7071	55	21	)	)	PUNCT
ejpam-7071	55	22	=	=	SYM
ejpam-7071	55	23	ergi	ergi	PROPN
ejpam-7071	55	24	(	(	PUNCT
ejpam-7071	55	25	z	z	NOUN
ejpam-7071	55	26	)	)	PUNCT
ejpam-7071	55	27	.	.	PUNCT
ejpam-7071	56	1	it	it	PRON
ejpam-7071	56	2	is	be	AUX
ejpam-7071	56	3	clear	clear	ADJ
ejpam-7071	56	4	that	that	SCONJ
ejpam-7071	56	5	the	the	DET
ejpam-7071	56	6	functions	function	NOUN
ejpam-7071	56	7	ergn	ergn	NOUN
ejpam-7071	56	8	(	(	PUNCT
ejpam-7071	56	9	z	z	NOUN
ejpam-7071	56	10	)	)	PUNCT
ejpam-7071	56	11	and	and	CCONJ
ejpam-7071	56	12	ergin	ergin	NOUN
ejpam-7071	56	13	(	(	PUNCT
ejpam-7071	56	14	z	z	NOUN
ejpam-7071	56	15	)	)	PUNCT
ejpam-7071	56	16	are	be	AUX
ejpam-7071	56	17	not	not	PART
ejpam-7071	56	18	members	member	NOUN
ejpam-7071	56	19	of	of	ADP
ejpam-7071	56	20	the	the	DET
ejpam-7071	56	21	class	class	NOUN
ejpam-7071	56	22	an	an	PRON
ejpam-7071	56	23	.	.	PUNCT
ejpam-7071	57	1	thus	thus	ADV
ejpam-7071	57	2	,	,	PUNCT
ejpam-7071	57	3	it	it	PRON
ejpam-7071	57	4	is	be	AUX
ejpam-7071	57	5	natural	natural	ADJ
ejpam-7071	57	6	to	to	PART
ejpam-7071	57	7	consider	consider	VERB
ejpam-7071	57	8	the	the	DET
ejpam-7071	57	9	following	follow	VERB
ejpam-7071	57	10	functions	function	NOUN
ejpam-7071	57	11	given	give	VERB
ejpam-7071	57	12	by	by	ADP
ejpam-7071	57	13	al	al	PROPN
ejpam-7071	57	14	-	-	PUNCT
ejpam-7071	57	15	hawary	hawary	PROPN
ejpam-7071	57	16	et	et	PROPN
ejpam-7071	57	17	.	.	PUNCT
ejpam-7071	58	1	al	al	PROPN
ejpam-7071	59	1	[	[	X
ejpam-7071	59	2	20	20	NUM
ejpam-7071	59	3	]	]	X
ejpam-7071	59	4	en	en	X
ejpam-7071	59	5	(	(	PUNCT
ejpam-7071	59	6	z	z	NOUN
ejpam-7071	59	7	)	)	PUNCT
ejpam-7071	59	8	=	=	SYM
ejpam-7071	59	9	√	√	PROPN
ejpam-7071	59	10	π	π	PROPN
ejpam-7071	59	11	n	n	X
ejpam-7071	59	12	!	!	PUNCT
ejpam-7071	59	13	z	z	NOUN
ejpam-7071	59	14	(	(	PUNCT
ejpam-7071	59	15	1−	1−	NUM
ejpam-7071	59	16	1	1	NUM
ejpam-7071	59	17	n	n	CCONJ
ejpam-7071	59	18	)	)	PUNCT
ejpam-7071	59	19	n	n	PRON
ejpam-7071	59	20	ergn	ergn	NOUN
ejpam-7071	59	21	(	(	PUNCT
ejpam-7071	59	22	z1	z1	PROPN
ejpam-7071	59	23	/	/	SYM
ejpam-7071	59	24	n	n	NOUN
ejpam-7071	59	25	)	)	PUNCT
ejpam-7071	59	26	=	=	PUNCT
ejpam-7071	60	1	z	z	NOUN
ejpam-7071	61	1	+	+	PUNCT
ejpam-7071	61	2	∞∑	∞∑	NUM
ejpam-7071	61	3	ρ=2	ρ=2	SYM
ejpam-7071	61	4	(	(	PUNCT
ejpam-7071	61	5	−1)ρ−1	−1)ρ−1	X
ejpam-7071	61	6	(	(	PUNCT
ejpam-7071	61	7	(	(	PUNCT
ejpam-7071	61	8	ρ−	ρ−	NOUN
ejpam-7071	61	9	1)n+	1)n+	NUM
ejpam-7071	61	10	1	1	NUM
ejpam-7071	61	11	)	)	PUNCT
ejpam-7071	61	12	(	(	PUNCT
ejpam-7071	61	13	ρ−	ρ−	NOUN
ejpam-7071	61	14	1	1	NUM
ejpam-7071	61	15	)	)	PUNCT
ejpam-7071	61	16	!	!	PUNCT
ejpam-7071	62	1	zρ	zρ	PROPN
ejpam-7071	62	2	,	,	PUNCT
ejpam-7071	62	3	(	(	PUNCT
ejpam-7071	62	4	n	n	X
ejpam-7071	62	5	∈	∈	PROPN
ejpam-7071	62	6	n	n	CCONJ
ejpam-7071	62	7	)	)	PUNCT
ejpam-7071	62	8	,	,	PUNCT
ejpam-7071	62	9	(	(	PUNCT
ejpam-7071	62	10	7	7	X
ejpam-7071	62	11	)	)	PUNCT
ejpam-7071	62	12	a.	a.	NOUN
ejpam-7071	62	13	alameer	alameer	NOUN
ejpam-7071	62	14	et	et	PROPN
ejpam-7071	63	1	al	al	PROPN
ejpam-7071	63	2	.	.	PUNCT
ejpam-7071	63	3	/	/	SYM
ejpam-7071	63	4	eur	eur	PROPN
ejpam-7071	63	5	.	.	PUNCT
ejpam-7071	64	1	j.	j.	PROPN
ejpam-7071	64	2	pure	pure	PROPN
ejpam-7071	64	3	appl	appl	PROPN
ejpam-7071	64	4	.	.	PROPN
ejpam-7071	64	5	math	math	PROPN
ejpam-7071	64	6	,	,	PUNCT
ejpam-7071	64	7	18	18	NUM
ejpam-7071	64	8	(	(	PUNCT
ejpam-7071	64	9	4	4	NUM
ejpam-7071	64	10	)	)	PUNCT
ejpam-7071	64	11	(	(	PUNCT
ejpam-7071	64	12	2025	2025	NUM
ejpam-7071	64	13	)	)	PUNCT
ejpam-7071	64	14	,	,	PUNCT
ejpam-7071	64	15	7071	7071	NUM
ejpam-7071	64	16	4	4	NUM
ejpam-7071	64	17	of	of	ADP
ejpam-7071	64	18	11	11	NUM
ejpam-7071	64	19	and	and	CCONJ
ejpam-7071	64	20	ein	ein	PROPN
ejpam-7071	64	21	(	(	PUNCT
ejpam-7071	64	22	z	z	NOUN
ejpam-7071	64	23	)	)	PUNCT
ejpam-7071	64	24	=	=	SYM
ejpam-7071	65	1	√	√	PROPN
ejpam-7071	65	2	π	π	PROPN
ejpam-7071	65	3	n	n	X
ejpam-7071	65	4	!	!	PUNCT
ejpam-7071	65	5	z(1−	z(1−	PROPN
ejpam-7071	65	6	1	1	NUM
ejpam-7071	65	7	n	n	CCONJ
ejpam-7071	65	8	)	)	PUNCT
ejpam-7071	65	9	erf	erf	NOUN
ejpam-7071	65	10	in	in	ADP
ejpam-7071	65	11	(	(	PUNCT
ejpam-7071	65	12	z1	z1	PROPN
ejpam-7071	65	13	/	/	SYM
ejpam-7071	65	14	n	n	NOUN
ejpam-7071	65	15	)	)	PUNCT
ejpam-7071	65	16	=	=	PUNCT
ejpam-7071	66	1	z	z	NOUN
ejpam-7071	67	1	+	+	NOUN
ejpam-7071	67	2	∞∑	∞∑	NUM
ejpam-7071	67	3	ρ=2	ρ=2	SYM
ejpam-7071	67	4	1	1	NUM
ejpam-7071	67	5	(	(	PUNCT
ejpam-7071	67	6	(	(	PUNCT
ejpam-7071	67	7	ρ−	ρ−	NOUN
ejpam-7071	67	8	1)n+	1)n+	NUM
ejpam-7071	67	9	1	1	NUM
ejpam-7071	67	10	)	)	PUNCT
ejpam-7071	67	11	(	(	PUNCT
ejpam-7071	67	12	ρ−	ρ−	NOUN
ejpam-7071	67	13	1	1	NUM
ejpam-7071	67	14	)	)	PUNCT
ejpam-7071	67	15	!	!	PUNCT
ejpam-7071	68	1	zρ	zρ	PROPN
ejpam-7071	68	2	,	,	PUNCT
ejpam-7071	68	3	(	(	PUNCT
ejpam-7071	68	4	n	n	X
ejpam-7071	68	5	∈	∈	PROPN
ejpam-7071	68	6	n	n	CCONJ
ejpam-7071	68	7	)	)	PUNCT
ejpam-7071	68	8	.	.	PUNCT
ejpam-7071	69	1	(	(	PUNCT
ejpam-7071	69	2	8)	8)	NUM
ejpam-7071	69	3	specifically	specifically	ADV
ejpam-7071	69	4	,	,	PUNCT
ejpam-7071	69	5	we	we	PRON
ejpam-7071	69	6	get	get	VERB
ejpam-7071	69	7	the	the	DET
ejpam-7071	69	8	normalizations	normalization	NOUN
ejpam-7071	69	9	e2	e2	VERB
ejpam-7071	69	10	g	g	PROPN
ejpam-7071	69	11	=	=	PUNCT
ejpam-7071	69	12	erg	erg	PROPN
ejpam-7071	69	13	and	and	CCONJ
ejpam-7071	69	14	ei2	ei2	PROPN
ejpam-7071	69	15	g	g	PROPN
ejpam-7071	69	16	=	=	SYM
ejpam-7071	69	17	ergi	ergi	PROPN
ejpam-7071	69	18	given	give	VERB
ejpam-7071	69	19	by	by	ADP
ejpam-7071	69	20	ramachandran	ramachandran	PROPN
ejpam-7071	69	21	et	et	PROPN
ejpam-7071	69	22	al	al	PROPN
ejpam-7071	69	23	.	.	PUNCT
ejpam-7071	70	1	[	[	X
ejpam-7071	70	2	21	21	NUM
ejpam-7071	70	3	]	]	PUNCT
ejpam-7071	70	4	and	and	CCONJ
ejpam-7071	70	5	is	be	AUX
ejpam-7071	70	6	the	the	DET
ejpam-7071	70	7	normalization	normalization	NOUN
ejpam-7071	70	8	given	give	VERB
ejpam-7071	70	9	by	by	ADP
ejpam-7071	70	10	mohammed	mohammed	PROPN
ejpam-7071	70	11	et	et	PROPN
ejpam-7071	70	12	al	al	PROPN
ejpam-7071	70	13	.	.	PUNCT
ejpam-7071	71	1	[	[	X
ejpam-7071	71	2	22	22	NUM
ejpam-7071	71	3	]	]	PUNCT
ejpam-7071	71	4	.	.	PUNCT
ejpam-7071	72	1	from	from	ADP
ejpam-7071	72	2	(	(	PUNCT
ejpam-7071	72	3	7	7	NUM
ejpam-7071	72	4	)	)	PUNCT
ejpam-7071	72	5	and	and	CCONJ
ejpam-7071	72	6	(	(	PUNCT
ejpam-7071	72	7	8)	8)	NUM
ejpam-7071	72	8	,	,	PUNCT
ejpam-7071	72	9	we	we	PRON
ejpam-7071	72	10	have	have	VERB
ejpam-7071	72	11	e1	e1	NOUN
ejpam-7071	72	12	g	g	PROPN
ejpam-7071	72	13	(	(	PUNCT
ejpam-7071	72	14	z	z	NOUN
ejpam-7071	72	15	)	)	PUNCT
ejpam-7071	72	16	=	=	SYM
ejpam-7071	73	1	√	√	NUM
ejpam-7071	73	2	πerg1	πerg1	NOUN
ejpam-7071	73	3	(	(	PUNCT
ejpam-7071	73	4	z	z	NOUN
ejpam-7071	73	5	)	)	PUNCT
ejpam-7071	73	6	=	=	SYM
ejpam-7071	73	7	1−	1−	NUM
ejpam-7071	73	8	ez	ez	PROPN
ejpam-7071	73	9	,	,	PUNCT
ejpam-7071	73	10	ei1	ei1	PROPN
ejpam-7071	73	11	g	g	PROPN
ejpam-7071	73	12	(	(	PUNCT
ejpam-7071	73	13	z	z	NOUN
ejpam-7071	73	14	)	)	PUNCT
ejpam-7071	73	15	=	=	SYM
ejpam-7071	73	16	√	√	PROPN
ejpam-7071	73	17	πergi1	πergi1	NOUN
ejpam-7071	73	18	(	(	PUNCT
ejpam-7071	73	19	z	z	NOUN
ejpam-7071	73	20	)	)	PUNCT
ejpam-7071	73	21	=	=	SYM
ejpam-7071	73	22	ez	ez	PROPN
ejpam-7071	74	1	−	−	PROPN
ejpam-7071	74	2	1	1	NUM
ejpam-7071	74	3	and	and	CCONJ
ejpam-7071	74	4	e2	e2	PROPN
ejpam-7071	74	5	g	g	PROPN
ejpam-7071	74	6	(	(	PUNCT
ejpam-7071	74	7	z	z	NOUN
ejpam-7071	74	8	)	)	PUNCT
ejpam-7071	74	9	=	=	PUNCT
ejpam-7071	75	1	√	√	NUM
ejpam-7071	75	2	πz	πz	PRON
ejpam-7071	75	3	2	2	NUM
ejpam-7071	75	4	erg2	erg2	NOUN
ejpam-7071	75	5	(	(	PUNCT
ejpam-7071	75	6	√	√	PROPN
ejpam-7071	75	7	z	z	NOUN
ejpam-7071	75	8	)	)	PUNCT
ejpam-7071	75	9	and	and	CCONJ
ejpam-7071	75	10	ei1	ei1	NOUN
ejpam-7071	75	11	g	g	PROPN
ejpam-7071	75	12	(	(	PUNCT
ejpam-7071	75	13	z	z	NOUN
ejpam-7071	75	14	)	)	PUNCT
ejpam-7071	75	15	=	=	PUNCT
ejpam-7071	76	1	√	√	NUM
ejpam-7071	76	2	πz	πz	PRON
ejpam-7071	76	3	2	2	NUM
ejpam-7071	76	4	ergi2	ergi2	NOUN
ejpam-7071	76	5	(	(	PUNCT
ejpam-7071	76	6	√	√	PROPN
ejpam-7071	76	7	z	z	NOUN
ejpam-7071	76	8	)	)	PUNCT
ejpam-7071	76	9	.	.	PUNCT
ejpam-7071	77	1	let	let	VERB
ejpam-7071	77	2	the	the	DET
ejpam-7071	77	3	function	function	NOUN
ejpam-7071	77	4	ϖin	ϖin	PROPN
ejpam-7071	77	5	(	(	PUNCT
ejpam-7071	77	6	z	z	AUX
ejpam-7071	77	7	)	)	PUNCT
ejpam-7071	77	8	be	be	AUX
ejpam-7071	77	9	defined	define	VERB
ejpam-7071	77	10	as	as	ADP
ejpam-7071	77	11	ϖin	ϖin	PROPN
ejpam-7071	77	12	(	(	PUNCT
ejpam-7071	77	13	z	z	NOUN
ejpam-7071	77	14	)	)	PUNCT
ejpam-7071	78	1	=	=	SYM
ejpam-7071	78	2	2z	2z	NOUN
ejpam-7071	79	1	−	−	PROPN
ejpam-7071	79	2	ein	ein	NOUN
ejpam-7071	79	3	(	(	PUNCT
ejpam-7071	79	4	z	z	NOUN
ejpam-7071	79	5	)	)	PUNCT
ejpam-7071	79	6	=	=	PUNCT
ejpam-7071	79	7	z	z	NOUN
ejpam-7071	80	1	−	−	NOUN
ejpam-7071	80	2	∞∑	∞∑	NUM
ejpam-7071	80	3	ρ=2	ρ=2	SYM
ejpam-7071	80	4	1	1	NUM
ejpam-7071	80	5	(	(	PUNCT
ejpam-7071	80	6	(	(	PUNCT
ejpam-7071	80	7	ρ−	ρ−	NOUN
ejpam-7071	80	8	1)n+	1)n+	NUM
ejpam-7071	80	9	1	1	NUM
ejpam-7071	80	10	)	)	PUNCT
ejpam-7071	80	11	(	(	PUNCT
ejpam-7071	80	12	ρ−	ρ−	NOUN
ejpam-7071	80	13	1	1	NUM
ejpam-7071	80	14	)	)	PUNCT
ejpam-7071	80	15	!	!	PUNCT
ejpam-7071	81	1	zρ	zρ	VERB
ejpam-7071	81	2	;	;	PUNCT
ejpam-7071	81	3	z	z	PROPN
ejpam-7071	81	4	∈	∈	NOUN
ejpam-7071	81	5	∆	∆	X
ejpam-7071	81	6	,	,	PUNCT
ejpam-7071	81	7	(	(	PUNCT
ejpam-7071	81	8	9	9	NUM
ejpam-7071	81	9	)	)	PUNCT
ejpam-7071	81	10	and	and	CCONJ
ejpam-7071	81	11	consider	consider	VERB
ejpam-7071	81	12	the	the	DET
ejpam-7071	81	13	linear	linear	ADJ
ejpam-7071	81	14	operator	operator	NOUN
ejpam-7071	81	15	iin	iin	NOUN
ejpam-7071	81	16	:	:	PUNCT
ejpam-7071	81	17	an	an	PRON
ejpam-7071	81	18	→	→	SYM
ejpam-7071	81	19	an	an	DET
ejpam-7071	81	20	defined	define	VERB
ejpam-7071	81	21	by	by	ADP
ejpam-7071	81	22	the	the	DET
ejpam-7071	81	23	convolution	convolution	NOUN
ejpam-7071	81	24	or	or	CCONJ
ejpam-7071	81	25	hadamard	hadamard	ADJ
ejpam-7071	81	26	product	product	NOUN
ejpam-7071	81	27	iin(z	iin(z	NOUN
ejpam-7071	81	28	)	)	PUNCT
ejpam-7071	81	29	=	=	SYM
ejpam-7071	82	1	ein	ein	NOUN
ejpam-7071	82	2	(	(	PUNCT
ejpam-7071	82	3	z	z	NOUN
ejpam-7071	82	4	)	)	PUNCT
ejpam-7071	82	5	∗	∗	NOUN
ejpam-7071	82	6	g(z	g(z	ADJ
ejpam-7071	82	7	)	)	PUNCT
ejpam-7071	82	8	=	=	SYM
ejpam-7071	82	9	z	z	NOUN
ejpam-7071	83	1	+	+	NOUN
ejpam-7071	83	2	∞∑	∞∑	NUM
ejpam-7071	83	3	ρ=2	ρ=2	SYM
ejpam-7071	83	4	1	1	NUM
ejpam-7071	83	5	(	(	PUNCT
ejpam-7071	83	6	(	(	PUNCT
ejpam-7071	83	7	ρ−	ρ−	NOUN
ejpam-7071	83	8	1)n+	1)n+	NUM
ejpam-7071	83	9	1	1	NUM
ejpam-7071	83	10	)	)	PUNCT
ejpam-7071	83	11	(	(	PUNCT
ejpam-7071	83	12	ρ−	ρ−	NOUN
ejpam-7071	83	13	1	1	NUM
ejpam-7071	83	14	)	)	PUNCT
ejpam-7071	83	15	!	!	PUNCT
ejpam-7071	84	1	aρz	aρz	PROPN
ejpam-7071	85	1	ρ	ρ	X
ejpam-7071	85	2	.	.	PUNCT
ejpam-7071	86	1	(	(	PUNCT
ejpam-7071	86	2	10	10	NUM
ejpam-7071	86	3	)	)	PUNCT
ejpam-7071	86	4	recently	recently	ADV
ejpam-7071	86	5	,	,	PUNCT
ejpam-7071	86	6	several	several	ADJ
ejpam-7071	86	7	academics	academic	NOUN
ejpam-7071	86	8	determined	determine	VERB
ejpam-7071	86	9	the	the	DET
ejpam-7071	86	10	necessary	necessary	ADJ
ejpam-7071	86	11	and	and	CCONJ
ejpam-7071	86	12	sufficient	sufficient	ADJ
ejpam-7071	86	13	conditions	condition	NOUN
ejpam-7071	86	14	using	use	VERB
ejpam-7071	86	15	rabotnov	rabotnov	NOUN
ejpam-7071	86	16	functions	function	NOUN
ejpam-7071	86	17	[	[	X
ejpam-7071	86	18	23	23	NUM
ejpam-7071	86	19	]	]	PUNCT
ejpam-7071	86	20	,	,	PUNCT
ejpam-7071	86	21	generalized	generalized	ADJ
ejpam-7071	86	22	bessel	bessel	NOUN
ejpam-7071	86	23	functions	function	NOUN
ejpam-7071	86	24	[	[	X
ejpam-7071	86	25	24	24	NUM
ejpam-7071	86	26	,	,	PUNCT
ejpam-7071	86	27	25	25	NUM
ejpam-7071	86	28	]	]	PUNCT
ejpam-7071	86	29	,	,	PUNCT
ejpam-7071	86	30	struve	struve	PROPN
ejpam-7071	86	31	functions	function	NOUN
ejpam-7071	87	1	[	[	X
ejpam-7071	87	2	26	26	NUM
ejpam-7071	87	3	,	,	PUNCT
ejpam-7071	87	4	27	27	NUM
ejpam-7071	87	5	]	]	PUNCT
ejpam-7071	87	6	,	,	PUNCT
ejpam-7071	87	7	hypergeometric	hypergeometric	ADJ
ejpam-7071	87	8	functions	function	NOUN
ejpam-7071	87	9	[	[	X
ejpam-7071	87	10	28	28	NUM
ejpam-7071	87	11	]	]	PUNCT
ejpam-7071	87	12	,	,	PUNCT
ejpam-7071	87	13	pascal	pascal	ADJ
ejpam-7071	87	14	distribution	distribution	NOUN
ejpam-7071	87	15	series	series	NOUN
ejpam-7071	87	16	[	[	X
ejpam-7071	87	17	29	29	NUM
ejpam-7071	87	18	,	,	PUNCT
ejpam-7071	87	19	30	30	NUM
ejpam-7071	87	20	]	]	PUNCT
ejpam-7071	87	21	,	,	PUNCT
ejpam-7071	87	22	poisson	poisson	NOUN
ejpam-7071	87	23	distribution	distribution	NOUN
ejpam-7071	87	24	series	series	NOUN
ejpam-7071	87	25	[	[	X
ejpam-7071	87	26	31	31	NUM
ejpam-7071	87	27	]	]	PUNCT
ejpam-7071	87	28	,	,	PUNCT
ejpam-7071	87	29	normalized	normalize	VERB
ejpam-7071	87	30	wright	wright	PROPN
ejpam-7071	87	31	functions	function	NOUN
ejpam-7071	87	32	[	[	X
ejpam-7071	87	33	32	32	NUM
ejpam-7071	87	34	]	]	PUNCT
ejpam-7071	87	35	,	,	PUNCT
ejpam-7071	87	36	ad	ad	NOUN
ejpam-7071	87	37	touchard	touchard	NOUN
ejpam-7071	87	38	polynomials	polynomial	NOUN
ejpam-7071	87	39	[	[	X
ejpam-7071	87	40	33	33	NUM
ejpam-7071	87	41	]	]	PUNCT
ejpam-7071	87	42	.	.	PUNCT
ejpam-7071	88	1	the	the	DET
ejpam-7071	88	2	remainder	remainder	NOUN
ejpam-7071	88	3	of	of	ADP
ejpam-7071	88	4	the	the	DET
ejpam-7071	88	5	document	document	NOUN
ejpam-7071	88	6	is	be	AUX
ejpam-7071	88	7	structured	structure	VERB
ejpam-7071	88	8	as	as	SCONJ
ejpam-7071	88	9	follows	follow	VERB
ejpam-7071	88	10	.	.	PUNCT
ejpam-7071	89	1	in	in	ADP
ejpam-7071	89	2	section	section	NOUN
ejpam-7071	89	3	2	2	NUM
ejpam-7071	89	4	,	,	PUNCT
ejpam-7071	89	5	we	we	PRON
ejpam-7071	89	6	derive	derive	VERB
ejpam-7071	89	7	the	the	DET
ejpam-7071	89	8	necessary	necessary	ADJ
ejpam-7071	89	9	and	and	CCONJ
ejpam-7071	89	10	sufficient	sufficient	ADJ
ejpam-7071	89	11	conditions	condition	NOUN
ejpam-7071	89	12	for	for	SCONJ
ejpam-7071	89	13	the	the	DET
ejpam-7071	89	14	function	function	NOUN
ejpam-7071	89	15	ϖin	ϖin	PROPN
ejpam-7071	89	16	to	to	PART
ejpam-7071	89	17	be	be	AUX
ejpam-7071	89	18	in	in	ADP
ejpam-7071	89	19	the	the	DET
ejpam-7071	89	20	class	class	NOUN
ejpam-7071	89	21	f(ℏ1	f(ℏ1	NOUN
ejpam-7071	89	22	,	,	PUNCT
ejpam-7071	89	23	ℏ2	ℏ2	NOUN
ejpam-7071	89	24	)	)	PUNCT
ejpam-7071	89	25	.	.	PUNCT
ejpam-7071	90	1	in	in	ADP
ejpam-7071	90	2	section	section	NOUN
ejpam-7071	90	3	3	3	NUM
ejpam-7071	90	4	,	,	PUNCT
ejpam-7071	90	5	we	we	PRON
ejpam-7071	90	6	will	will	AUX
ejpam-7071	90	7	study	study	VERB
ejpam-7071	90	8	the	the	DET
ejpam-7071	90	9	action	action	NOUN
ejpam-7071	90	10	of	of	ADP
ejpam-7071	90	11	the	the	DET
ejpam-7071	90	12	function	function	NOUN
ejpam-7071	90	13	iin(z	iin(z	NOUN
ejpam-7071	90	14	)	)	PUNCT
ejpam-7071	90	15	on	on	ADP
ejpam-7071	90	16	the	the	DET
ejpam-7071	90	17	class	class	NOUN
ejpam-7071	90	18	f(ℏ1	f(ℏ1	NOUN
ejpam-7071	90	19	,	,	PUNCT
ejpam-7071	90	20	ℏ2	ℏ2	NOUN
ejpam-7071	90	21	)	)	PUNCT
ejpam-7071	90	22	.	.	PUNCT
ejpam-7071	91	1	finally	finally	ADV
ejpam-7071	91	2	,	,	PUNCT
ejpam-7071	91	3	in	in	ADP
ejpam-7071	91	4	section	section	NOUN
ejpam-7071	91	5	4	4	NUM
ejpam-7071	91	6	,	,	PUNCT
ejpam-7071	91	7	we	we	PRON
ejpam-7071	91	8	give	give	VERB
ejpam-7071	91	9	a	a	DET
ejpam-7071	91	10	necessary	necessary	ADJ
ejpam-7071	91	11	and	and	CCONJ
ejpam-7071	91	12	sufficient	sufficient	ADJ
ejpam-7071	91	13	condition	condition	NOUN
ejpam-7071	91	14	for	for	ADP
ejpam-7071	91	15	an	an	DET
ejpam-7071	91	16	integral	integral	ADJ
ejpam-7071	91	17	operator	operator	NOUN
ejpam-7071	91	18	gin(z	gin(z	PROPN
ejpam-7071	91	19	)	)	PUNCT
ejpam-7071	91	20	:	:	PUNCT
ejpam-7071	92	1	=	=	X
ejpam-7071	92	2	∫	∫	PROPN
ejpam-7071	92	3	z	z	NOUN
ejpam-7071	92	4	0	0	NUM
ejpam-7071	92	5	ϖin(t	ϖin(t	NUM
ejpam-7071	92	6	)	)	PUNCT
ejpam-7071	92	7	t	t	PROPN
ejpam-7071	92	8	dt	dt	NOUN
ejpam-7071	92	9	to	to	PART
ejpam-7071	92	10	be	be	AUX
ejpam-7071	92	11	in	in	ADP
ejpam-7071	92	12	the	the	DET
ejpam-7071	92	13	class	class	NOUN
ejpam-7071	92	14	f(ℏ1	f(ℏ1	NOUN
ejpam-7071	92	15	,	,	PUNCT
ejpam-7071	92	16	ℏ2	ℏ2	NOUN
ejpam-7071	92	17	)	)	PUNCT
ejpam-7071	92	18	.	.	PUNCT
ejpam-7071	93	1	we	we	PRON
ejpam-7071	93	2	recall	recall	VERB
ejpam-7071	93	3	the	the	DET
ejpam-7071	93	4	following	follow	VERB
ejpam-7071	93	5	lemma	lemma	PROPN
ejpam-7071	93	6	,	,	PUNCT
ejpam-7071	93	7	which	which	PRON
ejpam-7071	93	8	will	will	AUX
ejpam-7071	93	9	be	be	AUX
ejpam-7071	93	10	helpful	helpful	ADJ
ejpam-7071	93	11	in	in	ADP
ejpam-7071	93	12	derive	derive	VERB
ejpam-7071	93	13	our	our	PRON
ejpam-7071	93	14	result	result	NOUN
ejpam-7071	93	15	in	in	ADP
ejpam-7071	93	16	section	section	NOUN
ejpam-7071	93	17	3	3	NUM
ejpam-7071	93	18	.	.	PUNCT
ejpam-7071	94	1	lemma	lemma	PROPN
ejpam-7071	94	2	2	2	NUM
ejpam-7071	94	3	.	.	PUNCT
ejpam-7071	95	1	[	[	X
ejpam-7071	95	2	3	3	X
ejpam-7071	95	3	]	]	X
ejpam-7071	95	4	if	if	SCONJ
ejpam-7071	95	5	g	g	PROPN
ejpam-7071	95	6	∈	∈	PROPN
ejpam-7071	95	7	gτ	gτ	PROPN
ejpam-7071	95	8	(	(	PUNCT
ejpam-7071	95	9	a1	a1	PROPN
ejpam-7071	95	10	,	,	PUNCT
ejpam-7071	95	11	a2	a2	PROPN
ejpam-7071	95	12	)	)	PUNCT
ejpam-7071	95	13	is	be	AUX
ejpam-7071	95	14	of	of	ADP
ejpam-7071	95	15	the	the	DET
ejpam-7071	95	16	form	form	NOUN
ejpam-7071	95	17	(	(	PUNCT
ejpam-7071	95	18	1	1	NUM
ejpam-7071	95	19	)	)	PUNCT
ejpam-7071	95	20	,	,	PUNCT
ejpam-7071	95	21	then	then	ADV
ejpam-7071	95	22	|aρ|	|aρ|	PROPN
ejpam-7071	95	23	≤	≤	NOUN
ejpam-7071	95	24	(	(	PUNCT
ejpam-7071	95	25	a1	a1	NOUN
ejpam-7071	95	26	−a2	−a2	PROPN
ejpam-7071	95	27	)	)	PUNCT
ejpam-7071	95	28	|τ	|τ	NOUN
ejpam-7071	95	29	|	|	NOUN
ejpam-7071	95	30	ρ	ρ	NOUN
ejpam-7071	95	31	;	;	PUNCT
ejpam-7071	95	32	ρ	ρ	PROPN
ejpam-7071	95	33	∈	∈	PROPN
ejpam-7071	95	34	n−	n−	PROPN
ejpam-7071	95	35	{	{	PUNCT
ejpam-7071	95	36	1	1	NUM
ejpam-7071	95	37	}	}	PUNCT
ejpam-7071	95	38	.	.	PUNCT
ejpam-7071	96	1	the	the	DET
ejpam-7071	96	2	result	result	NOUN
ejpam-7071	96	3	is	be	AUX
ejpam-7071	96	4	sharp	sharp	ADJ
ejpam-7071	96	5	.	.	PUNCT
ejpam-7071	97	1	a.	a.	PROPN
ejpam-7071	97	2	alameer	alameer	PROPN
ejpam-7071	97	3	et	et	PROPN
ejpam-7071	97	4	al	al	PROPN
ejpam-7071	97	5	.	.	PUNCT
ejpam-7071	97	6	/	/	SYM
ejpam-7071	97	7	eur	eur	PROPN
ejpam-7071	97	8	.	.	PUNCT
ejpam-7071	98	1	j.	j.	PROPN
ejpam-7071	98	2	pure	pure	PROPN
ejpam-7071	98	3	appl	appl	PROPN
ejpam-7071	98	4	.	.	PROPN
ejpam-7071	98	5	math	math	PROPN
ejpam-7071	98	6	,	,	PUNCT
ejpam-7071	98	7	18	18	NUM
ejpam-7071	98	8	(	(	PUNCT
ejpam-7071	98	9	4	4	NUM
ejpam-7071	98	10	)	)	PUNCT
ejpam-7071	98	11	(	(	PUNCT
ejpam-7071	98	12	2025	2025	NUM
ejpam-7071	98	13	)	)	PUNCT
ejpam-7071	98	14	,	,	PUNCT
ejpam-7071	98	15	7071	7071	NUM
ejpam-7071	98	16	5	5	NUM
ejpam-7071	98	17	of	of	ADP
ejpam-7071	98	18	11	11	NUM
ejpam-7071	98	19	we	we	PRON
ejpam-7071	98	20	employ	employ	VERB
ejpam-7071	98	21	the	the	DET
ejpam-7071	98	22	following	follow	VERB
ejpam-7071	98	23	well	well	ADV
ejpam-7071	98	24	-	-	PUNCT
ejpam-7071	98	25	known	know	VERB
ejpam-7071	98	26	series	series	NOUN
ejpam-7071	98	27	sums	sum	VERB
ejpam-7071	98	28	throughout	throughout	ADP
ejpam-7071	98	29	the	the	DET
ejpam-7071	98	30	sequel	sequel	NOUN
ejpam-7071	98	31	.	.	PUNCT
ejpam-7071	99	1	∞∑	∞∑	NUM
ejpam-7071	99	2	ρ=2	ρ=2	SYM
ejpam-7071	99	3	1	1	NUM
ejpam-7071	99	4	(	(	PUNCT
ejpam-7071	99	5	ρ−	ρ−	NOUN
ejpam-7071	99	6	1	1	NUM
ejpam-7071	99	7	)	)	PUNCT
ejpam-7071	99	8	2ρ	2ρ	NOUN
ejpam-7071	99	9	=	=	SYM
ejpam-7071	99	10	1	1	NUM
ejpam-7071	99	11	2	2	NUM
ejpam-7071	99	12	ln	ln	SYM
ejpam-7071	99	13	2	2	NUM
ejpam-7071	99	14	,	,	PUNCT
ejpam-7071	99	15	(	(	PUNCT
ejpam-7071	99	16	11	11	NUM
ejpam-7071	99	17	)	)	PUNCT
ejpam-7071	100	1	∞∑	∞∑	NUM
ejpam-7071	100	2	ρ=3	ρ=3	NUM
ejpam-7071	100	3	1	1	NUM
ejpam-7071	100	4	2ρ	2ρ	NOUN
ejpam-7071	100	5	(	(	PUNCT
ejpam-7071	100	6	ρ−	ρ−	NOUN
ejpam-7071	100	7	1	1	NUM
ejpam-7071	100	8	)	)	PUNCT
ejpam-7071	100	9	=	=	SYM
ejpam-7071	100	10	1	1	NUM
ejpam-7071	100	11	2	2	NUM
ejpam-7071	100	12	ln	ln	NOUN
ejpam-7071	100	13	2−	2−	NUM
ejpam-7071	100	14	1	1	NUM
ejpam-7071	100	15	4	4	NUM
ejpam-7071	100	16	,	,	PUNCT
ejpam-7071	100	17	(	(	PUNCT
ejpam-7071	100	18	12	12	NUM
ejpam-7071	100	19	)	)	PUNCT
ejpam-7071	100	20	and	and	CCONJ
ejpam-7071	100	21	∞∑	∞∑	NUM
ejpam-7071	100	22	ρ=4	ρ=4	DET
ejpam-7071	100	23	1	1	NUM
ejpam-7071	100	24	2ρ	2ρ	NOUN
ejpam-7071	100	25	(	(	PUNCT
ejpam-7071	100	26	ρ−	ρ−	NOUN
ejpam-7071	100	27	1	1	NUM
ejpam-7071	100	28	)	)	PUNCT
ejpam-7071	100	29	=	=	SYM
ejpam-7071	100	30	1	1	NUM
ejpam-7071	100	31	2	2	NUM
ejpam-7071	100	32	ln	ln	NOUN
ejpam-7071	100	33	2−	2−	NUM
ejpam-7071	100	34	1	1	NUM
ejpam-7071	100	35	4	4	NUM
ejpam-7071	100	36	−	−	NOUN
ejpam-7071	100	37	1	1	NUM
ejpam-7071	100	38	16	16	NUM
ejpam-7071	100	39	.	.	PUNCT
ejpam-7071	101	1	(	(	PUNCT
ejpam-7071	101	2	13	13	X
ejpam-7071	101	3	)	)	PUNCT
ejpam-7071	101	4	note	note	NOUN
ejpam-7071	101	5	that	that	SCONJ
ejpam-7071	101	6	∞∑	∞∑	NUM
ejpam-7071	101	7	ρ	ρ	PROPN
ejpam-7071	101	8	=	=	PROPN
ejpam-7071	101	9	j	j	NOUN
ejpam-7071	101	10	1	1	NUM
ejpam-7071	101	11	(	(	PUNCT
ejpam-7071	101	12	ρ−	ρ−	NOUN
ejpam-7071	101	13	1	1	NUM
ejpam-7071	101	14	)	)	PUNCT
ejpam-7071	101	15	2ρ	2ρ	NOUN
ejpam-7071	101	16	=	=	SYM
ejpam-7071	101	17	1	1	NUM
ejpam-7071	101	18	2	2	NUM
ejpam-7071	101	19	ln	ln	NUM
ejpam-7071	101	20	2−	2−	NUM
ejpam-7071	101	21	j−1∑	j−1∑	NOUN
ejpam-7071	101	22	ρ=2	ρ=2	SYM
ejpam-7071	101	23	1	1	NUM
ejpam-7071	101	24	(	(	PUNCT
ejpam-7071	101	25	ρ−	ρ−	NOUN
ejpam-7071	101	26	1	1	NUM
ejpam-7071	101	27	)	)	PUNCT
ejpam-7071	101	28	2ρ	2ρ	NOUN
ejpam-7071	101	29	,	,	PUNCT
ejpam-7071	101	30	j	j	PROPN
ejpam-7071	101	31	=	=	SYM
ejpam-7071	101	32	3	3	NUM
ejpam-7071	101	33	,	,	PUNCT
ejpam-7071	101	34	4	4	NUM
ejpam-7071	101	35	,	,	PUNCT
ejpam-7071	101	36	·	·	PUNCT
ejpam-7071	101	37	·	·	PUNCT
ejpam-7071	101	38	·	·	PUNCT
ejpam-7071	101	39	.	.	PUNCT
ejpam-7071	102	1	(	(	PUNCT
ejpam-7071	102	2	14	14	NUM
ejpam-7071	102	3	)	)	PUNCT
ejpam-7071	102	4	in	in	ADP
ejpam-7071	102	5	addition	addition	NOUN
ejpam-7071	102	6	,	,	PUNCT
ejpam-7071	102	7	we	we	PRON
ejpam-7071	102	8	need	need	VERB
ejpam-7071	102	9	the	the	DET
ejpam-7071	102	10	following	follow	VERB
ejpam-7071	102	11	inequalities	inequality	NOUN
ejpam-7071	102	12	.	.	PUNCT
ejpam-7071	103	1	(	(	PUNCT
ejpam-7071	103	2	ρ−	ρ−	NOUN
ejpam-7071	103	3	1)n+	1)n+	NUM
ejpam-7071	103	4	1	1	NUM
ejpam-7071	103	5	>	>	X
ejpam-7071	103	6	(	(	PUNCT
ejpam-7071	103	7	ρ−	ρ−	PROPN
ejpam-7071	103	8	1)n	1)n	NUM
ejpam-7071	103	9	(	(	PUNCT
ejpam-7071	103	10	ρ	ρ	PROPN
ejpam-7071	103	11	,	,	PUNCT
ejpam-7071	103	12	n	n	PROPN
ejpam-7071	103	13	∈	∈	PROPN
ejpam-7071	103	14	n	n	CCONJ
ejpam-7071	103	15	)	)	PUNCT
ejpam-7071	103	16	(	(	PUNCT
ejpam-7071	103	17	15	15	NUM
ejpam-7071	103	18	)	)	PUNCT
ejpam-7071	103	19	and	and	CCONJ
ejpam-7071	103	20	ρ	ρ	PROPN
ejpam-7071	103	21	!	!	PROPN
ejpam-7071	103	22	≥	≥	PROPN
ejpam-7071	103	23	2ρ−1	2ρ−1	NUM
ejpam-7071	103	24	(	(	PUNCT
ejpam-7071	103	25	ρ	ρ	PROPN
ejpam-7071	103	26	∈	∈	PROPN
ejpam-7071	103	27	n	n	CCONJ
ejpam-7071	103	28	)	)	PUNCT
ejpam-7071	103	29	.	.	PUNCT
ejpam-7071	104	1	(	(	PUNCT
ejpam-7071	104	2	16	16	NUM
ejpam-7071	104	3	)	)	PUNCT
ejpam-7071	104	4	2	2	NUM
ejpam-7071	104	5	.	.	NOUN
ejpam-7071	104	6	necessary	necessary	ADJ
ejpam-7071	104	7	and	and	CCONJ
ejpam-7071	104	8	sufficient	sufficient	ADJ
ejpam-7071	104	9	conditions	condition	NOUN
ejpam-7071	104	10	in	in	ADP
ejpam-7071	104	11	this	this	DET
ejpam-7071	104	12	section	section	NOUN
ejpam-7071	105	1	,	,	PUNCT
ejpam-7071	105	2	we	we	PRON
ejpam-7071	105	3	give	give	VERB
ejpam-7071	105	4	the	the	DET
ejpam-7071	105	5	necessary	necessary	ADJ
ejpam-7071	105	6	and	and	CCONJ
ejpam-7071	105	7	sufficient	sufficient	ADJ
ejpam-7071	105	8	conditions	condition	NOUN
ejpam-7071	105	9	for	for	SCONJ
ejpam-7071	105	10	the	the	DET
ejpam-7071	105	11	function	function	NOUN
ejpam-7071	105	12	ϖin	ϖin	PROPN
ejpam-7071	105	13	to	to	PART
ejpam-7071	105	14	be	be	AUX
ejpam-7071	105	15	in	in	ADP
ejpam-7071	105	16	the	the	DET
ejpam-7071	105	17	class	class	NOUN
ejpam-7071	105	18	f(ℏ1	f(ℏ1	NOUN
ejpam-7071	105	19	,	,	PUNCT
ejpam-7071	105	20	ℏ2	ℏ2	NOUN
ejpam-7071	105	21	)	)	PUNCT
ejpam-7071	105	22	.	.	PUNCT
ejpam-7071	106	1	theorem	theorem	NOUN
ejpam-7071	106	2	1	1	NUM
ejpam-7071	106	3	.	.	PUNCT
ejpam-7071	107	1	if	if	SCONJ
ejpam-7071	107	2	ℏ1	ℏ1	ADJ
ejpam-7071	107	3	,	,	PUNCT
ejpam-7071	107	4	ℏ2	ℏ2	NOUN
ejpam-7071	107	5	∈	∈	PROPN
ejpam-7071	108	1	[	[	X
ejpam-7071	108	2	0	0	NUM
ejpam-7071	108	3	,	,	PUNCT
ejpam-7071	108	4	1	1	NUM
ejpam-7071	108	5	)	)	PUNCT
ejpam-7071	108	6	and	and	CCONJ
ejpam-7071	108	7	n	n	PRON
ejpam-7071	108	8	∈	∈	PROPN
ejpam-7071	108	9	n	n	CCONJ
ejpam-7071	108	10	,	,	PUNCT
ejpam-7071	108	11	then	then	ADV
ejpam-7071	108	12	ϖin	ϖin	PROPN
ejpam-7071	109	1	(	(	PUNCT
ejpam-7071	109	2	z	z	NOUN
ejpam-7071	109	3	)	)	PUNCT
ejpam-7071	109	4	is	be	AUX
ejpam-7071	109	5	in	in	ADP
ejpam-7071	109	6	the	the	DET
ejpam-7071	109	7	class	class	NOUN
ejpam-7071	109	8	f(ℏ1	f(ℏ1	NOUN
ejpam-7071	109	9	,	,	PUNCT
ejpam-7071	109	10	ℏ2	ℏ2	NOUN
ejpam-7071	109	11	)	)	PUNCT
ejpam-7071	110	1	if	if	SCONJ
ejpam-7071	111	1	and	and	CCONJ
ejpam-7071	111	2	only	only	ADV
ejpam-7071	111	3	if	if	SCONJ
ejpam-7071	111	4	[	[	X
ejpam-7071	111	5	72ℏ2	72ℏ2	NUM
ejpam-7071	111	6	−	−	NUM
ejpam-7071	111	7	16ℏ1ℏ2	16ℏ1ℏ2	NUM
ejpam-7071	111	8	−	−	PROPN
ejpam-7071	111	9	6ℏ1	6ℏ1	NUM
ejpam-7071	111	10	+	+	CCONJ
ejpam-7071	111	11	22	22	NUM
ejpam-7071	111	12	]	]	X
ejpam-7071	111	13	ln	ln	NOUN
ejpam-7071	111	14	2−	2−	NUM
ejpam-7071	112	1	[	[	X
ejpam-7071	112	2	30ℏ2	30ℏ2	NUM
ejpam-7071	112	3	+	+	NUM
ejpam-7071	112	4	4(1−	4(1−	NUM
ejpam-7071	112	5	ℏ1ℏ2	ℏ1ℏ2	NOUN
ejpam-7071	112	6	)	)	PUNCT
ejpam-7071	112	7	]	]	PUNCT
ejpam-7071	112	8	≤	≤	NUM
ejpam-7071	112	9	n	n	CCONJ
ejpam-7071	112	10	(	(	PUNCT
ejpam-7071	112	11	1−	1−	NUM
ejpam-7071	112	12	ℏ1	ℏ1	PROPN
ejpam-7071	112	13	)	)	PUNCT
ejpam-7071	112	14	.	.	PUNCT
ejpam-7071	113	1	(	(	PUNCT
ejpam-7071	113	2	17	17	NUM
ejpam-7071	113	3	)	)	PUNCT
ejpam-7071	113	4	proof	proof	NOUN
ejpam-7071	113	5	.	.	PUNCT
ejpam-7071	114	1	since	since	SCONJ
ejpam-7071	114	2	ϖin	ϖin	PROPN
ejpam-7071	114	3	(	(	PUNCT
ejpam-7071	114	4	z	z	NOUN
ejpam-7071	114	5	)	)	PUNCT
ejpam-7071	114	6	=	=	PUNCT
ejpam-7071	114	7	z	z	NOUN
ejpam-7071	114	8	−	−	NOUN
ejpam-7071	114	9	∞∑	∞∑	NUM
ejpam-7071	114	10	ρ=2	ρ=2	SYM
ejpam-7071	114	11	1	1	NUM
ejpam-7071	114	12	(	(	PUNCT
ejpam-7071	114	13	(	(	PUNCT
ejpam-7071	114	14	ρ−	ρ−	NOUN
ejpam-7071	114	15	1)n+	1)n+	NUM
ejpam-7071	114	16	1	1	NUM
ejpam-7071	114	17	)	)	PUNCT
ejpam-7071	114	18	(	(	PUNCT
ejpam-7071	114	19	ρ−	ρ−	NOUN
ejpam-7071	114	20	1	1	NUM
ejpam-7071	114	21	)	)	PUNCT
ejpam-7071	114	22	!	!	PUNCT
ejpam-7071	115	1	zρ	zρ	PROPN
ejpam-7071	115	2	,	,	PUNCT
ejpam-7071	115	3	by	by	ADP
ejpam-7071	115	4	virtue	virtue	NOUN
ejpam-7071	115	5	of	of	ADP
ejpam-7071	115	6	lemma	lemma	PROPN
ejpam-7071	115	7	1	1	NUM
ejpam-7071	115	8	it	it	PRON
ejpam-7071	115	9	suffices	suffice	VERB
ejpam-7071	115	10	to	to	PART
ejpam-7071	115	11	show	show	VERB
ejpam-7071	115	12	that	that	SCONJ
ejpam-7071	115	13	l(γ	l(γ	PROPN
ejpam-7071	115	14	,	,	PUNCT
ejpam-7071	115	15	β	β	NOUN
ejpam-7071	115	16	)	)	PUNCT
ejpam-7071	115	17	≤	≤	NOUN
ejpam-7071	115	18	1−	1−	NUM
ejpam-7071	115	19	ℏ1	ℏ1	NOUN
ejpam-7071	115	20	,	,	PUNCT
ejpam-7071	115	21	where	where	SCONJ
ejpam-7071	115	22	l(ℏ1	l(ℏ1	NOUN
ejpam-7071	115	23	,	,	PUNCT
ejpam-7071	115	24	ℏ2	ℏ2	NOUN
ejpam-7071	115	25	)	)	PUNCT
ejpam-7071	115	26	:	:	PUNCT
ejpam-7071	116	1	=	=	NOUN
ejpam-7071	116	2	∞∑	∞∑	NUM
ejpam-7071	116	3	ρ=2	ρ=2	PUNCT
ejpam-7071	116	4	ρ(ρ−	ρ(ρ−	ADJ
ejpam-7071	116	5	ℏ1	ℏ1	PROPN
ejpam-7071	116	6	)	)	PUNCT
ejpam-7071	116	7	(	(	PUNCT
ejpam-7071	116	8	ℏ2(ρ−	ℏ2(ρ−	ADJ
ejpam-7071	116	9	1	1	X
ejpam-7071	116	10	)	)	PUNCT
ejpam-7071	116	11	+	+	CCONJ
ejpam-7071	116	12	1	1	X
ejpam-7071	116	13	)	)	SYM
ejpam-7071	116	14	1	1	NUM
ejpam-7071	116	15	(	(	PUNCT
ejpam-7071	116	16	(	(	PUNCT
ejpam-7071	116	17	ρ−	ρ−	NOUN
ejpam-7071	116	18	1)n+	1)n+	NUM
ejpam-7071	116	19	1	1	NUM
ejpam-7071	116	20	)	)	PUNCT
ejpam-7071	116	21	(	(	PUNCT
ejpam-7071	116	22	ρ−	ρ−	NOUN
ejpam-7071	116	23	1	1	NUM
ejpam-7071	116	24	)	)	PUNCT
ejpam-7071	116	25	!	!	PUNCT
ejpam-7071	116	26	.	.	PUNCT
ejpam-7071	117	1	writing	write	VERB
ejpam-7071	117	2	ρ	ρ	PROPN
ejpam-7071	117	3	=	=	SYM
ejpam-7071	117	4	(	(	PUNCT
ejpam-7071	117	5	ρ−	ρ−	NOUN
ejpam-7071	117	6	1	1	NUM
ejpam-7071	117	7	)	)	PUNCT
ejpam-7071	117	8	+	+	NUM
ejpam-7071	117	9	1	1	NUM
ejpam-7071	117	10	,	,	PUNCT
ejpam-7071	117	11	(	(	PUNCT
ejpam-7071	117	12	18	18	NUM
ejpam-7071	117	13	)	)	PUNCT
ejpam-7071	117	14	ρ2	ρ2	NOUN
ejpam-7071	117	15	=	=	SYM
ejpam-7071	117	16	(	(	PUNCT
ejpam-7071	117	17	ρ−	ρ−	NOUN
ejpam-7071	117	18	1)(ρ−	1)(ρ−	NUM
ejpam-7071	117	19	2	2	NUM
ejpam-7071	117	20	)	)	PUNCT
ejpam-7071	117	21	+	+	CCONJ
ejpam-7071	117	22	3(ρ−	3(ρ−	NUM
ejpam-7071	117	23	1	1	NUM
ejpam-7071	117	24	)	)	PUNCT
ejpam-7071	117	25	+	+	NUM
ejpam-7071	117	26	1	1	NUM
ejpam-7071	117	27	,	,	PUNCT
ejpam-7071	117	28	(	(	PUNCT
ejpam-7071	117	29	19	19	NUM
ejpam-7071	117	30	)	)	PUNCT
ejpam-7071	117	31	a.	a.	NOUN
ejpam-7071	117	32	alameer	alameer	NOUN
ejpam-7071	117	33	et	et	PROPN
ejpam-7071	117	34	al	al	PROPN
ejpam-7071	117	35	.	.	PUNCT
ejpam-7071	117	36	/	/	SYM
ejpam-7071	117	37	eur	eur	PROPN
ejpam-7071	117	38	.	.	PUNCT
ejpam-7071	118	1	j.	j.	PROPN
ejpam-7071	118	2	pure	pure	PROPN
ejpam-7071	118	3	appl	appl	PROPN
ejpam-7071	118	4	.	.	PROPN
ejpam-7071	118	5	math	math	PROPN
ejpam-7071	118	6	,	,	PUNCT
ejpam-7071	118	7	18	18	NUM
ejpam-7071	118	8	(	(	PUNCT
ejpam-7071	118	9	4	4	NUM
ejpam-7071	118	10	)	)	PUNCT
ejpam-7071	118	11	(	(	PUNCT
ejpam-7071	118	12	2025	2025	NUM
ejpam-7071	118	13	)	)	PUNCT
ejpam-7071	118	14	,	,	PUNCT
ejpam-7071	118	15	7071	7071	NUM
ejpam-7071	118	16	6	6	NUM
ejpam-7071	118	17	of	of	ADP
ejpam-7071	118	18	11	11	NUM
ejpam-7071	118	19	ρ3	ρ3	NOUN
ejpam-7071	118	20	=	=	PUNCT
ejpam-7071	118	21	(	(	PUNCT
ejpam-7071	118	22	ρ−	ρ−	NOUN
ejpam-7071	118	23	1)(ρ−	1)(ρ−	NUM
ejpam-7071	118	24	2)(ρ−	2)(ρ−	NUM
ejpam-7071	118	25	3	3	NUM
ejpam-7071	118	26	)	)	PUNCT
ejpam-7071	118	27	+	+	CCONJ
ejpam-7071	118	28	6(ρ−	6(ρ−	NUM
ejpam-7071	118	29	1)(ρ−	1)(ρ−	NUM
ejpam-7071	118	30	2	2	NUM
ejpam-7071	118	31	)	)	PUNCT
ejpam-7071	118	32	+	+	CCONJ
ejpam-7071	119	1	7(ρ−	7(ρ−	NUM
ejpam-7071	119	2	1	1	NUM
ejpam-7071	119	3	)	)	PUNCT
ejpam-7071	119	4	+	+	NUM
ejpam-7071	119	5	1	1	NUM
ejpam-7071	119	6	,	,	PUNCT
ejpam-7071	119	7	(	(	PUNCT
ejpam-7071	119	8	20	20	NUM
ejpam-7071	119	9	)	)	PUNCT
ejpam-7071	119	10	we	we	PRON
ejpam-7071	119	11	get	get	VERB
ejpam-7071	119	12	l(ℏ1	l(ℏ1	NOUN
ejpam-7071	119	13	,	,	PUNCT
ejpam-7071	119	14	ℏ2	ℏ2	NOUN
ejpam-7071	119	15	)	)	PUNCT
ejpam-7071	119	16	=	=	PUNCT
ejpam-7071	120	1	∞∑	∞∑	NUM
ejpam-7071	120	2	ρ=2	ρ=2	PUNCT
ejpam-7071	120	3	[	[	X
ejpam-7071	120	4	ℏ2ρ3	ℏ2ρ3	X
ejpam-7071	120	5	+	+	CCONJ
ejpam-7071	120	6	(	(	PUNCT
ejpam-7071	120	7	1−	1−	NUM
ejpam-7071	120	8	ℏ2(ℏ1	ℏ2(ℏ1	VERB
ejpam-7071	120	9	+	+	NUM
ejpam-7071	120	10	1))ρ2	1))ρ2	NUM
ejpam-7071	120	11	+	+	CCONJ
ejpam-7071	120	12	ℏ1(ℏ2	ℏ1(ℏ2	ADJ
ejpam-7071	120	13	−	−	PROPN
ejpam-7071	120	14	1))ρ	1))ρ	NUM
ejpam-7071	120	15	]	]	SYM
ejpam-7071	120	16	1	1	NUM
ejpam-7071	120	17	(	(	PUNCT
ejpam-7071	120	18	(	(	PUNCT
ejpam-7071	120	19	ρ−	ρ−	NOUN
ejpam-7071	120	20	1)n+	1)n+	NUM
ejpam-7071	120	21	1	1	NUM
ejpam-7071	120	22	)	)	PUNCT
ejpam-7071	120	23	(	(	PUNCT
ejpam-7071	120	24	ρ−	ρ−	NOUN
ejpam-7071	120	25	1	1	NUM
ejpam-7071	120	26	)	)	PUNCT
ejpam-7071	120	27	!	!	PUNCT
ejpam-7071	121	1	=	=	PRON
ejpam-7071	121	2	ℏ2	ℏ2	VERB
ejpam-7071	121	3	∞∑	∞∑	NUM
ejpam-7071	121	4	ρ=2	ρ=2	SYM
ejpam-7071	121	5	(	(	PUNCT
ejpam-7071	121	6	ρ−	ρ−	NOUN
ejpam-7071	121	7	1)(ρ−	1)(ρ−	NUM
ejpam-7071	121	8	2)(ρ−	2)(ρ−	NUM
ejpam-7071	121	9	3	3	NUM
ejpam-7071	121	10	)	)	PUNCT
ejpam-7071	121	11	1	1	NUM
ejpam-7071	121	12	(	(	PUNCT
ejpam-7071	121	13	(	(	PUNCT
ejpam-7071	121	14	ρ−	ρ−	NOUN
ejpam-7071	121	15	1)n+	1)n+	NUM
ejpam-7071	121	16	1	1	NUM
ejpam-7071	121	17	)	)	PUNCT
ejpam-7071	121	18	(	(	PUNCT
ejpam-7071	121	19	ρ−	ρ−	NOUN
ejpam-7071	121	20	1	1	NUM
ejpam-7071	121	21	)	)	PUNCT
ejpam-7071	121	22	!	!	PUNCT
ejpam-7071	122	1	+	+	CCONJ
ejpam-7071	122	2	(	(	PUNCT
ejpam-7071	122	3	ℏ2(5−	ℏ2(5−	X
ejpam-7071	122	4	ℏ1	ℏ1	VERB
ejpam-7071	122	5	)	)	PUNCT
ejpam-7071	122	6	+	+	NUM
ejpam-7071	122	7	1	1	X
ejpam-7071	122	8	)	)	PUNCT
ejpam-7071	123	1	∞∑	∞∑	NUM
ejpam-7071	123	2	ρ=2	ρ=2	SYM
ejpam-7071	123	3	(	(	PUNCT
ejpam-7071	123	4	ρ−	ρ−	NOUN
ejpam-7071	123	5	1)(ρ−	1)(ρ−	NUM
ejpam-7071	123	6	2	2	NUM
ejpam-7071	123	7	)	)	PUNCT
ejpam-7071	123	8	1	1	NUM
ejpam-7071	123	9	(	(	PUNCT
ejpam-7071	123	10	(	(	PUNCT
ejpam-7071	123	11	ρ−	ρ−	NOUN
ejpam-7071	123	12	1)n+	1)n+	NUM
ejpam-7071	123	13	1	1	NUM
ejpam-7071	123	14	)	)	PUNCT
ejpam-7071	123	15	(	(	PUNCT
ejpam-7071	123	16	ρ−	ρ−	NOUN
ejpam-7071	123	17	1	1	NUM
ejpam-7071	123	18	)	)	PUNCT
ejpam-7071	123	19	!	!	PUNCT
ejpam-7071	124	1	+	+	CCONJ
ejpam-7071	124	2	(	(	PUNCT
ejpam-7071	124	3	2ℏ2(2−	2ℏ2(2−	NUM
ejpam-7071	124	4	ℏ1	ℏ1	PROPN
ejpam-7071	124	5	)	)	PUNCT
ejpam-7071	124	6	+	+	CCONJ
ejpam-7071	124	7	3−	3−	NUM
ejpam-7071	124	8	ℏ1	ℏ1	NOUN
ejpam-7071	124	9	)	)	PUNCT
ejpam-7071	125	1	∞∑	∞∑	PROPN
ejpam-7071	125	2	ρ=2	ρ=2	SYM
ejpam-7071	125	3	(	(	PUNCT
ejpam-7071	125	4	ρ−	ρ−	NOUN
ejpam-7071	125	5	1	1	NUM
ejpam-7071	125	6	)	)	PUNCT
ejpam-7071	125	7	1	1	NUM
ejpam-7071	125	8	(	(	PUNCT
ejpam-7071	125	9	(	(	PUNCT
ejpam-7071	125	10	ρ−	ρ−	NOUN
ejpam-7071	125	11	1)n+	1)n+	NUM
ejpam-7071	125	12	1	1	NUM
ejpam-7071	125	13	)	)	PUNCT
ejpam-7071	125	14	(	(	PUNCT
ejpam-7071	125	15	ρ−	ρ−	NOUN
ejpam-7071	125	16	1	1	NUM
ejpam-7071	125	17	)	)	PUNCT
ejpam-7071	125	18	!	!	PUNCT
ejpam-7071	126	1	+	+	CCONJ
ejpam-7071	126	2	(	(	PUNCT
ejpam-7071	126	3	1−	1−	NUM
ejpam-7071	126	4	ℏ1	ℏ1	ADJ
ejpam-7071	126	5	)	)	PUNCT
ejpam-7071	126	6	∞∑	∞∑	NUM
ejpam-7071	126	7	ρ=2	ρ=2	SYM
ejpam-7071	126	8	1	1	NUM
ejpam-7071	126	9	(	(	PUNCT
ejpam-7071	126	10	(	(	PUNCT
ejpam-7071	126	11	ρ−	ρ−	NOUN
ejpam-7071	126	12	1)n+	1)n+	NUM
ejpam-7071	126	13	1	1	NUM
ejpam-7071	126	14	)	)	PUNCT
ejpam-7071	126	15	(	(	PUNCT
ejpam-7071	126	16	ρ−	ρ−	NOUN
ejpam-7071	126	17	1	1	NUM
ejpam-7071	126	18	)	)	PUNCT
ejpam-7071	126	19	!	!	PUNCT
ejpam-7071	127	1	=	=	PUNCT
ejpam-7071	128	1	ℏ2	ℏ2	VERB
ejpam-7071	128	2	∞∑	∞∑	ADJ
ejpam-7071	128	3	ρ=4	ρ=4	NOUN
ejpam-7071	128	4	1	1	NUM
ejpam-7071	128	5	(	(	PUNCT
ejpam-7071	128	6	(	(	PUNCT
ejpam-7071	128	7	ρ−	ρ−	NOUN
ejpam-7071	128	8	1)n+	1)n+	NUM
ejpam-7071	128	9	1	1	NUM
ejpam-7071	128	10	)	)	PUNCT
ejpam-7071	128	11	(	(	PUNCT
ejpam-7071	128	12	ρ−	ρ−	NOUN
ejpam-7071	128	13	4	4	NUM
ejpam-7071	128	14	)	)	PUNCT
ejpam-7071	128	15	!	!	PUNCT
ejpam-7071	129	1	+	+	CCONJ
ejpam-7071	129	2	(	(	PUNCT
ejpam-7071	129	3	ℏ2(5−	ℏ2(5−	X
ejpam-7071	129	4	ℏ1	ℏ1	VERB
ejpam-7071	129	5	)	)	PUNCT
ejpam-7071	129	6	+	+	NUM
ejpam-7071	129	7	1	1	X
ejpam-7071	129	8	)	)	PUNCT
ejpam-7071	129	9	∞∑	∞∑	NUM
ejpam-7071	129	10	ρ=3	ρ=3	NUM
ejpam-7071	129	11	1	1	NUM
ejpam-7071	129	12	(	(	PUNCT
ejpam-7071	129	13	(	(	PUNCT
ejpam-7071	129	14	ρ−	ρ−	NOUN
ejpam-7071	129	15	1)n+	1)n+	NUM
ejpam-7071	129	16	1	1	NUM
ejpam-7071	129	17	)	)	PUNCT
ejpam-7071	129	18	(	(	PUNCT
ejpam-7071	129	19	ρ−	ρ−	NOUN
ejpam-7071	129	20	3	3	NUM
ejpam-7071	129	21	)	)	PUNCT
ejpam-7071	129	22	!	!	PUNCT
ejpam-7071	130	1	+	+	CCONJ
ejpam-7071	130	2	(	(	PUNCT
ejpam-7071	130	3	2ℏ2(2−	2ℏ2(2−	NUM
ejpam-7071	130	4	ℏ1	ℏ1	PROPN
ejpam-7071	130	5	)	)	PUNCT
ejpam-7071	130	6	+	+	CCONJ
ejpam-7071	130	7	3−	3−	NUM
ejpam-7071	130	8	ℏ1	ℏ1	NOUN
ejpam-7071	130	9	)	)	PUNCT
ejpam-7071	130	10	∞∑	∞∑	NUM
ejpam-7071	130	11	ρ=2	ρ=2	SYM
ejpam-7071	130	12	1	1	NUM
ejpam-7071	130	13	(	(	PUNCT
ejpam-7071	130	14	(	(	PUNCT
ejpam-7071	130	15	ρ−	ρ−	NOUN
ejpam-7071	130	16	1)n+	1)n+	NUM
ejpam-7071	130	17	1	1	NUM
ejpam-7071	130	18	)	)	PUNCT
ejpam-7071	130	19	(	(	PUNCT
ejpam-7071	130	20	ρ−	ρ−	NOUN
ejpam-7071	130	21	2	2	NUM
ejpam-7071	130	22	)	)	PUNCT
ejpam-7071	130	23	!	!	PUNCT
ejpam-7071	131	1	+	+	CCONJ
ejpam-7071	131	2	(	(	PUNCT
ejpam-7071	131	3	1−	1−	NUM
ejpam-7071	131	4	ℏ1	ℏ1	ADJ
ejpam-7071	131	5	)	)	PUNCT
ejpam-7071	131	6	∞∑	∞∑	NUM
ejpam-7071	131	7	ρ=2	ρ=2	SYM
ejpam-7071	131	8	1	1	NUM
ejpam-7071	131	9	(	(	PUNCT
ejpam-7071	131	10	(	(	PUNCT
ejpam-7071	131	11	ρ−	ρ−	NOUN
ejpam-7071	131	12	1)n+	1)n+	NUM
ejpam-7071	131	13	1	1	NUM
ejpam-7071	131	14	)	)	PUNCT
ejpam-7071	131	15	(	(	PUNCT
ejpam-7071	131	16	ρ−	ρ−	NOUN
ejpam-7071	131	17	1	1	NUM
ejpam-7071	131	18	)	)	PUNCT
ejpam-7071	131	19	!	!	PUNCT
ejpam-7071	131	20	.	.	PUNCT
ejpam-7071	132	1	by	by	ADP
ejpam-7071	132	2	(	(	PUNCT
ejpam-7071	132	3	15	15	NUM
ejpam-7071	132	4	)	)	PUNCT
ejpam-7071	132	5	,	,	PUNCT
ejpam-7071	132	6	we	we	PRON
ejpam-7071	132	7	get	get	VERB
ejpam-7071	132	8	l(ℏ1	l(ℏ1	NOUN
ejpam-7071	132	9	,	,	PUNCT
ejpam-7071	132	10	ℏ2	ℏ2	NOUN
ejpam-7071	132	11	)	)	PUNCT
ejpam-7071	132	12	≤	≤	NUM
ejpam-7071	132	13	ℏ2	ℏ2	NOUN
ejpam-7071	132	14	n	n	PROPN
ejpam-7071	132	15	∞∑	∞∑	NUM
ejpam-7071	132	16	ρ=4	ρ=4	NOUN
ejpam-7071	132	17	1	1	NUM
ejpam-7071	132	18	(	(	PUNCT
ejpam-7071	132	19	ρ−	ρ−	NOUN
ejpam-7071	132	20	1	1	NUM
ejpam-7071	132	21	)	)	PUNCT
ejpam-7071	132	22	(	(	PUNCT
ejpam-7071	132	23	ρ−	ρ−	NOUN
ejpam-7071	132	24	4	4	NUM
ejpam-7071	132	25	)	)	PUNCT
ejpam-7071	132	26	!	!	PUNCT
ejpam-7071	133	1	+	+	CCONJ
ejpam-7071	133	2	ℏ2(5−	ℏ2(5−	X
ejpam-7071	133	3	ℏ1	ℏ1	PROPN
ejpam-7071	133	4	)	)	PUNCT
ejpam-7071	133	5	+	+	CCONJ
ejpam-7071	134	1	1	1	NUM
ejpam-7071	134	2	n	n	DET
ejpam-7071	134	3	∞∑	∞∑	NUM
ejpam-7071	134	4	ρ=3	ρ=3	ADJ
ejpam-7071	134	5	1	1	X
ejpam-7071	134	6	(	(	PUNCT
ejpam-7071	134	7	ρ−	ρ−	NOUN
ejpam-7071	134	8	1	1	NUM
ejpam-7071	134	9	)	)	PUNCT
ejpam-7071	134	10	(	(	PUNCT
ejpam-7071	134	11	ρ−	ρ−	NOUN
ejpam-7071	134	12	3	3	NUM
ejpam-7071	134	13	)	)	PUNCT
ejpam-7071	134	14	!	!	PUNCT
ejpam-7071	135	1	+	+	CCONJ
ejpam-7071	135	2	2ℏ2(2−	2ℏ2(2−	NUM
ejpam-7071	135	3	ℏ1	ℏ1	PROPN
ejpam-7071	135	4	)	)	PUNCT
ejpam-7071	135	5	+	+	CCONJ
ejpam-7071	135	6	3−	3−	NUM
ejpam-7071	135	7	ℏ1	ℏ1	ADJ
ejpam-7071	135	8	n	n	CCONJ
ejpam-7071	135	9	∞∑	∞∑	NUM
ejpam-7071	135	10	ρ=2	ρ=2	SYM
ejpam-7071	135	11	1	1	NUM
ejpam-7071	135	12	(	(	PUNCT
ejpam-7071	135	13	ρ−	ρ−	NOUN
ejpam-7071	135	14	1	1	NUM
ejpam-7071	135	15	)	)	PUNCT
ejpam-7071	135	16	(	(	PUNCT
ejpam-7071	135	17	ρ−	ρ−	NOUN
ejpam-7071	135	18	2	2	NUM
ejpam-7071	135	19	)	)	PUNCT
ejpam-7071	135	20	!	!	PUNCT
ejpam-7071	136	1	+	+	CCONJ
ejpam-7071	136	2	1−	1−	NUM
ejpam-7071	136	3	ℏ1	ℏ1	PROPN
ejpam-7071	136	4	n	n	CCONJ
ejpam-7071	136	5	∞∑	∞∑	NUM
ejpam-7071	136	6	ρ=2	ρ=2	SYM
ejpam-7071	136	7	1	1	NUM
ejpam-7071	136	8	(	(	PUNCT
ejpam-7071	136	9	ρ−	ρ−	NOUN
ejpam-7071	136	10	1	1	NUM
ejpam-7071	136	11	)	)	PUNCT
ejpam-7071	136	12	(	(	PUNCT
ejpam-7071	136	13	ρ−	ρ−	NOUN
ejpam-7071	136	14	1	1	NUM
ejpam-7071	136	15	)	)	PUNCT
ejpam-7071	136	16	!	!	PUNCT
ejpam-7071	136	17	.	.	PUNCT
ejpam-7071	137	1	by	by	ADP
ejpam-7071	137	2	(	(	PUNCT
ejpam-7071	137	3	16	16	NUM
ejpam-7071	137	4	)	)	PUNCT
ejpam-7071	137	5	,	,	PUNCT
ejpam-7071	137	6	we	we	PRON
ejpam-7071	137	7	get	get	VERB
ejpam-7071	137	8	l(ℏ1	l(ℏ1	NOUN
ejpam-7071	137	9	,	,	PUNCT
ejpam-7071	137	10	ℏ2	ℏ2	NOUN
ejpam-7071	137	11	)	)	PUNCT
ejpam-7071	137	12	≤	≤	NOUN
ejpam-7071	137	13	32ℏ2	32ℏ2	NUM
ejpam-7071	137	14	n	n	NOUN
ejpam-7071	137	15	∞∑	∞∑	NUM
ejpam-7071	137	16	ρ=4	ρ=4	NOUN
ejpam-7071	137	17	1	1	NUM
ejpam-7071	137	18	(	(	PUNCT
ejpam-7071	137	19	ρ−	ρ−	NOUN
ejpam-7071	137	20	1	1	NUM
ejpam-7071	137	21	)	)	PUNCT
ejpam-7071	137	22	2ρ	2ρ	NOUN
ejpam-7071	138	1	+	+	CCONJ
ejpam-7071	138	2	16	16	NUM
ejpam-7071	138	3	(	(	PUNCT
ejpam-7071	138	4	ℏ2(5−	ℏ2(5−	X
ejpam-7071	138	5	ℏ1	ℏ1	ADJ
ejpam-7071	138	6	)	)	PUNCT
ejpam-7071	138	7	+	+	NUM
ejpam-7071	138	8	1	1	X
ejpam-7071	138	9	)	)	PUNCT
ejpam-7071	138	10	n	n	NOUN
ejpam-7071	138	11	∞∑	∞∑	NUM
ejpam-7071	138	12	ρ=3	ρ=3	ADJ
ejpam-7071	138	13	1	1	X
ejpam-7071	138	14	(	(	PUNCT
ejpam-7071	138	15	ρ−	ρ−	NOUN
ejpam-7071	138	16	1	1	NUM
ejpam-7071	138	17	)	)	PUNCT
ejpam-7071	138	18	2ρ	2ρ	NOUN
ejpam-7071	138	19	+	+	CCONJ
ejpam-7071	138	20	8	8	NUM
ejpam-7071	138	21	(	(	PUNCT
ejpam-7071	138	22	2ℏ2(2−	2ℏ2(2−	NUM
ejpam-7071	138	23	ℏ1	ℏ1	PROPN
ejpam-7071	138	24	)	)	PUNCT
ejpam-7071	138	25	+	+	CCONJ
ejpam-7071	138	26	3−	3−	NUM
ejpam-7071	138	27	ℏ1	ℏ1	ADJ
ejpam-7071	138	28	)	)	PUNCT
ejpam-7071	138	29	n	n	NOUN
ejpam-7071	138	30	∞∑	∞∑	NUM
ejpam-7071	138	31	ρ=2	ρ=2	SYM
ejpam-7071	138	32	1	1	NUM
ejpam-7071	138	33	(	(	PUNCT
ejpam-7071	138	34	ρ−	ρ−	NOUN
ejpam-7071	138	35	1	1	NUM
ejpam-7071	138	36	)	)	PUNCT
ejpam-7071	138	37	2ρ	2ρ	NOUN
ejpam-7071	138	38	+	+	CCONJ
ejpam-7071	138	39	4	4	NUM
ejpam-7071	138	40	(	(	PUNCT
ejpam-7071	138	41	1−	1−	NUM
ejpam-7071	138	42	ℏ1	ℏ1	PROPN
ejpam-7071	138	43	)	)	PUNCT
ejpam-7071	138	44	n	n	NOUN
ejpam-7071	138	45	∞∑	∞∑	NUM
ejpam-7071	138	46	ρ=2	ρ=2	SYM
ejpam-7071	138	47	1	1	NUM
ejpam-7071	138	48	(	(	PUNCT
ejpam-7071	138	49	ρ−	ρ−	NOUN
ejpam-7071	138	50	1	1	NUM
ejpam-7071	138	51	)	)	PUNCT
ejpam-7071	138	52	2ρ	2ρ	NOUN
ejpam-7071	138	53	.	.	PUNCT
ejpam-7071	139	1	using	use	VERB
ejpam-7071	139	2	the	the	DET
ejpam-7071	139	3	series	series	NOUN
ejpam-7071	139	4	sums	sum	NOUN
ejpam-7071	139	5	(	(	PUNCT
ejpam-7071	139	6	11	11	NUM
ejpam-7071	139	7	)	)	PUNCT
ejpam-7071	139	8	,	,	PUNCT
ejpam-7071	139	9	(	(	PUNCT
ejpam-7071	139	10	12	12	NUM
ejpam-7071	139	11	)	)	PUNCT
ejpam-7071	139	12	and	and	CCONJ
ejpam-7071	139	13	(	(	PUNCT
ejpam-7071	139	14	13	13	NUM
ejpam-7071	139	15	)	)	PUNCT
ejpam-7071	139	16	,	,	PUNCT
ejpam-7071	139	17	we	we	PRON
ejpam-7071	139	18	get	get	VERB
ejpam-7071	139	19	l(ℏ1	l(ℏ1	NOUN
ejpam-7071	139	20	,	,	PUNCT
ejpam-7071	139	21	ℏ2	ℏ2	NOUN
ejpam-7071	139	22	)	)	PUNCT
ejpam-7071	140	1	=	=	PUNCT
ejpam-7071	140	2	ℏ2	ℏ2	NOUN
ejpam-7071	140	3	n	n	CCONJ
ejpam-7071	140	4	(	(	PUNCT
ejpam-7071	140	5	16	16	NUM
ejpam-7071	140	6	ln	ln	NUM
ejpam-7071	140	7	2−	2−	NUM
ejpam-7071	140	8	8−	8−	NUM
ejpam-7071	140	9	2	2	NUM
ejpam-7071	140	10	)	)	PUNCT
ejpam-7071	140	11	+	+	CCONJ
ejpam-7071	140	12	ℏ2(5−	ℏ2(5−	X
ejpam-7071	140	13	ℏ1	ℏ1	PROPN
ejpam-7071	140	14	)	)	PUNCT
ejpam-7071	140	15	+	+	CCONJ
ejpam-7071	140	16	1	1	NUM
ejpam-7071	140	17	n	n	NOUN
ejpam-7071	140	18	(	(	PUNCT
ejpam-7071	140	19	8	8	NUM
ejpam-7071	140	20	ln	ln	NOUN
ejpam-7071	140	21	2−	2−	NUM
ejpam-7071	140	22	4	4	NUM
ejpam-7071	140	23	)	)	PUNCT
ejpam-7071	140	24	a.	a.	NOUN
ejpam-7071	140	25	alameer	alameer	NOUN
ejpam-7071	140	26	et	et	PROPN
ejpam-7071	140	27	al	al	PROPN
ejpam-7071	140	28	.	.	PUNCT
ejpam-7071	140	29	/	/	SYM
ejpam-7071	140	30	eur	eur	PROPN
ejpam-7071	140	31	.	.	PUNCT
ejpam-7071	141	1	j.	j.	PROPN
ejpam-7071	141	2	pure	pure	PROPN
ejpam-7071	141	3	appl	appl	PROPN
ejpam-7071	141	4	.	.	PROPN
ejpam-7071	141	5	math	math	PROPN
ejpam-7071	141	6	,	,	PUNCT
ejpam-7071	141	7	18	18	NUM
ejpam-7071	141	8	(	(	PUNCT
ejpam-7071	141	9	4	4	NUM
ejpam-7071	141	10	)	)	PUNCT
ejpam-7071	141	11	(	(	PUNCT
ejpam-7071	141	12	2025	2025	NUM
ejpam-7071	141	13	)	)	PUNCT
ejpam-7071	141	14	,	,	PUNCT
ejpam-7071	141	15	7071	7071	NUM
ejpam-7071	141	16	7	7	NUM
ejpam-7071	141	17	of	of	ADP
ejpam-7071	141	18	11	11	NUM
ejpam-7071	141	19	+	+	CCONJ
ejpam-7071	141	20	2ℏ2(2−	2ℏ2(2−	NUM
ejpam-7071	141	21	ℏ1	ℏ1	PROPN
ejpam-7071	141	22	)	)	PUNCT
ejpam-7071	141	23	+	+	CCONJ
ejpam-7071	141	24	3−	3−	NUM
ejpam-7071	141	25	ℏ1	ℏ1	ADJ
ejpam-7071	141	26	n	n	CCONJ
ejpam-7071	141	27	(	(	PUNCT
ejpam-7071	141	28	4	4	NUM
ejpam-7071	141	29	ln	ln	NOUN
ejpam-7071	141	30	2	2	NUM
ejpam-7071	141	31	)	)	PUNCT
ejpam-7071	141	32	+	+	SYM
ejpam-7071	141	33	1−	1−	NUM
ejpam-7071	141	34	ℏ1	ℏ1	PROPN
ejpam-7071	141	35	n	n	CCONJ
ejpam-7071	141	36	(	(	PUNCT
ejpam-7071	141	37	2	2	NUM
ejpam-7071	141	38	ln	ln	NOUN
ejpam-7071	141	39	2	2	NUM
ejpam-7071	141	40	)	)	PUNCT
ejpam-7071	141	41	=	=	SYM
ejpam-7071	141	42	(	(	PUNCT
ejpam-7071	141	43	72ℏ2	72ℏ2	NUM
ejpam-7071	141	44	−	−	NUM
ejpam-7071	141	45	16ℏ1ℏ2	16ℏ1ℏ2	NUM
ejpam-7071	141	46	−	−	NUM
ejpam-7071	141	47	6ℏ1	6ℏ1	NUM
ejpam-7071	141	48	+	+	NUM
ejpam-7071	141	49	22	22	NUM
ejpam-7071	141	50	n	n	NOUN
ejpam-7071	141	51	)	)	PUNCT
ejpam-7071	142	1	ln	ln	ADV
ejpam-7071	142	2	2−	2−	NUM
ejpam-7071	142	3	30ℏ2	30ℏ2	NUM
ejpam-7071	142	4	+	+	NUM
ejpam-7071	142	5	4(1−	4(1−	NUM
ejpam-7071	142	6	ℏ1ℏ2	ℏ1ℏ2	NOUN
ejpam-7071	142	7	)	)	PUNCT
ejpam-7071	142	8	n	n	NOUN
ejpam-7071	142	9	.	.	PUNCT
ejpam-7071	143	1	but	but	CCONJ
ejpam-7071	143	2	this	this	DET
ejpam-7071	143	3	expression	expression	NOUN
ejpam-7071	143	4	is	be	AUX
ejpam-7071	143	5	bounded	bound	VERB
ejpam-7071	143	6	above	above	ADV
ejpam-7071	143	7	by	by	ADP
ejpam-7071	143	8	1−	1−	NUM
ejpam-7071	143	9	ℏ1	ℏ1	PROPN
ejpam-7071	143	10	if	if	SCONJ
ejpam-7071	144	1	and	and	CCONJ
ejpam-7071	144	2	only	only	ADV
ejpam-7071	144	3	if	if	SCONJ
ejpam-7071	144	4	(	(	PUNCT
ejpam-7071	144	5	17	17	NUM
ejpam-7071	144	6	)	)	PUNCT
ejpam-7071	144	7	holds	hold	VERB
ejpam-7071	144	8	.	.	PUNCT
ejpam-7071	145	1	3	3	X
ejpam-7071	145	2	.	.	X
ejpam-7071	145	3	an	an	DET
ejpam-7071	145	4	inclusion	inclusion	NOUN
ejpam-7071	145	5	property	property	NOUN
ejpam-7071	145	6	making	making	NOUN
ejpam-7071	145	7	use	use	NOUN
ejpam-7071	145	8	of	of	ADP
ejpam-7071	145	9	lemma	lemma	PROPN
ejpam-7071	145	10	2	2	NUM
ejpam-7071	145	11	,	,	PUNCT
ejpam-7071	145	12	we	we	PRON
ejpam-7071	145	13	will	will	AUX
ejpam-7071	145	14	study	study	VERB
ejpam-7071	145	15	the	the	DET
ejpam-7071	145	16	action	action	NOUN
ejpam-7071	145	17	of	of	ADP
ejpam-7071	145	18	the	the	DET
ejpam-7071	145	19	function	function	NOUN
ejpam-7071	145	20	iin(z	iin(z	NOUN
ejpam-7071	145	21	)	)	PUNCT
ejpam-7071	145	22	on	on	ADP
ejpam-7071	145	23	the	the	DET
ejpam-7071	145	24	class	class	NOUN
ejpam-7071	145	25	f(ℏ1	f(ℏ1	NOUN
ejpam-7071	145	26	,	,	PUNCT
ejpam-7071	145	27	ℏ2	ℏ2	NOUN
ejpam-7071	145	28	)	)	PUNCT
ejpam-7071	145	29	.	.	PUNCT
ejpam-7071	146	1	theorem	theorem	NOUN
ejpam-7071	146	2	2	2	NUM
ejpam-7071	146	3	.	.	PUNCT
ejpam-7071	147	1	let	let	VERB
ejpam-7071	147	2	ℏ1	ℏ1	NOUN
ejpam-7071	147	3	,	,	PUNCT
ejpam-7071	147	4	ℏ2	ℏ2	NOUN
ejpam-7071	147	5	∈	∈	PROPN
ejpam-7071	148	1	[	[	X
ejpam-7071	148	2	0	0	NUM
ejpam-7071	148	3	,	,	PUNCT
ejpam-7071	148	4	1	1	NUM
ejpam-7071	148	5	)	)	PUNCT
ejpam-7071	148	6	and	and	CCONJ
ejpam-7071	148	7	n	n	PRON
ejpam-7071	148	8	∈	∈	PROPN
ejpam-7071	148	9	n.	n.	NOUN
ejpam-7071	148	10	if	if	SCONJ
ejpam-7071	148	11	g	g	PROPN
ejpam-7071	148	12	∈	∈	PROPN
ejpam-7071	148	13	gτ	gτ	PROPN
ejpam-7071	148	14	(	(	PUNCT
ejpam-7071	148	15	a1	a1	PROPN
ejpam-7071	148	16	,	,	PUNCT
ejpam-7071	148	17	a2	a2	PROPN
ejpam-7071	148	18	)	)	PUNCT
ejpam-7071	148	19	,	,	PUNCT
ejpam-7071	148	20	then	then	ADV
ejpam-7071	148	21	iin(z	iin(z	VERB
ejpam-7071	148	22	)	)	PUNCT
ejpam-7071	148	23	is	be	AUX
ejpam-7071	148	24	in	in	ADP
ejpam-7071	148	25	the	the	DET
ejpam-7071	148	26	class	class	NOUN
ejpam-7071	148	27	f(ℏ1	f(ℏ1	NOUN
ejpam-7071	148	28	,	,	PUNCT
ejpam-7071	148	29	ℏ2	ℏ2	NOUN
ejpam-7071	148	30	)	)	PUNCT
ejpam-7071	148	31	if	if	SCONJ
ejpam-7071	148	32	(	(	PUNCT
ejpam-7071	148	33	8ℏ2	8ℏ2	NUM
ejpam-7071	148	34	−	−	NOUN
ejpam-7071	148	35	2ℏ1ℏ2	2ℏ1ℏ2	NUM
ejpam-7071	148	36	−	−	PROPN
ejpam-7071	148	37	ℏ1	ℏ1	PROPN
ejpam-7071	148	38	+	+	CCONJ
ejpam-7071	148	39	3	3	X
ejpam-7071	148	40	)	)	PUNCT
ejpam-7071	148	41	ln	ln	NOUN
ejpam-7071	148	42	2−	2−	NUM
ejpam-7071	148	43	2ℏ2	2ℏ2	NUM
ejpam-7071	148	44	≤	≤	NUM
ejpam-7071	148	45	n	n	CCONJ
ejpam-7071	148	46	(	(	PUNCT
ejpam-7071	148	47	1−	1−	NUM
ejpam-7071	148	48	γ	γ	NOUN
ejpam-7071	148	49	)	)	PUNCT
ejpam-7071	148	50	2(a1	2(a1	NUM
ejpam-7071	148	51	−a2)|τ	−a2)|τ	NOUN
ejpam-7071	149	1	|	|	ADV
ejpam-7071	149	2	.	.	PUNCT
ejpam-7071	150	1	(	(	PUNCT
ejpam-7071	150	2	21	21	NUM
ejpam-7071	150	3	)	)	PUNCT
ejpam-7071	150	4	proof	proof	NOUN
ejpam-7071	150	5	.	.	PUNCT
ejpam-7071	151	1	in	in	ADP
ejpam-7071	151	2	view	view	NOUN
ejpam-7071	151	3	of	of	ADP
ejpam-7071	151	4	lemma	lemma	PROPN
ejpam-7071	151	5	1	1	NUM
ejpam-7071	151	6	,	,	PUNCT
ejpam-7071	151	7	it	it	PRON
ejpam-7071	151	8	suffices	suffice	VERB
ejpam-7071	151	9	to	to	PART
ejpam-7071	151	10	show	show	VERB
ejpam-7071	151	11	that	that	SCONJ
ejpam-7071	151	12	m(ℏ1	m(ℏ1	ADJ
ejpam-7071	151	13	,	,	PUNCT
ejpam-7071	151	14	ℏ2	ℏ2	NOUN
ejpam-7071	151	15	)	)	PUNCT
ejpam-7071	151	16	:	:	PUNCT
ejpam-7071	152	1	=	=	NOUN
ejpam-7071	152	2	∞∑	∞∑	NUM
ejpam-7071	152	3	ρ=2	ρ=2	PUNCT
ejpam-7071	152	4	ρ(ρ−	ρ(ρ−	ADJ
ejpam-7071	152	5	ℏ1	ℏ1	PROPN
ejpam-7071	152	6	)	)	PUNCT
ejpam-7071	152	7	(	(	PUNCT
ejpam-7071	152	8	ℏ2(ρ−	ℏ2(ρ−	ADJ
ejpam-7071	152	9	1	1	X
ejpam-7071	152	10	)	)	PUNCT
ejpam-7071	152	11	+	+	CCONJ
ejpam-7071	152	12	1	1	X
ejpam-7071	152	13	)	)	SYM
ejpam-7071	152	14	1	1	NUM
ejpam-7071	152	15	(	(	PUNCT
ejpam-7071	152	16	(	(	PUNCT
ejpam-7071	152	17	ρ−	ρ−	NOUN
ejpam-7071	152	18	1)n+	1)n+	NUM
ejpam-7071	152	19	1	1	NUM
ejpam-7071	152	20	)	)	PUNCT
ejpam-7071	152	21	(	(	PUNCT
ejpam-7071	152	22	ρ−	ρ−	NOUN
ejpam-7071	152	23	1	1	NUM
ejpam-7071	152	24	)	)	PUNCT
ejpam-7071	152	25	!	!	PUNCT
ejpam-7071	153	1	|aρ|	|aρ|	ADJ
ejpam-7071	153	2	≤	≤	NOUN
ejpam-7071	153	3	1−	1−	NUM
ejpam-7071	153	4	γ	γ	X
ejpam-7071	153	5	.	.	PUNCT
ejpam-7071	154	1	since	since	SCONJ
ejpam-7071	154	2	g	g	PROPN
ejpam-7071	154	3	∈	∈	PROPN
ejpam-7071	154	4	gτ	gτ	PROPN
ejpam-7071	154	5	(	(	PUNCT
ejpam-7071	154	6	a1	a1	PROPN
ejpam-7071	154	7	,	,	PUNCT
ejpam-7071	154	8	a2	a2	PROPN
ejpam-7071	154	9	)	)	PUNCT
ejpam-7071	154	10	,	,	PUNCT
ejpam-7071	154	11	then	then	ADV
ejpam-7071	154	12	by	by	ADP
ejpam-7071	154	13	lemma	lemma	PROPN
ejpam-7071	154	14	2	2	NUM
ejpam-7071	154	15	,	,	PUNCT
ejpam-7071	154	16	we	we	PRON
ejpam-7071	154	17	have	have	VERB
ejpam-7071	154	18	|aρ|	|aρ|	ADJ
ejpam-7071	154	19	≤	≤	NOUN
ejpam-7071	154	20	(	(	PUNCT
ejpam-7071	154	21	a1	a1	NOUN
ejpam-7071	154	22	−a2	−a2	PROPN
ejpam-7071	154	23	)	)	PUNCT
ejpam-7071	154	24	|τ	|τ	PROPN
ejpam-7071	154	25	|	|	NOUN
ejpam-7071	154	26	ρ	ρ	NOUN
ejpam-7071	154	27	.	.	PUNCT
ejpam-7071	155	1	(	(	PUNCT
ejpam-7071	155	2	22	22	NUM
ejpam-7071	155	3	)	)	PUNCT
ejpam-7071	155	4	thus	thus	ADV
ejpam-7071	155	5	,	,	PUNCT
ejpam-7071	155	6	we	we	PRON
ejpam-7071	155	7	have	have	VERB
ejpam-7071	155	8	m(ℏ1	m(ℏ1	ADJ
ejpam-7071	155	9	,	,	PUNCT
ejpam-7071	155	10	ℏ2	ℏ2	NOUN
ejpam-7071	155	11	)	)	PUNCT
ejpam-7071	155	12	=	=	PUNCT
ejpam-7071	156	1	∞∑	∞∑	NUM
ejpam-7071	156	2	ρ=2	ρ=2	PUNCT
ejpam-7071	156	3	[	[	X
ejpam-7071	156	4	ℏ2ρ3	ℏ2ρ3	X
ejpam-7071	156	5	+	+	CCONJ
ejpam-7071	156	6	(	(	PUNCT
ejpam-7071	156	7	1−	1−	NUM
ejpam-7071	156	8	ℏ2(ℏ1	ℏ2(ℏ1	VERB
ejpam-7071	156	9	+	+	NUM
ejpam-7071	156	10	1))ρ2	1))ρ2	NUM
ejpam-7071	156	11	+	+	CCONJ
ejpam-7071	156	12	ℏ1(ℏ2	ℏ1(ℏ2	ADJ
ejpam-7071	156	13	−	−	PROPN
ejpam-7071	156	14	1))ρ	1))ρ	NUM
ejpam-7071	156	15	]	]	SYM
ejpam-7071	156	16	1	1	NUM
ejpam-7071	156	17	(	(	PUNCT
ejpam-7071	156	18	(	(	PUNCT
ejpam-7071	156	19	ρ−	ρ−	NOUN
ejpam-7071	156	20	1)n+	1)n+	NUM
ejpam-7071	156	21	1	1	NUM
ejpam-7071	156	22	)	)	PUNCT
ejpam-7071	156	23	(	(	PUNCT
ejpam-7071	156	24	ρ−	ρ−	NOUN
ejpam-7071	156	25	1	1	NUM
ejpam-7071	156	26	)	)	PUNCT
ejpam-7071	156	27	!	!	PUNCT
ejpam-7071	157	1	|aρ|	|aρ|	ADJ
ejpam-7071	157	2	≤	≤	NOUN
ejpam-7071	157	3	(	(	PUNCT
ejpam-7071	157	4	a1	a1	NOUN
ejpam-7071	157	5	−a2)|τ	−a2)|τ	NOUN
ejpam-7071	157	6	|	|	ADV
ejpam-7071	157	7	∞∑	∞∑	NUM
ejpam-7071	157	8	ρ=2	ρ=2	PUNCT
ejpam-7071	157	9	[	[	X
ejpam-7071	157	10	ℏ2ρ2	ℏ2ρ2	X
ejpam-7071	157	11	+	+	CCONJ
ejpam-7071	157	12	(	(	PUNCT
ejpam-7071	157	13	1−	1−	NUM
ejpam-7071	157	14	ℏ2(ℏ1	ℏ2(ℏ1	VERB
ejpam-7071	157	15	+	+	NUM
ejpam-7071	157	16	1))ρ	1))ρ	NUM
ejpam-7071	157	17	+	+	CCONJ
ejpam-7071	157	18	ℏ1(ℏ2	ℏ1(ℏ2	PRON
ejpam-7071	157	19	−	−	PROPN
ejpam-7071	157	20	1	1	NUM
ejpam-7071	157	21	)	)	PUNCT
ejpam-7071	157	22	)	)	PUNCT
ejpam-7071	157	23	]	]	PUNCT
ejpam-7071	157	24	1	1	X
ejpam-7071	157	25	(	(	PUNCT
ejpam-7071	157	26	(	(	PUNCT
ejpam-7071	157	27	ρ−	ρ−	NOUN
ejpam-7071	157	28	1)n+	1)n+	NUM
ejpam-7071	157	29	1	1	NUM
ejpam-7071	157	30	)	)	PUNCT
ejpam-7071	157	31	(	(	PUNCT
ejpam-7071	157	32	ρ−	ρ−	NOUN
ejpam-7071	157	33	1	1	NUM
ejpam-7071	157	34	)	)	PUNCT
ejpam-7071	157	35	!	!	PUNCT
ejpam-7071	157	36	.	.	PUNCT
ejpam-7071	158	1	by	by	ADP
ejpam-7071	158	2	(	(	PUNCT
ejpam-7071	158	3	18	18	NUM
ejpam-7071	158	4	)	)	PUNCT
ejpam-7071	158	5	and	and	CCONJ
ejpam-7071	158	6	(	(	PUNCT
ejpam-7071	158	7	19	19	NUM
ejpam-7071	158	8	)	)	PUNCT
ejpam-7071	158	9	,	,	PUNCT
ejpam-7071	158	10	we	we	PRON
ejpam-7071	158	11	get	get	VERB
ejpam-7071	158	12	m(ℏ1	m(ℏ1	ADJ
ejpam-7071	158	13	,	,	PUNCT
ejpam-7071	158	14	ℏ2	ℏ2	NOUN
ejpam-7071	158	15	)	)	PUNCT
ejpam-7071	158	16	≤	≤	NOUN
ejpam-7071	158	17	(	(	PUNCT
ejpam-7071	158	18	a1	a1	NOUN
ejpam-7071	158	19	−a2)|τ	−a2)|τ	NOUN
ejpam-7071	159	1	|	|	ADV
ejpam-7071	159	2	∞∑	∞∑	NUM
ejpam-7071	159	3	ρ=2	ρ=2	PUNCT
ejpam-7071	159	4	[	[	X
ejpam-7071	159	5	ℏ2(ρ−	ℏ2(ρ−	ADJ
ejpam-7071	159	6	1)(ρ−	1)(ρ−	NUM
ejpam-7071	159	7	2	2	NUM
ejpam-7071	159	8	)	)	PUNCT
ejpam-7071	159	9	+	+	CCONJ
ejpam-7071	159	10	(	(	PUNCT
ejpam-7071	159	11	ℏ2(2−	ℏ2(2−	PROPN
ejpam-7071	159	12	ℏ1	ℏ1	PROPN
ejpam-7071	159	13	)	)	PUNCT
ejpam-7071	159	14	+	+	CCONJ
ejpam-7071	159	15	1)(ρ−	1)(ρ−	NUM
ejpam-7071	159	16	1	1	NUM
ejpam-7071	159	17	)	)	PUNCT
ejpam-7071	159	18	+	+	CCONJ
ejpam-7071	159	19	1−	1−	NUM
ejpam-7071	159	20	ℏ1	ℏ1	PROPN
ejpam-7071	159	21	]	]	X
ejpam-7071	159	22	×	×	NOUN
ejpam-7071	159	23	1	1	NUM
ejpam-7071	159	24	(	(	PUNCT
ejpam-7071	159	25	(	(	PUNCT
ejpam-7071	159	26	ρ−	ρ−	NOUN
ejpam-7071	159	27	1)n+	1)n+	NUM
ejpam-7071	159	28	1	1	NUM
ejpam-7071	159	29	)	)	PUNCT
ejpam-7071	159	30	(	(	PUNCT
ejpam-7071	159	31	ρ−	ρ−	NOUN
ejpam-7071	159	32	1	1	NUM
ejpam-7071	159	33	)	)	PUNCT
ejpam-7071	159	34	!	!	PUNCT
ejpam-7071	160	1	=	=	PUNCT
ejpam-7071	161	1	(	(	PUNCT
ejpam-7071	161	2	a1	a1	NOUN
ejpam-7071	161	3	−a2)|τ	−a2)|τ	NOUN
ejpam-7071	162	1	|	|	ADV
ejpam-7071	162	2			PROPN
ejpam-7071	162	3	∞∑	∞∑	NUM
ejpam-7071	162	4	ρ=3	ρ=3	X
ejpam-7071	162	5	ℏ2	ℏ2	NOUN
ejpam-7071	162	6	(	(	PUNCT
ejpam-7071	162	7	(	(	PUNCT
ejpam-7071	162	8	ρ−	ρ−	NOUN
ejpam-7071	162	9	1)n+	1)n+	NUM
ejpam-7071	162	10	1	1	NUM
ejpam-7071	162	11	)	)	PUNCT
ejpam-7071	162	12	(	(	PUNCT
ejpam-7071	162	13	ρ−	ρ−	NOUN
ejpam-7071	162	14	3	3	NUM
ejpam-7071	162	15	)	)	PUNCT
ejpam-7071	162	16	!	!	PUNCT
ejpam-7071	163	1	+	+	PUNCT
ejpam-7071	163	2	∞∑	∞∑	NUM
ejpam-7071	163	3	ρ=2	ρ=2	NUM
ejpam-7071	163	4	ℏ2(2−	ℏ2(2−	NOUN
ejpam-7071	163	5	ℏ1	ℏ1	PROPN
ejpam-7071	163	6	)	)	PUNCT
ejpam-7071	163	7	+	+	NUM
ejpam-7071	163	8	1	1	NUM
ejpam-7071	163	9	(	(	PUNCT
ejpam-7071	163	10	(	(	PUNCT
ejpam-7071	163	11	ρ−	ρ−	NOUN
ejpam-7071	163	12	1)n+	1)n+	NUM
ejpam-7071	163	13	1	1	NUM
ejpam-7071	163	14	)	)	PUNCT
ejpam-7071	163	15	(	(	PUNCT
ejpam-7071	163	16	ρ−	ρ−	NOUN
ejpam-7071	163	17	2	2	NUM
ejpam-7071	163	18	)	)	PUNCT
ejpam-7071	163	19	!	!	PUNCT
ejpam-7071	164	1	a.	a.	PROPN
ejpam-7071	164	2	alameer	alameer	PROPN
ejpam-7071	164	3	et	et	PROPN
ejpam-7071	164	4	al	al	PROPN
ejpam-7071	164	5	.	.	PUNCT
ejpam-7071	164	6	/	/	SYM
ejpam-7071	164	7	eur	eur	PROPN
ejpam-7071	164	8	.	.	PUNCT
ejpam-7071	165	1	j.	j.	PROPN
ejpam-7071	165	2	pure	pure	PROPN
ejpam-7071	165	3	appl	appl	PROPN
ejpam-7071	165	4	.	.	PROPN
ejpam-7071	165	5	math	math	PROPN
ejpam-7071	165	6	,	,	PUNCT
ejpam-7071	165	7	18	18	NUM
ejpam-7071	165	8	(	(	PUNCT
ejpam-7071	165	9	4	4	NUM
ejpam-7071	165	10	)	)	PUNCT
ejpam-7071	165	11	(	(	PUNCT
ejpam-7071	165	12	2025	2025	NUM
ejpam-7071	165	13	)	)	PUNCT
ejpam-7071	165	14	,	,	PUNCT
ejpam-7071	165	15	7071	7071	NUM
ejpam-7071	165	16	8	8	NUM
ejpam-7071	165	17	of	of	ADP
ejpam-7071	165	18	11	11	NUM
ejpam-7071	165	19	+	+	CCONJ
ejpam-7071	165	20	∞∑	∞∑	NUM
ejpam-7071	165	21	ρ=2	ρ=2	SYM
ejpam-7071	165	22	1−	1−	NUM
ejpam-7071	165	23	ℏ1	ℏ1	PROPN
ejpam-7071	165	24	(	(	PUNCT
ejpam-7071	165	25	(	(	PUNCT
ejpam-7071	165	26	ρ−	ρ−	NOUN
ejpam-7071	165	27	1)n+	1)n+	NUM
ejpam-7071	165	28	1)ρ	1)ρ	NOUN
ejpam-7071	165	29	!	!	PUNCT
ejpam-7071	166	1			PROPN
ejpam-7071	166	2	.	.	PUNCT
ejpam-7071	167	1	by	by	ADP
ejpam-7071	167	2	(	(	PUNCT
ejpam-7071	167	3	15	15	NUM
ejpam-7071	167	4	)	)	PUNCT
ejpam-7071	167	5	and	and	CCONJ
ejpam-7071	167	6	(	(	PUNCT
ejpam-7071	167	7	16	16	NUM
ejpam-7071	167	8	)	)	PUNCT
ejpam-7071	167	9	,	,	PUNCT
ejpam-7071	167	10	we	we	PRON
ejpam-7071	167	11	get	get	VERB
ejpam-7071	167	12	m(ℏ1	m(ℏ1	ADJ
ejpam-7071	167	13	,	,	PUNCT
ejpam-7071	167	14	ℏ2	ℏ2	NOUN
ejpam-7071	167	15	)	)	PUNCT
ejpam-7071	167	16	≤	≤	NOUN
ejpam-7071	167	17	(	(	PUNCT
ejpam-7071	167	18	a1	a1	NOUN
ejpam-7071	167	19	−a2)|τ	−a2)|τ	NOUN
ejpam-7071	168	1	|	|	ADV
ejpam-7071	168	2	n	n	PRON
ejpam-7071	168	3	16	16	VERB
ejpam-7071	168	4	∞∑	∞∑	NUM
ejpam-7071	168	5	ρ=3	ρ=3	X
ejpam-7071	169	1	ℏ2	ℏ2	NOUN
ejpam-7071	169	2	(	(	PUNCT
ejpam-7071	169	3	ρ−	ρ−	NOUN
ejpam-7071	169	4	1	1	NUM
ejpam-7071	169	5	)	)	PUNCT
ejpam-7071	169	6	2ρ	2ρ	NOUN
ejpam-7071	169	7	+	+	CCONJ
ejpam-7071	169	8	8	8	NUM
ejpam-7071	169	9	∞∑	∞∑	NUM
ejpam-7071	169	10	ρ=2	ρ=2	PUNCT
ejpam-7071	169	11	ℏ2(2−	ℏ2(2−	NOUN
ejpam-7071	169	12	ℏ1	ℏ1	PROPN
ejpam-7071	169	13	)	)	PUNCT
ejpam-7071	169	14	+	+	NUM
ejpam-7071	169	15	1	1	NUM
ejpam-7071	169	16	(	(	PUNCT
ejpam-7071	169	17	ρ−	ρ−	NOUN
ejpam-7071	169	18	1	1	NUM
ejpam-7071	169	19	)	)	PUNCT
ejpam-7071	169	20	2ρ	2ρ	NOUN
ejpam-7071	169	21	+	+	CCONJ
ejpam-7071	169	22	4	4	NUM
ejpam-7071	169	23	∞∑	∞∑	NUM
ejpam-7071	169	24	ρ=2	ρ=2	SYM
ejpam-7071	169	25	1−	1−	NUM
ejpam-7071	169	26	ℏ1	ℏ1	PROPN
ejpam-7071	169	27	(	(	PUNCT
ejpam-7071	169	28	ρ−	ρ−	NOUN
ejpam-7071	169	29	1	1	NUM
ejpam-7071	169	30	)	)	PUNCT
ejpam-7071	169	31	2ρ	2ρ	NOUN
ejpam-7071	169	32			PROPN
ejpam-7071	169	33	.	.	PUNCT
ejpam-7071	170	1	by	by	ADP
ejpam-7071	170	2	(	(	PUNCT
ejpam-7071	170	3	11	11	NUM
ejpam-7071	170	4	)	)	PUNCT
ejpam-7071	170	5	and	and	CCONJ
ejpam-7071	170	6	(	(	PUNCT
ejpam-7071	170	7	12	12	NUM
ejpam-7071	170	8	)	)	PUNCT
ejpam-7071	170	9	,	,	PUNCT
ejpam-7071	170	10	we	we	PRON
ejpam-7071	170	11	get	get	VERB
ejpam-7071	170	12	m(ℏ1	m(ℏ1	ADJ
ejpam-7071	170	13	,	,	PUNCT
ejpam-7071	170	14	ℏ2	ℏ2	NOUN
ejpam-7071	170	15	)	)	PUNCT
ejpam-7071	170	16	≤	≤	NOUN
ejpam-7071	170	17	(	(	PUNCT
ejpam-7071	170	18	a1	a1	NOUN
ejpam-7071	170	19	−a2)|τ	−a2)|τ	NOUN
ejpam-7071	171	1	|	|	ADV
ejpam-7071	172	1	n	n	CCONJ
ejpam-7071	173	1	[	[	X
ejpam-7071	173	2	2	2	NUM
ejpam-7071	173	3	(	(	PUNCT
ejpam-7071	173	4	8ℏ2	8ℏ2	NUM
ejpam-7071	173	5	−	−	NOUN
ejpam-7071	173	6	2ℏ1ℏ2	2ℏ1ℏ2	NUM
ejpam-7071	173	7	−	−	PROPN
ejpam-7071	174	1	ℏ1	ℏ1	PROPN
ejpam-7071	174	2	+	+	CCONJ
ejpam-7071	174	3	3	3	X
ejpam-7071	174	4	)	)	PUNCT
ejpam-7071	174	5	ln	ln	NOUN
ejpam-7071	174	6	2−	2−	NUM
ejpam-7071	174	7	4ℏ2	4ℏ2	NUM
ejpam-7071	174	8	]	]	PUNCT
ejpam-7071	174	9	.	.	PUNCT
ejpam-7071	175	1	but	but	CCONJ
ejpam-7071	175	2	this	this	DET
ejpam-7071	175	3	last	last	ADJ
ejpam-7071	175	4	expression	expression	NOUN
ejpam-7071	175	5	is	be	AUX
ejpam-7071	175	6	bounded	bound	VERB
ejpam-7071	175	7	by	by	ADP
ejpam-7071	175	8	1−	1−	NUM
ejpam-7071	175	9	ℏ1	ℏ1	PROPN
ejpam-7071	175	10	,	,	PUNCT
ejpam-7071	175	11	if	if	SCONJ
ejpam-7071	175	12	(	(	PUNCT
ejpam-7071	175	13	21	21	NUM
ejpam-7071	175	14	)	)	PUNCT
ejpam-7071	175	15	holds	hold	VERB
ejpam-7071	175	16	.	.	PUNCT
ejpam-7071	176	1	4	4	X
ejpam-7071	176	2	.	.	X
ejpam-7071	176	3	an	an	DET
ejpam-7071	176	4	integral	integral	ADJ
ejpam-7071	176	5	operator	operator	NOUN
ejpam-7071	176	6	theorem	theorem	VERB
ejpam-7071	176	7	3	3	X
ejpam-7071	176	8	.	.	PUNCT
ejpam-7071	177	1	let	let	VERB
ejpam-7071	177	2	ℏ1	ℏ1	NOUN
ejpam-7071	177	3	,	,	PUNCT
ejpam-7071	177	4	ℏ2	ℏ2	NOUN
ejpam-7071	177	5	∈	∈	PROPN
ejpam-7071	178	1	[	[	X
ejpam-7071	178	2	0	0	NUM
ejpam-7071	178	3	,	,	PUNCT
ejpam-7071	178	4	1	1	NUM
ejpam-7071	178	5	)	)	PUNCT
ejpam-7071	178	6	and	and	CCONJ
ejpam-7071	178	7	n	n	PRON
ejpam-7071	178	8	∈	∈	NOUN
ejpam-7071	178	9	n.the	n.the	DET
ejpam-7071	178	10	integral	integral	ADJ
ejpam-7071	178	11	operator	operator	NOUN
ejpam-7071	178	12	gin(z	gin(z	PROPN
ejpam-7071	178	13	)	)	PUNCT
ejpam-7071	178	14	:	:	PUNCT
ejpam-7071	179	1	=	=	PUNCT
ejpam-7071	179	2	∫	∫	PROPN
ejpam-7071	180	1	z	z	NOUN
ejpam-7071	180	2	0	0	NUM
ejpam-7071	180	3	ϖin(t	ϖin(t	NUM
ejpam-7071	180	4	)	)	PUNCT
ejpam-7071	180	5	t	t	NOUN
ejpam-7071	180	6	dt	dt	PROPN
ejpam-7071	180	7	,	,	PUNCT
ejpam-7071	180	8	z	z	PROPN
ejpam-7071	180	9	∈	∈	PROPN
ejpam-7071	180	10	∆	∆	X
ejpam-7071	180	11	,	,	PUNCT
ejpam-7071	180	12	(	(	PUNCT
ejpam-7071	180	13	23	23	NUM
ejpam-7071	180	14	)	)	PUNCT
ejpam-7071	180	15	is	be	AUX
ejpam-7071	180	16	in	in	ADP
ejpam-7071	180	17	the	the	DET
ejpam-7071	180	18	class	class	NOUN
ejpam-7071	180	19	f(ℏ1	f(ℏ1	NOUN
ejpam-7071	180	20	,	,	PUNCT
ejpam-7071	180	21	ℏ2	ℏ2	NOUN
ejpam-7071	180	22	)	)	PUNCT
ejpam-7071	180	23	if	if	SCONJ
ejpam-7071	181	1	and	and	CCONJ
ejpam-7071	181	2	only	only	ADV
ejpam-7071	181	3	if	if	SCONJ
ejpam-7071	181	4	the	the	DET
ejpam-7071	181	5	inequality	inequality	NOUN
ejpam-7071	181	6	(	(	PUNCT
ejpam-7071	181	7	8ℏ2	8ℏ2	NUM
ejpam-7071	181	8	−	−	NOUN
ejpam-7071	181	9	2ℏ1ℏ2	2ℏ1ℏ2	NUM
ejpam-7071	181	10	−	−	PROPN
ejpam-7071	181	11	ℏ1	ℏ1	PROPN
ejpam-7071	181	12	+	+	CCONJ
ejpam-7071	181	13	3	3	X
ejpam-7071	181	14	)	)	PUNCT
ejpam-7071	181	15	ln	ln	NOUN
ejpam-7071	181	16	2−	2−	NUM
ejpam-7071	181	17	2ℏ2	2ℏ2	NUM
ejpam-7071	181	18	≤	≤	NUM
ejpam-7071	181	19	n	n	CCONJ
ejpam-7071	181	20	(	(	PUNCT
ejpam-7071	181	21	1−	1−	NUM
ejpam-7071	181	22	γ	γ	NOUN
ejpam-7071	181	23	)	)	PUNCT
ejpam-7071	181	24	2	2	NUM
ejpam-7071	181	25	(	(	PUNCT
ejpam-7071	181	26	24	24	NUM
ejpam-7071	181	27	)	)	PUNCT
ejpam-7071	181	28	holds	hold	VERB
ejpam-7071	181	29	.	.	PUNCT
ejpam-7071	182	1	proof	proof	NOUN
ejpam-7071	182	2	.	.	PUNCT
ejpam-7071	183	1	according	accord	VERB
ejpam-7071	183	2	to	to	ADP
ejpam-7071	183	3	(	(	PUNCT
ejpam-7071	183	4	9	9	X
ejpam-7071	183	5	)	)	PUNCT
ejpam-7071	183	6	it	it	PRON
ejpam-7071	183	7	follows	follow	VERB
ejpam-7071	183	8	that	that	SCONJ
ejpam-7071	183	9	gin(z	gin(z	PROPN
ejpam-7071	183	10	)	)	PUNCT
ejpam-7071	183	11	=	=	PUNCT
ejpam-7071	184	1	z	z	NOUN
ejpam-7071	185	1	−	−	NOUN
ejpam-7071	185	2	∞∑	∞∑	NUM
ejpam-7071	185	3	ρ=2	ρ=2	SYM
ejpam-7071	185	4	1	1	NUM
ejpam-7071	185	5	(	(	PUNCT
ejpam-7071	185	6	(	(	PUNCT
ejpam-7071	185	7	ρ−	ρ−	NOUN
ejpam-7071	185	8	1)n+	1)n+	NUM
ejpam-7071	185	9	1	1	NUM
ejpam-7071	185	10	)	)	PUNCT
ejpam-7071	185	11	(	(	PUNCT
ejpam-7071	185	12	ρ−	ρ−	NOUN
ejpam-7071	185	13	1	1	NUM
ejpam-7071	185	14	)	)	PUNCT
ejpam-7071	185	15	!	!	PUNCT
ejpam-7071	186	1	zρ	zρ	PROPN
ejpam-7071	186	2	ρ	ρ	PROPN
ejpam-7071	186	3	,	,	PUNCT
ejpam-7071	186	4	z	z	PROPN
ejpam-7071	186	5	∈	∈	PROPN
ejpam-7071	187	1	∆.	∆.	NOUN
ejpam-7071	187	2	using	use	VERB
ejpam-7071	187	3	lemma	lemma	PROPN
ejpam-7071	187	4	1	1	NUM
ejpam-7071	187	5	,	,	PUNCT
ejpam-7071	187	6	the	the	DET
ejpam-7071	187	7	function	function	NOUN
ejpam-7071	187	8	gin(z	gin(z	PROPN
ejpam-7071	187	9	)	)	PUNCT
ejpam-7071	187	10	belongs	belong	VERB
ejpam-7071	187	11	to	to	ADP
ejpam-7071	187	12	f(ℏ1	f(ℏ1	ADJ
ejpam-7071	187	13	,	,	PUNCT
ejpam-7071	187	14	ℏ2	ℏ2	NOUN
ejpam-7071	187	15	)	)	PUNCT
ejpam-7071	187	16	if	if	SCONJ
ejpam-7071	187	17	and	and	CCONJ
ejpam-7071	187	18	only	only	ADV
ejpam-7071	187	19	if	if	SCONJ
ejpam-7071	187	20	∞∑	∞∑	PRON
ejpam-7071	187	21	ρ=2	ρ=2	PUNCT
ejpam-7071	187	22	[	[	X
ejpam-7071	187	23	ρ(ρ−	ρ(ρ−	ADJ
ejpam-7071	187	24	ℏ1	ℏ1	NOUN
ejpam-7071	187	25	)	)	PUNCT
ejpam-7071	187	26	(	(	PUNCT
ejpam-7071	187	27	ℏ2(ρ−	ℏ2(ρ−	ADJ
ejpam-7071	187	28	1	1	X
ejpam-7071	187	29	)	)	PUNCT
ejpam-7071	187	30	+	+	CCONJ
ejpam-7071	187	31	1	1	NUM
ejpam-7071	187	32	)	)	PUNCT
ejpam-7071	187	33	]	]	PUNCT
ejpam-7071	188	1	1	1	NUM
ejpam-7071	188	2	ρ((ρ−	ρ((ρ−	PROPN
ejpam-7071	188	3	1)n+	1)n+	NUM
ejpam-7071	188	4	1	1	NUM
ejpam-7071	188	5	)	)	PUNCT
ejpam-7071	188	6	(	(	PUNCT
ejpam-7071	188	7	ρ−	ρ−	NOUN
ejpam-7071	188	8	1	1	NUM
ejpam-7071	188	9	)	)	PUNCT
ejpam-7071	188	10	!	!	PUNCT
ejpam-7071	189	1	≤	≤	NUM
ejpam-7071	189	2	1−	1−	NUM
ejpam-7071	189	3	ℏ1	ℏ1	PROPN
ejpam-7071	189	4	.	.	PUNCT
ejpam-7071	190	1	by	by	ADP
ejpam-7071	190	2	a	a	DET
ejpam-7071	190	3	similar	similar	ADJ
ejpam-7071	190	4	proof	proof	NOUN
ejpam-7071	190	5	of	of	ADP
ejpam-7071	190	6	theorem	theorem	NOUN
ejpam-7071	190	7	2	2	NUM
ejpam-7071	190	8	we	we	PRON
ejpam-7071	190	9	get	get	VERB
ejpam-7071	190	10	that	that	DET
ejpam-7071	190	11	gin	gin	NOUN
ejpam-7071	190	12	∈	∈	PROPN
ejpam-7071	190	13	f(ℏ1	f(ℏ1	NOUN
ejpam-7071	190	14	,	,	PUNCT
ejpam-7071	190	15	ℏ2	ℏ2	NOUN
ejpam-7071	190	16	)	)	PUNCT
ejpam-7071	190	17	if	if	SCONJ
ejpam-7071	190	18	and	and	CCONJ
ejpam-7071	190	19	only	only	ADV
ejpam-7071	190	20	if	if	SCONJ
ejpam-7071	190	21	(	(	PUNCT
ejpam-7071	190	22	24	24	NUM
ejpam-7071	190	23	)	)	PUNCT
ejpam-7071	190	24	holds	hold	VERB
ejpam-7071	190	25	.	.	PUNCT
ejpam-7071	191	1	we	we	PRON
ejpam-7071	191	2	obtain	obtain	VERB
ejpam-7071	191	3	many	many	ADJ
ejpam-7071	191	4	corollaries	corollary	NOUN
ejpam-7071	191	5	by	by	ADP
ejpam-7071	191	6	specializing	specialize	VERB
ejpam-7071	191	7	the	the	DET
ejpam-7071	191	8	parameters	parameter	NOUN
ejpam-7071	191	9	ℏ1	ℏ1	ADJ
ejpam-7071	191	10	and	and	CCONJ
ejpam-7071	191	11	ℏ2	ℏ2	NOUN
ejpam-7071	191	12	in	in	ADP
ejpam-7071	191	13	our	our	PRON
ejpam-7071	191	14	theorems	theorem	NOUN
ejpam-7071	191	15	,	,	PUNCT
ejpam-7071	191	16	for	for	ADP
ejpam-7071	191	17	example	example	NOUN
ejpam-7071	191	18	,	,	PUNCT
ejpam-7071	191	19	if	if	SCONJ
ejpam-7071	191	20	ℏ2	ℏ2	NOUN
ejpam-7071	191	21	=	=	SYM
ejpam-7071	191	22	0	0	NUM
ejpam-7071	191	23	,	,	PUNCT
ejpam-7071	191	24	we	we	PRON
ejpam-7071	191	25	get	get	VERB
ejpam-7071	191	26	the	the	DET
ejpam-7071	191	27	following	follow	VERB
ejpam-7071	191	28	corollary	corollary	NOUN
ejpam-7071	191	29	.	.	PUNCT
ejpam-7071	192	1	corollary	corollary	ADJ
ejpam-7071	192	2	1	1	NUM
ejpam-7071	192	3	.	.	PUNCT
ejpam-7071	193	1	if	if	SCONJ
ejpam-7071	193	2	n	n	PRON
ejpam-7071	193	3	∈	∈	PROPN
ejpam-7071	193	4	n	n	CCONJ
ejpam-7071	193	5	and	and	CCONJ
ejpam-7071	193	6	ℏ1	ℏ1	PROPN
ejpam-7071	193	7	∈	∈	PROPN
ejpam-7071	194	1	[	[	X
ejpam-7071	194	2	0	0	NUM
ejpam-7071	194	3	,	,	PUNCT
ejpam-7071	194	4	1	1	NUM
ejpam-7071	194	5	)	)	PUNCT
ejpam-7071	194	6	,	,	PUNCT
ejpam-7071	194	7	then	then	ADV
ejpam-7071	195	1	a.	a.	PROPN
ejpam-7071	195	2	alameer	alameer	PROPN
ejpam-7071	195	3	et	et	PROPN
ejpam-7071	195	4	al	al	PROPN
ejpam-7071	195	5	.	.	PUNCT
ejpam-7071	195	6	/	/	SYM
ejpam-7071	195	7	eur	eur	PROPN
ejpam-7071	195	8	.	.	PUNCT
ejpam-7071	196	1	j.	j.	PROPN
ejpam-7071	196	2	pure	pure	PROPN
ejpam-7071	196	3	appl	appl	PROPN
ejpam-7071	196	4	.	.	PROPN
ejpam-7071	196	5	math	math	PROPN
ejpam-7071	196	6	,	,	PUNCT
ejpam-7071	196	7	18	18	NUM
ejpam-7071	196	8	(	(	PUNCT
ejpam-7071	196	9	4	4	NUM
ejpam-7071	196	10	)	)	PUNCT
ejpam-7071	196	11	(	(	PUNCT
ejpam-7071	196	12	2025	2025	NUM
ejpam-7071	196	13	)	)	PUNCT
ejpam-7071	196	14	,	,	PUNCT
ejpam-7071	196	15	7071	7071	NUM
ejpam-7071	196	16	9	9	NUM
ejpam-7071	196	17	of	of	ADP
ejpam-7071	196	18	11	11	NUM
ejpam-7071	196	19	(	(	PUNCT
ejpam-7071	196	20	i	i	NOUN
ejpam-7071	196	21	)	)	PUNCT
ejpam-7071	196	22	ϖin	ϖin	PROPN
ejpam-7071	196	23	(	(	PUNCT
ejpam-7071	196	24	z	z	NOUN
ejpam-7071	196	25	)	)	PUNCT
ejpam-7071	196	26	∈	∈	PROPN
ejpam-7071	196	27	k(ℏ1	k(ℏ1	PROPN
ejpam-7071	196	28	)	)	PUNCT
ejpam-7071	197	1	if	if	SCONJ
ejpam-7071	197	2	and	and	CCONJ
ejpam-7071	197	3	only	only	ADV
ejpam-7071	197	4	if	if	SCONJ
ejpam-7071	197	5	[	[	X
ejpam-7071	197	6	22−	22−	NUM
ejpam-7071	197	7	6ℏ1	6ℏ1	NUM
ejpam-7071	197	8	]	]	PUNCT
ejpam-7071	197	9	ln	ln	NOUN
ejpam-7071	197	10	2−	2−	NUM
ejpam-7071	197	11	4	4	NUM
ejpam-7071	197	12	≤	≤	NUM
ejpam-7071	197	13	n	n	CCONJ
ejpam-7071	197	14	(	(	PUNCT
ejpam-7071	197	15	1−	1−	NUM
ejpam-7071	197	16	ℏ1	ℏ1	PROPN
ejpam-7071	197	17	)	)	PUNCT
ejpam-7071	197	18	.	.	PUNCT
ejpam-7071	198	1	(	(	PUNCT
ejpam-7071	198	2	ii	ii	NOUN
ejpam-7071	198	3	)	)	PUNCT
ejpam-7071	198	4	for	for	ADP
ejpam-7071	198	5	g	g	PROPN
ejpam-7071	198	6	∈	∈	PROPN
ejpam-7071	198	7	gτ	gτ	PROPN
ejpam-7071	198	8	(	(	PUNCT
ejpam-7071	198	9	a1	a1	PROPN
ejpam-7071	198	10	,	,	PUNCT
ejpam-7071	198	11	a2	a2	PROPN
ejpam-7071	198	12	)	)	PUNCT
ejpam-7071	198	13	,	,	PUNCT
ejpam-7071	198	14	iin(z	iin(z	PROPN
ejpam-7071	198	15	)	)	PUNCT
ejpam-7071	198	16	∈	∈	PROPN
ejpam-7071	198	17	k(ℏ1	k(ℏ1	PROPN
ejpam-7071	198	18	)	)	PUNCT
ejpam-7071	199	1	if	if	SCONJ
ejpam-7071	199	2	and	and	CCONJ
ejpam-7071	199	3	only	only	ADV
ejpam-7071	199	4	if	if	SCONJ
ejpam-7071	199	5	(	(	PUNCT
ejpam-7071	199	6	3−	3−	NUM
ejpam-7071	199	7	ℏ1	ℏ1	ADJ
ejpam-7071	199	8	)	)	PUNCT
ejpam-7071	199	9	ln	ln	ADJ
ejpam-7071	199	10	2	2	NUM
ejpam-7071	199	11	≤	≤	NOUN
ejpam-7071	199	12	n	n	CCONJ
ejpam-7071	199	13	(	(	PUNCT
ejpam-7071	199	14	1−	1−	NUM
ejpam-7071	199	15	ℏ1	ℏ1	PROPN
ejpam-7071	199	16	)	)	PUNCT
ejpam-7071	199	17	2(a1	2(a1	NUM
ejpam-7071	199	18	−a2)|τ	−a2)|τ	NOUN
ejpam-7071	199	19	|	|	ADV
ejpam-7071	199	20	.	.	PUNCT
ejpam-7071	200	1	(	(	PUNCT
ejpam-7071	200	2	iii	iii	X
ejpam-7071	200	3	)	)	PUNCT
ejpam-7071	200	4	gin(z	gin(z	PROPN
ejpam-7071	200	5	)	)	PUNCT
ejpam-7071	200	6	∈	∈	PROPN
ejpam-7071	200	7	k(ℏ1	k(ℏ1	PROPN
ejpam-7071	200	8	)	)	PUNCT
ejpam-7071	201	1	if	if	SCONJ
ejpam-7071	201	2	and	and	CCONJ
ejpam-7071	201	3	only	only	ADV
ejpam-7071	201	4	if	if	SCONJ
ejpam-7071	201	5	(	(	PUNCT
ejpam-7071	201	6	3−	3−	NUM
ejpam-7071	201	7	ℏ1	ℏ1	ADJ
ejpam-7071	201	8	)	)	PUNCT
ejpam-7071	201	9	ln	ln	ADJ
ejpam-7071	201	10	2	2	NUM
ejpam-7071	201	11	≤	≤	NOUN
ejpam-7071	201	12	n	n	CCONJ
ejpam-7071	201	13	(	(	PUNCT
ejpam-7071	201	14	1−	1−	NUM
ejpam-7071	201	15	ℏ1	ℏ1	PROPN
ejpam-7071	201	16	)	)	PUNCT
ejpam-7071	201	17	2	2	NUM
ejpam-7071	201	18	.	.	X
ejpam-7071	202	1	5	5	X
ejpam-7071	202	2	.	.	X
ejpam-7071	202	3	conclusion	conclusion	NOUN
ejpam-7071	202	4	for	for	ADP
ejpam-7071	202	5	the	the	DET
ejpam-7071	202	6	generalized	generalize	VERB
ejpam-7071	202	7	normalized	normalize	VERB
ejpam-7071	202	8	imaginary	imaginary	ADJ
ejpam-7071	202	9	error	error	NOUN
ejpam-7071	202	10	function	function	NOUN
ejpam-7071	202	11	ϖin	ϖin	NOUN
ejpam-7071	202	12	to	to	PART
ejpam-7071	202	13	belong	belong	VERB
ejpam-7071	202	14	to	to	ADP
ejpam-7071	202	15	the	the	DET
ejpam-7071	202	16	class	class	NOUN
ejpam-7071	202	17	f(ℏ1	f(ℏ1	NOUN
ejpam-7071	202	18	,	,	PUNCT
ejpam-7071	202	19	ℏ2	ℏ2	NOUN
ejpam-7071	202	20	)	)	PUNCT
ejpam-7071	202	21	of	of	ADP
ejpam-7071	202	22	analytic	analytic	ADJ
ejpam-7071	202	23	functions	function	NOUN
ejpam-7071	202	24	defined	define	VERB
ejpam-7071	202	25	on	on	ADP
ejpam-7071	202	26	the	the	DET
ejpam-7071	202	27	open	open	ADJ
ejpam-7071	202	28	unit	unit	NOUN
ejpam-7071	202	29	disk	disk	NOUN
ejpam-7071	202	30	∆	∆	PROPN
ejpam-7071	202	31	,	,	PUNCT
ejpam-7071	202	32	we	we	PRON
ejpam-7071	202	33	establish	establish	VERB
ejpam-7071	202	34	necessary	necessary	ADJ
ejpam-7071	202	35	and	and	CCONJ
ejpam-7071	202	36	sufficient	sufficient	ADJ
ejpam-7071	202	37	criteria	criterion	NOUN
ejpam-7071	202	38	.	.	PUNCT
ejpam-7071	203	1	we	we	PRON
ejpam-7071	203	2	also	also	ADV
ejpam-7071	203	3	investigate	investigate	VERB
ejpam-7071	203	4	the	the	DET
ejpam-7071	203	5	action	action	NOUN
ejpam-7071	203	6	of	of	ADP
ejpam-7071	203	7	the	the	DET
ejpam-7071	203	8	function	function	NOUN
ejpam-7071	203	9	iin(z	iin(z	NOUN
ejpam-7071	203	10	)	)	PUNCT
ejpam-7071	203	11	on	on	ADP
ejpam-7071	203	12	the	the	DET
ejpam-7071	203	13	class	class	NOUN
ejpam-7071	203	14	f(ℏ1	f(ℏ1	NOUN
ejpam-7071	203	15	,	,	PUNCT
ejpam-7071	203	16	ℏ2	ℏ2	NOUN
ejpam-7071	203	17	)	)	PUNCT
ejpam-7071	203	18	.	.	PUNCT
ejpam-7071	204	1	furthermore	furthermore	ADV
ejpam-7071	204	2	,	,	PUNCT
ejpam-7071	204	3	we	we	PRON
ejpam-7071	204	4	derive	derive	VERB
ejpam-7071	204	5	a	a	DET
ejpam-7071	204	6	necessary	necessary	ADJ
ejpam-7071	204	7	and	and	CCONJ
ejpam-7071	204	8	sufficient	sufficient	ADJ
ejpam-7071	204	9	condition	condition	NOUN
ejpam-7071	204	10	for	for	ADP
ejpam-7071	204	11	the	the	DET
ejpam-7071	204	12	integral	integral	ADJ
ejpam-7071	204	13	operator	operator	NOUN
ejpam-7071	204	14	gin(z	gin(z	PROPN
ejpam-7071	204	15	)	)	PUNCT
ejpam-7071	204	16	to	to	PART
ejpam-7071	204	17	lie	lie	VERB
ejpam-7071	204	18	in	in	ADP
ejpam-7071	204	19	the	the	DET
ejpam-7071	204	20	same	same	ADJ
ejpam-7071	204	21	class	class	NOUN
ejpam-7071	204	22	.	.	PUNCT
ejpam-7071	205	1	this	this	DET
ejpam-7071	205	2	study	study	NOUN
ejpam-7071	205	3	may	may	AUX
ejpam-7071	205	4	further	far	ADV
ejpam-7071	205	5	motivate	motivate	VERB
ejpam-7071	205	6	researchers	researcher	NOUN
ejpam-7071	205	7	to	to	PART
ejpam-7071	205	8	derive	derive	VERB
ejpam-7071	205	9	new	new	ADJ
ejpam-7071	205	10	criteria	criterion	NOUN
ejpam-7071	205	11	under	under	ADP
ejpam-7071	205	12	which	which	PRON
ejpam-7071	205	13	the	the	DET
ejpam-7071	205	14	generalized	generalize	VERB
ejpam-7071	205	15	normalized	normalize	VERB
ejpam-7071	205	16	imaginary	imaginary	ADJ
ejpam-7071	205	17	error	error	NOUN
ejpam-7071	205	18	function	function	NOUN
ejpam-7071	205	19	ϖin	ϖin	PROPN
ejpam-7071	205	20	belongs	belong	VERB
ejpam-7071	205	21	to	to	ADP
ejpam-7071	205	22	other	other	ADJ
ejpam-7071	205	23	families	family	NOUN
ejpam-7071	205	24	of	of	ADP
ejpam-7071	205	25	analytic	analytic	ADJ
ejpam-7071	205	26	functions	function	NOUN
ejpam-7071	205	27	defined	define	VERB
ejpam-7071	205	28	on	on	ADP
ejpam-7071	205	29	∆.	∆.	ADJ
ejpam-7071	205	30	references	reference	NOUN
ejpam-7071	205	31	[	[	X
ejpam-7071	205	32	1	1	NUM
ejpam-7071	205	33	]	]	PUNCT
ejpam-7071	205	34	m.	m.	NOUN
ejpam-7071	205	35	kamali	kamali	PROPN
ejpam-7071	205	36	and	and	CCONJ
ejpam-7071	205	37	s.	s.	PROPN
ejpam-7071	205	38	akbulut	akbulut	PROPN
ejpam-7071	205	39	.	.	PUNCT
ejpam-7071	206	1	on	on	ADP
ejpam-7071	206	2	a	a	DET
ejpam-7071	206	3	subclass	subclass	NOUN
ejpam-7071	206	4	of	of	ADP
ejpam-7071	206	5	certain	certain	ADJ
ejpam-7071	206	6	convex	convex	NOUN
ejpam-7071	206	7	functions	function	NOUN
ejpam-7071	206	8	with	with	ADP
ejpam-7071	206	9	negative	negative	ADJ
ejpam-7071	206	10	coefficients	coefficient	NOUN
ejpam-7071	206	11	.	.	PUNCT
ejpam-7071	207	1	applied	apply	VERB
ejpam-7071	207	2	mathematics	mathematic	NOUN
ejpam-7071	207	3	and	and	CCONJ
ejpam-7071	207	4	computation	computation	NOUN
ejpam-7071	207	5	,	,	PUNCT
ejpam-7071	207	6	145(2	145(2	NUM
ejpam-7071	207	7	-	-	SYM
ejpam-7071	207	8	3):341–350	3):341–350	NUM
ejpam-7071	207	9	,	,	PUNCT
ejpam-7071	207	10	2003	2003	NUM
ejpam-7071	207	11	.	.	PUNCT
ejpam-7071	208	1	[	[	X
ejpam-7071	208	2	2	2	X
ejpam-7071	208	3	]	]	PUNCT
ejpam-7071	208	4	h.	h.	PROPN
ejpam-7071	208	5	silverman	silverman	PROPN
ejpam-7071	208	6	.	.	PUNCT
ejpam-7071	209	1	univalent	univalent	ADJ
ejpam-7071	209	2	functions	function	NOUN
ejpam-7071	209	3	with	with	ADP
ejpam-7071	209	4	negative	negative	ADJ
ejpam-7071	209	5	coefficients	coefficient	NOUN
ejpam-7071	209	6	.	.	PUNCT
ejpam-7071	210	1	proceedings	proceeding	NOUN
ejpam-7071	210	2	of	of	ADP
ejpam-7071	210	3	the	the	DET
ejpam-7071	210	4	american	american	PROPN
ejpam-7071	210	5	mathematical	mathematical	PROPN
ejpam-7071	210	6	society	society	NOUN
ejpam-7071	210	7	,	,	PUNCT
ejpam-7071	210	8	51(1):109–116	51(1):109–116	PROPN
ejpam-7071	210	9	,	,	PUNCT
ejpam-7071	210	10	1975	1975	NUM
ejpam-7071	210	11	.	.	PUNCT
ejpam-7071	211	1	[	[	X
ejpam-7071	211	2	3	3	X
ejpam-7071	211	3	]	]	PUNCT
ejpam-7071	211	4	k.	k.	PROPN
ejpam-7071	211	5	k.	k.	PROPN
ejpam-7071	212	1	dixit	dixit	PROPN
ejpam-7071	212	2	and	and	CCONJ
ejpam-7071	212	3	s.	s.	PROPN
ejpam-7071	212	4	k.	k.	PROPN
ejpam-7071	212	5	pal	pal	PROPN
ejpam-7071	212	6	.	.	PUNCT
ejpam-7071	213	1	on	on	ADP
ejpam-7071	213	2	a	a	DET
ejpam-7071	213	3	class	class	NOUN
ejpam-7071	213	4	of	of	ADP
ejpam-7071	213	5	univalent	univalent	ADJ
ejpam-7071	213	6	functions	function	NOUN
ejpam-7071	213	7	related	relate	VERB
ejpam-7071	213	8	to	to	ADP
ejpam-7071	213	9	complex	complex	ADJ
ejpam-7071	213	10	order	order	NOUN
ejpam-7071	213	11	.	.	PUNCT
ejpam-7071	214	1	indian	indian	ADJ
ejpam-7071	214	2	journal	journal	PROPN
ejpam-7071	214	3	of	of	ADP
ejpam-7071	214	4	pure	pure	ADJ
ejpam-7071	214	5	and	and	CCONJ
ejpam-7071	214	6	applied	applied	ADJ
ejpam-7071	214	7	mathematics	mathematic	NOUN
ejpam-7071	214	8	,	,	PUNCT
ejpam-7071	214	9	26(9):889–896	26(9):889–896	PROPN
ejpam-7071	214	10	,	,	PUNCT
ejpam-7071	214	11	1995	1995	NUM
ejpam-7071	214	12	.	.	PUNCT
ejpam-7071	215	1	[	[	X
ejpam-7071	215	2	4	4	NUM
ejpam-7071	215	3	]	]	PUNCT
ejpam-7071	215	4	a.	a.	NOUN
ejpam-7071	215	5	a.	a.	PROPN
ejpam-7071	215	6	amourah	amourah	PROPN
ejpam-7071	215	7	,	,	PUNCT
ejpam-7071	215	8	f.	f.	PROPN
ejpam-7071	215	9	yousef	yousef	PROPN
ejpam-7071	215	10	,	,	PUNCT
ejpam-7071	215	11	t.	t.	PROPN
ejpam-7071	215	12	al	al	PROPN
ejpam-7071	215	13	-	-	PUNCT
ejpam-7071	215	14	hawary	hawary	PROPN
ejpam-7071	215	15	,	,	PUNCT
ejpam-7071	215	16	and	and	CCONJ
ejpam-7071	215	17	m.	m.	NOUN
ejpam-7071	215	18	darus	darus	NOUN
ejpam-7071	215	19	.	.	PUNCT
ejpam-7071	216	1	on	on	ADP
ejpam-7071	216	2	a	a	DET
ejpam-7071	216	3	class	class	NOUN
ejpam-7071	216	4	of	of	ADP
ejpam-7071	216	5	p	p	NOUN
ejpam-7071	216	6	valent	valent	NOUN
ejpam-7071	216	7	nonbazilevič	nonbazilevič	NOUN
ejpam-7071	216	8	functions	function	NOUN
ejpam-7071	216	9	of	of	ADP
ejpam-7071	216	10	order	order	NOUN
ejpam-7071	216	11	µ+	µ+	DET
ejpam-7071	216	12	iβ	iβ	PROPN
ejpam-7071	216	13	.	.	PROPN
ejpam-7071	216	14	international	international	ADJ
ejpam-7071	216	15	journal	journal	PROPN
ejpam-7071	216	16	of	of	ADP
ejpam-7071	216	17	mathematical	mathematical	ADJ
ejpam-7071	216	18	analysis	analysis	NOUN
ejpam-7071	216	19	,	,	PUNCT
ejpam-7071	216	20	10(15):701–710	10(15):701–710	NUM
ejpam-7071	216	21	,	,	PUNCT
ejpam-7071	216	22	2016	2016	NUM
ejpam-7071	216	23	.	.	PUNCT
ejpam-7071	217	1	[	[	X
ejpam-7071	217	2	5	5	NUM
ejpam-7071	217	3	]	]	PUNCT
ejpam-7071	217	4	a.	a.	NOUN
ejpam-7071	217	5	a.	a.	NOUN
ejpam-7071	217	6	attiya	attiya	PROPN
ejpam-7071	217	7	.	.	PUNCT
ejpam-7071	218	1	some	some	DET
ejpam-7071	218	2	applications	application	NOUN
ejpam-7071	218	3	of	of	ADP
ejpam-7071	218	4	mittag	mittag	ADJ
ejpam-7071	218	5	-	-	PUNCT
ejpam-7071	218	6	leffler	leffler	NOUN
ejpam-7071	218	7	function	function	NOUN
ejpam-7071	218	8	in	in	ADP
ejpam-7071	218	9	the	the	DET
ejpam-7071	218	10	unit	unit	NOUN
ejpam-7071	218	11	disk	disk	NOUN
ejpam-7071	218	12	.	.	PUNCT
ejpam-7071	219	1	filomat	filomat	PROPN
ejpam-7071	219	2	,	,	PUNCT
ejpam-7071	219	3	30(7):2075–2081	30(7):2075–2081	NUM
ejpam-7071	219	4	,	,	PUNCT
ejpam-7071	219	5	2016	2016	NUM
ejpam-7071	219	6	.	.	PUNCT
ejpam-7071	220	1	[	[	X
ejpam-7071	220	2	6	6	NUM
ejpam-7071	220	3	]	]	PUNCT
ejpam-7071	220	4	f.	f.	PROPN
ejpam-7071	220	5	yousef	yousef	PROPN
ejpam-7071	220	6	,	,	PUNCT
ejpam-7071	220	7	a.	a.	NOUN
ejpam-7071	220	8	a.	a.	PROPN
ejpam-7071	220	9	amourah	amourah	PROPN
ejpam-7071	220	10	,	,	PUNCT
ejpam-7071	220	11	and	and	CCONJ
ejpam-7071	220	12	m.	m.	NOUN
ejpam-7071	220	13	darus	darus	NOUN
ejpam-7071	220	14	.	.	PUNCT
ejpam-7071	221	1	differential	differential	ADJ
ejpam-7071	221	2	sandwich	sandwich	NOUN
ejpam-7071	221	3	theorems	theorem	NOUN
ejpam-7071	221	4	for	for	ADP
ejpam-7071	221	5	pvalent	pvalent	NOUN
ejpam-7071	221	6	functions	function	NOUN
ejpam-7071	221	7	associated	associate	VERB
ejpam-7071	221	8	with	with	ADP
ejpam-7071	221	9	a	a	DET
ejpam-7071	221	10	certain	certain	ADJ
ejpam-7071	221	11	generalized	generalized	ADJ
ejpam-7071	221	12	differential	differential	NOUN
ejpam-7071	221	13	operator	operator	NOUN
ejpam-7071	221	14	and	and	CCONJ
ejpam-7071	221	15	integral	integral	ADJ
ejpam-7071	221	16	operator	operator	NOUN
ejpam-7071	221	17	.	.	PUNCT
ejpam-7071	222	1	italian	italian	ADJ
ejpam-7071	222	2	journal	journal	NOUN
ejpam-7071	222	3	of	of	ADP
ejpam-7071	222	4	pure	pure	ADJ
ejpam-7071	222	5	and	and	CCONJ
ejpam-7071	222	6	applied	applied	ADJ
ejpam-7071	222	7	mathematics	mathematic	NOUN
ejpam-7071	222	8	,	,	PUNCT
ejpam-7071	222	9	36:543–556	36:543–556	NUM
ejpam-7071	222	10	,	,	PUNCT
ejpam-7071	222	11	2016	2016	NUM
ejpam-7071	222	12	.	.	PUNCT
ejpam-7071	223	1	[	[	X
ejpam-7071	223	2	7	7	X
ejpam-7071	223	3	]	]	X
ejpam-7071	223	4	m.	m.	NOUN
ejpam-7071	223	5	el	el	PROPN
ejpam-7071	223	6	-	-	PUNCT
ejpam-7071	223	7	ityan	ityan	NOUN
ejpam-7071	223	8	,	,	PUNCT
ejpam-7071	223	9	m.	m.	NOUN
ejpam-7071	223	10	a.	a.	PROPN
ejpam-7071	223	11	sabri	sabri	PROPN
ejpam-7071	223	12	,	,	PUNCT
ejpam-7071	223	13	h.	h.	PROPN
ejpam-7071	223	14	suha	suha	PROPN
ejpam-7071	223	15	,	,	PUNCT
ejpam-7071	223	16	b.	b.	PROPN
ejpam-7071	223	17	basem	basem	PROPN
ejpam-7071	223	18	,	,	PUNCT
ejpam-7071	223	19	t.	t.	PROPN
ejpam-7071	223	20	al	al	PROPN
ejpam-7071	223	21	-	-	PUNCT
ejpam-7071	223	22	hawary	hawary	PROPN
ejpam-7071	223	23	,	,	PUNCT
ejpam-7071	223	24	and	and	CCONJ
ejpam-7071	223	25	f.	f.	PROPN
ejpam-7071	223	26	yousef	yousef	PROPN
ejpam-7071	223	27	.	.	PUNCT
ejpam-7071	224	1	thirdorder	thirdorder	PROPN
ejpam-7071	224	2	hankel	hankel	NOUN
ejpam-7071	224	3	determinant	determinant	ADJ
ejpam-7071	224	4	for	for	ADP
ejpam-7071	224	5	a	a	DET
ejpam-7071	224	6	class	class	NOUN
ejpam-7071	224	7	of	of	ADP
ejpam-7071	224	8	bi	bi	ADJ
ejpam-7071	224	9	-	-	ADJ
ejpam-7071	224	10	univalent	univalent	ADJ
ejpam-7071	224	11	functions	function	NOUN
ejpam-7071	224	12	associated	associate	VERB
ejpam-7071	224	13	with	with	ADP
ejpam-7071	224	14	sine	sine	ADJ
ejpam-7071	224	15	function	function	NOUN
ejpam-7071	224	16	.	.	PUNCT
ejpam-7071	225	1	mathematics	mathematic	NOUN
ejpam-7071	225	2	,	,	PUNCT
ejpam-7071	225	3	13(17):2887	13(17):2887	NUM
ejpam-7071	225	4	,	,	PUNCT
ejpam-7071	225	5	2025	2025	NUM
ejpam-7071	225	6	.	.	PUNCT
ejpam-7071	226	1	[	[	X
ejpam-7071	226	2	8	8	NUM
ejpam-7071	226	3	]	]	PUNCT
ejpam-7071	226	4	t.	t.	PROPN
ejpam-7071	226	5	al	al	PROPN
ejpam-7071	226	6	-	-	PUNCT
ejpam-7071	226	7	hawary	hawary	PROPN
ejpam-7071	226	8	,	,	PUNCT
ejpam-7071	226	9	b.	b.	PROPN
ejpam-7071	226	10	a.	a.	PROPN
ejpam-7071	226	11	frasin	frasin	PROPN
ejpam-7071	226	12	,	,	PUNCT
ejpam-7071	226	13	and	and	CCONJ
ejpam-7071	226	14	f.	f.	PROPN
ejpam-7071	226	15	yousef	yousef	PROPN
ejpam-7071	226	16	.	.	PUNCT
ejpam-7071	227	1	coefficients	coefficient	NOUN
ejpam-7071	227	2	estimates	estimate	NOUN
ejpam-7071	227	3	for	for	ADP
ejpam-7071	227	4	certain	certain	ADJ
ejpam-7071	227	5	classes	class	NOUN
ejpam-7071	227	6	of	of	ADP
ejpam-7071	227	7	analytic	analytic	ADJ
ejpam-7071	227	8	functions	function	NOUN
ejpam-7071	227	9	of	of	ADP
ejpam-7071	227	10	complex	complex	ADJ
ejpam-7071	227	11	order	order	NOUN
ejpam-7071	227	12	.	.	PUNCT
ejpam-7071	228	1	afrika	afrika	ADJ
ejpam-7071	228	2	matematika	matematika	PROPN
ejpam-7071	228	3	,	,	PUNCT
ejpam-7071	228	4	29(7):1265–1271	29(7):1265–1271	NUM
ejpam-7071	228	5	,	,	PUNCT
ejpam-7071	228	6	2018	2018	NUM
ejpam-7071	228	7	.	.	PUNCT
ejpam-7071	229	1	a.	a.	NOUN
ejpam-7071	229	2	alameer	alameer	PROPN
ejpam-7071	229	3	et	et	PROPN
ejpam-7071	229	4	al	al	PROPN
ejpam-7071	229	5	.	.	PUNCT
ejpam-7071	229	6	/	/	SYM
ejpam-7071	229	7	eur	eur	PROPN
ejpam-7071	229	8	.	.	PUNCT
ejpam-7071	230	1	j.	j.	PROPN
ejpam-7071	230	2	pure	pure	PROPN
ejpam-7071	230	3	appl	appl	PROPN
ejpam-7071	230	4	.	.	PROPN
ejpam-7071	230	5	math	math	PROPN
ejpam-7071	230	6	,	,	PUNCT
ejpam-7071	230	7	18	18	NUM
ejpam-7071	230	8	(	(	PUNCT
ejpam-7071	230	9	4	4	NUM
ejpam-7071	230	10	)	)	PUNCT
ejpam-7071	230	11	(	(	PUNCT
ejpam-7071	230	12	2025	2025	NUM
ejpam-7071	230	13	)	)	PUNCT
ejpam-7071	230	14	,	,	PUNCT
ejpam-7071	230	15	7071	7071	NUM
ejpam-7071	230	16	10	10	NUM
ejpam-7071	230	17	of	of	ADP
ejpam-7071	230	18	11	11	NUM
ejpam-7071	230	19	[	[	X
ejpam-7071	230	20	9	9	NUM
ejpam-7071	230	21	]	]	PUNCT
ejpam-7071	230	22	a.	a.	NOUN
ejpam-7071	230	23	o.	o.	PROPN
ejpam-7071	230	24	mostafa	mostafa	PROPN
ejpam-7071	230	25	.	.	PUNCT
ejpam-7071	231	1	a	a	DET
ejpam-7071	231	2	study	study	NOUN
ejpam-7071	231	3	on	on	ADP
ejpam-7071	231	4	starlike	starlike	NOUN
ejpam-7071	231	5	and	and	CCONJ
ejpam-7071	231	6	convex	convex	NOUN
ejpam-7071	231	7	properties	property	NOUN
ejpam-7071	231	8	for	for	ADP
ejpam-7071	231	9	hypergeometric	hypergeometric	ADJ
ejpam-7071	231	10	functions	function	NOUN
ejpam-7071	231	11	.	.	PUNCT
ejpam-7071	232	1	j.	j.	PROPN
ejpam-7071	232	2	inequal	inequal	PROPN
ejpam-7071	232	3	.	.	PUNCT
ejpam-7071	233	1	pure	pure	ADJ
ejpam-7071	233	2	appl	appl	PROPN
ejpam-7071	233	3	.	.	PUNCT
ejpam-7071	233	4	math	math	PROPN
ejpam-7071	233	5	.	.	PUNCT
ejpam-7071	233	6	,	,	PUNCT
ejpam-7071	234	1	10(3):1–16	10(3):1–16	NUM
ejpam-7071	234	2	,	,	PUNCT
ejpam-7071	234	3	2009	2009	NUM
ejpam-7071	234	4	.	.	PUNCT
ejpam-7071	235	1	[	[	X
ejpam-7071	235	2	10	10	NUM
ejpam-7071	235	3	]	]	X
ejpam-7071	235	4	e.	e.	PROPN
ejpam-7071	235	5	merkes	merkes	PROPN
ejpam-7071	235	6	and	and	CCONJ
ejpam-7071	235	7	b.	b.	PROPN
ejpam-7071	235	8	t.	t.	PROPN
ejpam-7071	235	9	scott	scott	PROPN
ejpam-7071	235	10	.	.	PUNCT
ejpam-7071	236	1	starlike	starlike	ADJ
ejpam-7071	236	2	hypergeometric	hypergeometric	ADJ
ejpam-7071	236	3	functions	function	NOUN
ejpam-7071	236	4	.	.	PUNCT
ejpam-7071	237	1	proceedings	proceeding	NOUN
ejpam-7071	237	2	of	of	ADP
ejpam-7071	237	3	the	the	DET
ejpam-7071	237	4	american	american	PROPN
ejpam-7071	237	5	mathematical	mathematical	PROPN
ejpam-7071	237	6	society	society	NOUN
ejpam-7071	237	7	,	,	PUNCT
ejpam-7071	237	8	12(6):885–888	12(6):885–888	PROPN
ejpam-7071	237	9	,	,	PUNCT
ejpam-7071	237	10	1961	1961	NUM
ejpam-7071	237	11	.	.	PUNCT
ejpam-7071	238	1	[	[	X
ejpam-7071	238	2	11	11	NUM
ejpam-7071	238	3	]	]	PUNCT
ejpam-7071	238	4	m.	m.	NOUN
ejpam-7071	238	5	illafe	illafe	NOUN
ejpam-7071	238	6	,	,	PUNCT
ejpam-7071	238	7	a.	a.	PROPN
ejpam-7071	238	8	hussen	hussen	PROPN
ejpam-7071	238	9	,	,	PUNCT
ejpam-7071	238	10	m.	m.	NOUN
ejpam-7071	238	11	h.	h.	PROPN
ejpam-7071	238	12	mohd	mohd	PROPN
ejpam-7071	238	13	,	,	PUNCT
ejpam-7071	238	14	and	and	CCONJ
ejpam-7071	238	15	f.	f.	PROPN
ejpam-7071	238	16	yousef	yousef	PROPN
ejpam-7071	238	17	.	.	PUNCT
ejpam-7071	239	1	on	on	ADP
ejpam-7071	239	2	a	a	DET
ejpam-7071	239	3	subclass	subclass	NOUN
ejpam-7071	239	4	of	of	ADP
ejpam-7071	239	5	bi	bi	ADJ
ejpam-7071	239	6	-	-	ADJ
ejpam-7071	239	7	univalent	univalent	ADJ
ejpam-7071	239	8	functions	function	NOUN
ejpam-7071	239	9	affiliated	affiliate	VERB
ejpam-7071	239	10	with	with	ADP
ejpam-7071	239	11	bell	bell	NOUN
ejpam-7071	239	12	and	and	CCONJ
ejpam-7071	239	13	gegenbauer	gegenbauer	NOUN
ejpam-7071	239	14	polynomials	polynomial	NOUN
ejpam-7071	239	15	.	.	PUNCT
ejpam-7071	240	1	boletim	boletim	PROPN
ejpam-7071	240	2	da	da	PROPN
ejpam-7071	240	3	sociedade	sociedade	PROPN
ejpam-7071	240	4	paranaense	paranaense	PROPN
ejpam-7071	240	5	de	de	PROPN
ejpam-7071	240	6	matematica	matematica	PROPN
ejpam-7071	240	7	,	,	PUNCT
ejpam-7071	240	8	43:1–10	43:1–10	NOUN
ejpam-7071	240	9	,	,	PUNCT
ejpam-7071	240	10	2025	2025	NUM
ejpam-7071	240	11	.	.	PUNCT
ejpam-7071	241	1	[	[	X
ejpam-7071	241	2	12	12	NUM
ejpam-7071	241	3	]	]	PUNCT
ejpam-7071	241	4	m.	m.	NOUN
ejpam-7071	241	5	illafe	illafe	NOUN
ejpam-7071	241	6	,	,	PUNCT
ejpam-7071	241	7	m.	m.	NOUN
ejpam-7071	241	8	h.	h.	PROPN
ejpam-7071	241	9	mohd	mohd	PROPN
ejpam-7071	241	10	,	,	PUNCT
ejpam-7071	241	11	f.	f.	PROPN
ejpam-7071	241	12	yousef	yousef	PROPN
ejpam-7071	241	13	,	,	PUNCT
ejpam-7071	241	14	and	and	CCONJ
ejpam-7071	241	15	s.	s.	PROPN
ejpam-7071	241	16	supramaniam	supramaniam	PROPN
ejpam-7071	241	17	.	.	PUNCT
ejpam-7071	242	1	a	a	DET
ejpam-7071	242	2	subclass	subclass	NOUN
ejpam-7071	242	3	of	of	ADP
ejpam-7071	242	4	bi	bi	ADJ
ejpam-7071	242	5	-	-	ADJ
ejpam-7071	242	6	univalent	univalent	ADJ
ejpam-7071	242	7	functions	function	NOUN
ejpam-7071	242	8	defined	define	VERB
ejpam-7071	242	9	by	by	ADP
ejpam-7071	242	10	asymmetric	asymmetric	ADJ
ejpam-7071	242	11	q	q	ADJ
ejpam-7071	242	12	-	-	ADJ
ejpam-7071	242	13	derivative	derivative	ADJ
ejpam-7071	242	14	operator	operator	NOUN
ejpam-7071	242	15	and	and	CCONJ
ejpam-7071	242	16	gegenbauer	gegenbauer	NOUN
ejpam-7071	242	17	polynomials	polynomial	NOUN
ejpam-7071	242	18	.	.	PUNCT
ejpam-7071	243	1	european	european	PROPN
ejpam-7071	243	2	journal	journal	PROPN
ejpam-7071	243	3	of	of	ADP
ejpam-7071	243	4	pure	pure	ADJ
ejpam-7071	243	5	and	and	CCONJ
ejpam-7071	243	6	applied	applied	ADJ
ejpam-7071	243	7	mathematics	mathematic	NOUN
ejpam-7071	243	8	,	,	PUNCT
ejpam-7071	243	9	17(4):2467–2480	17(4):2467–2480	NUM
ejpam-7071	243	10	,	,	PUNCT
ejpam-7071	243	11	2024	2024	NUM
ejpam-7071	243	12	.	.	PUNCT
ejpam-7071	244	1	[	[	X
ejpam-7071	244	2	13	13	NUM
ejpam-7071	244	3	]	]	PUNCT
ejpam-7071	244	4	m.	m.	NOUN
ejpam-7071	244	5	illafe	illafe	NOUN
ejpam-7071	244	6	,	,	PUNCT
ejpam-7071	244	7	m.	m.	NOUN
ejpam-7071	244	8	haji	haji	PROPN
ejpam-7071	244	9	mohd	mohd	PROPN
ejpam-7071	244	10	,	,	PUNCT
ejpam-7071	244	11	f.	f.	PROPN
ejpam-7071	244	12	yousef	yousef	PROPN
ejpam-7071	244	13	,	,	PUNCT
ejpam-7071	244	14	and	and	CCONJ
ejpam-7071	244	15	s.	s.	PROPN
ejpam-7071	244	16	supramaniam	supramaniam	PROPN
ejpam-7071	244	17	.	.	PUNCT
ejpam-7071	245	1	bounds	bound	VERB
ejpam-7071	245	2	for	for	ADP
ejpam-7071	245	3	the	the	DET
ejpam-7071	245	4	second	second	ADJ
ejpam-7071	245	5	hankel	hankel	NOUN
ejpam-7071	245	6	determinant	determinant	ADJ
ejpam-7071	245	7	of	of	ADP
ejpam-7071	245	8	a	a	DET
ejpam-7071	245	9	general	general	ADJ
ejpam-7071	245	10	subclass	subclass	NOUN
ejpam-7071	245	11	of	of	ADP
ejpam-7071	245	12	bi	bi	ADJ
ejpam-7071	245	13	-	-	ADJ
ejpam-7071	245	14	univalent	univalent	ADJ
ejpam-7071	245	15	functions	function	NOUN
ejpam-7071	245	16	.	.	PUNCT
ejpam-7071	246	1	international	international	ADJ
ejpam-7071	246	2	journal	journal	PROPN
ejpam-7071	246	3	of	of	ADP
ejpam-7071	246	4	mathematics	mathematic	NOUN
ejpam-7071	246	5	,	,	PUNCT
ejpam-7071	246	6	engineering	engineering	NOUN
ejpam-7071	246	7	,	,	PUNCT
ejpam-7071	246	8	and	and	CCONJ
ejpam-7071	246	9	management	management	NOUN
ejpam-7071	246	10	sciences	science	NOUN
ejpam-7071	246	11	,	,	PUNCT
ejpam-7071	246	12	9(5):1226–1239	9(5):1226–1239	NUM
ejpam-7071	246	13	,	,	PUNCT
ejpam-7071	246	14	2024	2024	NUM
ejpam-7071	246	15	.	.	PUNCT
ejpam-7071	247	1	[	[	X
ejpam-7071	247	2	14	14	NUM
ejpam-7071	247	3	]	]	X
ejpam-7071	247	4	n.	n.	PROPN
ejpam-7071	247	5	e.	e.	PROPN
ejpam-7071	247	6	cho	cho	PROPN
ejpam-7071	247	7	,	,	PUNCT
ejpam-7071	247	8	s.	s.	PROPN
ejpam-7071	247	9	y.	y.	PROPN
ejpam-7071	247	10	woo	woo	PROPN
ejpam-7071	247	11	,	,	PUNCT
ejpam-7071	247	12	and	and	CCONJ
ejpam-7071	247	13	s.	s.	PROPN
ejpam-7071	247	14	owa	owa	PROPN
ejpam-7071	247	15	.	.	PROPN
ejpam-7071	247	16	uniform	uniform	PROPN
ejpam-7071	247	17	convexity	convexity	NOUN
ejpam-7071	247	18	properties	property	NOUN
ejpam-7071	247	19	for	for	ADP
ejpam-7071	247	20	hypergeometric	hypergeometric	ADJ
ejpam-7071	247	21	functions	function	NOUN
ejpam-7071	247	22	.	.	PUNCT
ejpam-7071	248	1	fractional	fractional	ADJ
ejpam-7071	248	2	calculus	calculus	NOUN
ejpam-7071	248	3	and	and	CCONJ
ejpam-7071	248	4	applied	apply	VERB
ejpam-7071	248	5	analysis	analysis	NOUN
ejpam-7071	248	6	,	,	PUNCT
ejpam-7071	248	7	5(3):303–314	5(3):303–314	NUM
ejpam-7071	248	8	,	,	PUNCT
ejpam-7071	248	9	2002	2002	NUM
ejpam-7071	248	10	.	.	PUNCT
ejpam-7071	249	1	[	[	X
ejpam-7071	249	2	15	15	X
ejpam-7071	249	3	]	]	PUNCT
ejpam-7071	249	4	t.	t.	PROPN
ejpam-7071	249	5	al	al	PROPN
ejpam-7071	249	6	-	-	PUNCT
ejpam-7071	249	7	hawary	hawary	PROPN
ejpam-7071	249	8	,	,	PUNCT
ejpam-7071	249	9	a.	a.	PROPN
ejpam-7071	249	10	amourah	amourah	PROPN
ejpam-7071	249	11	,	,	PUNCT
ejpam-7071	249	12	and	and	CCONJ
ejpam-7071	249	13	b.	b.	PROPN
ejpam-7071	249	14	a.	a.	PROPN
ejpam-7071	249	15	frasin	frasin	PROPN
ejpam-7071	249	16	.	.	PUNCT
ejpam-7071	250	1	fekete	fekete	PROPN
ejpam-7071	250	2	–	–	PUNCT
ejpam-7071	250	3	szegö	szegö	VERB
ejpam-7071	250	4	inequality	inequality	NOUN
ejpam-7071	250	5	for	for	ADP
ejpam-7071	250	6	bi	bi	ADJ
ejpam-7071	250	7	-	-	ADJ
ejpam-7071	250	8	univalent	univalent	ADJ
ejpam-7071	250	9	functions	function	NOUN
ejpam-7071	250	10	by	by	ADP
ejpam-7071	250	11	means	mean	NOUN
ejpam-7071	250	12	of	of	ADP
ejpam-7071	250	13	horadam	horadam	NOUN
ejpam-7071	250	14	polynomials	polynomial	NOUN
ejpam-7071	250	15	.	.	PUNCT
ejpam-7071	251	1	boletin	boletin	PROPN
ejpam-7071	251	2	de	de	X
ejpam-7071	251	3	la	la	PROPN
ejpam-7071	251	4	sociedad	sociedad	PROPN
ejpam-7071	251	5	matematica	matematica	PROPN
ejpam-7071	251	6	mexicana	mexicana	PROPN
ejpam-7071	251	7	,	,	PUNCT
ejpam-7071	251	8	27(3):79	27(3):79	NUM
ejpam-7071	251	9	,	,	PUNCT
ejpam-7071	251	10	2021	2021	NUM
ejpam-7071	251	11	.	.	PUNCT
ejpam-7071	252	1	[	[	X
ejpam-7071	252	2	16	16	NUM
ejpam-7071	252	3	]	]	X
ejpam-7071	252	4	m.	m.	NOUN
ejpam-7071	252	5	abramowitz	abramowitz	PROPN
ejpam-7071	252	6	and	and	CCONJ
ejpam-7071	252	7	i.	i.	PROPN
ejpam-7071	252	8	a.	a.	PROPN
ejpam-7071	252	9	stegun	stegun	PROPN
ejpam-7071	252	10	.	.	PUNCT
ejpam-7071	253	1	handbook	handbook	NOUN
ejpam-7071	253	2	of	of	ADP
ejpam-7071	253	3	mathematical	mathematical	ADJ
ejpam-7071	253	4	functions	function	NOUN
ejpam-7071	253	5	with	with	ADP
ejpam-7071	253	6	formulas	formula	NOUN
ejpam-7071	253	7	,	,	PUNCT
ejpam-7071	253	8	graphs	graph	NOUN
ejpam-7071	253	9	and	and	CCONJ
ejpam-7071	253	10	matematical	matematical	ADJ
ejpam-7071	253	11	tables	table	NOUN
ejpam-7071	253	12	.	.	PUNCT
ejpam-7071	254	1	dorer	dorer	PROPN
ejpam-7071	254	2	publications	publications	PROPN
ejpam-7071	254	3	inc	inc	PROPN
ejpam-7071	254	4	.	.	PROPN
ejpam-7071	254	5	,	,	PUNCT
ejpam-7071	254	6	new	new	PROPN
ejpam-7071	254	7	york	york	PROPN
ejpam-7071	254	8	,	,	PUNCT
ejpam-7071	254	9	1965	1965	NUM
ejpam-7071	255	1	.	.	PUNCT
ejpam-7071	256	1	[	[	X
ejpam-7071	256	2	17	17	NUM
ejpam-7071	256	3	]	]	X
ejpam-7071	256	4	h.	h.	PROPN
ejpam-7071	256	5	alzer	alzer	PROPN
ejpam-7071	256	6	.	.	PUNCT
ejpam-7071	257	1	error	error	NOUN
ejpam-7071	257	2	functions	function	NOUN
ejpam-7071	257	3	inequalities	inequality	NOUN
ejpam-7071	257	4	.	.	PUNCT
ejpam-7071	258	1	advances	advance	NOUN
ejpam-7071	258	2	in	in	ADP
ejpam-7071	258	3	computational	computational	ADJ
ejpam-7071	258	4	mathematics	mathematic	NOUN
ejpam-7071	258	5	,	,	PUNCT
ejpam-7071	258	6	33(3):349–379	33(3):349–379	PROPN
ejpam-7071	258	7	,	,	PUNCT
ejpam-7071	258	8	2010	2010	NUM
ejpam-7071	258	9	.	.	PUNCT
ejpam-7071	259	1	[	[	X
ejpam-7071	259	2	18	18	NUM
ejpam-7071	259	3	]	]	X
ejpam-7071	259	4	d.	d.	PROPN
ejpam-7071	259	5	coman	coman	PROPN
ejpam-7071	259	6	.	.	PUNCT
ejpam-7071	260	1	the	the	DET
ejpam-7071	260	2	radius	radius	NOUN
ejpam-7071	260	3	of	of	ADP
ejpam-7071	260	4	starlikeness	starlikeness	NOUN
ejpam-7071	260	5	for	for	ADP
ejpam-7071	260	6	error	error	NOUN
ejpam-7071	260	7	function	function	NOUN
ejpam-7071	260	8	.	.	PUNCT
ejpam-7071	261	1	stud	stud	PROPN
ejpam-7071	261	2	.	.	PUNCT
ejpam-7071	262	1	univ	univ	PROPN
ejpam-7071	262	2	.	.	PUNCT
ejpam-7071	263	1	babes	babe	NOUN
ejpam-7071	263	2	-	-	PUNCT
ejpam-7071	263	3	bolyai	bolyai	NOUN
ejpam-7071	263	4	math	math	NOUN
ejpam-7071	263	5	,	,	PUNCT
ejpam-7071	263	6	36(2):13–16	36(2):13–16	NUM
ejpam-7071	263	7	,	,	PUNCT
ejpam-7071	263	8	1991	1991	NUM
ejpam-7071	263	9	.	.	PUNCT
ejpam-7071	264	1	[	[	X
ejpam-7071	264	2	19	19	NUM
ejpam-7071	264	3	]	]	PUNCT
ejpam-7071	264	4	a.	a.	NOUN
ejpam-7071	264	5	elbert	elbert	NOUN
ejpam-7071	264	6	and	and	CCONJ
ejpam-7071	264	7	a.	a.	NOUN
ejpam-7071	264	8	laforgia	laforgia	NOUN
ejpam-7071	264	9	.	.	PUNCT
ejpam-7071	265	1	the	the	DET
ejpam-7071	265	2	zeros	zero	NOUN
ejpam-7071	265	3	of	of	ADP
ejpam-7071	265	4	the	the	DET
ejpam-7071	265	5	complementary	complementary	ADJ
ejpam-7071	265	6	error	error	NOUN
ejpam-7071	265	7	function	function	NOUN
ejpam-7071	265	8	.	.	PUNCT
ejpam-7071	266	1	numerical	numerical	ADJ
ejpam-7071	266	2	algorithms	algorithms	PROPN
ejpam-7071	266	3	,	,	PUNCT
ejpam-7071	266	4	49(1):153–157	49(1):153–157	NOUN
ejpam-7071	266	5	,	,	PUNCT
ejpam-7071	266	6	2008	2008	NUM
ejpam-7071	266	7	.	.	PUNCT
ejpam-7071	267	1	[	[	X
ejpam-7071	267	2	20	20	NUM
ejpam-7071	267	3	]	]	PUNCT
ejpam-7071	267	4	t.	t.	PROPN
ejpam-7071	267	5	al	al	PROPN
ejpam-7071	267	6	-	-	PUNCT
ejpam-7071	267	7	hawary	hawary	PROPN
ejpam-7071	267	8	,	,	PUNCT
ejpam-7071	267	9	b.a	b.a	PROPN
ejpam-7071	267	10	.	.	PROPN
ejpam-7071	267	11	frasin	frasin	PROPN
ejpam-7071	267	12	and	and	CCONJ
ejpam-7071	267	13	j.	j.	PROPN
ejpam-7071	267	14	salah	salah	PROPN
ejpam-7071	267	15	.	.	PUNCT
ejpam-7071	268	1	comprehensive	comprehensive	ADJ
ejpam-7071	268	2	subfamilies	subfamily	NOUN
ejpam-7071	268	3	of	of	ADP
ejpam-7071	268	4	bi	bi	ADJ
ejpam-7071	268	5	-	-	ADJ
ejpam-7071	268	6	univalent	univalent	ADJ
ejpam-7071	268	7	functions	function	NOUN
ejpam-7071	268	8	defined	define	VERB
ejpam-7071	268	9	by	by	ADP
ejpam-7071	268	10	error	error	NOUN
ejpam-7071	268	11	function	function	NOUN
ejpam-7071	268	12	subordinate	subordinate	NOUN
ejpam-7071	268	13	to	to	PART
ejpam-7071	268	14	euler	euler	VERB
ejpam-7071	268	15	polynomials	polynomial	NOUN
ejpam-7071	268	16	.	.	PUNCT
ejpam-7071	269	1	symmetry	symmetry	PROPN
ejpam-7071	269	2	,	,	PUNCT
ejpam-7071	269	3	17(2):256	17(2):256	NUM
ejpam-7071	269	4	,	,	PUNCT
ejpam-7071	269	5	2025	2025	NUM
ejpam-7071	269	6	.	.	PUNCT
ejpam-7071	270	1	[	[	X
ejpam-7071	270	2	21	21	NUM
ejpam-7071	270	3	]	]	X
ejpam-7071	270	4	c.	c.	PROPN
ejpam-7071	270	5	ramachandran	ramachandran	PROPN
ejpam-7071	270	6	,	,	PUNCT
ejpam-7071	270	7	l.	l.	PROPN
ejpam-7071	270	8	vanitha	vanitha	PROPN
ejpam-7071	270	9	,	,	PUNCT
ejpam-7071	270	10	and	and	CCONJ
ejpam-7071	270	11	s.	s.	PROPN
ejpam-7071	270	12	kanas	kanas	PROPN
ejpam-7071	270	13	.	.	PUNCT
ejpam-7071	271	1	certain	certain	ADJ
ejpam-7071	271	2	results	result	NOUN
ejpam-7071	271	3	on	on	ADP
ejpam-7071	271	4	q	q	ADJ
ejpam-7071	271	5	-	-	PUNCT
ejpam-7071	271	6	starlike	starlike	ADJ
ejpam-7071	271	7	and	and	CCONJ
ejpam-7071	271	8	qconvex	qconvex	NOUN
ejpam-7071	271	9	error	error	NOUN
ejpam-7071	271	10	functions	function	NOUN
ejpam-7071	271	11	.	.	PUNCT
ejpam-7071	272	1	mathematica	mathematica	PROPN
ejpam-7071	272	2	slovaca	slovaca	PROPN
ejpam-7071	272	3	,	,	PUNCT
ejpam-7071	272	4	68(2):361–368	68(2):361–368	PROPN
ejpam-7071	272	5	,	,	PUNCT
ejpam-7071	272	6	2018	2018	NUM
ejpam-7071	272	7	.	.	PUNCT
ejpam-7071	273	1	[	[	X
ejpam-7071	273	2	22	22	NUM
ejpam-7071	273	3	]	]	X
ejpam-7071	273	4	n.	n.	PROPN
ejpam-7071	273	5	h.	h.	PROPN
ejpam-7071	273	6	mohammed	mohammed	PROPN
ejpam-7071	273	7	,	,	PUNCT
ejpam-7071	273	8	n.	n.	PROPN
ejpam-7071	273	9	e.	e.	PROPN
ejpam-7071	273	10	cho	cho	PROPN
ejpam-7071	273	11	,	,	PUNCT
ejpam-7071	273	12	e.	e.	PROPN
ejpam-7071	273	13	a.	a.	PROPN
ejpam-7071	273	14	adegani	adegani	PROPN
ejpam-7071	273	15	,	,	PUNCT
ejpam-7071	273	16	and	and	CCONJ
ejpam-7071	273	17	t.	t.	PROPN
ejpam-7071	273	18	bulboaca	bulboaca	PROPN
ejpam-7071	273	19	.	.	PUNCT
ejpam-7071	274	1	geometric	geometric	ADJ
ejpam-7071	274	2	properties	property	NOUN
ejpam-7071	274	3	of	of	ADP
ejpam-7071	274	4	normalized	normalize	VERB
ejpam-7071	274	5	imaginary	imaginary	ADJ
ejpam-7071	274	6	error	error	NOUN
ejpam-7071	274	7	function	function	NOUN
ejpam-7071	274	8	.	.	PUNCT
ejpam-7071	275	1	studia	studia	PROPN
ejpam-7071	275	2	universitatis	universitatis	PROPN
ejpam-7071	275	3	babes	babes	PROPN
ejpam-7071	275	4	-	-	PUNCT
ejpam-7071	275	5	bolyai	bolyai	NOUN
ejpam-7071	275	6	matematica	matematica	PROPN
ejpam-7071	275	7	,	,	PUNCT
ejpam-7071	275	8	67(2):455–462	67(2):455–462	PROPN
ejpam-7071	275	9	,	,	PUNCT
ejpam-7071	275	10	2022	2022	NUM
ejpam-7071	275	11	.	.	PUNCT
ejpam-7071	276	1	[	[	X
ejpam-7071	276	2	23	23	NUM
ejpam-7071	276	3	]	]	PUNCT
ejpam-7071	276	4	a.	a.	NOUN
ejpam-7071	276	5	fallatah	fallatah	PROPN
ejpam-7071	276	6	,	,	PUNCT
ejpam-7071	276	7	t.	t.	PROPN
ejpam-7071	276	8	al	al	PROPN
ejpam-7071	276	9	-	-	PUNCT
ejpam-7071	276	10	hawary	hawary	PROPN
ejpam-7071	276	11	,	,	PUNCT
ejpam-7071	276	12	m.	m.	NOUN
ejpam-7071	276	13	o.	o.	PROPN
ejpam-7071	276	14	massa’deh	massa’deh	PROPN
ejpam-7071	276	15	,	,	PUNCT
ejpam-7071	276	16	and	and	CCONJ
ejpam-7071	276	17	f.	f.	PROPN
ejpam-7071	276	18	yousef	yousef	PROPN
ejpam-7071	276	19	.	.	PUNCT
ejpam-7071	277	1	subfamilies	subfamily	NOUN
ejpam-7071	277	2	of	of	ADP
ejpam-7071	277	3	analytic	analytic	ADJ
ejpam-7071	277	4	functions	function	NOUN
ejpam-7071	277	5	associated	associate	VERB
ejpam-7071	277	6	with	with	ADP
ejpam-7071	277	7	rabotnov	rabotnov	NOUN
ejpam-7071	277	8	function	function	NOUN
ejpam-7071	277	9	.	.	PUNCT
ejpam-7071	278	1	international	international	ADJ
ejpam-7071	278	2	journal	journal	PROPN
ejpam-7071	278	3	of	of	ADP
ejpam-7071	278	4	neutrosophic	neutrosophic	ADJ
ejpam-7071	278	5	science	science	NOUN
ejpam-7071	278	6	,	,	PUNCT
ejpam-7071	278	7	26(1):33–39	26(1):33–39	NUM
ejpam-7071	278	8	,	,	PUNCT
ejpam-7071	278	9	2025	2025	NUM
ejpam-7071	278	10	.	.	PUNCT
ejpam-7071	279	1	[	[	X
ejpam-7071	279	2	24	24	NUM
ejpam-7071	279	3	]	]	PUNCT
ejpam-7071	279	4	b.	b.	PROPN
ejpam-7071	279	5	a.	a.	PROPN
ejpam-7071	279	6	frasin	frasin	PROPN
ejpam-7071	279	7	,	,	PUNCT
ejpam-7071	279	8	f.	f.	PROPN
ejpam-7071	279	9	yousef	yousef	PROPN
ejpam-7071	279	10	,	,	PUNCT
ejpam-7071	279	11	t.	t.	PROPN
ejpam-7071	279	12	al	al	PROPN
ejpam-7071	279	13	-	-	PUNCT
ejpam-7071	279	14	hawary	hawary	PROPN
ejpam-7071	279	15	,	,	PUNCT
ejpam-7071	279	16	and	and	CCONJ
ejpam-7071	279	17	i.	i.	PROPN
ejpam-7071	279	18	aldawish	aldawish	PROPN
ejpam-7071	279	19	.	.	PUNCT
ejpam-7071	280	1	application	application	NOUN
ejpam-7071	280	2	of	of	ADP
ejpam-7071	280	3	generalized	generalized	ADJ
ejpam-7071	280	4	bessel	bessel	NOUN
ejpam-7071	280	5	functions	function	NOUN
ejpam-7071	280	6	to	to	ADP
ejpam-7071	280	7	classes	class	NOUN
ejpam-7071	280	8	of	of	ADP
ejpam-7071	280	9	analytic	analytic	ADJ
ejpam-7071	280	10	functions	function	NOUN
ejpam-7071	280	11	.	.	PUNCT
ejpam-7071	281	1	afrika	afrika	ADJ
ejpam-7071	281	2	matematika	matematika	PROPN
ejpam-7071	281	3	,	,	PUNCT
ejpam-7071	281	4	32(3):431–439	32(3):431–439	NOUN
ejpam-7071	281	5	,	,	PUNCT
ejpam-7071	281	6	2021	2021	NUM
ejpam-7071	281	7	.	.	PUNCT
ejpam-7071	282	1	[	[	X
ejpam-7071	282	2	25	25	NUM
ejpam-7071	282	3	]	]	X
ejpam-7071	282	4	s.	s.	PROPN
ejpam-7071	282	5	r.	r.	PROPN
ejpam-7071	282	6	mondal	mondal	PROPN
ejpam-7071	282	7	and	and	CCONJ
ejpam-7071	282	8	a.	a.	NOUN
ejpam-7071	282	9	swaminathan	swaminathan	ADV
ejpam-7071	282	10	.	.	PUNCT
ejpam-7071	283	1	geometric	geometric	ADJ
ejpam-7071	283	2	properties	property	NOUN
ejpam-7071	283	3	of	of	ADP
ejpam-7071	283	4	generalized	generalized	ADJ
ejpam-7071	283	5	bessel	bessel	NOUN
ejpam-7071	283	6	functions	function	NOUN
ejpam-7071	283	7	.	.	PUNCT
ejpam-7071	284	1	bull	bull	NOUN
ejpam-7071	284	2	.	.	PUNCT
ejpam-7071	285	1	malays	malays	PROPN
ejpam-7071	285	2	.	.	PUNCT
ejpam-7071	286	1	math	math	NOUN
ejpam-7071	286	2	.	.	PUNCT
ejpam-7071	287	1	sci	sci	PROPN
ejpam-7071	287	2	.	.	PROPN
ejpam-7071	287	3	soc	soc	PROPN
ejpam-7071	287	4	.	.	PUNCT
ejpam-7071	287	5	,	,	PUNCT
ejpam-7071	287	6	35(1):179–194	35(1):179–194	PROPN
ejpam-7071	287	7	,	,	PUNCT
ejpam-7071	287	8	2012	2012	NUM
ejpam-7071	287	9	.	.	PUNCT
ejpam-7071	288	1	a.	a.	NOUN
ejpam-7071	288	2	alameer	alameer	PROPN
ejpam-7071	288	3	et	et	PROPN
ejpam-7071	288	4	al	al	PROPN
ejpam-7071	288	5	.	.	PUNCT
ejpam-7071	288	6	/	/	SYM
ejpam-7071	288	7	eur	eur	PROPN
ejpam-7071	288	8	.	.	PUNCT
ejpam-7071	289	1	j.	j.	PROPN
ejpam-7071	289	2	pure	pure	PROPN
ejpam-7071	289	3	appl	appl	PROPN
ejpam-7071	289	4	.	.	PROPN
ejpam-7071	289	5	math	math	PROPN
ejpam-7071	289	6	,	,	PUNCT
ejpam-7071	289	7	18	18	NUM
ejpam-7071	289	8	(	(	PUNCT
ejpam-7071	289	9	4	4	NUM
ejpam-7071	289	10	)	)	PUNCT
ejpam-7071	289	11	(	(	PUNCT
ejpam-7071	289	12	2025	2025	NUM
ejpam-7071	289	13	)	)	PUNCT
ejpam-7071	289	14	,	,	PUNCT
ejpam-7071	289	15	7071	7071	NUM
ejpam-7071	289	16	11	11	NUM
ejpam-7071	289	17	of	of	ADP
ejpam-7071	289	18	11	11	NUM
ejpam-7071	289	19	[	[	SYM
ejpam-7071	289	20	26	26	NUM
ejpam-7071	289	21	]	]	X
ejpam-7071	289	22	b.	b.	PROPN
ejpam-7071	289	23	a.	a.	PROPN
ejpam-7071	289	24	frasin	frasin	PROPN
ejpam-7071	289	25	,	,	PUNCT
ejpam-7071	289	26	t.	t.	PROPN
ejpam-7071	289	27	al	al	PROPN
ejpam-7071	289	28	-	-	PUNCT
ejpam-7071	289	29	hawary	hawary	PROPN
ejpam-7071	289	30	,	,	PUNCT
ejpam-7071	289	31	f.	f.	PROPN
ejpam-7071	289	32	yousef	yousef	PROPN
ejpam-7071	289	33	,	,	PUNCT
ejpam-7071	289	34	and	and	CCONJ
ejpam-7071	289	35	i.	i.	PROPN
ejpam-7071	289	36	aldawish	aldawish	PROPN
ejpam-7071	289	37	.	.	PUNCT
ejpam-7071	290	1	on	on	ADP
ejpam-7071	290	2	subclasses	subclass	NOUN
ejpam-7071	290	3	of	of	ADP
ejpam-7071	290	4	analytic	analytic	ADJ
ejpam-7071	290	5	functions	function	NOUN
ejpam-7071	290	6	associated	associate	VERB
ejpam-7071	290	7	with	with	ADP
ejpam-7071	290	8	struve	struve	PROPN
ejpam-7071	290	9	functions	function	NOUN
ejpam-7071	290	10	.	.	PUNCT
ejpam-7071	291	1	nonlinear	nonlinear	ADJ
ejpam-7071	291	2	functional	functional	ADJ
ejpam-7071	291	3	analysis	analysis	NOUN
ejpam-7071	291	4	and	and	CCONJ
ejpam-7071	291	5	applications	application	NOUN
ejpam-7071	291	6	,	,	PUNCT
ejpam-7071	291	7	27(1):99–110	27(1):99–110	NUM
ejpam-7071	291	8	,	,	PUNCT
ejpam-7071	291	9	2022	2022	NUM
ejpam-7071	291	10	.	.	PUNCT
ejpam-7071	292	1	[	[	X
ejpam-7071	292	2	27	27	NUM
ejpam-7071	292	3	]	]	PUNCT
ejpam-7071	292	4	t.	t.	PROPN
ejpam-7071	292	5	janani	janani	PROPN
ejpam-7071	292	6	and	and	CCONJ
ejpam-7071	292	7	g.	g.	PROPN
ejpam-7071	292	8	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-7071	292	9	.	.	PUNCT
ejpam-7071	293	1	inclusion	inclusion	NOUN
ejpam-7071	293	2	results	result	NOUN
ejpam-7071	293	3	on	on	ADP
ejpam-7071	293	4	subclasses	subclass	NOUN
ejpam-7071	293	5	of	of	ADP
ejpam-7071	293	6	starlike	starlike	NOUN
ejpam-7071	293	7	and	and	CCONJ
ejpam-7071	293	8	convex	convex	NOUN
ejpam-7071	293	9	functions	function	NOUN
ejpam-7071	293	10	associated	associate	VERB
ejpam-7071	293	11	with	with	ADP
ejpam-7071	293	12	struve	struve	PROPN
ejpam-7071	293	13	functions	function	NOUN
ejpam-7071	293	14	.	.	PUNCT
ejpam-7071	294	1	italian	italian	ADJ
ejpam-7071	294	2	journal	journal	NOUN
ejpam-7071	294	3	of	of	ADP
ejpam-7071	294	4	pure	pure	ADJ
ejpam-7071	294	5	and	and	CCONJ
ejpam-7071	294	6	applied	applied	ADJ
ejpam-7071	294	7	mathematics	mathematic	NOUN
ejpam-7071	294	8	,	,	PUNCT
ejpam-7071	294	9	32:467–476	32:467–476	PROPN
ejpam-7071	294	10	,	,	PUNCT
ejpam-7071	294	11	2014	2014	NUM
ejpam-7071	294	12	.	.	PUNCT
ejpam-7071	295	1	[	[	X
ejpam-7071	295	2	28	28	NUM
ejpam-7071	295	3	]	]	X
ejpam-7071	295	4	b.a	b.a	PROPN
ejpam-7071	295	5	.	.	PROPN
ejpam-7071	295	6	frasin	frasin	PROPN
ejpam-7071	295	7	,	,	PUNCT
ejpam-7071	295	8	t.	t.	PROPN
ejpam-7071	295	9	al	al	PROPN
ejpam-7071	295	10	-	-	PUNCT
ejpam-7071	295	11	hawary	hawary	PROPN
ejpam-7071	295	12	,	,	PUNCT
ejpam-7071	295	13	and	and	CCONJ
ejpam-7071	295	14	f.	f.	PROPN
ejpam-7071	295	15	yousef	yousef	PROPN
ejpam-7071	295	16	.	.	PUNCT
ejpam-7071	296	1	necessary	necessary	ADJ
ejpam-7071	296	2	and	and	CCONJ
ejpam-7071	296	3	sufficient	sufficient	ADJ
ejpam-7071	296	4	conditions	condition	NOUN
ejpam-7071	296	5	for	for	ADP
ejpam-7071	296	6	hypergeometric	hypergeometric	ADJ
ejpam-7071	296	7	functions	function	NOUN
ejpam-7071	296	8	to	to	PART
ejpam-7071	296	9	be	be	AUX
ejpam-7071	296	10	in	in	ADP
ejpam-7071	296	11	a	a	DET
ejpam-7071	296	12	subclass	subclass	NOUN
ejpam-7071	296	13	of	of	ADP
ejpam-7071	296	14	analytic	analytic	ADJ
ejpam-7071	296	15	functions	function	NOUN
ejpam-7071	296	16	.	.	PUNCT
ejpam-7071	297	1	afrika	afrika	PROPN
ejpam-7071	297	2	matematika	matematika	PROPN
ejpam-7071	297	3	,	,	PUNCT
ejpam-7071	297	4	30(1):223–230	30(1):223–230	PROPN
ejpam-7071	297	5	,	,	PUNCT
ejpam-7071	297	6	2019	2019	NUM
ejpam-7071	297	7	.	.	PUNCT
ejpam-7071	298	1	[	[	X
ejpam-7071	298	2	29	29	NUM
ejpam-7071	298	3	]	]	X
ejpam-7071	298	4	g.	g.	PROPN
ejpam-7071	298	5	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-7071	298	6	,	,	PUNCT
ejpam-7071	298	7	b.	b.	PROPN
ejpam-7071	298	8	a.	a.	PROPN
ejpam-7071	298	9	frasin	frasin	PROPN
ejpam-7071	298	10	,	,	PUNCT
ejpam-7071	298	11	and	and	CCONJ
ejpam-7071	298	12	t.	t.	PROPN
ejpam-7071	298	13	al	al	PROPN
ejpam-7071	298	14	-	-	PUNCT
ejpam-7071	298	15	hawary	hawary	PROPN
ejpam-7071	298	16	.	.	PUNCT
ejpam-7071	299	1	uniformly	uniformly	ADV
ejpam-7071	299	2	convex	convex	VERB
ejpam-7071	299	3	spiral	spiral	ADJ
ejpam-7071	299	4	functions	function	NOUN
ejpam-7071	299	5	and	and	CCONJ
ejpam-7071	299	6	uniformly	uniformly	ADV
ejpam-7071	299	7	spirallike	spirallike	ADJ
ejpam-7071	299	8	function	function	NOUN
ejpam-7071	299	9	associated	associate	VERB
ejpam-7071	299	10	with	with	ADP
ejpam-7071	299	11	pascal	pascal	ADJ
ejpam-7071	299	12	distribution	distribution	NOUN
ejpam-7071	299	13	series	series	NOUN
ejpam-7071	299	14	.	.	PUNCT
ejpam-7071	300	1	mat	mat	PROPN
ejpam-7071	300	2	.	.	PROPN
ejpam-7071	300	3	bohem	bohem	PROPN
ejpam-7071	300	4	.	.	PROPN
ejpam-7071	300	5	,	,	PUNCT
ejpam-7071	300	6	23:1–11	23:1–11	PROPN
ejpam-7071	300	7	,	,	PUNCT
ejpam-7071	300	8	2021	2021	NUM
ejpam-7071	300	9	.	.	PUNCT
ejpam-7071	301	1	[	[	X
ejpam-7071	301	2	30	30	NUM
ejpam-7071	301	3	]	]	X
ejpam-7071	301	4	s.	s.	PROPN
ejpam-7071	301	5	m.	m.	PROPN
ejpam-7071	301	6	el	el	PROPN
ejpam-7071	301	7	-	-	PUNCT
ejpam-7071	301	8	deeb	deeb	PROPN
ejpam-7071	301	9	,	,	PUNCT
ejpam-7071	301	10	t.	t.	PROPN
ejpam-7071	301	11	bulboacă	bulboacă	PROPN
ejpam-7071	301	12	and	and	CCONJ
ejpam-7071	301	13	j.	j.	PROPN
ejpam-7071	301	14	dziok	dziok	PROPN
ejpam-7071	301	15	.	.	PUNCT
ejpam-7071	302	1	pascal	pascal	ADJ
ejpam-7071	302	2	distribution	distribution	NOUN
ejpam-7071	302	3	series	series	NOUN
ejpam-7071	302	4	connected	connect	VERB
ejpam-7071	302	5	with	with	ADP
ejpam-7071	302	6	certain	certain	ADJ
ejpam-7071	302	7	subclasses	subclass	NOUN
ejpam-7071	302	8	of	of	ADP
ejpam-7071	302	9	univalent	univalent	ADJ
ejpam-7071	302	10	functions	function	NOUN
ejpam-7071	302	11	.	.	PUNCT
ejpam-7071	303	1	kyungpook	kyungpook	PROPN
ejpam-7071	303	2	mathematical	mathematical	PROPN
ejpam-7071	303	3	journal	journal	PROPN
ejpam-7071	303	4	,	,	PUNCT
ejpam-7071	303	5	59(2):301–314	59(2):301–314	PROPN
ejpam-7071	303	6	,	,	PUNCT
ejpam-7071	303	7	2019	2019	NUM
ejpam-7071	303	8	.	.	PUNCT
ejpam-7071	304	1	[	[	X
ejpam-7071	304	2	31	31	NUM
ejpam-7071	304	3	]	]	PUNCT
ejpam-7071	304	4	r.	r.	PROPN
ejpam-7071	304	5	m.	m.	PROPN
ejpam-7071	304	6	el	el	PROPN
ejpam-7071	304	7	-	-	NOUN
ejpam-7071	304	8	ashwah	ashwah	NOUN
ejpam-7071	304	9	and	and	CCONJ
ejpam-7071	304	10	w.	w.	PROPN
ejpam-7071	304	11	y	y	PROPN
ejpam-7071	304	12	kota	kota	PROPN
ejpam-7071	304	13	.	.	PUNCT
ejpam-7071	305	1	some	some	DET
ejpam-7071	305	2	condition	condition	NOUN
ejpam-7071	305	3	on	on	ADP
ejpam-7071	305	4	a	a	DET
ejpam-7071	305	5	poisson	poisson	NOUN
ejpam-7071	305	6	distribution	distribution	NOUN
ejpam-7071	305	7	series	series	NOUN
ejpam-7071	305	8	to	to	PART
ejpam-7071	305	9	be	be	AUX
ejpam-7071	305	10	in	in	ADP
ejpam-7071	305	11	subclasses	subclass	NOUN
ejpam-7071	305	12	of	of	ADP
ejpam-7071	305	13	univalent	univalent	ADJ
ejpam-7071	305	14	functions	function	NOUN
ejpam-7071	305	15	.	.	PUNCT
ejpam-7071	306	1	acta	acta	PROPN
ejpam-7071	306	2	univ	univ	PROPN
ejpam-7071	306	3	.	.	PUNCT
ejpam-7071	307	1	apulensis	apulensis	NOUN
ejpam-7071	307	2	,	,	PUNCT
ejpam-7071	307	3	51:89–103	51:89–103	NUM
ejpam-7071	307	4	,	,	PUNCT
ejpam-7071	307	5	2017	2017	NUM
ejpam-7071	307	6	.	.	PUNCT
ejpam-7071	308	1	[	[	X
ejpam-7071	308	2	32	32	NUM
ejpam-7071	308	3	]	]	PUNCT
ejpam-7071	308	4	t.	t.	PROPN
ejpam-7071	308	5	al	al	PROPN
ejpam-7071	308	6	-	-	PUNCT
ejpam-7071	308	7	hawary	hawary	PROPN
ejpam-7071	308	8	,	,	PUNCT
ejpam-7071	308	9	i.	i.	PROPN
ejpam-7071	308	10	aldawish	aldawish	PROPN
ejpam-7071	308	11	,	,	PUNCT
ejpam-7071	308	12	b.	b.	PROPN
ejpam-7071	308	13	a.	a.	PROPN
ejpam-7071	308	14	frasin	frasin	PROPN
ejpam-7071	308	15	,	,	PUNCT
ejpam-7071	308	16	o.	o.	PROPN
ejpam-7071	308	17	alkam	alkam	PROPN
ejpam-7071	308	18	,	,	PUNCT
ejpam-7071	308	19	and	and	CCONJ
ejpam-7071	308	20	f.	f.	PROPN
ejpam-7071	308	21	yousef	yousef	PROPN
ejpam-7071	308	22	.	.	PUNCT
ejpam-7071	309	1	necessary	necessary	ADJ
ejpam-7071	309	2	and	and	CCONJ
ejpam-7071	309	3	sufficient	sufficient	ADJ
ejpam-7071	309	4	conditions	condition	NOUN
ejpam-7071	309	5	for	for	SCONJ
ejpam-7071	309	6	normalized	normalize	VERB
ejpam-7071	309	7	wright	wright	PROPN
ejpam-7071	309	8	functions	function	NOUN
ejpam-7071	309	9	to	to	PART
ejpam-7071	309	10	be	be	AUX
ejpam-7071	309	11	in	in	ADP
ejpam-7071	309	12	certain	certain	ADJ
ejpam-7071	309	13	classes	class	NOUN
ejpam-7071	309	14	of	of	ADP
ejpam-7071	309	15	analytic	analytic	ADJ
ejpam-7071	309	16	functions	function	NOUN
ejpam-7071	309	17	.	.	PUNCT
ejpam-7071	310	1	mathematics	mathematic	NOUN
ejpam-7071	310	2	,	,	PUNCT
ejpam-7071	310	3	10(24):4693	10(24):4693	NUM
ejpam-7071	310	4	,	,	PUNCT
ejpam-7071	310	5	2022	2022	NUM
ejpam-7071	310	6	.	.	PUNCT
ejpam-7071	311	1	[	[	X
ejpam-7071	311	2	33	33	NUM
ejpam-7071	311	3	]	]	PUNCT
ejpam-7071	311	4	t.	t.	PROPN
ejpam-7071	311	5	al	al	PROPN
ejpam-7071	311	6	-	-	PUNCT
ejpam-7071	311	7	hawary	hawary	PROPN
ejpam-7071	311	8	,	,	PUNCT
ejpam-7071	311	9	m.	m.	NOUN
ejpam-7071	311	10	illafe	illafe	NOUN
ejpam-7071	311	11	,	,	PUNCT
ejpam-7071	311	12	and	and	CCONJ
ejpam-7071	311	13	f.	f.	PROPN
ejpam-7071	311	14	yousef	yousef	PROPN
ejpam-7071	311	15	.	.	PUNCT
ejpam-7071	312	1	certain	certain	ADJ
ejpam-7071	312	2	constraints	constraint	NOUN
ejpam-7071	312	3	for	for	ADP
ejpam-7071	312	4	functions	function	NOUN
ejpam-7071	312	5	provided	provide	VERB
ejpam-7071	312	6	by	by	ADP
ejpam-7071	312	7	touchard	touchard	NOUN
ejpam-7071	312	8	polynomials	polynomial	NOUN
ejpam-7071	312	9	.	.	PUNCT
ejpam-7071	313	1	international	international	ADJ
ejpam-7071	313	2	journal	journal	PROPN
ejpam-7071	313	3	of	of	ADP
ejpam-7071	313	4	mathematics	mathematics	PROPN
ejpam-7071	313	5	and	and	CCONJ
ejpam-7071	313	6	mathematical	mathematical	ADJ
ejpam-7071	313	7	sciences	science	NOUN
ejpam-7071	313	8	,	,	PUNCT
ejpam-7071	313	9	2025(1):2581058	2025(1):2581058	NUM
ejpam-7071	313	10	,	,	PUNCT
ejpam-7071	313	11	2025	2025	NUM
ejpam-7071	313	12	.	.	PUNCT