id	sid	tid	token	lemma	pos
ejpam-4815	1	1	european	european	PROPN
ejpam-4815	1	2	journal	journal	PROPN
ejpam-4815	1	3	of	of	ADP
ejpam-4815	1	4	pure	pure	ADJ
ejpam-4815	1	5	and	and	CCONJ
ejpam-4815	1	6	applied	apply	VERB
ejpam-4815	1	7	mathematics	mathematic	NOUN
ejpam-4815	1	8	vol	vol	NOUN
ejpam-4815	1	9	.	.	PUNCT
ejpam-4815	2	1	16	16	NUM
ejpam-4815	2	2	,	,	PUNCT
ejpam-4815	2	3	no	no	INTJ
ejpam-4815	2	4	.	.	NOUN
ejpam-4815	2	5	3	3	NUM
ejpam-4815	2	6	,	,	PUNCT
ejpam-4815	2	7	2023	2023	NUM
ejpam-4815	2	8	,	,	PUNCT
ejpam-4815	2	9	1508	1508	NUM
ejpam-4815	2	10	-	-	SYM
ejpam-4815	2	11	1517	1517	NUM
ejpam-4815	2	12	issn	issn	PROPN
ejpam-4815	2	13	1307	1307	NUM
ejpam-4815	2	14	-	-	SYM
ejpam-4815	2	15	5543	5543	NUM
ejpam-4815	2	16	–	–	PUNCT
ejpam-4815	2	17	ejpam.com	ejpam.com	X
ejpam-4815	2	18	published	publish	VERB
ejpam-4815	2	19	by	by	ADP
ejpam-4815	2	20	new	new	PROPN
ejpam-4815	2	21	york	york	PROPN
ejpam-4815	2	22	business	business	PROPN
ejpam-4815	2	23	global	global	ADJ
ejpam-4815	2	24	approximation	approximation	NOUN
ejpam-4815	2	25	of	of	ADP
ejpam-4815	2	26	generalized	generalized	ADJ
ejpam-4815	2	27	biaxisymmetric	biaxisymmetric	ADJ
ejpam-4815	2	28	potentials	potential	NOUN
ejpam-4815	2	29	in	in	ADP
ejpam-4815	2	30	lβ	lβ	ADJ
ejpam-4815	2	31	-	-	ADJ
ejpam-4815	2	32	norm	norm	NOUN
ejpam-4815	2	33	devendra	devendra	PROPN
ejpam-4815	2	34	kumar1,2	kumar1,2	PROPN
ejpam-4815	2	35	1	1	NUM
ejpam-4815	2	36	department	department	NOUN
ejpam-4815	2	37	of	of	ADP
ejpam-4815	2	38	mathematics	mathematic	NOUN
ejpam-4815	2	39	,	,	PUNCT
ejpam-4815	2	40	faculty	faculty	NOUN
ejpam-4815	2	41	of	of	ADP
ejpam-4815	2	42	sciences	sciences	PROPN
ejpam-4815	2	43	al	al	PROPN
ejpam-4815	2	44	-	-	PUNCT
ejpam-4815	2	45	baha	baha	PROPN
ejpam-4815	2	46	university	university	PROPN
ejpam-4815	2	47	,	,	PUNCT
ejpam-4815	2	48	p.o.box-7738	p.o.box-7738	PROPN
ejpam-4815	2	49	alaqiq	alaqiq	PROPN
ejpam-4815	2	50	,	,	PUNCT
ejpam-4815	2	51	al	al	PROPN
ejpam-4815	2	52	-	-	PUNCT
ejpam-4815	2	53	baha-65799	baha-65799	NOUN
ejpam-4815	2	54	,	,	PUNCT
ejpam-4815	2	55	saudi	saudi	PROPN
ejpam-4815	2	56	arabia	arabia	PROPN
ejpam-4815	2	57	2	2	NUM
ejpam-4815	2	58	research	research	NOUN
ejpam-4815	2	59	and	and	CCONJ
ejpam-4815	2	60	post	post	VERB
ejpam-4815	2	61	graduate	graduate	ADJ
ejpam-4815	2	62	studies	study	NOUN
ejpam-4815	2	63	,	,	PUNCT
ejpam-4815	2	64	department	department	NOUN
ejpam-4815	2	65	of	of	ADP
ejpam-4815	2	66	mathematics	mathematic	NOUN
ejpam-4815	2	67	,	,	PUNCT
ejpam-4815	2	68	m.	m.	NOUN
ejpam-4815	2	69	m.	m.	PROPN
ejpam-4815	2	70	h.	h.	PROPN
ejpam-4815	2	71	college	college	PROPN
ejpam-4815	2	72	,	,	PUNCT
ejpam-4815	2	73	model	model	NOUN
ejpam-4815	2	74	town	town	NOUN
ejpam-4815	2	75	,	,	PUNCT
ejpam-4815	2	76	ghaziabad-201001	ghaziabad-201001	NOUN
ejpam-4815	2	77	,	,	PUNCT
ejpam-4815	2	78	u.p	u.p	PROPN
ejpam-4815	2	79	.	.	PROPN
ejpam-4815	2	80	,	,	PUNCT
ejpam-4815	2	81	india	india	PROPN
ejpam-4815	2	82	abstract	abstract	PROPN
ejpam-4815	2	83	.	.	PUNCT
ejpam-4815	3	1	let	let	VERB
ejpam-4815	3	2	f	f	PRON
ejpam-4815	3	3	be	be	AUX
ejpam-4815	3	4	a	a	DET
ejpam-4815	3	5	real	real	ADV
ejpam-4815	3	6	valued	value	VERB
ejpam-4815	3	7	generalized	generalized	ADJ
ejpam-4815	3	8	biaxisymmetric	biaxisymmetric	ADJ
ejpam-4815	3	9	potential	potential	NOUN
ejpam-4815	3	10	(	(	PUNCT
ejpam-4815	3	11	gbasp	gbasp	NOUN
ejpam-4815	3	12	)	)	PUNCT
ejpam-4815	3	13	in	in	ADP
ejpam-4815	3	14	lβ	lβ	PROPN
ejpam-4815	3	15	on	on	ADP
ejpam-4815	3	16	sr	sr	PROPN
ejpam-4815	3	17	,	,	PUNCT
ejpam-4815	3	18	the	the	DET
ejpam-4815	3	19	open	open	ADJ
ejpam-4815	3	20	sphere	sphere	NOUN
ejpam-4815	3	21	of	of	ADP
ejpam-4815	3	22	radius	radius	NOUN
ejpam-4815	3	23	r	r	NOUN
ejpam-4815	3	24	about	about	ADP
ejpam-4815	3	25	the	the	DET
ejpam-4815	3	26	origin	origin	NOUN
ejpam-4815	3	27	.	.	PUNCT
ejpam-4815	4	1	in	in	ADP
ejpam-4815	4	2	this	this	DET
ejpam-4815	4	3	paper	paper	NOUN
ejpam-4815	4	4	we	we	PRON
ejpam-4815	4	5	have	have	AUX
ejpam-4815	4	6	obtained	obtain	VERB
ejpam-4815	4	7	the	the	DET
ejpam-4815	4	8	necessary	necessary	ADJ
ejpam-4815	4	9	and	and	CCONJ
ejpam-4815	4	10	sufficient	sufficient	ADJ
ejpam-4815	4	11	conditions	condition	NOUN
ejpam-4815	4	12	on	on	ADP
ejpam-4815	4	13	the	the	DET
ejpam-4815	4	14	rate	rate	NOUN
ejpam-4815	4	15	of	of	ADP
ejpam-4815	4	16	decrease	decrease	NOUN
ejpam-4815	4	17	of	of	ADP
ejpam-4815	4	18	a	a	DET
ejpam-4815	4	19	sequence	sequence	NOUN
ejpam-4815	4	20	of	of	ADP
ejpam-4815	4	21	best	good	ADJ
ejpam-4815	4	22	harmonic	harmonic	ADJ
ejpam-4815	4	23	polynomial	polynomial	ADJ
ejpam-4815	4	24	approximates	approximate	NOUN
ejpam-4815	4	25	to	to	ADP
ejpam-4815	4	26	f	f	PROPN
ejpam-4815	4	27	such	such	ADJ
ejpam-4815	4	28	that	that	SCONJ
ejpam-4815	4	29	f	f	PROPN
ejpam-4815	4	30	is	be	AUX
ejpam-4815	4	31	harmonically	harmonically	ADV
ejpam-4815	4	32	continues	continue	VERB
ejpam-4815	4	33	as	as	ADP
ejpam-4815	4	34	an	an	DET
ejpam-4815	4	35	entire	entire	ADJ
ejpam-4815	4	36	function	function	NOUN
ejpam-4815	4	37	gbasp	gbasp	NOUN
ejpam-4815	4	38	and	and	CCONJ
ejpam-4815	4	39	determine	determine	VERB
ejpam-4815	4	40	their	their	PRON
ejpam-4815	4	41	(	(	PUNCT
ejpam-4815	4	42	p	p	NOUN
ejpam-4815	4	43	,	,	PUNCT
ejpam-4815	4	44	q)order	q)order	NOUN
ejpam-4815	4	45	and	and	CCONJ
ejpam-4815	4	46	generalized	generalize	VERB
ejpam-4815	4	47	(	(	PUNCT
ejpam-4815	4	48	p	p	NOUN
ejpam-4815	4	49	,	,	PUNCT
ejpam-4815	4	50	q)-type	q)-type	PUNCT
ejpam-4815	4	51	with	with	ADP
ejpam-4815	4	52	respect	respect	NOUN
ejpam-4815	4	53	to	to	PART
ejpam-4815	4	54	proximate	proximate	VERB
ejpam-4815	4	55	order	order	NOUN
ejpam-4815	4	56	ρ(r	ρ(r	NOUN
ejpam-4815	4	57	)	)	PUNCT
ejpam-4815	4	58	.	.	PUNCT
ejpam-4815	5	1	2020	2020	NUM
ejpam-4815	5	2	mathematics	mathematic	NOUN
ejpam-4815	5	3	subject	subject	NOUN
ejpam-4815	5	4	classifications	classification	NOUN
ejpam-4815	5	5	:	:	PUNCT
ejpam-4815	5	6	41a15	41a15	ADJ
ejpam-4815	5	7	,	,	PUNCT
ejpam-4815	5	8	30b10	30b10	NUM
ejpam-4815	5	9	.	.	PUNCT
ejpam-4815	6	1	key	key	ADJ
ejpam-4815	6	2	words	word	NOUN
ejpam-4815	6	3	and	and	CCONJ
ejpam-4815	6	4	phrases	phrase	NOUN
ejpam-4815	6	5	:	:	PUNCT
ejpam-4815	6	6	entire	entire	ADJ
ejpam-4815	6	7	functions	function	NOUN
ejpam-4815	6	8	,	,	PUNCT
ejpam-4815	6	9	generalized	generalize	VERB
ejpam-4815	6	10	biaxisymmetric	biaxisymmetric	ADJ
ejpam-4815	6	11	potentials	potential	NOUN
ejpam-4815	6	12	,	,	PUNCT
ejpam-4815	6	13	harmonic	harmonic	ADJ
ejpam-4815	6	14	polynomial	polynomial	ADJ
ejpam-4815	6	15	approximation	approximation	NOUN
ejpam-4815	6	16	error	error	NOUN
ejpam-4815	6	17	,	,	PUNCT
ejpam-4815	6	18	lβ	lβ	PROPN
ejpam-4815	6	19	-	-	ADJ
ejpam-4815	6	20	norm	norm	ADJ
ejpam-4815	6	21	1	1	NUM
ejpam-4815	6	22	≤	≤	NOUN
ejpam-4815	6	23	β	β	X
ejpam-4815	6	24	<	<	X
ejpam-4815	6	25	∞	∞	PROPN
ejpam-4815	6	26	,	,	PUNCT
ejpam-4815	6	27	proximate	proximate	VERB
ejpam-4815	6	28	order	order	NOUN
ejpam-4815	6	29	and	and	CCONJ
ejpam-4815	6	30	jacobi	jacobi	PROPN
ejpam-4815	6	31	polynomials	polynomial	NOUN
ejpam-4815	6	32	.	.	PUNCT
ejpam-4815	7	1	1	1	X
ejpam-4815	7	2	.	.	X
ejpam-4815	7	3	introduction	introduction	NOUN
ejpam-4815	7	4	let	let	VERB
ejpam-4815	7	5	f	f	PROPN
ejpam-4815	7	6	=	=	SYM
ejpam-4815	7	7	f	f	PROPN
ejpam-4815	7	8	(	(	PUNCT
ejpam-4815	7	9	x	x	NOUN
ejpam-4815	7	10	,	,	PUNCT
ejpam-4815	7	11	y	y	NOUN
ejpam-4815	7	12	)	)	PUNCT
ejpam-4815	7	13	be	be	VERB
ejpam-4815	7	14	a	a	DET
ejpam-4815	7	15	real	real	ADV
ejpam-4815	7	16	-	-	PUNCT
ejpam-4815	7	17	valued	value	VERB
ejpam-4815	7	18	regular	regular	ADJ
ejpam-4815	7	19	solution	solution	NOUN
ejpam-4815	7	20	of	of	ADP
ejpam-4815	7	21	the	the	DET
ejpam-4815	7	22	generalized	generalized	ADJ
ejpam-4815	7	23	biaxisymmetric	biaxisymmetric	ADJ
ejpam-4815	7	24	potential	potential	NOUN
ejpam-4815	7	25	(	(	PUNCT
ejpam-4815	7	26	gbasp	gbasp	NOUN
ejpam-4815	7	27	)	)	PUNCT
ejpam-4815	7	28	equation	equation	NOUN
ejpam-4815	7	29	∂2f	∂2f	VERB
ejpam-4815	7	30	∂x2	∂x2	NOUN
ejpam-4815	7	31	+	+	SYM
ejpam-4815	7	32	2µ	2µ	NUM
ejpam-4815	7	33	y	y	PROPN
ejpam-4815	7	34	∂f	∂f	PROPN
ejpam-4815	7	35	∂y	∂y	PRON
ejpam-4815	8	1	+	+	CCONJ
ejpam-4815	8	2	∂2f	∂2f	VERB
ejpam-4815	8	3	∂y2	∂y2	ADJ
ejpam-4815	8	4	+	+	CCONJ
ejpam-4815	8	5	2ν	2ν	NOUN
ejpam-4815	8	6	x	x	SYM
ejpam-4815	8	7	∂f	∂f	PROPN
ejpam-4815	8	8	∂x	∂x	PROPN
ejpam-4815	8	9	=	=	SYM
ejpam-4815	8	10	0	0	NUM
ejpam-4815	8	11	,	,	PUNCT
ejpam-4815	8	12	µ	µ	NOUN
ejpam-4815	8	13	,	,	PUNCT
ejpam-4815	8	14	ν	ν	X
ejpam-4815	8	15	>	>	X
ejpam-4815	8	16	0	0	NUM
ejpam-4815	8	17	,	,	PUNCT
ejpam-4815	8	18	(	(	PUNCT
ejpam-4815	8	19	1.1	1.1	NUM
ejpam-4815	8	20	)	)	PUNCT
ejpam-4815	8	21	which	which	PRON
ejpam-4815	8	22	are	be	AUX
ejpam-4815	8	23	even	even	ADV
ejpam-4815	8	24	in	in	ADP
ejpam-4815	8	25	x	x	PUNCT
ejpam-4815	8	26	and	and	CCONJ
ejpam-4815	8	27	y.	y.	NOUN
ejpam-4815	8	28	a	a	DET
ejpam-4815	8	29	polynomial	polynomial	NOUN
ejpam-4815	8	30	of	of	ADP
ejpam-4815	8	31	degree	degree	NOUN
ejpam-4815	8	32	n	n	X
ejpam-4815	8	33	which	which	PRON
ejpam-4815	8	34	is	be	AUX
ejpam-4815	8	35	even	even	ADV
ejpam-4815	8	36	in	in	ADP
ejpam-4815	8	37	x	x	SYM
ejpam-4815	8	38	and	and	CCONJ
ejpam-4815	8	39	y	y	PROPN
ejpam-4815	8	40	is	be	AUX
ejpam-4815	8	41	said	say	VERB
ejpam-4815	8	42	to	to	PART
ejpam-4815	8	43	be	be	AUX
ejpam-4815	8	44	a	a	DET
ejpam-4815	8	45	gbasp	gbasp	ADJ
ejpam-4815	8	46	polynomial	polynomial	NOUN
ejpam-4815	8	47	of	of	ADP
ejpam-4815	8	48	degree	degree	NOUN
ejpam-4815	8	49	n	n	NOUN
ejpam-4815	8	50	if	if	SCONJ
ejpam-4815	8	51	it	it	PRON
ejpam-4815	8	52	satisfies	satisfy	VERB
ejpam-4815	8	53	(	(	PUNCT
ejpam-4815	8	54	1.1	1.1	NUM
ejpam-4815	8	55	)	)	PUNCT
ejpam-4815	8	56	.	.	PUNCT
ejpam-4815	9	1	a	a	DET
ejpam-4815	9	2	gbasp	gbasp	NOUN
ejpam-4815	9	3	f	f	NOUN
ejpam-4815	9	4	,	,	PUNCT
ejpam-4815	9	5	regular	regular	ADJ
ejpam-4815	9	6	about	about	ADP
ejpam-4815	9	7	origin	origin	NOUN
ejpam-4815	9	8	,	,	PUNCT
ejpam-4815	9	9	have	have	VERB
ejpam-4815	9	10	local	local	ADJ
ejpam-4815	9	11	expansions	expansion	NOUN
ejpam-4815	9	12	of	of	ADP
ejpam-4815	9	13	the	the	DET
ejpam-4815	9	14	form	form	NOUN
ejpam-4815	9	15	f	f	X
ejpam-4815	9	16	(	(	PUNCT
ejpam-4815	9	17	x	x	PROPN
ejpam-4815	9	18	,	,	PUNCT
ejpam-4815	9	19	y	y	NOUN
ejpam-4815	9	20	)	)	PUNCT
ejpam-4815	9	21	=	=	PUNCT
ejpam-4815	10	1	∞∑	∞∑	PRON
ejpam-4815	10	2	n=0	n=0	NUM
ejpam-4815	10	3	anr	anr	NOUN
ejpam-4815	10	4	(	(	PUNCT
ejpam-4815	10	5	µ−	µ−	PROPN
ejpam-4815	10	6	1	1	NUM
ejpam-4815	10	7	2	2	NUM
ejpam-4815	10	8	,	,	PUNCT
ejpam-4815	10	9	ν−	ν−	PROPN
ejpam-4815	10	10	1	1	NUM
ejpam-4815	10	11	2	2	NUM
ejpam-4815	10	12	)	)	PUNCT
ejpam-4815	10	13	n	n	CCONJ
ejpam-4815	10	14	(	(	PUNCT
ejpam-4815	10	15	x	x	NOUN
ejpam-4815	10	16	,	,	PUNCT
ejpam-4815	10	17	y	y	PROPN
ejpam-4815	10	18	)	)	PUNCT
ejpam-4815	10	19	,	,	PUNCT
ejpam-4815	10	20	(	(	PUNCT
ejpam-4815	10	21	1.2	1.2	NUM
ejpam-4815	10	22	)	)	PUNCT
ejpam-4815	10	23	doi	doi	NOUN
ejpam-4815	10	24	:	:	PUNCT
ejpam-4815	10	25	https://doi.org/10.29020/nybg.ejpam.v16i3.4815	https://doi.org/10.29020/nybg.ejpam.v16i3.4815	NOUN
ejpam-4815	10	26	email	email	NOUN
ejpam-4815	10	27	address	address	NOUN
ejpam-4815	10	28	:	:	PUNCT
ejpam-4815	10	29	d	d	X
ejpam-4815	10	30	kumar001@rediffmail.com	kumar001@rediffmail.com	PROPN
ejpam-4815	10	31	(	(	PUNCT
ejpam-4815	10	32	d.	d.	PROPN
ejpam-4815	10	33	kumar	kumar	PROPN
ejpam-4815	10	34	)	)	PUNCT
ejpam-4815	10	35	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4815	10	36	1508	1508	NUM
ejpam-4815	11	1	©	©	ADP
ejpam-4815	11	2	2023	2023	NUM
ejpam-4815	11	3	ejpam	ejpam	NOUN
ejpam-4815	11	4	all	all	DET
ejpam-4815	11	5	rights	right	NOUN
ejpam-4815	11	6	reserved	reserve	VERB
ejpam-4815	11	7	.	.	PUNCT
ejpam-4815	12	1	d.	d.	PROPN
ejpam-4815	12	2	kumar	kumar	PROPN
ejpam-4815	12	3	/	/	SYM
ejpam-4815	12	4	eur	eur	PROPN
ejpam-4815	12	5	.	.	PUNCT
ejpam-4815	13	1	j.	j.	PROPN
ejpam-4815	13	2	pure	pure	PROPN
ejpam-4815	13	3	appl	appl	PROPN
ejpam-4815	13	4	.	.	PROPN
ejpam-4815	13	5	math	math	PROPN
ejpam-4815	13	6	,	,	PUNCT
ejpam-4815	13	7	16	16	NUM
ejpam-4815	13	8	(	(	PUNCT
ejpam-4815	13	9	3	3	NUM
ejpam-4815	13	10	)	)	PUNCT
ejpam-4815	13	11	(	(	PUNCT
ejpam-4815	13	12	2023	2023	NUM
ejpam-4815	13	13	)	)	PUNCT
ejpam-4815	13	14	,	,	PUNCT
ejpam-4815	13	15	1508	1508	NUM
ejpam-4815	13	16	-	-	SYM
ejpam-4815	13	17	1517	1517	NUM
ejpam-4815	13	18	1509	1509	NUM
ejpam-4815	13	19	r	r	NOUN
ejpam-4815	13	20	(	(	PUNCT
ejpam-4815	13	21	µ−	µ−	PROPN
ejpam-4815	13	22	1	1	NUM
ejpam-4815	13	23	2	2	NUM
ejpam-4815	13	24	,	,	PUNCT
ejpam-4815	13	25	ν−	ν−	PROPN
ejpam-4815	13	26	1	1	NUM
ejpam-4815	13	27	2	2	NUM
ejpam-4815	13	28	)	)	PUNCT
ejpam-4815	13	29	n	n	CCONJ
ejpam-4815	13	30	(	(	PUNCT
ejpam-4815	13	31	x	x	NOUN
ejpam-4815	13	32	,	,	PUNCT
ejpam-4815	13	33	y	y	NOUN
ejpam-4815	13	34	)	)	PUNCT
ejpam-4815	13	35	=	=	SYM
ejpam-4815	14	1	(	(	PUNCT
ejpam-4815	14	2	x2	x2	PROPN
ejpam-4815	14	3	+	+	NUM
ejpam-4815	14	4	y2)np	y2)np	PROPN
ejpam-4815	14	5	(	(	PUNCT
ejpam-4815	14	6	µ−	µ−	PROPN
ejpam-4815	14	7	1	1	NUM
ejpam-4815	14	8	2	2	NUM
ejpam-4815	14	9	,	,	PUNCT
ejpam-4815	14	10	ν−	ν−	PROPN
ejpam-4815	14	11	1	1	NUM
ejpam-4815	14	12	2	2	NUM
ejpam-4815	14	13	)	)	PUNCT
ejpam-4815	14	14	n	n	CCONJ
ejpam-4815	14	15	(	(	PUNCT
ejpam-4815	14	16	(	(	PUNCT
ejpam-4815	14	17	x	x	SYM
ejpam-4815	14	18	2−y2	2−y2	NUM
ejpam-4815	14	19	)	)	PUNCT
ejpam-4815	14	20	(	(	PUNCT
ejpam-4815	14	21	x2+y2	x2+y2	NOUN
ejpam-4815	14	22	)	)	PUNCT
ejpam-4815	14	23	)	)	PUNCT
ejpam-4815	14	24	/p	/p	PUNCT
ejpam-4815	15	1	(	(	PUNCT
ejpam-4815	15	2	µ−	µ−	PROPN
ejpam-4815	15	3	1	1	NUM
ejpam-4815	15	4	2	2	NUM
ejpam-4815	15	5	,	,	PUNCT
ejpam-4815	15	6	ν−	ν−	PROPN
ejpam-4815	15	7	1	1	NUM
ejpam-4815	15	8	2	2	NUM
ejpam-4815	15	9	)	)	PUNCT
ejpam-4815	15	10	n	n	CCONJ
ejpam-4815	15	11	(	(	PUNCT
ejpam-4815	15	12	1	1	NUM
ejpam-4815	15	13	)	)	PUNCT
ejpam-4815	15	14	,	,	PUNCT
ejpam-4815	15	15	where	where	SCONJ
ejpam-4815	15	16	x	x	X
ejpam-4815	15	17	=	=	SYM
ejpam-4815	15	18	r	r	NOUN
ejpam-4815	15	19	cos	cos	PROPN
ejpam-4815	15	20	θ	θ	PROPN
ejpam-4815	15	21	,	,	PUNCT
ejpam-4815	15	22	y	y	NOUN
ejpam-4815	15	23	=	=	PUNCT
ejpam-4815	15	24	r	r	NOUN
ejpam-4815	15	25	sin	sin	NOUN
ejpam-4815	15	26	θ	θ	PROPN
ejpam-4815	15	27	and	and	CCONJ
ejpam-4815	15	28	p	p	PROPN
ejpam-4815	15	29	(	(	PUNCT
ejpam-4815	15	30	µ−	µ−	PROPN
ejpam-4815	15	31	1	1	NUM
ejpam-4815	15	32	2	2	NUM
ejpam-4815	15	33	,	,	PUNCT
ejpam-4815	15	34	ν−	ν−	PROPN
ejpam-4815	15	35	1	1	NUM
ejpam-4815	15	36	2	2	NUM
ejpam-4815	15	37	)	)	PUNCT
ejpam-4815	15	38	n	n	CCONJ
ejpam-4815	15	39	(	(	PUNCT
ejpam-4815	15	40	t	t	NOUN
ejpam-4815	15	41	)	)	PUNCT
ejpam-4815	15	42	are	be	AUX
ejpam-4815	15	43	jacobi	jacobi	NOUN
ejpam-4815	15	44	polynomials	polynomial	NOUN
ejpam-4815	15	45	[	[	X
ejpam-4815	15	46	1	1	NUM
ejpam-4815	15	47	,	,	PUNCT
ejpam-4815	15	48	17	17	NUM
ejpam-4815	15	49	]	]	PUNCT
ejpam-4815	15	50	.	.	PUNCT
ejpam-4815	16	1	the	the	DET
ejpam-4815	16	2	series	series	NOUN
ejpam-4815	16	3	(	(	PUNCT
ejpam-4815	16	4	1.2	1.2	NUM
ejpam-4815	16	5	)	)	PUNCT
ejpam-4815	16	6	can	can	AUX
ejpam-4815	16	7	be	be	AUX
ejpam-4815	16	8	represented	represent	VERB
ejpam-4815	16	9	in	in	ADP
ejpam-4815	16	10	(	(	PUNCT
ejpam-4815	16	11	r	r	NOUN
ejpam-4815	16	12	,	,	PUNCT
ejpam-4815	16	13	θ	θ	NOUN
ejpam-4815	16	14	)	)	PUNCT
ejpam-4815	16	15	by	by	ADP
ejpam-4815	16	16	f	f	PROPN
ejpam-4815	16	17	≡	≡	PROPN
ejpam-4815	16	18	f	f	PROPN
ejpam-4815	16	19	(	(	PUNCT
ejpam-4815	16	20	r	r	NOUN
ejpam-4815	16	21	,	,	PUNCT
ejpam-4815	16	22	θ	θ	NOUN
ejpam-4815	16	23	)	)	PUNCT
ejpam-4815	16	24	=	=	SYM
ejpam-4815	17	1	∞∑	∞∑	PRON
ejpam-4815	17	2	n=0	n=0	NUM
ejpam-4815	17	3	anr	anr	NOUN
ejpam-4815	17	4	2np	2np	NOUN
ejpam-4815	17	5	(	(	PUNCT
ejpam-4815	17	6	µ−	µ−	PROPN
ejpam-4815	17	7	1	1	NUM
ejpam-4815	17	8	2	2	NUM
ejpam-4815	17	9	,	,	PUNCT
ejpam-4815	17	10	ν−	ν−	PROPN
ejpam-4815	17	11	1	1	NUM
ejpam-4815	17	12	2	2	NUM
ejpam-4815	17	13	)	)	PUNCT
ejpam-4815	17	14	n	n	CCONJ
ejpam-4815	17	15	(	(	PUNCT
ejpam-4815	17	16	cos	cos	ADJ
ejpam-4815	17	17	2θ	2θ	NUM
ejpam-4815	17	18	)	)	PUNCT
ejpam-4815	17	19	.	.	PUNCT
ejpam-4815	18	1	let	let	VERB
ejpam-4815	18	2	sr	sr	PROPN
ejpam-4815	18	3	=	=	PRON
ejpam-4815	18	4	{	{	PUNCT
ejpam-4815	18	5	(	(	PUNCT
ejpam-4815	18	6	x	x	NOUN
ejpam-4815	18	7	,	,	PUNCT
ejpam-4815	18	8	y	y	PROPN
ejpam-4815	18	9	)	)	PUNCT
ejpam-4815	18	10	:	:	PUNCT
ejpam-4815	19	1	x2	x2	INTJ
ejpam-4815	20	1	+	+	CCONJ
ejpam-4815	20	2	y2	y2	NOUN
ejpam-4815	20	3	<	<	X
ejpam-4815	20	4	r2	r2	PROPN
ejpam-4815	20	5	}	}	PUNCT
ejpam-4815	20	6	,	,	PUNCT
ejpam-4815	20	7	0	0	NUM
ejpam-4815	20	8	<	<	X
ejpam-4815	20	9	r	r	NOUN
ejpam-4815	20	10	≤	≤	NUM
ejpam-4815	20	11	∞	∞	PROPN
ejpam-4815	20	12	,	,	PUNCT
ejpam-4815	20	13	be	be	AUX
ejpam-4815	20	14	the	the	DET
ejpam-4815	20	15	open	open	ADJ
ejpam-4815	20	16	sphere	sphere	NOUN
ejpam-4815	20	17	of	of	ADP
ejpam-4815	20	18	radius	radius	NOUN
ejpam-4815	20	19	r	r	NOUN
ejpam-4815	20	20	about	about	ADP
ejpam-4815	20	21	the	the	DET
ejpam-4815	20	22	origin	origin	NOUN
ejpam-4815	20	23	and	and	CCONJ
ejpam-4815	20	24	sr	sr	PROPN
ejpam-4815	20	25	be	be	AUX
ejpam-4815	20	26	the	the	DET
ejpam-4815	20	27	closure	closure	NOUN
ejpam-4815	20	28	of	of	ADP
ejpam-4815	20	29	sr	sr	PROPN
ejpam-4815	20	30	.	.	PUNCT
ejpam-4815	21	1	in	in	ADP
ejpam-4815	21	2	this	this	DET
ejpam-4815	21	3	paper	paper	NOUN
ejpam-4815	21	4	we	we	PRON
ejpam-4815	21	5	consider	consider	VERB
ejpam-4815	21	6	those	those	DET
ejpam-4815	21	7	gbasp	gbasp	NOUN
ejpam-4815	21	8	f	f	PROPN
ejpam-4815	21	9	∈	∈	PROPN
ejpam-4815	21	10	lβ(sr	lβ(sr	PROPN
ejpam-4815	21	11	)	)	PUNCT
ejpam-4815	21	12	,	,	PUNCT
ejpam-4815	21	13	1	1	NUM
ejpam-4815	21	14	≤	≤	NUM
ejpam-4815	21	15	β	β	X
ejpam-4815	21	16	<	<	X
ejpam-4815	21	17	∞	∞	PROPN
ejpam-4815	21	18	,	,	PUNCT
ejpam-4815	21	19	that	that	PRON
ejpam-4815	21	20	harmonically	harmonically	ADV
ejpam-4815	21	21	continue	continue	VERB
ejpam-4815	21	22	as	as	ADP
ejpam-4815	21	23	an	an	DET
ejpam-4815	21	24	entire	entire	ADJ
ejpam-4815	21	25	function	function	NOUN
ejpam-4815	21	26	gbasp	gbasp	NOUN
ejpam-4815	21	27	.	.	PUNCT
ejpam-4815	22	1	the	the	DET
ejpam-4815	22	2	characteristic	characteristic	ADJ
ejpam-4815	22	3	feature	feature	NOUN
ejpam-4815	22	4	follows	follow	VERB
ejpam-4815	22	5	from	from	ADP
ejpam-4815	22	6	the	the	DET
ejpam-4815	22	7	rate	rate	NOUN
ejpam-4815	22	8	of	of	ADP
ejpam-4815	22	9	convergence	convergence	NOUN
ejpam-4815	22	10	of	of	ADP
ejpam-4815	22	11	a	a	DET
ejpam-4815	22	12	sequence	sequence	NOUN
ejpam-4815	22	13	of	of	ADP
ejpam-4815	22	14	best	good	ADJ
ejpam-4815	22	15	gbasp	gbasp	ADJ
ejpam-4815	22	16	polynomial	polynomial	ADJ
ejpam-4815	22	17	approximates	approximate	NOUN
ejpam-4815	22	18	to	to	ADP
ejpam-4815	22	19	f	f	PROPN
ejpam-4815	22	20	in	in	ADP
ejpam-4815	22	21	lβ(sr	lβ(sr	PROPN
ejpam-4815	22	22	)	)	PUNCT
ejpam-4815	22	23	.	.	PUNCT
ejpam-4815	23	1	the	the	DET
ejpam-4815	23	2	concepts	concept	NOUN
ejpam-4815	23	3	of	of	ADP
ejpam-4815	23	4	index	index	NOUN
ejpam-4815	23	5	-	-	PUNCT
ejpam-4815	23	6	pair	pair	NOUN
ejpam-4815	23	7	(	(	PUNCT
ejpam-4815	23	8	p	p	X
ejpam-4815	23	9	,	,	PUNCT
ejpam-4815	23	10	q	q	NOUN
ejpam-4815	23	11	)	)	PUNCT
ejpam-4815	23	12	,	,	PUNCT
ejpam-4815	23	13	p	p	NOUN
ejpam-4815	23	14	≥	≥	NOUN
ejpam-4815	23	15	q	q	NOUN
ejpam-4815	23	16	≥	≥	NUM
ejpam-4815	23	17	1	1	NUM
ejpam-4815	23	18	,	,	PUNCT
ejpam-4815	23	19	(	(	PUNCT
ejpam-4815	23	20	p	p	NOUN
ejpam-4815	23	21	,	,	PUNCT
ejpam-4815	23	22	q)-order	q)-order	PUNCT
ejpam-4815	23	23	and	and	CCONJ
ejpam-4815	23	24	(	(	PUNCT
ejpam-4815	23	25	p	p	X
ejpam-4815	23	26	,	,	PUNCT
ejpam-4815	23	27	q)-type	q)-type	PUNCT
ejpam-4815	23	28	were	be	AUX
ejpam-4815	23	29	introduced	introduce	VERB
ejpam-4815	23	30	by	by	ADP
ejpam-4815	23	31	juneja	juneja	PROPN
ejpam-4815	23	32	et	et	PROPN
ejpam-4815	23	33	al	al	PROPN
ejpam-4815	23	34	.	.	PUNCT
ejpam-4815	24	1	[	[	X
ejpam-4815	24	2	15	15	NUM
ejpam-4815	24	3	,	,	PUNCT
ejpam-4815	24	4	16	16	NUM
ejpam-4815	24	5	]	]	PUNCT
ejpam-4815	24	6	.	.	PUNCT
ejpam-4815	25	1	following	follow	VERB
ejpam-4815	25	2	the	the	DET
ejpam-4815	25	3	juneja	juneja	NOUN
ejpam-4815	25	4	et	et	PROPN
ejpam-4815	25	5	al	al	PROPN
ejpam-4815	25	6	.	.	PUNCT
ejpam-4815	26	1	[	[	X
ejpam-4815	26	2	15	15	NUM
ejpam-4815	26	3	,	,	PUNCT
ejpam-4815	26	4	16	16	NUM
ejpam-4815	26	5	]	]	X
ejpam-4815	26	6	the	the	DET
ejpam-4815	26	7	(	(	PUNCT
ejpam-4815	26	8	p	p	NOUN
ejpam-4815	26	9	,	,	PUNCT
ejpam-4815	26	10	q)-order	q)-order	NOUN
ejpam-4815	26	11	of	of	ADP
ejpam-4815	26	12	an	an	DET
ejpam-4815	26	13	entire	entire	ADJ
ejpam-4815	26	14	gbasp	gbasp	NOUN
ejpam-4815	26	15	function	function	NOUN
ejpam-4815	26	16	is	be	AUX
ejpam-4815	26	17	defined	define	VERB
ejpam-4815	26	18	as	as	ADP
ejpam-4815	26	19	lim	lim	PROPN
ejpam-4815	26	20	sup	sup	PROPN
ejpam-4815	26	21	r→∞	r→∞	PROPN
ejpam-4815	26	22	log[p]m(r	log[p]m(r	NOUN
ejpam-4815	26	23	,	,	PUNCT
ejpam-4815	26	24	f	f	PROPN
ejpam-4815	26	25	)	)	PUNCT
ejpam-4815	26	26	log[q	log[q	NOUN
ejpam-4815	26	27	]	]	X
ejpam-4815	26	28	r	r	NOUN
ejpam-4815	26	29	=	=	SYM
ejpam-4815	26	30	ρ(p	ρ(p	PROPN
ejpam-4815	26	31	,	,	PUNCT
ejpam-4815	26	32	q	q	X
ejpam-4815	26	33	)	)	PUNCT
ejpam-4815	26	34	≡	≡	PROPN
ejpam-4815	26	35	ρ	ρ	PROPN
ejpam-4815	26	36	,	,	PUNCT
ejpam-4815	26	37	and	and	CCONJ
ejpam-4815	26	38	,	,	PUNCT
ejpam-4815	26	39	the	the	DET
ejpam-4815	26	40	function	function	NOUN
ejpam-4815	26	41	having	have	VERB
ejpam-4815	26	42	(	(	PUNCT
ejpam-4815	26	43	p	p	NOUN
ejpam-4815	26	44	,	,	PUNCT
ejpam-4815	26	45	q)-order	q)-order	PUNCT
ejpam-4815	26	46	ρ(b	ρ(b	PROPN
ejpam-4815	26	47	<	<	X
ejpam-4815	26	48	ρ(p	ρ(p	PROPN
ejpam-4815	26	49	,	,	PUNCT
ejpam-4815	26	50	q	q	NOUN
ejpam-4815	26	51	)	)	PUNCT
ejpam-4815	26	52	<	<	X
ejpam-4815	26	53	∞	∞	NUM
ejpam-4815	26	54	)	)	PUNCT
ejpam-4815	26	55	is	be	AUX
ejpam-4815	26	56	said	say	VERB
ejpam-4815	26	57	to	to	PART
ejpam-4815	26	58	be	be	AUX
ejpam-4815	26	59	of	of	ADP
ejpam-4815	26	60	(	(	PUNCT
ejpam-4815	26	61	p	p	X
ejpam-4815	26	62	,	,	PUNCT
ejpam-4815	26	63	q)-type	q)-type	PUNCT
ejpam-4815	26	64	t	t	NOUN
ejpam-4815	26	65	if	if	SCONJ
ejpam-4815	26	66	lim	lim	PROPN
ejpam-4815	26	67	sup	sup	PROPN
ejpam-4815	26	68	r→∞	r→∞	X
ejpam-4815	26	69	log[p−1]m(r	log[p−1]m(r	PROPN
ejpam-4815	26	70	,	,	PUNCT
ejpam-4815	26	71	f	f	PROPN
ejpam-4815	26	72	)	)	PUNCT
ejpam-4815	27	1	(	(	PUNCT
ejpam-4815	27	2	log[q−1	log[q−1	X
ejpam-4815	27	3	]	]	PUNCT
ejpam-4815	27	4	r)ρ	r)ρ	NOUN
ejpam-4815	27	5	=	=	SYM
ejpam-4815	27	6	t	t	PROPN
ejpam-4815	27	7	(	(	PUNCT
ejpam-4815	27	8	p	p	X
ejpam-4815	27	9	,	,	PUNCT
ejpam-4815	27	10	q	q	ADJ
ejpam-4815	27	11	)	)	PUNCT
ejpam-4815	27	12	≡	≡	PROPN
ejpam-4815	27	13	t	t	PROPN
ejpam-4815	27	14	,	,	PUNCT
ejpam-4815	27	15	where	where	SCONJ
ejpam-4815	27	16	m(r	m(r	PROPN
ejpam-4815	27	17	,	,	PUNCT
ejpam-4815	27	18	f	f	X
ejpam-4815	27	19	)	)	PUNCT
ejpam-4815	27	20	=	=	SYM
ejpam-4815	28	1	maxx2+y2	maxx2+y2	PROPN
ejpam-4815	28	2	<	<	X
ejpam-4815	28	3	r2{|f	r2{|f	NOUN
ejpam-4815	28	4	(	(	PUNCT
ejpam-4815	28	5	x	x	X
ejpam-4815	28	6	,	,	PUNCT
ejpam-4815	28	7	y)|	y)|	PROPN
ejpam-4815	28	8	}	}	PUNCT
ejpam-4815	28	9	,	,	PUNCT
ejpam-4815	28	10	b=1	b=1	PUNCT
ejpam-4815	28	11	if	if	SCONJ
ejpam-4815	28	12	p	p	NOUN
ejpam-4815	28	13	=	=	X
ejpam-4815	28	14	q	q	X
ejpam-4815	28	15	and	and	CCONJ
ejpam-4815	28	16	b=0	b=0	PROPN
ejpam-4815	28	17	otherwise	otherwise	ADV
ejpam-4815	28	18	.	.	PUNCT
ejpam-4815	29	1	for	for	SCONJ
ejpam-4815	29	2	entire	entire	ADJ
ejpam-4815	29	3	function	function	NOUN
ejpam-4815	29	4	gbasp	gbasp	NOUN
ejpam-4815	29	5	the	the	DET
ejpam-4815	29	6	growth	growth	NOUN
ejpam-4815	29	7	of	of	ADP
ejpam-4815	29	8	this	this	DET
ejpam-4815	29	9	sequence	sequence	NOUN
ejpam-4815	29	10	is	be	AUX
ejpam-4815	29	11	used	use	VERB
ejpam-4815	29	12	to	to	PART
ejpam-4815	29	13	calculate	calculate	VERB
ejpam-4815	29	14	the	the	DET
ejpam-4815	29	15	(	(	PUNCT
ejpam-4815	29	16	p	p	NOUN
ejpam-4815	29	17	,	,	PUNCT
ejpam-4815	29	18	q)order	q)order	NOUN
ejpam-4815	29	19	and	and	CCONJ
ejpam-4815	29	20	generalized	generalize	VERB
ejpam-4815	29	21	(	(	PUNCT
ejpam-4815	29	22	p	p	NOUN
ejpam-4815	29	23	,	,	PUNCT
ejpam-4815	29	24	q)-type	q)-type	PUNCT
ejpam-4815	29	25	with	with	ADP
ejpam-4815	29	26	respect	respect	NOUN
ejpam-4815	29	27	to	to	PART
ejpam-4815	29	28	proximate	proximate	VERB
ejpam-4815	29	29	order	order	NOUN
ejpam-4815	29	30	ρp	ρp	NOUN
ejpam-4815	29	31	,	,	PUNCT
ejpam-4815	29	32	q(r	q(r	PROPN
ejpam-4815	29	33	)	)	PUNCT
ejpam-4815	29	34	.	.	PUNCT
ejpam-4815	30	1	the	the	DET
ejpam-4815	30	2	function	function	NOUN
ejpam-4815	30	3	in	in	ADP
ejpam-4815	30	4	the	the	DET
ejpam-4815	30	5	class	class	NOUN
ejpam-4815	30	6	lβ(s∞	lβ(s∞	PROPN
ejpam-4815	30	7	)	)	PUNCT
ejpam-4815	30	8	are	be	AUX
ejpam-4815	30	9	called	call	VERB
ejpam-4815	30	10	entire	entire	ADJ
ejpam-4815	30	11	gbasp	gbasp	NOUN
ejpam-4815	30	12	.	.	PUNCT
ejpam-4815	31	1	the	the	DET
ejpam-4815	31	2	growth	growth	NOUN
ejpam-4815	31	3	parameters	parameter	NOUN
ejpam-4815	31	4	(	(	PUNCT
ejpam-4815	31	5	p	p	X
ejpam-4815	31	6	,	,	PUNCT
ejpam-4815	31	7	q)-order	q)-order	ADJ
ejpam-4815	31	8	ρ(p	ρ(p	NUM
ejpam-4815	31	9	,	,	PUNCT
ejpam-4815	31	10	q	q	NOUN
ejpam-4815	31	11	)	)	PUNCT
ejpam-4815	31	12	and	and	CCONJ
ejpam-4815	31	13	(	(	PUNCT
ejpam-4815	31	14	p	p	X
ejpam-4815	31	15	,	,	PUNCT
ejpam-4815	31	16	q)-type	q)-type	PUNCT
ejpam-4815	31	17	t	t	NOUN
ejpam-4815	31	18	(	(	PUNCT
ejpam-4815	31	19	p	p	X
ejpam-4815	31	20	,	,	PUNCT
ejpam-4815	31	21	q	q	NOUN
ejpam-4815	31	22	)	)	PUNCT
ejpam-4815	31	23	of	of	ADP
ejpam-4815	31	24	entire	entire	ADJ
ejpam-4815	31	25	function	function	NOUN
ejpam-4815	31	26	gbasp	gbasp	NOUN
ejpam-4815	31	27	f	f	PROPN
ejpam-4815	31	28	for	for	ADP
ejpam-4815	31	29	(	(	PUNCT
ejpam-4815	31	30	p	p	X
ejpam-4815	31	31	,	,	PUNCT
ejpam-4815	31	32	q	q	NOUN
ejpam-4815	31	33	)	)	PUNCT
ejpam-4815	31	34	=	=	SYM
ejpam-4815	31	35	(	(	PUNCT
ejpam-4815	31	36	2	2	NUM
ejpam-4815	31	37	,	,	PUNCT
ejpam-4815	31	38	1	1	NUM
ejpam-4815	31	39	)	)	PUNCT
ejpam-4815	31	40	have	have	AUX
ejpam-4815	31	41	been	be	AUX
ejpam-4815	31	42	studied	study	VERB
ejpam-4815	31	43	in	in	ADP
ejpam-4815	31	44	lβ(sr	lβ(sr	PROPN
ejpam-4815	31	45	)	)	PUNCT
ejpam-4815	31	46	by	by	ADP
ejpam-4815	31	47	mccoy	mccoy	PROPN
ejpam-4815	32	1	[	[	X
ejpam-4815	32	2	14	14	NUM
ejpam-4815	32	3	]	]	PUNCT
ejpam-4815	32	4	,	,	PUNCT
ejpam-4815	32	5	but	but	CCONJ
ejpam-4815	32	6	these	these	DET
ejpam-4815	32	7	concepts	concept	NOUN
ejpam-4815	32	8	are	be	AUX
ejpam-4815	32	9	inadequate	inadequate	ADJ
ejpam-4815	32	10	to	to	PART
ejpam-4815	32	11	compare	compare	VERB
ejpam-4815	32	12	the	the	DET
ejpam-4815	32	13	growth	growth	NOUN
ejpam-4815	32	14	of	of	ADP
ejpam-4815	32	15	those	those	DET
ejpam-4815	32	16	entire	entire	ADJ
ejpam-4815	32	17	function	function	NOUN
ejpam-4815	32	18	gbasp	gbasp	NOUN
ejpam-4815	32	19	which	which	PRON
ejpam-4815	32	20	are	be	AUX
ejpam-4815	32	21	of	of	ADP
ejpam-4815	32	22	the	the	DET
ejpam-4815	32	23	same	same	ADJ
ejpam-4815	32	24	order	order	NOUN
ejpam-4815	32	25	but	but	CCONJ
ejpam-4815	32	26	of	of	ADP
ejpam-4815	32	27	infinite	infinite	ADJ
ejpam-4815	32	28	type	type	NOUN
ejpam-4815	32	29	.	.	PUNCT
ejpam-4815	33	1	hence	hence	ADV
ejpam-4815	33	2	,	,	PUNCT
ejpam-4815	33	3	for	for	ADP
ejpam-4815	33	4	a	a	DET
ejpam-4815	33	5	refinement	refinement	NOUN
ejpam-4815	33	6	of	of	ADP
ejpam-4815	33	7	the	the	DET
ejpam-4815	33	8	above	above	ADJ
ejpam-4815	33	9	scale	scale	NOUN
ejpam-4815	33	10	one	one	PRON
ejpam-4815	33	11	may	may	AUX
ejpam-4815	33	12	utilize	utilize	VERB
ejpam-4815	33	13	the	the	DET
ejpam-4815	33	14	concept	concept	NOUN
ejpam-4815	33	15	of	of	ADP
ejpam-4815	33	16	proximate	proximate	NOUN
ejpam-4815	33	17	order	order	NOUN
ejpam-4815	33	18	cf	cf	NOUN
ejpam-4815	33	19	.	.	PUNCT
ejpam-4815	34	1	[	[	X
ejpam-4815	34	2	4	4	NUM
ejpam-4815	34	3	,	,	PUNCT
ejpam-4815	34	4	11	11	NUM
ejpam-4815	34	5	]	]	PUNCT
ejpam-4815	34	6	.	.	PUNCT
ejpam-4815	35	1	a	a	DET
ejpam-4815	35	2	positive	positive	ADJ
ejpam-4815	35	3	function	function	NOUN
ejpam-4815	35	4	ρ(r	ρ(r	PROPN
ejpam-4815	35	5	)	)	PUNCT
ejpam-4815	35	6	defined	define	VERB
ejpam-4815	35	7	on	on	ADP
ejpam-4815	35	8	[	[	X
ejpam-4815	35	9	r0,∞	r0,∞	X
ejpam-4815	35	10	)	)	PUNCT
ejpam-4815	35	11	,	,	PUNCT
ejpam-4815	35	12	r0	r0	NOUN
ejpam-4815	35	13	>	>	X
ejpam-4815	35	14	exp[q−1	exp[q−1	X
ejpam-4815	35	15	]	]	X
ejpam-4815	35	16	1	1	NUM
ejpam-4815	35	17	,	,	PUNCT
ejpam-4815	35	18	is	be	AUX
ejpam-4815	35	19	said	say	VERB
ejpam-4815	35	20	to	to	PART
ejpam-4815	35	21	be	be	AUX
ejpam-4815	35	22	a	a	DET
ejpam-4815	35	23	proximate	proximate	NOUN
ejpam-4815	35	24	order	order	NOUN
ejpam-4815	35	25	of	of	ADP
ejpam-4815	35	26	an	an	DET
ejpam-4815	35	27	entire	entire	ADJ
ejpam-4815	35	28	function	function	NOUN
ejpam-4815	35	29	with	with	ADP
ejpam-4815	35	30	index	index	NOUN
ejpam-4815	35	31	-	-	PUNCT
ejpam-4815	35	32	pair	pair	NOUN
ejpam-4815	35	33	(	(	PUNCT
ejpam-4815	35	34	p	p	X
ejpam-4815	35	35	,	,	PUNCT
ejpam-4815	35	36	q	q	NOUN
ejpam-4815	35	37	)	)	PUNCT
ejpam-4815	36	1	if	if	SCONJ
ejpam-4815	36	2	(	(	PUNCT
ejpam-4815	36	3	i	i	NOUN
ejpam-4815	36	4	)	)	PUNCT
ejpam-4815	36	5	ρ(r	ρ(r	PROPN
ejpam-4815	36	6	)	)	PUNCT
ejpam-4815	36	7	→	→	SYM
ejpam-4815	36	8	ρ(p	ρ(p	PROPN
ejpam-4815	36	9	,	,	PUNCT
ejpam-4815	36	10	q	q	X
ejpam-4815	36	11	)	)	PUNCT
ejpam-4815	36	12	≡	≡	PROPN
ejpam-4815	36	13	ρ	ρ	PROPN
ejpam-4815	36	14	as	as	ADP
ejpam-4815	36	15	r	r	NOUN
ejpam-4815	36	16	→	→	SYM
ejpam-4815	36	17	∞	∞	PROPN
ejpam-4815	36	18	,	,	PUNCT
ejpam-4815	36	19	b	b	X
ejpam-4815	36	20	<	<	X
ejpam-4815	36	21	ρ	ρ	X
ejpam-4815	36	22	<	<	X
ejpam-4815	36	23	∞	∞	PROPN
ejpam-4815	36	24	;	;	PUNCT
ejpam-4815	36	25	(	(	PUNCT
ejpam-4815	36	26	ii	ii	NOUN
ejpam-4815	36	27	)	)	PUNCT
ejpam-4815	36	28	∧	∧	PROPN
ejpam-4815	36	29	[	[	X
ejpam-4815	36	30	q](r)ρ	q](r)ρ	NUM
ejpam-4815	36	31	′(r	′(r	NOUN
ejpam-4815	36	32	)	)	PUNCT
ejpam-4815	36	33	→	→	SYM
ejpam-4815	36	34	0	0	NUM
ejpam-4815	36	35	r	r	NOUN
ejpam-4815	36	36	→	→	SYM
ejpam-4815	36	37	∞	∞	PROPN
ejpam-4815	36	38	,	,	PUNCT
ejpam-4815	36	39	where	where	SCONJ
ejpam-4815	36	40	ρ′(r	ρ′(r	NOUN
ejpam-4815	36	41	)	)	PUNCT
ejpam-4815	36	42	denotes	denote	VERB
ejpam-4815	36	43	the	the	DET
ejpam-4815	36	44	derivative	derivative	NOUN
ejpam-4815	36	45	of	of	ADP
ejpam-4815	36	46	ρ(r	ρ(r	PROPN
ejpam-4815	36	47	)	)	PUNCT
ejpam-4815	36	48	,	,	PUNCT
ejpam-4815	36	49	and	and	CCONJ
ejpam-4815	36	50	∧	∧	PROPN
ejpam-4815	36	51	[	[	X
ejpam-4815	36	52	q](r	q](r	NOUN
ejpam-4815	36	53	)	)	PUNCT
ejpam-4815	36	54	=	=	VERB
ejpam-4815	37	1	∏q	∏q	NOUN
ejpam-4815	38	1	i=0	i=0	ADJ
ejpam-4815	38	2	log	log	NOUN
ejpam-4815	38	3	[	[	X
ejpam-4815	38	4	i	i	X
ejpam-4815	38	5	]	]	PUNCT
ejpam-4815	38	6	r.	r.	X
ejpam-4815	38	7	the	the	DET
ejpam-4815	38	8	(	(	PUNCT
ejpam-4815	38	9	p	p	NOUN
ejpam-4815	38	10	,	,	PUNCT
ejpam-4815	38	11	q)-type	q)-type	PUNCT
ejpam-4815	38	12	t	t	PROPN
ejpam-4815	38	13	∗	∗	NOUN
ejpam-4815	38	14	of	of	ADP
ejpam-4815	38	15	f	f	PROPN
ejpam-4815	38	16	with	with	ADP
ejpam-4815	38	17	respect	respect	NOUN
ejpam-4815	38	18	to	to	ADP
ejpam-4815	38	19	a	a	DET
ejpam-4815	38	20	given	give	VERB
ejpam-4815	38	21	proximate	proximate	NOUN
ejpam-4815	38	22	order	order	NOUN
ejpam-4815	38	23	ρ(r	ρ(r	NOUN
ejpam-4815	38	24	)	)	PUNCT
ejpam-4815	38	25	is	be	AUX
ejpam-4815	38	26	defined	define	VERB
ejpam-4815	38	27	as	as	ADP
ejpam-4815	38	28	lim	lim	PROPN
ejpam-4815	38	29	sup	sup	PROPN
ejpam-4815	38	30	r→∞	r→∞	X
ejpam-4815	38	31	log[p−1]m(r	log[p−1]m(r	PROPN
ejpam-4815	38	32	,	,	PUNCT
ejpam-4815	38	33	f	f	PROPN
ejpam-4815	38	34	)	)	PUNCT
ejpam-4815	38	35	(	(	PUNCT
ejpam-4815	38	36	log[q−1	log[q−1	X
ejpam-4815	38	37	]	]	PUNCT
ejpam-4815	38	38	r)ρ(r	r)ρ(r	PROPN
ejpam-4815	38	39	)	)	PUNCT
ejpam-4815	38	40	=	=	SYM
ejpam-4815	38	41	t	t	PROPN
ejpam-4815	38	42	∗(p	∗(p	PROPN
ejpam-4815	38	43	,	,	PUNCT
ejpam-4815	38	44	q	q	X
ejpam-4815	38	45	)	)	PUNCT
ejpam-4815	38	46	≡	≡	PROPN
ejpam-4815	38	47	t	t	PROPN
ejpam-4815	38	48	∗.	∗.	PUNCT
ejpam-4815	38	49	if	if	SCONJ
ejpam-4815	38	50	the	the	DET
ejpam-4815	38	51	quantity	quantity	NOUN
ejpam-4815	38	52	t	t	PROPN
ejpam-4815	38	53	∗	∗	NOUN
ejpam-4815	38	54	is	be	AUX
ejpam-4815	38	55	different	different	ADJ
ejpam-4815	38	56	from	from	ADP
ejpam-4815	38	57	zero	zero	NUM
ejpam-4815	38	58	and	and	CCONJ
ejpam-4815	38	59	infinity	infinity	NOUN
ejpam-4815	38	60	then	then	ADV
ejpam-4815	38	61	ρ(r	ρ(r	PROPN
ejpam-4815	38	62	)	)	PUNCT
ejpam-4815	38	63	is	be	AUX
ejpam-4815	38	64	said	say	VERB
ejpam-4815	38	65	to	to	PART
ejpam-4815	38	66	be	be	AUX
ejpam-4815	38	67	the	the	DET
ejpam-4815	38	68	proximate	proximate	NOUN
ejpam-4815	38	69	order	order	NOUN
ejpam-4815	38	70	of	of	ADP
ejpam-4815	38	71	a	a	DET
ejpam-4815	38	72	given	give	VERB
ejpam-4815	38	73	gbasp	gbasp	NOUN
ejpam-4815	38	74	function	function	NOUN
ejpam-4815	38	75	f	f	PROPN
ejpam-4815	38	76	with	with	ADP
ejpam-4815	38	77	index	index	NOUN
ejpam-4815	38	78	-	-	PUNCT
ejpam-4815	38	79	pair	pair	NOUN
ejpam-4815	38	80	(	(	PUNCT
ejpam-4815	38	81	p	p	X
ejpam-4815	38	82	,	,	PUNCT
ejpam-4815	38	83	q	q	NOUN
ejpam-4815	38	84	)	)	PUNCT
ejpam-4815	38	85	.	.	PUNCT
ejpam-4815	39	1	d.	d.	PROPN
ejpam-4815	39	2	kumar	kumar	PROPN
ejpam-4815	39	3	/	/	SYM
ejpam-4815	39	4	eur	eur	PROPN
ejpam-4815	39	5	.	.	PUNCT
ejpam-4815	40	1	j.	j.	PROPN
ejpam-4815	40	2	pure	pure	PROPN
ejpam-4815	40	3	appl	appl	PROPN
ejpam-4815	40	4	.	.	PROPN
ejpam-4815	40	5	math	math	PROPN
ejpam-4815	40	6	,	,	PUNCT
ejpam-4815	40	7	16	16	NUM
ejpam-4815	40	8	(	(	PUNCT
ejpam-4815	40	9	3	3	NUM
ejpam-4815	40	10	)	)	PUNCT
ejpam-4815	40	11	(	(	PUNCT
ejpam-4815	40	12	2023	2023	NUM
ejpam-4815	40	13	)	)	PUNCT
ejpam-4815	40	14	,	,	PUNCT
ejpam-4815	40	15	1508	1508	NUM
ejpam-4815	40	16	-	-	SYM
ejpam-4815	40	17	1517	1517	NUM
ejpam-4815	40	18	1510	1510	NUM
ejpam-4815	40	19	p.a	p.a	PROPN
ejpam-4815	40	20	.	.	PUNCT
ejpam-4815	40	21	mccoy	mccoy	PROPN
ejpam-4815	41	1	[	[	X
ejpam-4815	41	2	14	14	NUM
ejpam-4815	41	3	]	]	PUNCT
ejpam-4815	41	4	obtained	obtain	VERB
ejpam-4815	41	5	the	the	DET
ejpam-4815	41	6	results	result	NOUN
ejpam-4815	41	7	by	by	ADP
ejpam-4815	41	8	using	use	VERB
ejpam-4815	41	9	integral	integral	ADJ
ejpam-4815	41	10	operator	operator	NOUN
ejpam-4815	41	11	method	method	NOUN
ejpam-4815	41	12	[	[	X
ejpam-4815	41	13	2	2	NUM
ejpam-4815	41	14	,	,	PUNCT
ejpam-4815	41	15	4	4	NUM
ejpam-4815	41	16	,	,	PUNCT
ejpam-4815	41	17	6–8	6–8	NOUN
ejpam-4815	41	18	]	]	X
ejpam-4815	41	19	,	,	PUNCT
ejpam-4815	41	20	but	but	CCONJ
ejpam-4815	41	21	our	our	PRON
ejpam-4815	41	22	method	method	NOUN
ejpam-4815	41	23	is	be	AUX
ejpam-4815	41	24	different	different	ADJ
ejpam-4815	41	25	from	from	ADP
ejpam-4815	41	26	mccoy	mccoy	PROPN
ejpam-4815	42	1	[	[	X
ejpam-4815	42	2	14	14	NUM
ejpam-4815	42	3	]	]	PUNCT
ejpam-4815	42	4	and	and	CCONJ
ejpam-4815	42	5	the	the	DET
ejpam-4815	42	6	results	result	NOUN
ejpam-4815	42	7	are	be	AUX
ejpam-4815	42	8	the	the	DET
ejpam-4815	42	9	extension	extension	NOUN
ejpam-4815	42	10	of	of	ADP
ejpam-4815	42	11	those	those	PRON
ejpam-4815	42	12	of	of	ADP
ejpam-4815	42	13	mccoy	mccoy	PROPN
ejpam-4815	43	1	[	[	X
ejpam-4815	43	2	14	14	NUM
ejpam-4815	43	3	]	]	PUNCT
ejpam-4815	43	4	.	.	PUNCT
ejpam-4815	44	1	for	for	ADP
ejpam-4815	44	2	the	the	DET
ejpam-4815	44	3	purpose	purpose	NOUN
ejpam-4815	44	4	of	of	ADP
ejpam-4815	44	5	motivation	motivation	NOUN
ejpam-4815	44	6	,	,	PUNCT
ejpam-4815	44	7	it	it	PRON
ejpam-4815	44	8	is	be	AUX
ejpam-4815	44	9	significant	significant	ADJ
ejpam-4815	44	10	to	to	PART
ejpam-4815	44	11	mention	mention	VERB
ejpam-4815	44	12	that	that	SCONJ
ejpam-4815	44	13	the	the	DET
ejpam-4815	44	14	euler	euler	PROPN
ejpam-4815	44	15	-	-	PUNCT
ejpam-4815	44	16	poisson	poisson	NOUN
ejpam-4815	44	17	darboux	darboux	VERB
ejpam-4815	44	18	equation	equation	NOUN
ejpam-4815	44	19	,	,	PUNCT
ejpam-4815	44	20	arising	arise	VERB
ejpam-4815	44	21	in	in	ADP
ejpam-4815	44	22	gas	gas	NOUN
ejpam-4815	44	23	dynamics	dynamic	NOUN
ejpam-4815	44	24	,	,	PUNCT
ejpam-4815	44	25	is	be	AUX
ejpam-4815	44	26	viewed	view	VERB
ejpam-4815	44	27	in	in	ADP
ejpam-4815	44	28	terms	term	NOUN
ejpam-4815	44	29	of	of	ADP
ejpam-4815	44	30	equation	equation	NOUN
ejpam-4815	44	31	(	(	PUNCT
ejpam-4815	44	32	1.1	1.1	NUM
ejpam-4815	44	33	)	)	PUNCT
ejpam-4815	44	34	after	after	ADP
ejpam-4815	44	35	a	a	DET
ejpam-4815	44	36	transformation	transformation	NOUN
ejpam-4815	44	37	and	and	CCONJ
ejpam-4815	44	38	has	have	VERB
ejpam-4815	44	39	a	a	DET
ejpam-4815	44	40	variety	variety	NOUN
ejpam-4815	44	41	of	of	ADP
ejpam-4815	44	42	physical	physical	ADJ
ejpam-4815	44	43	interpretations	interpretation	NOUN
ejpam-4815	44	44	.	.	PUNCT
ejpam-4815	45	1	the	the	DET
ejpam-4815	45	2	solution	solution	NOUN
ejpam-4815	45	3	of	of	ADP
ejpam-4815	45	4	equation	equation	NOUN
ejpam-4815	45	5	(	(	PUNCT
ejpam-4815	45	6	1.1	1.1	NUM
ejpam-4815	45	7	)	)	PUNCT
ejpam-4815	45	8	which	which	PRON
ejpam-4815	45	9	satisfies	satisfy	VERB
ejpam-4815	45	10	a	a	DET
ejpam-4815	45	11	suitable	suitable	ADJ
ejpam-4815	45	12	radiation	radiation	NOUN
ejpam-4815	45	13	condition	condition	NOUN
ejpam-4815	45	14	,	,	PUNCT
ejpam-4815	45	15	corresponding	correspond	VERB
ejpam-4815	45	16	to	to	ADP
ejpam-4815	45	17	scattered	scatter	VERB
ejpam-4815	45	18	waves	wave	NOUN
ejpam-4815	45	19	,	,	PUNCT
ejpam-4815	45	20	and	and	CCONJ
ejpam-4815	45	21	their	their	PRON
ejpam-4815	45	22	singularities	singularity	NOUN
ejpam-4815	45	23	are	be	AUX
ejpam-4815	45	24	related	relate	VERB
ejpam-4815	45	25	to	to	ADP
ejpam-4815	45	26	the	the	DET
ejpam-4815	45	27	quantum	quantum	ADJ
ejpam-4815	45	28	states	state	NOUN
ejpam-4815	45	29	of	of	ADP
ejpam-4815	45	30	the	the	DET
ejpam-4815	45	31	scattered	scatter	VERB
ejpam-4815	45	32	particles	particle	NOUN
ejpam-4815	45	33	.	.	PUNCT
ejpam-4815	46	1	the	the	DET
ejpam-4815	46	2	gbasp	gbasp	NOUN
ejpam-4815	46	3	play	play	VERB
ejpam-4815	46	4	an	an	DET
ejpam-4815	46	5	important	important	ADJ
ejpam-4815	46	6	role	role	NOUN
ejpam-4815	46	7	in	in	ADP
ejpam-4815	46	8	many	many	ADJ
ejpam-4815	46	9	aspects	aspect	NOUN
ejpam-4815	46	10	of	of	ADP
ejpam-4815	46	11	mathematical	mathematical	ADJ
ejpam-4815	46	12	physics	physics	NOUN
ejpam-4815	46	13	,	,	PUNCT
ejpam-4815	46	14	in	in	ADP
ejpam-4815	46	15	particular	particular	ADJ
ejpam-4815	46	16	,	,	PUNCT
ejpam-4815	46	17	in	in	ADP
ejpam-4815	46	18	an	an	DET
ejpam-4815	46	19	understanding	understanding	NOUN
ejpam-4815	46	20	of	of	ADP
ejpam-4815	46	21	compressible	compressible	ADJ
ejpam-4815	46	22	flow	flow	NOUN
ejpam-4815	46	23	in	in	ADP
ejpam-4815	46	24	the	the	DET
ejpam-4815	46	25	transonic	transonic	ADJ
ejpam-4815	46	26	region	region	NOUN
ejpam-4815	46	27	(	(	PUNCT
ejpam-4815	46	28	see	see	VERB
ejpam-4815	46	29	[	[	X
ejpam-4815	46	30	14	14	NUM
ejpam-4815	46	31	]	]	NUM
ejpam-4815	46	32	)	)	PUNCT
ejpam-4815	46	33	.	.	PUNCT
ejpam-4815	47	1	the	the	DET
ejpam-4815	47	2	limit	limit	NOUN
ejpam-4815	47	3	µ	µ	DET
ejpam-4815	47	4	↓	↓	NOUN
ejpam-4815	47	5	ν	ν	NOUN
ejpam-4815	47	6	produces	produce	VERB
ejpam-4815	47	7	the	the	DET
ejpam-4815	47	8	generalized	generalized	ADJ
ejpam-4815	47	9	axisymmetric	axisymmetric	ADJ
ejpam-4815	47	10	potential	potential	ADJ
ejpam-4815	47	11	equation	equation	NOUN
ejpam-4815	47	12	.	.	PUNCT
ejpam-4815	48	1	reduction	reduction	NOUN
ejpam-4815	48	2	of	of	ADP
ejpam-4815	48	3	the	the	DET
ejpam-4815	48	4	gbasp	gbasp	ADJ
ejpam-4815	48	5	equation	equation	NOUN
ejpam-4815	48	6	to	to	ADP
ejpam-4815	48	7	the	the	DET
ejpam-4815	48	8	harmonic	harmonic	ADJ
ejpam-4815	48	9	function	function	NOUN
ejpam-4815	48	10	follows	follow	VERB
ejpam-4815	48	11	from	from	ADP
ejpam-4815	48	12	the	the	DET
ejpam-4815	48	13	limit	limit	NOUN
ejpam-4815	48	14	µ	µ	X
ejpam-4815	48	15	↓	↓	NOUN
ejpam-4815	48	16	0	0	NUM
ejpam-4815	48	17	that	that	PRON
ejpam-4815	48	18	also	also	ADV
ejpam-4815	48	19	reduces	reduce	VERB
ejpam-4815	48	20	the	the	DET
ejpam-4815	48	21	zonal	zonal	ADJ
ejpam-4815	48	22	harmonics	harmonic	NOUN
ejpam-4815	48	23	to	to	ADP
ejpam-4815	48	24	the	the	DET
ejpam-4815	48	25	circular	circular	ADJ
ejpam-4815	48	26	harmonics	harmonic	NOUN
ejpam-4815	48	27	.	.	PUNCT
ejpam-4815	49	1	these	these	DET
ejpam-4815	49	2	functions	function	NOUN
ejpam-4815	49	3	form	form	VERB
ejpam-4815	49	4	complete	complete	ADJ
ejpam-4815	49	5	sets	set	NOUN
ejpam-4815	49	6	for	for	ADP
ejpam-4815	49	7	even	even	ADV
ejpam-4815	49	8	harmonic	harmonic	ADJ
ejpam-4815	49	9	,	,	PUNCT
ejpam-4815	49	10	respectively	respectively	ADV
ejpam-4815	49	11	analytic	analytic	ADJ
ejpam-4815	49	12	functions	function	NOUN
ejpam-4815	49	13	,	,	PUNCT
ejpam-4815	49	14	regular	regular	ADV
ejpam-4815	49	15	at	at	ADP
ejpam-4815	49	16	the	the	DET
ejpam-4815	49	17	origin	origin	NOUN
ejpam-4815	49	18	.	.	PUNCT
ejpam-4815	50	1	the	the	DET
ejpam-4815	50	2	gbasp	gbasp	NOUN
ejpam-4815	50	3	functions	function	NOUN
ejpam-4815	50	4	,	,	PUNCT
ejpam-4815	50	5	then	then	ADV
ejpam-4815	50	6	,	,	PUNCT
ejpam-4815	50	7	are	be	AUX
ejpam-4815	50	8	natural	natural	ADJ
ejpam-4815	50	9	extensions	extension	NOUN
ejpam-4815	50	10	of	of	ADP
ejpam-4815	50	11	harmonic	harmonic	ADJ
ejpam-4815	50	12	or	or	CCONJ
ejpam-4815	50	13	analytic	analytic	ADJ
ejpam-4815	50	14	functions	function	NOUN
ejpam-4815	50	15	.	.	PUNCT
ejpam-4815	51	1	let	let	AUX
ejpam-4815	51	2	aβ(sr	aβ(sr	ADJ
ejpam-4815	51	3	)	)	PUNCT
ejpam-4815	51	4	denote	denote	VERB
ejpam-4815	51	5	the	the	DET
ejpam-4815	51	6	space	space	NOUN
ejpam-4815	51	7	of	of	ADP
ejpam-4815	51	8	gbasp	gbasp	NOUN
ejpam-4815	51	9	that	that	PRON
ejpam-4815	51	10	is	be	AUX
ejpam-4815	51	11	regular	regular	ADJ
ejpam-4815	51	12	and	and	CCONJ
ejpam-4815	51	13	analytic	analytic	ADJ
ejpam-4815	51	14	in	in	ADP
ejpam-4815	51	15	sr	sr	PROPN
ejpam-4815	51	16	with	with	ADP
ejpam-4815	51	17	finite	finite	NOUN
ejpam-4815	51	18	norm	norm	NOUN
ejpam-4815	51	19	∥	∥	PROPN
ejpam-4815	51	20	f	f	PROPN
ejpam-4815	51	21	∥β	∥β	PROPN
ejpam-4815	51	22	,	,	PUNCT
ejpam-4815	51	23	r=	r=	PUNCT
ejpam-4815	51	24	[	[	PUNCT
ejpam-4815	51	25	∫	∫	PROPN
ejpam-4815	51	26	∫	∫	PROPN
ejpam-4815	51	27	sr	sr	PROPN
ejpam-4815	51	28	|f	|f	PROPN
ejpam-4815	51	29	|pdxdy	|pdxdy	PROPN
ejpam-4815	51	30	]	]	X
ejpam-4815	51	31	1	1	NUM
ejpam-4815	51	32	β	β	X
ejpam-4815	51	33	,	,	PUNCT
ejpam-4815	51	34	1	1	NUM
ejpam-4815	51	35	≤	≤	NUM
ejpam-4815	51	36	β	β	X
ejpam-4815	51	37	<	<	X
ejpam-4815	51	38	∞	∞	PROPN
ejpam-4815	51	39	,	,	PUNCT
ejpam-4815	51	40	where	where	SCONJ
ejpam-4815	51	41	∥	∥	X
ejpam-4815	51	42	.	.	PUNCT
ejpam-4815	52	1	∥β	∥β	NOUN
ejpam-4815	52	2	,	,	PUNCT
ejpam-4815	52	3	r	r	NOUN
ejpam-4815	52	4	denotes	denote	VERB
ejpam-4815	52	5	the	the	DET
ejpam-4815	52	6	lβ	lβ	PROPN
ejpam-4815	52	7	-	-	NOUN
ejpam-4815	52	8	norm	norm	NOUN
ejpam-4815	52	9	.	.	PUNCT
ejpam-4815	53	1	the	the	DET
ejpam-4815	53	2	best	good	ADJ
ejpam-4815	53	3	polynomial	polynomial	ADJ
ejpam-4815	53	4	approximation	approximation	NOUN
ejpam-4815	53	5	error	error	NOUN
ejpam-4815	53	6	for	for	ADP
ejpam-4815	53	7	the	the	DET
ejpam-4815	53	8	gbasp	gbasp	NOUN
ejpam-4815	53	9	is	be	AUX
ejpam-4815	53	10	defined	define	VERB
ejpam-4815	53	11	by	by	ADP
ejpam-4815	53	12	eβ	eβ	NOUN
ejpam-4815	53	13	n(f	n(f	PROPN
ejpam-4815	53	14	,	,	PUNCT
ejpam-4815	53	15	r	r	NOUN
ejpam-4815	53	16	)	)	PUNCT
ejpam-4815	53	17	=	=	SYM
ejpam-4815	53	18	inf	inf	PROPN
ejpam-4815	53	19	gr	gr	NOUN
ejpam-4815	53	20	,	,	PUNCT
ejpam-4815	53	21	n∈pr	n∈pr	NOUN
ejpam-4815	53	22	,	,	PUNCT
ejpam-4815	53	23	n	n	CCONJ
ejpam-4815	53	24	{	{	PUNCT
ejpam-4815	53	25	||f	||f	PROPN
ejpam-4815	53	26	−	−	PROPN
ejpam-4815	53	27	gr	gr	NOUN
ejpam-4815	53	28	,	,	PUNCT
ejpam-4815	53	29	n||β	n||β	NOUN
ejpam-4815	53	30	,	,	PUNCT
ejpam-4815	53	31	r	r	NOUN
ejpam-4815	53	32	}	}	PUNCT
ejpam-4815	53	33	,	,	PUNCT
ejpam-4815	53	34	n	n	NOUN
ejpam-4815	53	35	=	=	SYM
ejpam-4815	53	36	0	0	NUM
ejpam-4815	53	37	,	,	PUNCT
ejpam-4815	53	38	1	1	NUM
ejpam-4815	53	39	,	,	PUNCT
ejpam-4815	53	40	.	.	PUNCT
ejpam-4815	53	41	.	.	PUNCT
ejpam-4815	54	1	.	.	PUNCT
ejpam-4815	55	1	,	,	PUNCT
ejpam-4815	55	2	(	(	PUNCT
ejpam-4815	55	3	1.3	1.3	NUM
ejpam-4815	55	4	)	)	PUNCT
ejpam-4815	55	5	with	with	ADP
ejpam-4815	55	6	pr	pr	NOUN
ejpam-4815	55	7	,	,	PUNCT
ejpam-4815	55	8	n	n	NOUN
ejpam-4815	55	9	=	=	SYM
ejpam-4815	55	10	pr	pr	NOUN
ejpam-4815	55	11	,	,	PUNCT
ejpam-4815	55	12	n(z	n(z	PROPN
ejpam-4815	55	13	)	)	PUNCT
ejpam-4815	56	1	=	=	SYM
ejpam-4815	56	2	pn	pn	PROPN
ejpam-4815	56	3	(	(	PUNCT
ejpam-4815	56	4	z	z	NOUN
ejpam-4815	56	5	r	r	NOUN
ejpam-4815	56	6	)	)	PUNCT
ejpam-4815	56	7	;	;	PUNCT
ejpam-4815	56	8	where	where	SCONJ
ejpam-4815	56	9	pn	pn	PROPN
ejpam-4815	56	10	denotes	denote	VERB
ejpam-4815	56	11	the	the	DET
ejpam-4815	56	12	set	set	NOUN
ejpam-4815	56	13	of	of	ADP
ejpam-4815	56	14	all	all	DET
ejpam-4815	56	15	gbasp	gbasp	ADJ
ejpam-4815	56	16	polynomials	polynomial	NOUN
ejpam-4815	56	17	of	of	ADP
ejpam-4815	56	18	degree	degree	NOUN
ejpam-4815	56	19	no	no	ADV
ejpam-4815	56	20	higher	high	ADJ
ejpam-4815	56	21	than	than	ADP
ejpam-4815	56	22	n.	n.	NOUN
ejpam-4815	56	23	for	for	ADP
ejpam-4815	56	24	β	β	X
ejpam-4815	56	25	=	=	SYM
ejpam-4815	56	26	∞	∞	PROPN
ejpam-4815	56	27	,	,	PUNCT
ejpam-4815	56	28	the	the	DET
ejpam-4815	56	29	above	above	ADJ
ejpam-4815	56	30	norm	norm	NOUN
ejpam-4815	56	31	is	be	AUX
ejpam-4815	56	32	sup	sup	NOUN
ejpam-4815	56	33	norm	norm	NOUN
ejpam-4815	56	34	.	.	PUNCT
ejpam-4815	57	1	for	for	ADP
ejpam-4815	57	2	each	each	DET
ejpam-4815	57	3	n	n	NOUN
ejpam-4815	57	4	there	there	PRON
ejpam-4815	57	5	is	be	VERB
ejpam-4815	57	6	an	an	DET
ejpam-4815	57	7	extremal	extremal	ADJ
ejpam-4815	57	8	gbasp	gbasp	NOUN
ejpam-4815	57	9	polynomial	polynomial	PROPN
ejpam-4815	57	10	g∗r	g∗r	PROPN
ejpam-4815	57	11	,	,	PUNCT
ejpam-4815	57	12	n	n	PRON
ejpam-4815	57	13	∈	∈	PROPN
ejpam-4815	57	14	pr	pr	NOUN
ejpam-4815	57	15	,	,	PUNCT
ejpam-4815	57	16	n	n	X
ejpam-4815	57	17	for	for	ADP
ejpam-4815	57	18	which	which	PRON
ejpam-4815	57	19	∥	∥	NUM
ejpam-4815	57	20	f	f	X
ejpam-4815	58	1	−	−	PROPN
ejpam-4815	58	2	g∗r	g∗r	PROPN
ejpam-4815	58	3	,	,	PUNCT
ejpam-4815	58	4	n	n	X
ejpam-4815	58	5	∥β	∥β	PROPN
ejpam-4815	58	6	,	,	PUNCT
ejpam-4815	58	7	r=	r=	PROPN
ejpam-4815	58	8	eβ	eβ	ADP
ejpam-4815	58	9	n(f	n(f	PROPN
ejpam-4815	58	10	,	,	PUNCT
ejpam-4815	58	11	r	r	NOUN
ejpam-4815	58	12	)	)	PUNCT
ejpam-4815	58	13	.	.	PUNCT
ejpam-4815	59	1	for	for	ADP
ejpam-4815	59	2	gbasp	gbasp	NOUN
ejpam-4815	59	3	functions	function	NOUN
ejpam-4815	59	4	there	there	PRON
ejpam-4815	59	5	is	be	VERB
ejpam-4815	59	6	a	a	DET
ejpam-4815	59	7	large	large	ADJ
ejpam-4815	59	8	literature	literature	NOUN
ejpam-4815	59	9	concerning	concern	VERB
ejpam-4815	59	10	the	the	DET
ejpam-4815	59	11	growth	growth	NOUN
ejpam-4815	59	12	and	and	CCONJ
ejpam-4815	59	13	approximation	approximation	NOUN
ejpam-4815	59	14	of	of	ADP
ejpam-4815	59	15	this	this	DET
ejpam-4815	59	16	topic	topic	NOUN
ejpam-4815	59	17	.	.	PUNCT
ejpam-4815	60	1	kasana	kasana	PROPN
ejpam-4815	60	2	and	and	CCONJ
ejpam-4815	60	3	kumar	kumar	PROPN
ejpam-4815	61	1	[	[	X
ejpam-4815	61	2	10	10	NUM
ejpam-4815	61	3	]	]	PUNCT
ejpam-4815	61	4	studied	study	VERB
ejpam-4815	61	5	the	the	DET
ejpam-4815	61	6	growth	growth	NOUN
ejpam-4815	61	7	and	and	CCONJ
ejpam-4815	61	8	approximation	approximation	NOUN
ejpam-4815	61	9	of	of	ADP
ejpam-4815	61	10	solutions	solution	NOUN
ejpam-4815	61	11	(	(	PUNCT
ejpam-4815	61	12	not	not	PART
ejpam-4815	61	13	necessarily	necessarily	ADV
ejpam-4815	61	14	entire	entire	ADJ
ejpam-4815	61	15	)	)	PUNCT
ejpam-4815	61	16	of	of	ADP
ejpam-4815	61	17	certain	certain	ADJ
ejpam-4815	61	18	elliptic	elliptic	ADJ
ejpam-4815	61	19	partial	partial	ADJ
ejpam-4815	61	20	differential	differential	NOUN
ejpam-4815	61	21	equations	equation	NOUN
ejpam-4815	61	22	.	.	PUNCT
ejpam-4815	62	1	they	they	PRON
ejpam-4815	62	2	obtained	obtain	VERB
ejpam-4815	62	3	the	the	DET
ejpam-4815	62	4	characterization	characterization	NOUN
ejpam-4815	62	5	of	of	ADP
ejpam-4815	62	6	q	q	NOUN
ejpam-4815	62	7	-	-	PUNCT
ejpam-4815	62	8	type	type	NOUN
ejpam-4815	62	9	and	and	CCONJ
ejpam-4815	62	10	lower	low	ADJ
ejpam-4815	62	11	q	q	ADJ
ejpam-4815	62	12	-	-	PUNCT
ejpam-4815	62	13	type	type	NOUN
ejpam-4815	62	14	(	(	PUNCT
ejpam-4815	62	15	q	q	NOUN
ejpam-4815	62	16	≥	≥	NOUN
ejpam-4815	62	17	2	2	NUM
ejpam-4815	62	18	)	)	PUNCT
ejpam-4815	62	19	of	of	ADP
ejpam-4815	62	20	a	a	DET
ejpam-4815	62	21	gbasp	gbasp	NOUN
ejpam-4815	62	22	having	have	VERB
ejpam-4815	62	23	fast	fast	ADJ
ejpam-4815	62	24	rates	rate	NOUN
ejpam-4815	62	25	of	of	ADP
ejpam-4815	62	26	growth	growth	NOUN
ejpam-4815	62	27	in	in	ADP
ejpam-4815	62	28	terms	term	NOUN
ejpam-4815	62	29	of	of	ADP
ejpam-4815	62	30	ratio	ratio	NOUN
ejpam-4815	62	31	of	of	ADP
ejpam-4815	62	32	approximation	approximation	NOUN
ejpam-4815	62	33	errors	error	NOUN
ejpam-4815	62	34	in	in	ADP
ejpam-4815	62	35	lβnorm	lβnorm	NOUN
ejpam-4815	62	36	.	.	PUNCT
ejpam-4815	63	1	in	in	ADP
ejpam-4815	63	2	[	[	X
ejpam-4815	63	3	12	12	NUM
ejpam-4815	63	4	]	]	PUNCT
ejpam-4815	63	5	,	,	PUNCT
ejpam-4815	63	6	kumar	kumar	PROPN
ejpam-4815	63	7	obtained	obtain	VERB
ejpam-4815	63	8	some	some	DET
ejpam-4815	63	9	results	result	NOUN
ejpam-4815	63	10	for	for	ADP
ejpam-4815	63	11	gbasp	gbasp	NOUN
ejpam-4815	63	12	and	and	CCONJ
ejpam-4815	63	13	the	the	DET
ejpam-4815	63	14	polynomial	polynomial	ADJ
ejpam-4815	63	15	approximation	approximation	NOUN
ejpam-4815	63	16	of	of	ADP
ejpam-4815	63	17	pseudo	pseudo	NOUN
ejpam-4815	63	18	analytic	analytic	ADJ
ejpam-4815	63	19	functions	function	NOUN
ejpam-4815	63	20	,	,	PUNCT
ejpam-4815	63	21	while	while	SCONJ
ejpam-4815	63	22	in	in	ADP
ejpam-4815	63	23	[	[	PUNCT
ejpam-4815	63	24	13	13	NUM
ejpam-4815	63	25	]	]	X
ejpam-4815	63	26	kumar	kumar	PROPN
ejpam-4815	63	27	obtained	obtain	VERB
ejpam-4815	63	28	the	the	DET
ejpam-4815	63	29	characterization	characterization	NOUN
ejpam-4815	63	30	of	of	ADP
ejpam-4815	63	31	growth	growth	NOUN
ejpam-4815	63	32	parameters	parameter	NOUN
ejpam-4815	63	33	in	in	ADP
ejpam-4815	63	34	terms	term	NOUN
ejpam-4815	63	35	of	of	ADP
ejpam-4815	63	36	axially	axially	ADV
ejpam-4815	63	37	symmetric	symmetric	ADJ
ejpam-4815	63	38	harmonic	harmonic	ADJ
ejpam-4815	63	39	polynomial	polynomial	ADJ
ejpam-4815	63	40	and	and	CCONJ
ejpam-4815	63	41	lagrange	lagrange	NOUN
ejpam-4815	63	42	polynomials	polynomial	NOUN
ejpam-4815	63	43	approximation	approximation	NOUN
ejpam-4815	63	44	errors	error	NOUN
ejpam-4815	63	45	in	in	ADP
ejpam-4815	63	46	n	n	NOUN
ejpam-4815	63	47	-	-	PUNCT
ejpam-4815	63	48	dimensions	dimension	NOUN
ejpam-4815	63	49	.	.	PUNCT
ejpam-4815	64	1	in	in	ADP
ejpam-4815	64	2	the	the	DET
ejpam-4815	64	3	present	present	ADJ
ejpam-4815	64	4	paper	paper	NOUN
ejpam-4815	64	5	,	,	PUNCT
ejpam-4815	64	6	using	use	VERB
ejpam-4815	64	7	a	a	DET
ejpam-4815	64	8	different	different	ADJ
ejpam-4815	64	9	technique	technique	NOUN
ejpam-4815	64	10	,	,	PUNCT
ejpam-4815	64	11	we	we	PRON
ejpam-4815	64	12	derive	derive	VERB
ejpam-4815	64	13	formulae	formulae	NOUN
ejpam-4815	64	14	for	for	ADP
ejpam-4815	64	15	the	the	DET
ejpam-4815	64	16	(	(	PUNCT
ejpam-4815	64	17	p	p	NOUN
ejpam-4815	64	18	,	,	PUNCT
ejpam-4815	64	19	q)-order	q)-order	PUNCT
ejpam-4815	64	20	and	and	CCONJ
ejpam-4815	64	21	generalized	generalize	VERB
ejpam-4815	64	22	(	(	PUNCT
ejpam-4815	64	23	p	p	NOUN
ejpam-4815	64	24	,	,	PUNCT
ejpam-4815	64	25	q)-type	q)-type	PUNCT
ejpam-4815	64	26	with	with	ADP
ejpam-4815	64	27	respect	respect	NOUN
ejpam-4815	64	28	to	to	ADP
ejpam-4815	64	29	a	a	DET
ejpam-4815	64	30	proximate	proximate	NOUN
ejpam-4815	64	31	order	order	NOUN
ejpam-4815	64	32	,	,	PUNCT
ejpam-4815	64	33	of	of	ADP
ejpam-4815	64	34	entire	entire	ADJ
ejpam-4815	64	35	gbasp	gbasp	NOUN
ejpam-4815	64	36	functions	function	NOUN
ejpam-4815	64	37	in	in	ADP
ejpam-4815	64	38	terms	term	NOUN
ejpam-4815	64	39	of	of	ADP
ejpam-4815	64	40	gbasp	gbasp	NOUN
ejpam-4815	64	41	polynomials	polynomial	NOUN
ejpam-4815	64	42	approximation	approximation	NOUN
ejpam-4815	64	43	errors	error	NOUN
ejpam-4815	64	44	in	in	ADP
ejpam-4815	64	45	lβnorm	lβnorm	NOUN
ejpam-4815	64	46	.	.	PUNCT
ejpam-4815	65	1	our	our	PRON
ejpam-4815	65	2	results	result	NOUN
ejpam-4815	65	3	extend	extend	VERB
ejpam-4815	65	4	and	and	CCONJ
ejpam-4815	65	5	improve	improve	VERB
ejpam-4815	65	6	the	the	DET
ejpam-4815	65	7	results	result	NOUN
ejpam-4815	65	8	obtained	obtain	VERB
ejpam-4815	65	9	by	by	ADP
ejpam-4815	65	10	mccoy	mccoy	PROPN
ejpam-4815	66	1	[	[	X
ejpam-4815	66	2	14	14	NUM
ejpam-4815	66	3	]	]	PUNCT
ejpam-4815	66	4	.	.	PUNCT
ejpam-4815	67	1	d.	d.	PROPN
ejpam-4815	67	2	kumar	kumar	PROPN
ejpam-4815	67	3	/	/	SYM
ejpam-4815	67	4	eur	eur	PROPN
ejpam-4815	67	5	.	.	PUNCT
ejpam-4815	68	1	j.	j.	PROPN
ejpam-4815	68	2	pure	pure	PROPN
ejpam-4815	68	3	appl	appl	PROPN
ejpam-4815	68	4	.	.	PROPN
ejpam-4815	68	5	math	math	PROPN
ejpam-4815	68	6	,	,	PUNCT
ejpam-4815	68	7	16	16	NUM
ejpam-4815	68	8	(	(	PUNCT
ejpam-4815	68	9	3	3	NUM
ejpam-4815	68	10	)	)	PUNCT
ejpam-4815	68	11	(	(	PUNCT
ejpam-4815	68	12	2023	2023	NUM
ejpam-4815	68	13	)	)	PUNCT
ejpam-4815	68	14	,	,	PUNCT
ejpam-4815	68	15	1508	1508	NUM
ejpam-4815	68	16	-	-	SYM
ejpam-4815	68	17	1517	1517	NUM
ejpam-4815	68	18	1511	1511	NUM
ejpam-4815	68	19	2	2	NUM
ejpam-4815	68	20	.	.	PUNCT
ejpam-4815	69	1	lemmas	lemmas	PROPN
ejpam-4815	69	2	and	and	CCONJ
ejpam-4815	69	3	results	result	NOUN
ejpam-4815	69	4	to	to	PART
ejpam-4815	69	5	prove	prove	VERB
ejpam-4815	69	6	our	our	PRON
ejpam-4815	69	7	main	main	ADJ
ejpam-4815	69	8	results	result	NOUN
ejpam-4815	69	9	the	the	DET
ejpam-4815	69	10	following	follow	VERB
ejpam-4815	69	11	lemmas	lemma	NOUN
ejpam-4815	69	12	are	be	AUX
ejpam-4815	69	13	required	require	VERB
ejpam-4815	69	14	.	.	PUNCT
ejpam-4815	70	1	lemma	lemma	PROPN
ejpam-4815	70	2	2.1	2.1	NUM
ejpam-4815	70	3	.	.	PUNCT
ejpam-4815	71	1	let	let	VERB
ejpam-4815	71	2	f	f	PROPN
ejpam-4815	71	3	∈	∈	PROPN
ejpam-4815	71	4	aβ(sr	aβ(sr	PROPN
ejpam-4815	71	5	)	)	PUNCT
ejpam-4815	71	6	,	,	PUNCT
ejpam-4815	71	7	then	then	ADV
ejpam-4815	71	8	for	for	ADP
ejpam-4815	71	9	all	all	DET
ejpam-4815	71	10	n	n	PRON
ejpam-4815	71	11	∈	∈	PRON
ejpam-4815	71	12	n	n	CCONJ
ejpam-4815	71	13	the	the	DET
ejpam-4815	71	14	following	follow	VERB
ejpam-4815	71	15	inequality	inequality	NOUN
ejpam-4815	71	16	holds	hold	VERB
ejpam-4815	71	17	:	:	PUNCT
ejpam-4815	72	1	|an|r2n+2	|an|r2n+2	NOUN
ejpam-4815	72	2	0	0	NUM
ejpam-4815	72	3	≤	≤	NOUN
ejpam-4815	72	4	(	(	PUNCT
ejpam-4815	72	5	πr2	πr2	NOUN
ejpam-4815	72	6	0	0	NUM
ejpam-4815	72	7	)	)	PUNCT
ejpam-4815	72	8	1	1	NUM
ejpam-4815	72	9	η	η	PROPN
ejpam-4815	72	10	(	(	PUNCT
ejpam-4815	72	11	2n+	2n+	NUM
ejpam-4815	72	12	2)((2n+	2)((2n+	NUM
ejpam-4815	72	13	µ+	µ+	PRON
ejpam-4815	72	14	ν)c(n	ν)c(n	PROPN
ejpam-4815	72	15	,	,	PUNCT
ejpam-4815	72	16	µ	µ	NOUN
ejpam-4815	72	17	,	,	PUNCT
ejpam-4815	72	18	ν))γ(n+	ν))γ(n+	ADJ
ejpam-4815	72	19	α+	α+	DET
ejpam-4815	72	20	1	1	NUM
ejpam-4815	72	21	)	)	PUNCT
ejpam-4815	72	22	γ(α+	γ(α+	PRON
ejpam-4815	72	23	1)γ(n+	1)γ(n+	PROPN
ejpam-4815	72	24	1	1	NUM
ejpam-4815	72	25	)	)	PUNCT
ejpam-4815	72	26	eβ	eβ	ADP
ejpam-4815	72	27	n−1(f	n−1(f	PROPN
ejpam-4815	72	28	,	,	PUNCT
ejpam-4815	72	29	r0	r0	NOUN
ejpam-4815	72	30	)	)	PUNCT
ejpam-4815	72	31	where	where	SCONJ
ejpam-4815	72	32	c(n	c(n	PROPN
ejpam-4815	72	33	,	,	PUNCT
ejpam-4815	72	34	µ	µ	NOUN
ejpam-4815	72	35	,	,	PUNCT
ejpam-4815	72	36	ν	ν	NOUN
ejpam-4815	72	37	)	)	PUNCT
ejpam-4815	72	38	=	=	SYM
ejpam-4815	72	39	γ(n+	γ(n+	NUM
ejpam-4815	72	40	1)γ(n+	1)γ(n+	PROPN
ejpam-4815	72	41	µ+	µ+	PUNCT
ejpam-4815	72	42	ν	ν	NOUN
ejpam-4815	72	43	)	)	PUNCT
ejpam-4815	72	44	γ(n+	γ(n+	NOUN
ejpam-4815	72	45	µ+	µ+	PUNCT
ejpam-4815	72	46	1	1	NUM
ejpam-4815	72	47	2)γ(n+	2)γ(n+	PROPN
ejpam-4815	72	48	ν	ν	NOUN
ejpam-4815	72	49	+	+	CCONJ
ejpam-4815	72	50	1	1	NUM
ejpam-4815	72	51	2	2	NUM
ejpam-4815	72	52	)	)	PUNCT
ejpam-4815	72	53	,	,	PUNCT
ejpam-4815	72	54	α	α	X
ejpam-4815	72	55	=	=	PUNCT
ejpam-4815	72	56	max(µ−	max(µ−	NOUN
ejpam-4815	72	57	1	1	NUM
ejpam-4815	72	58	2	2	NUM
ejpam-4815	72	59	,	,	PUNCT
ejpam-4815	72	60	ν	ν	X
ejpam-4815	72	61	−	−	PROPN
ejpam-4815	72	62	1	1	NUM
ejpam-4815	72	63	2	2	NUM
ejpam-4815	72	64	)	)	PUNCT
ejpam-4815	72	65	and	and	CCONJ
ejpam-4815	72	66	1	1	NUM
ejpam-4815	72	67	η	η	X
ejpam-4815	72	68	+	+	PROPN
ejpam-4815	72	69	1	1	NUM
ejpam-4815	72	70	β	β	X
ejpam-4815	72	71	=	=	SYM
ejpam-4815	72	72	1	1	X
ejpam-4815	72	73	.	.	PUNCT
ejpam-4815	73	1	proof	proof	NOUN
ejpam-4815	73	2	.	.	PUNCT
ejpam-4815	74	1	from	from	ADP
ejpam-4815	74	2	the	the	DET
ejpam-4815	74	3	orthogonality	orthogonality	NOUN
ejpam-4815	74	4	property	property	NOUN
ejpam-4815	74	5	of	of	ADP
ejpam-4815	74	6	jacobi	jacobi	PROPN
ejpam-4815	74	7	polynomials	polynomial	NOUN
ejpam-4815	74	8	and	and	CCONJ
ejpam-4815	74	9	uniform	uniform	ADJ
ejpam-4815	74	10	convergence	convergence	NOUN
ejpam-4815	74	11	of	of	ADP
ejpam-4815	74	12	the	the	DET
ejpam-4815	74	13	series	series	NOUN
ejpam-4815	74	14	(	(	PUNCT
ejpam-4815	74	15	1.2	1.2	NUM
ejpam-4815	74	16	)	)	PUNCT
ejpam-4815	74	17	on	on	ADP
ejpam-4815	74	18	sr	sr	PROPN
ejpam-4815	74	19	,	,	PUNCT
ejpam-4815	74	20	we	we	PRON
ejpam-4815	74	21	have	have	VERB
ejpam-4815	74	22	anτ	anτ	NOUN
ejpam-4815	74	23	2n	2n	NUM
ejpam-4815	74	24	=	=	NOUN
ejpam-4815	74	25	2(2n+	2(2n+	NUM
ejpam-4815	74	26	µ+	µ+	X
ejpam-4815	74	27	ν)c(n	ν)c(n	PROPN
ejpam-4815	74	28	,	,	PUNCT
ejpam-4815	74	29	µ	µ	NOUN
ejpam-4815	74	30	,	,	PUNCT
ejpam-4815	74	31	ν	ν	NOUN
ejpam-4815	74	32	)	)	PUNCT
ejpam-4815	74	33	∫	∫	PROPN
ejpam-4815	75	1	π	π	PROPN
ejpam-4815	75	2	2	2	NUM
ejpam-4815	75	3	0	0	NUM
ejpam-4815	75	4	(	(	PUNCT
ejpam-4815	75	5	f	f	PROPN
ejpam-4815	75	6	(	(	PUNCT
ejpam-4815	75	7	τ	τ	PROPN
ejpam-4815	75	8	,	,	PUNCT
ejpam-4815	75	9	θ)−	θ)−	PROPN
ejpam-4815	75	10	g∗τ	g∗τ	NOUN
ejpam-4815	75	11	,	,	PUNCT
ejpam-4815	75	12	n−1(τ	n−1(τ	PROPN
ejpam-4815	75	13	,	,	PUNCT
ejpam-4815	75	14	θ))×	θ))×	PROPN
ejpam-4815	75	15	×	×	PROPN
ejpam-4815	75	16	p	p	X
ejpam-4815	75	17	(	(	PUNCT
ejpam-4815	75	18	µ−	µ−	PROPN
ejpam-4815	75	19	1	1	NUM
ejpam-4815	75	20	2	2	NUM
ejpam-4815	75	21	,	,	PUNCT
ejpam-4815	75	22	ν−	ν−	PROPN
ejpam-4815	75	23	1	1	NUM
ejpam-4815	75	24	2	2	NUM
ejpam-4815	75	25	)	)	PUNCT
ejpam-4815	75	26	n	n	CCONJ
ejpam-4815	75	27	(	(	PUNCT
ejpam-4815	75	28	cos	cos	NOUN
ejpam-4815	75	29	2θ	2θ	NUM
ejpam-4815	75	30	)	)	PUNCT
ejpam-4815	75	31	sin2µ	sin2µ	X
ejpam-4815	76	1	θ	θ	X
ejpam-4815	77	1	cos2ν	cos2ν	PUNCT
ejpam-4815	77	2	θdθ	θdθ	NOUN
ejpam-4815	77	3	,	,	PUNCT
ejpam-4815	77	4	(	(	PUNCT
ejpam-4815	77	5	2.1	2.1	NUM
ejpam-4815	77	6	)	)	PUNCT
ejpam-4815	77	7	where	where	SCONJ
ejpam-4815	77	8	g∗τ	g∗τ	NOUN
ejpam-4815	77	9	,	,	PUNCT
ejpam-4815	77	10	n−1	n−1	PROPN
ejpam-4815	77	11	∈	∈	PROPN
ejpam-4815	77	12	pτ	pτ	NOUN
ejpam-4815	77	13	,	,	PUNCT
ejpam-4815	77	14	n−1	n−1	PROPN
ejpam-4815	77	15	,	,	PUNCT
ejpam-4815	77	16	0	0	NUM
ejpam-4815	77	17	<	<	X
ejpam-4815	77	18	τ	τ	X
ejpam-4815	77	19	<	<	X
ejpam-4815	77	20	r0	r0	NOUN
ejpam-4815	77	21	.	.	PUNCT
ejpam-4815	78	1	using	use	VERB
ejpam-4815	78	2	[	[	X
ejpam-4815	78	3	3	3	NUM
ejpam-4815	78	4	,	,	PUNCT
ejpam-4815	78	5	p.168	p.168	NOUN
ejpam-4815	78	6	]	]	X
ejpam-4815	78	7	max	max	PROPN
ejpam-4815	78	8	−1≤t≤1	−1≤t≤1	PROPN
ejpam-4815	78	9	|p	|p	X
ejpam-4815	78	10	(	(	PUNCT
ejpam-4815	78	11	µ−	µ−	PROPN
ejpam-4815	78	12	1	1	NUM
ejpam-4815	78	13	2	2	NUM
ejpam-4815	78	14	,	,	PUNCT
ejpam-4815	78	15	ν−	ν−	PROPN
ejpam-4815	78	16	1	1	NUM
ejpam-4815	78	17	2	2	NUM
ejpam-4815	78	18	)	)	PUNCT
ejpam-4815	78	19	(	(	PUNCT
ejpam-4815	78	20	t)|	t)|	NOUN
ejpam-4815	78	21	=	=	SYM
ejpam-4815	78	22	γ(n+	γ(n+	NOUN
ejpam-4815	78	23	α+	α+	NOUN
ejpam-4815	78	24	1	1	NUM
ejpam-4815	78	25	)	)	PUNCT
ejpam-4815	78	26	γ(α+	γ(α+	PRON
ejpam-4815	78	27	1)γ(n+	1)γ(n+	PROPN
ejpam-4815	78	28	1	1	NUM
ejpam-4815	78	29	)	)	PUNCT
ejpam-4815	78	30	(	(	PUNCT
ejpam-4815	78	31	2.2	2.2	NUM
ejpam-4815	78	32	)	)	PUNCT
ejpam-4815	78	33	in	in	ADP
ejpam-4815	78	34	(	(	PUNCT
ejpam-4815	78	35	2.1	2.1	NUM
ejpam-4815	78	36	)	)	PUNCT
ejpam-4815	78	37	,	,	PUNCT
ejpam-4815	78	38	we	we	PRON
ejpam-4815	78	39	obtain	obtain	VERB
ejpam-4815	78	40	|an|τ2n	|an|τ2n	X
ejpam-4815	78	41	=	=	SYM
ejpam-4815	78	42	(	(	PUNCT
ejpam-4815	78	43	2n+	2n+	NUM
ejpam-4815	78	44	µ+	µ+	PRON
ejpam-4815	78	45	ν)c(n	ν)c(n	PROPN
ejpam-4815	78	46	,	,	PUNCT
ejpam-4815	78	47	µ	µ	X
ejpam-4815	78	48	,	,	PUNCT
ejpam-4815	78	49	ν)γ(n+	ν)γ(n+	X
ejpam-4815	78	50	α+	α+	X
ejpam-4815	78	51	1	1	NUM
ejpam-4815	78	52	)	)	PUNCT
ejpam-4815	78	53	2γ(α+	2γ(α+	PROPN
ejpam-4815	78	54	1)γ(n+	1)γ(n+	NUM
ejpam-4815	78	55	1	1	NUM
ejpam-4815	78	56	)	)	PUNCT
ejpam-4815	78	57	∫	∫	PROPN
ejpam-4815	78	58	2π	2π	PROPN
ejpam-4815	78	59	0	0	NUM
ejpam-4815	79	1	|(f	|(f	PROPN
ejpam-4815	79	2	(	(	PUNCT
ejpam-4815	79	3	τ	τ	PROPN
ejpam-4815	79	4	,	,	PUNCT
ejpam-4815	79	5	θ)−	θ)−	PROPN
ejpam-4815	79	6	g∗τ	g∗τ	NOUN
ejpam-4815	79	7	,	,	PUNCT
ejpam-4815	79	8	n−1(τ	n−1(τ	PROPN
ejpam-4815	79	9	,	,	PUNCT
ejpam-4815	79	10	θ))|dθ	θ))|dθ	PROPN
ejpam-4815	79	11	,	,	PUNCT
ejpam-4815	79	12	since	since	SCONJ
ejpam-4815	79	13	f	f	PROPN
ejpam-4815	79	14	and	and	CCONJ
ejpam-4815	79	15	g∗τ	g∗τ	NOUN
ejpam-4815	79	16	,	,	PUNCT
ejpam-4815	79	17	n−1	n−1	PROPN
ejpam-4815	79	18	are	be	AUX
ejpam-4815	79	19	even	even	ADV
ejpam-4815	79	20	in	in	ADP
ejpam-4815	79	21	x	x	PUNCT
ejpam-4815	79	22	and	and	CCONJ
ejpam-4815	79	23	y.	y.	PROPN
ejpam-4815	79	24	multiplying	multiply	VERB
ejpam-4815	79	25	both	both	DET
ejpam-4815	79	26	sides	side	NOUN
ejpam-4815	79	27	of	of	ADP
ejpam-4815	79	28	the	the	DET
ejpam-4815	79	29	above	above	ADJ
ejpam-4815	79	30	inequality	inequality	NOUN
ejpam-4815	79	31	by	by	ADP
ejpam-4815	79	32	τdτ	τdτ	NOUN
ejpam-4815	79	33	and	and	CCONJ
ejpam-4815	79	34	integrating	integrate	VERB
ejpam-4815	79	35	from	from	ADP
ejpam-4815	79	36	0	0	NUM
ejpam-4815	79	37	to	to	PART
ejpam-4815	79	38	r0	r0	VERB
ejpam-4815	79	39	,	,	PUNCT
ejpam-4815	79	40	we	we	PRON
ejpam-4815	79	41	get	get	VERB
ejpam-4815	79	42	|an|r0	|an|r0	NOUN
ejpam-4815	79	43	2n+2	2n+2	PROPN
ejpam-4815	79	44	=	=	SYM
ejpam-4815	80	1	2(n+	2(n+	NUM
ejpam-4815	80	2	1)(2n+	1)(2n+	PROPN
ejpam-4815	80	3	µ+	µ+	X
ejpam-4815	80	4	ν)c(n	ν)c(n	PROPN
ejpam-4815	80	5	,	,	PUNCT
ejpam-4815	80	6	µ	µ	X
ejpam-4815	80	7	,	,	PUNCT
ejpam-4815	80	8	ν)γ(n+	ν)γ(n+	X
ejpam-4815	80	9	α+	α+	X
ejpam-4815	80	10	1	1	NUM
ejpam-4815	80	11	)	)	PUNCT
ejpam-4815	80	12	2γ(α+	2γ(α+	PROPN
ejpam-4815	80	13	1)γ(n+	1)γ(n+	NUM
ejpam-4815	80	14	1	1	NUM
ejpam-4815	80	15	)	)	PUNCT
ejpam-4815	81	1	×	×	NOUN
ejpam-4815	81	2	×	×	NOUN
ejpam-4815	81	3	∫	∫	PROPN
ejpam-4815	81	4	∫	∫	PROPN
ejpam-4815	81	5	sr0	sr0	PROPN
ejpam-4815	81	6	|(f	|(f	PROPN
ejpam-4815	81	7	(	(	PUNCT
ejpam-4815	81	8	x	x	X
ejpam-4815	81	9	,	,	PUNCT
ejpam-4815	81	10	y)−	y)−	PROPN
ejpam-4815	81	11	g∗r0,n−1(x	g∗r0,n−1(x	NOUN
ejpam-4815	81	12	,	,	PUNCT
ejpam-4815	81	13	y))|dxdy	y))|dxdy	X
ejpam-4815	81	14	.	.	PUNCT
ejpam-4815	81	15	(	(	PUNCT
ejpam-4815	81	16	2.3	2.3	NUM
ejpam-4815	81	17	)	)	PUNCT
ejpam-4815	81	18	for	for	ADP
ejpam-4815	81	19	f	f	PROPN
ejpam-4815	81	20	∈	∈	PROPN
ejpam-4815	81	21	aβ(sr0	aβ(sr0	PROPN
ejpam-4815	81	22	)	)	PUNCT
ejpam-4815	81	23	,	,	PUNCT
ejpam-4815	81	24	there	there	PRON
ejpam-4815	81	25	exists	exist	VERB
ejpam-4815	81	26	g∗r0,n−1	g∗r0,n−1	PROPN
ejpam-4815	81	27	∈	∈	PROPN
ejpam-4815	81	28	pr0,n−1	pr0,n−1	PROPN
ejpam-4815	81	29	such	such	ADJ
ejpam-4815	81	30	that	that	SCONJ
ejpam-4815	81	31	2eβ	2eβ	PROPN
ejpam-4815	81	32	n−1(f	n−1(f	PROPN
ejpam-4815	81	33	,	,	PUNCT
ejpam-4815	81	34	r0	r0	NOUN
ejpam-4815	81	35	)	)	PUNCT
ejpam-4815	81	36	≥	≥	NOUN
ejpam-4815	81	37	∥	∥	X
ejpam-4815	81	38	f	f	X
ejpam-4815	81	39	−	−	X
ejpam-4815	81	40	g∗r0,n−1	g∗r0,n−1	PROPN
ejpam-4815	81	41	∥β	∥β	PROPN
ejpam-4815	81	42	,	,	PUNCT
ejpam-4815	81	43	r0	r0	NOUN
ejpam-4815	81	44	≥	≥	NUM
ejpam-4815	81	45	(	(	PUNCT
ejpam-4815	81	46	∫	∫	PROPN
ejpam-4815	81	47	∫	∫	PROPN
ejpam-4815	81	48	sr0	sr0	PROPN
ejpam-4815	81	49	|(f	|(f	PROPN
ejpam-4815	81	50	(	(	PUNCT
ejpam-4815	81	51	x	x	X
ejpam-4815	81	52	,	,	PUNCT
ejpam-4815	81	53	y)−	y)−	PROPN
ejpam-4815	81	54	g∗r0,n−1(x	g∗r0,n−1(x	NOUN
ejpam-4815	81	55	,	,	PUNCT
ejpam-4815	81	56	y))|βdxdy	y))|βdxdy	NOUN
ejpam-4815	81	57	)	)	PUNCT
ejpam-4815	81	58	1	1	NUM
ejpam-4815	81	59	β	β	X
ejpam-4815	81	60	≥	≥	NUM
ejpam-4815	81	61	1	1	NUM
ejpam-4815	81	62	(	(	PUNCT
ejpam-4815	81	63	πr2	πr2	NOUN
ejpam-4815	81	64	0	0	NUM
ejpam-4815	81	65	)	)	PUNCT
ejpam-4815	81	66	1	1	NUM
ejpam-4815	81	67	η	η	PROPN
ejpam-4815	81	68	∫	∫	PROPN
ejpam-4815	81	69	∫	∫	PROPN
ejpam-4815	81	70	sr0	sr0	PROPN
ejpam-4815	81	71	|(f	|(f	PROPN
ejpam-4815	81	72	(	(	PUNCT
ejpam-4815	81	73	x	x	X
ejpam-4815	81	74	,	,	PUNCT
ejpam-4815	81	75	y)−	y)−	PROPN
ejpam-4815	81	76	g∗r0,n−1(x	g∗r0,n−1(x	NOUN
ejpam-4815	81	77	,	,	PUNCT
ejpam-4815	81	78	y))|dxdy	y))|dxdy	X
ejpam-4815	81	79	.	.	PUNCT
ejpam-4815	82	1	(	(	PUNCT
ejpam-4815	82	2	2.4	2.4	NUM
ejpam-4815	82	3	)	)	PUNCT
ejpam-4815	82	4	d.	d.	PROPN
ejpam-4815	82	5	kumar	kumar	PROPN
ejpam-4815	82	6	/	/	SYM
ejpam-4815	82	7	eur	eur	PROPN
ejpam-4815	82	8	.	.	PUNCT
ejpam-4815	83	1	j.	j.	PROPN
ejpam-4815	83	2	pure	pure	PROPN
ejpam-4815	83	3	appl	appl	PROPN
ejpam-4815	83	4	.	.	PROPN
ejpam-4815	83	5	math	math	PROPN
ejpam-4815	83	6	,	,	PUNCT
ejpam-4815	83	7	16	16	NUM
ejpam-4815	83	8	(	(	PUNCT
ejpam-4815	83	9	3	3	NUM
ejpam-4815	83	10	)	)	PUNCT
ejpam-4815	83	11	(	(	PUNCT
ejpam-4815	83	12	2023	2023	NUM
ejpam-4815	83	13	)	)	PUNCT
ejpam-4815	83	14	,	,	PUNCT
ejpam-4815	83	15	1508	1508	NUM
ejpam-4815	83	16	-	-	SYM
ejpam-4815	83	17	1517	1517	NUM
ejpam-4815	83	18	1512	1512	NUM
ejpam-4815	83	19	now	now	ADV
ejpam-4815	83	20	combining	combine	VERB
ejpam-4815	83	21	(	(	PUNCT
ejpam-4815	83	22	2.3	2.3	NUM
ejpam-4815	83	23	)	)	PUNCT
ejpam-4815	83	24	and	and	CCONJ
ejpam-4815	83	25	(	(	PUNCT
ejpam-4815	83	26	2.4	2.4	NUM
ejpam-4815	83	27	)	)	PUNCT
ejpam-4815	83	28	we	we	PRON
ejpam-4815	83	29	get	get	VERB
ejpam-4815	83	30	the	the	DET
ejpam-4815	83	31	required	require	VERB
ejpam-4815	83	32	result	result	NOUN
ejpam-4815	83	33	.	.	PUNCT
ejpam-4815	84	1	let	let	AUX
ejpam-4815	84	2	w	w	NOUN
ejpam-4815	84	3	=	=	SYM
ejpam-4815	84	4	ψ(z	ψ(z	PROPN
ejpam-4815	84	5	)	)	PUNCT
ejpam-4815	84	6	be	be	VERB
ejpam-4815	84	7	the	the	DET
ejpam-4815	84	8	univalent	univalent	ADJ
ejpam-4815	84	9	function	function	NOUN
ejpam-4815	84	10	mapping	map	VERB
ejpam-4815	84	11	the	the	DET
ejpam-4815	84	12	complement	complement	NOUN
ejpam-4815	84	13	of	of	ADP
ejpam-4815	84	14	sr	sr	PROPN
ejpam-4815	84	15	on	on	ADP
ejpam-4815	84	16	|w|	|w|	PROPN
ejpam-4815	84	17	>	>	SYM
ejpam-4815	84	18	1	1	NUM
ejpam-4815	84	19	such	such	ADJ
ejpam-4815	84	20	that	that	SCONJ
ejpam-4815	84	21	ψ(∞	ψ(∞	NOUN
ejpam-4815	84	22	)	)	PUNCT
ejpam-4815	85	1	=	=	SYM
ejpam-4815	85	2	∞	∞	PROPN
ejpam-4815	85	3	and	and	CCONJ
ejpam-4815	85	4	ψ′(∞	ψ′(∞	ADP
ejpam-4815	85	5	)	)	PUNCT
ejpam-4815	85	6	>	>	X
ejpam-4815	85	7	0	0	X
ejpam-4815	85	8	.	.	PUNCT
ejpam-4815	86	1	set	set	VERB
ejpam-4815	86	2	sr	sr	PROPN
ejpam-4815	86	3	=	=	PUNCT
ejpam-4815	86	4	{	{	PUNCT
ejpam-4815	86	5	z	z	NOUN
ejpam-4815	86	6	:	:	PUNCT
ejpam-4815	86	7	ψ(z	ψ(z	PROPN
ejpam-4815	86	8	)	)	PUNCT
ejpam-4815	86	9	=	=	SYM
ejpam-4815	87	1	r	r	NOUN
ejpam-4815	87	2	,	,	PUNCT
ejpam-4815	87	3	r	r	NOUN
ejpam-4815	87	4	>	>	X
ejpam-4815	87	5	1	1	NUM
ejpam-4815	87	6	}	}	PUNCT
ejpam-4815	87	7	.	.	PUNCT
ejpam-4815	88	1	then	then	ADV
ejpam-4815	88	2	lemma	lemma	PROPN
ejpam-4815	88	3	2.2	2.2	NUM
ejpam-4815	88	4	.	.	PUNCT
ejpam-4815	89	1	let	let	VERB
ejpam-4815	89	2	f	f	PROPN
ejpam-4815	89	3	∈	∈	PROPN
ejpam-4815	89	4	aβ(sr	aβ(sr	NOUN
ejpam-4815	89	5	)	)	PUNCT
ejpam-4815	89	6	be	be	VERB
ejpam-4815	89	7	an	an	DET
ejpam-4815	89	8	entire	entire	ADJ
ejpam-4815	89	9	gbasp	gbasp	NOUN
ejpam-4815	89	10	function	function	NOUN
ejpam-4815	89	11	of	of	ADP
ejpam-4815	89	12	(	(	PUNCT
ejpam-4815	89	13	p	p	X
ejpam-4815	89	14	,	,	PUNCT
ejpam-4815	89	15	q)-order	q)-order	PUNCT
ejpam-4815	89	16	ρ	ρ	PROPN
ejpam-4815	89	17	and	and	CCONJ
ejpam-4815	89	18	generalized	generalized	ADJ
ejpam-4815	89	19	(	(	PUNCT
ejpam-4815	89	20	p	p	NOUN
ejpam-4815	89	21	,	,	PUNCT
ejpam-4815	89	22	q)-type	q)-type	PUNCT
ejpam-4815	89	23	t	t	PROPN
ejpam-4815	89	24	∗	∗	NOUN
ejpam-4815	89	25	with	with	ADP
ejpam-4815	89	26	respect	respect	NOUN
ejpam-4815	89	27	to	to	ADP
ejpam-4815	89	28	ρ(r	ρ(r	PROPN
ejpam-4815	89	29	)	)	PUNCT
ejpam-4815	89	30	.	.	PUNCT
ejpam-4815	90	1	then	then	ADV
ejpam-4815	90	2	lim	lim	PROPN
ejpam-4815	90	3	sup	sup	PROPN
ejpam-4815	90	4	r→∞	r→∞	PROPN
ejpam-4815	90	5	log[p]m(r	log[p]m(r	NOUN
ejpam-4815	90	6	,	,	PUNCT
ejpam-4815	90	7	f	f	PROPN
ejpam-4815	90	8	)	)	PUNCT
ejpam-4815	90	9	log[q	log[q	NOUN
ejpam-4815	90	10	]	]	X
ejpam-4815	90	11	r	r	NOUN
ejpam-4815	90	12	=	=	SYM
ejpam-4815	90	13	ρ	ρ	PROPN
ejpam-4815	90	14	,	,	PUNCT
ejpam-4815	90	15	lim	lim	PROPN
ejpam-4815	90	16	sup	sup	PROPN
ejpam-4815	90	17	r→∞	r→∞	X
ejpam-4815	90	18	log[p−1]m(r	log[p−1]m(r	PROPN
ejpam-4815	90	19	,	,	PUNCT
ejpam-4815	90	20	f	f	PROPN
ejpam-4815	90	21	)	)	PUNCT
ejpam-4815	90	22	(	(	PUNCT
ejpam-4815	90	23	log[q−1	log[q−1	X
ejpam-4815	90	24	]	]	PUNCT
ejpam-4815	90	25	r)ρ(r	r)ρ(r	PROPN
ejpam-4815	90	26	)	)	PUNCT
ejpam-4815	90	27	=	=	SYM
ejpam-4815	90	28	t	t	PROPN
ejpam-4815	90	29	∗	∗	NOUN
ejpam-4815	90	30	γ	γ	X
ejpam-4815	90	31	,	,	PUNCT
ejpam-4815	90	32	where	where	SCONJ
ejpam-4815	90	33	m(r	m(r	PROPN
ejpam-4815	90	34	,	,	PUNCT
ejpam-4815	90	35	f	f	X
ejpam-4815	90	36	)	)	PUNCT
ejpam-4815	90	37	=	=	PROPN
ejpam-4815	91	1	maxz∈sr	maxz∈sr	X
ejpam-4815	91	2	|f	|f	PROPN
ejpam-4815	92	1	|	|	ADV
ejpam-4815	92	2	,	,	PUNCT
ejpam-4815	92	3	γ	γ	NOUN
ejpam-4815	92	4	=	=	SYM
ejpam-4815	92	5	r−ρ	r−ρ	PROPN
ejpam-4815	92	6	for	for	ADP
ejpam-4815	92	7	q	q	NOUN
ejpam-4815	92	8	=	=	SYM
ejpam-4815	92	9	1	1	NUM
ejpam-4815	92	10	and	and	CCONJ
ejpam-4815	92	11	γ	γ	X
ejpam-4815	92	12	=	=	SYM
ejpam-4815	92	13	1	1	NUM
ejpam-4815	92	14	,	,	PUNCT
ejpam-4815	92	15	otherwise	otherwise	ADV
ejpam-4815	92	16	.	.	PUNCT
ejpam-4815	93	1	this	this	DET
ejpam-4815	93	2	lemma	lemma	PROPN
ejpam-4815	93	3	is	be	AUX
ejpam-4815	93	4	an	an	DET
ejpam-4815	93	5	immediate	immediate	ADJ
ejpam-4815	93	6	consequence	consequence	NOUN
ejpam-4815	93	7	of	of	ADP
ejpam-4815	93	8	[	[	X
ejpam-4815	93	9	18	18	NUM
ejpam-4815	93	10	,	,	PUNCT
ejpam-4815	93	11	lemma	lemma	PROPN
ejpam-4815	93	12	3.1	3.1	NUM
ejpam-4815	93	13	]	]	PUNCT
ejpam-4815	93	14	.	.	PUNCT
ejpam-4815	94	1	lemma	lemma	PROPN
ejpam-4815	94	2	2.3	2.3	NUM
ejpam-4815	94	3	.	.	PUNCT
ejpam-4815	95	1	let	let	VERB
ejpam-4815	95	2	f	f	PROPN
ejpam-4815	95	3	∈	∈	PROPN
ejpam-4815	95	4	aβ(sr	aβ(sr	PROPN
ejpam-4815	95	5	)	)	PUNCT
ejpam-4815	95	6	,	,	PUNCT
ejpam-4815	95	7	r	r	NOUN
ejpam-4815	95	8	′	′	NUM
ejpam-4815	95	9	>	>	X
ejpam-4815	95	10	1	1	NUM
ejpam-4815	95	11	,	,	PUNCT
ejpam-4815	95	12	be	be	AUX
ejpam-4815	95	13	an	an	DET
ejpam-4815	95	14	entire	entire	ADJ
ejpam-4815	95	15	gbasp	gbasp	NOUN
ejpam-4815	95	16	function	function	NOUN
ejpam-4815	95	17	.	.	PUNCT
ejpam-4815	96	1	then	then	ADV
ejpam-4815	96	2	,	,	PUNCT
ejpam-4815	96	3	for	for	ADP
ejpam-4815	96	4	all	all	DET
ejpam-4815	96	5	sufficiently	sufficiently	ADV
ejpam-4815	96	6	large	large	ADJ
ejpam-4815	96	7	values	value	NOUN
ejpam-4815	96	8	of	of	ADP
ejpam-4815	96	9	n	n	CCONJ
ejpam-4815	96	10	,	,	PUNCT
ejpam-4815	96	11	we	we	PRON
ejpam-4815	96	12	have	have	VERB
ejpam-4815	96	13	eβ	eβ	ADP
ejpam-4815	96	14	n(f	n(f	PROPN
ejpam-4815	96	15	,	,	PUNCT
ejpam-4815	96	16	r	r	NOUN
ejpam-4815	96	17	)	)	PUNCT
ejpam-4815	96	18	≤	≤	NOUN
ejpam-4815	96	19	km(r	km(r	PROPN
ejpam-4815	96	20	,	,	PUNCT
ejpam-4815	96	21	f	f	PROPN
ejpam-4815	96	22	)	)	PUNCT
ejpam-4815	96	23	(	(	PUNCT
ejpam-4815	96	24	n+	n+	NUM
ejpam-4815	96	25	1)α+	1)α+	NUM
ejpam-4815	96	26	1	1	NUM
ejpam-4815	96	27	2	2	NUM
ejpam-4815	96	28	(	(	PUNCT
ejpam-4815	96	29	r′r	r′r	NOUN
ejpam-4815	96	30	r	r	NOUN
ejpam-4815	96	31	)	)	PUNCT
ejpam-4815	96	32	2(n+1	2(n+1	NUM
ejpam-4815	96	33	)	)	PUNCT
ejpam-4815	96	34	,	,	PUNCT
ejpam-4815	96	35	(	(	PUNCT
ejpam-4815	96	36	2.5	2.5	NUM
ejpam-4815	96	37	)	)	PUNCT
ejpam-4815	96	38	where	where	SCONJ
ejpam-4815	96	39	k	k	PROPN
ejpam-4815	96	40	is	be	AUX
ejpam-4815	96	41	a	a	DET
ejpam-4815	96	42	constant	constant	ADJ
ejpam-4815	96	43	independent	independent	NOUN
ejpam-4815	96	44	of	of	ADP
ejpam-4815	96	45	n	n	PROPN
ejpam-4815	96	46	and	and	CCONJ
ejpam-4815	96	47	r	r	NOUN
ejpam-4815	96	48	and	and	CCONJ
ejpam-4815	96	49	r	r	NOUN
ejpam-4815	96	50	>	>	X
ejpam-4815	96	51	2r′r	2r′r	NUM
ejpam-4815	96	52	.	.	PUNCT
ejpam-4815	97	1	proof	proof	NOUN
ejpam-4815	97	2	.	.	PUNCT
ejpam-4815	98	1	let	let	VERB
ejpam-4815	98	2	us	we	PRON
ejpam-4815	98	3	consider	consider	VERB
ejpam-4815	98	4	the	the	DET
ejpam-4815	98	5	gbasp	gbasp	ADJ
ejpam-4815	98	6	polynomial	polynomial	PROPN
ejpam-4815	98	7	gn	gn	PROPN
ejpam-4815	98	8	,	,	PUNCT
ejpam-4815	99	1	r	r	NOUN
ejpam-4815	99	2	=	=	SYM
ejpam-4815	99	3	∞∑	∞∑	PRON
ejpam-4815	99	4	k=0	k=0	PROPN
ejpam-4815	99	5	akr	akr	NOUN
ejpam-4815	99	6	2kp	2kp	NOUN
ejpam-4815	99	7	(	(	PUNCT
ejpam-4815	99	8	µ−	µ−	PROPN
ejpam-4815	99	9	1	1	NUM
ejpam-4815	99	10	2	2	NUM
ejpam-4815	99	11	,	,	PUNCT
ejpam-4815	99	12	ν−	ν−	PROPN
ejpam-4815	99	13	1	1	NUM
ejpam-4815	99	14	2	2	NUM
ejpam-4815	99	15	)	)	PUNCT
ejpam-4815	99	16	k	k	NOUN
ejpam-4815	99	17	(	(	PUNCT
ejpam-4815	99	18	cos	cos	PROPN
ejpam-4815	99	19	2θ	2θ	NUM
ejpam-4815	99	20	)	)	PUNCT
ejpam-4815	99	21	.	.	PUNCT
ejpam-4815	100	1	then	then	ADV
ejpam-4815	100	2	gn	gn	PROPN
ejpam-4815	100	3	,	,	PUNCT
ejpam-4815	100	4	r	r	PROPN
ejpam-4815	100	5	∈	∈	PROPN
ejpam-4815	100	6	pn	pn	PROPN
ejpam-4815	100	7	,	,	PUNCT
ejpam-4815	100	8	r.	r.	PROPN
ejpam-4815	100	9	using	use	VERB
ejpam-4815	100	10	the	the	DET
ejpam-4815	100	11	definition	definition	NOUN
ejpam-4815	100	12	of	of	ADP
ejpam-4815	100	13	approximation	approximation	NOUN
ejpam-4815	100	14	error	error	NOUN
ejpam-4815	100	15	eβ	eβ	NOUN
ejpam-4815	100	16	n(f	n(f	PROPN
ejpam-4815	100	17	,	,	PUNCT
ejpam-4815	100	18	r	r	NOUN
ejpam-4815	100	19	)	)	PUNCT
ejpam-4815	100	20	for	for	ADP
ejpam-4815	100	21	all	all	DET
ejpam-4815	100	22	r	r	NOUN
ejpam-4815	100	23	,	,	PUNCT
ejpam-4815	100	24	0	0	NUM
ejpam-4815	100	25	<	<	X
ejpam-4815	100	26	r	r	X
ejpam-4815	100	27	<	<	X
ejpam-4815	100	28	r	r	NOUN
ejpam-4815	100	29	,	,	PUNCT
ejpam-4815	100	30	we	we	PRON
ejpam-4815	100	31	get	get	VERB
ejpam-4815	100	32	eβ	eβ	ADP
ejpam-4815	100	33	n(f	n(f	PROPN
ejpam-4815	100	34	,	,	PUNCT
ejpam-4815	100	35	r	r	NOUN
ejpam-4815	100	36	)	)	PUNCT
ejpam-4815	101	1	≤|f	≤|f	PROPN
ejpam-4815	101	2	−	−	PROPN
ejpam-4815	101	3	gn	gn	PROPN
ejpam-4815	101	4	,	,	PUNCT
ejpam-4815	101	5	r|β	r|β	NOUN
ejpam-4815	101	6	,	,	PUNCT
ejpam-4815	101	7	r	r	NOUN
ejpam-4815	101	8	≤	≤	NOUN
ejpam-4815	102	1	∞∑	∞∑	NUM
ejpam-4815	102	2	k	k	X
ejpam-4815	102	3	=	=	PROPN
ejpam-4815	102	4	n+1	n+1	PROPN
ejpam-4815	102	5	|ak|r2k|p	|ak|r2k|p	NUM
ejpam-4815	102	6	(	(	PUNCT
ejpam-4815	102	7	µ−	µ−	PROPN
ejpam-4815	102	8	1	1	NUM
ejpam-4815	102	9	2	2	NUM
ejpam-4815	102	10	,	,	PUNCT
ejpam-4815	102	11	ν−	ν−	PROPN
ejpam-4815	102	12	1	1	NUM
ejpam-4815	102	13	2	2	NUM
ejpam-4815	102	14	)	)	PUNCT
ejpam-4815	102	15	k	k	NOUN
ejpam-4815	103	1	(	(	PUNCT
ejpam-4815	103	2	cos	cos	PROPN
ejpam-4815	103	3	2θ)|	2θ)|	PROPN
ejpam-4815	103	4	≤	≤	ADV
ejpam-4815	103	5	1	1	NUM
ejpam-4815	103	6	γ(α+	γ(α+	DET
ejpam-4815	103	7	1	1	NUM
ejpam-4815	103	8	)	)	PUNCT
ejpam-4815	103	9	∞∑	∞∑	NUM
ejpam-4815	103	10	k	k	X
ejpam-4815	103	11	=	=	PROPN
ejpam-4815	103	12	n+1	n+1	PROPN
ejpam-4815	103	13	|ak|r2kγ(k	|ak|r2kγ(k	NOUN
ejpam-4815	103	14	+	+	CCONJ
ejpam-4815	103	15	α+	α+	PUNCT
ejpam-4815	103	16	1	1	X
ejpam-4815	103	17	)	)	PUNCT
ejpam-4815	103	18	γ(k	γ(k	NOUN
ejpam-4815	103	19	+	+	CCONJ
ejpam-4815	103	20	1	1	NUM
ejpam-4815	103	21	)	)	PUNCT
ejpam-4815	103	22	.	.	PUNCT
ejpam-4815	104	1	(	(	PUNCT
ejpam-4815	104	2	2.6	2.6	NUM
ejpam-4815	104	3	)	)	PUNCT
ejpam-4815	104	4	for	for	ADP
ejpam-4815	104	5	f	f	PROPN
ejpam-4815	104	6	∈	∈	PROPN
ejpam-4815	104	7	aβ(sr	aβ(sr	PROPN
ejpam-4815	104	8	)	)	PUNCT
ejpam-4815	104	9	,	,	PUNCT
ejpam-4815	104	10	we	we	PRON
ejpam-4815	104	11	have	have	VERB
ejpam-4815	104	12	[	[	X
ejpam-4815	104	13	5	5	NUM
ejpam-4815	104	14	]	]	SYM
ejpam-4815	104	15	|ak|	|ak|	PROPN
ejpam-4815	104	16	≤	≤	PROPN
ejpam-4815	104	17	m(r	m(r	PROPN
ejpam-4815	104	18	,	,	PUNCT
ejpam-4815	104	19	f	f	NOUN
ejpam-4815	104	20	)	)	PUNCT
ejpam-4815	105	1	r2k	r2k	PROPN
ejpam-4815	105	2	[	[	X
ejpam-4815	105	3	(	(	PUNCT
ejpam-4815	105	4	2k	2k	NUM
ejpam-4815	105	5	+	+	CCONJ
ejpam-4815	105	6	µ+	µ+	X
ejpam-4815	105	7	ν)c(k	ν)c(k	PROPN
ejpam-4815	105	8	,	,	PUNCT
ejpam-4815	105	9	µ	µ	NOUN
ejpam-4815	105	10	,	,	PUNCT
ejpam-4815	105	11	ν)c(µ	ν)c(µ	NOUN
ejpam-4815	105	12	,	,	PUNCT
ejpam-4815	105	13	ν	ν	NOUN
ejpam-4815	105	14	)	)	PUNCT
ejpam-4815	105	15	]	]	PUNCT
ejpam-4815	105	16	1	1	NUM
ejpam-4815	105	17	2	2	NUM
ejpam-4815	105	18	(	(	PUNCT
ejpam-4815	105	19	2.7	2.7	NUM
ejpam-4815	105	20	)	)	PUNCT
ejpam-4815	105	21	d.	d.	PROPN
ejpam-4815	105	22	kumar	kumar	PROPN
ejpam-4815	105	23	/	/	SYM
ejpam-4815	105	24	eur	eur	PROPN
ejpam-4815	105	25	.	.	PUNCT
ejpam-4815	106	1	j.	j.	PROPN
ejpam-4815	106	2	pure	pure	PROPN
ejpam-4815	106	3	appl	appl	PROPN
ejpam-4815	106	4	.	.	PROPN
ejpam-4815	106	5	math	math	PROPN
ejpam-4815	106	6	,	,	PUNCT
ejpam-4815	106	7	16	16	NUM
ejpam-4815	106	8	(	(	PUNCT
ejpam-4815	106	9	3	3	NUM
ejpam-4815	106	10	)	)	PUNCT
ejpam-4815	106	11	(	(	PUNCT
ejpam-4815	106	12	2023	2023	NUM
ejpam-4815	106	13	)	)	PUNCT
ejpam-4815	106	14	,	,	PUNCT
ejpam-4815	106	15	1508	1508	NUM
ejpam-4815	106	16	-	-	SYM
ejpam-4815	106	17	1517	1517	NUM
ejpam-4815	106	18	1513	1513	NUM
ejpam-4815	106	19	for	for	ADP
ejpam-4815	106	20	every	every	DET
ejpam-4815	106	21	r	r	NOUN
ejpam-4815	106	22	<	<	X
ejpam-4815	106	23	r.	r.	PROPN
ejpam-4815	106	24	combining	combine	VERB
ejpam-4815	106	25	(	(	PUNCT
ejpam-4815	106	26	2.6	2.6	NUM
ejpam-4815	106	27	)	)	PUNCT
ejpam-4815	106	28	and	and	CCONJ
ejpam-4815	106	29	(	(	PUNCT
ejpam-4815	106	30	2.7	2.7	NUM
ejpam-4815	106	31	)	)	PUNCT
ejpam-4815	106	32	we	we	PRON
ejpam-4815	106	33	get	get	VERB
ejpam-4815	106	34	eβ	eβ	ADP
ejpam-4815	106	35	n(f	n(f	PROPN
ejpam-4815	106	36	,	,	PUNCT
ejpam-4815	106	37	r	r	NOUN
ejpam-4815	106	38	)	)	PUNCT
ejpam-4815	106	39	≤	≤	PROPN
ejpam-4815	106	40	m(r	m(r	PROPN
ejpam-4815	106	41	,	,	PUNCT
ejpam-4815	106	42	f	f	PROPN
ejpam-4815	106	43	)	)	PUNCT
ejpam-4815	107	1	γ(α+	γ(α+	DET
ejpam-4815	107	2	1	1	NUM
ejpam-4815	107	3	)	)	PUNCT
ejpam-4815	107	4	(	(	PUNCT
ejpam-4815	107	5	c(µ	c(µ	X
ejpam-4815	107	6	,	,	PUNCT
ejpam-4815	107	7	ν	ν	NOUN
ejpam-4815	107	8	)	)	PUNCT
ejpam-4815	107	9	)	)	PUNCT
ejpam-4815	108	1	1	1	NUM
ejpam-4815	108	2	2	2	NUM
ejpam-4815	108	3	∞∑	∞∑	NUM
ejpam-4815	108	4	k	k	X
ejpam-4815	108	5	=	=	X
ejpam-4815	108	6	n+1	n+1	PROPN
ejpam-4815	108	7	γ(k	γ(k	PROPN
ejpam-4815	108	8	+	+	CCONJ
ejpam-4815	108	9	α+	α+	PUNCT
ejpam-4815	108	10	1	1	X
ejpam-4815	108	11	)	)	PUNCT
ejpam-4815	108	12	γ(k	γ(k	NOUN
ejpam-4815	108	13	+	+	CCONJ
ejpam-4815	108	14	1	1	X
ejpam-4815	108	15	)	)	PUNCT
ejpam-4815	109	1	[	[	X
ejpam-4815	109	2	(	(	PUNCT
ejpam-4815	109	3	2k+	2k+	NUM
ejpam-4815	109	4	µ+	µ+	NOUN
ejpam-4815	109	5	ν)c(k	ν)c(k	PROPN
ejpam-4815	109	6	,	,	PUNCT
ejpam-4815	109	7	µ	µ	NOUN
ejpam-4815	109	8	,	,	PUNCT
ejpam-4815	109	9	ν	ν	NOUN
ejpam-4815	109	10	)	)	PUNCT
ejpam-4815	109	11	]	]	PUNCT
ejpam-4815	109	12	1	1	NUM
ejpam-4815	109	13	2	2	NUM
ejpam-4815	109	14	(	(	PUNCT
ejpam-4815	109	15	r	r	NOUN
ejpam-4815	109	16	r	r	NOUN
ejpam-4815	109	17	)	)	PUNCT
ejpam-4815	109	18	2k	2k	NUM
ejpam-4815	109	19	.	.	PUNCT
ejpam-4815	110	1	(	(	PUNCT
ejpam-4815	110	2	2.8	2.8	NUM
ejpam-4815	110	3	)	)	PUNCT
ejpam-4815	110	4	since	since	SCONJ
ejpam-4815	110	5	γ(x+a	γ(x+a	NOUN
ejpam-4815	110	6	)	)	PUNCT
ejpam-4815	110	7	γ(x	γ(x	NOUN
ejpam-4815	110	8	)	)	PUNCT
ejpam-4815	110	9	∼	∼	NOUN
ejpam-4815	110	10	xa	xa	PROPN
ejpam-4815	110	11	as	as	ADP
ejpam-4815	110	12	x→	x→	PROPN
ejpam-4815	110	13	∞	∞	PROPN
ejpam-4815	110	14	,	,	PUNCT
ejpam-4815	110	15	we	we	PRON
ejpam-4815	110	16	have	have	AUX
ejpam-4815	110	17	γ(k	γ(k	NOUN
ejpam-4815	110	18	+	+	CCONJ
ejpam-4815	110	19	α+	α+	PUNCT
ejpam-4815	110	20	1	1	X
ejpam-4815	110	21	)	)	PUNCT
ejpam-4815	110	22	γ(k	γ(k	NOUN
ejpam-4815	110	23	+	+	CCONJ
ejpam-4815	110	24	1	1	X
ejpam-4815	110	25	)	)	PUNCT
ejpam-4815	111	1	[	[	X
ejpam-4815	111	2	(	(	PUNCT
ejpam-4815	111	3	2k	2k	NUM
ejpam-4815	111	4	+	+	CCONJ
ejpam-4815	111	5	µ+	µ+	X
ejpam-4815	111	6	ν)c(k	ν)c(k	PROPN
ejpam-4815	111	7	,	,	PUNCT
ejpam-4815	111	8	µ	µ	NOUN
ejpam-4815	111	9	,	,	PUNCT
ejpam-4815	111	10	ν	ν	NOUN
ejpam-4815	111	11	)	)	PUNCT
ejpam-4815	111	12	]	]	PUNCT
ejpam-4815	111	13	1	1	NUM
ejpam-4815	111	14	2	2	NUM
ejpam-4815	111	15	∼	∼	NOUN
ejpam-4815	111	16	√	√	NOUN
ejpam-4815	111	17	2kα+	2kα+	NUM
ejpam-4815	111	18	1	1	NUM
ejpam-4815	111	19	2	2	NUM
ejpam-4815	111	20	as	as	ADP
ejpam-4815	111	21	k	k	PROPN
ejpam-4815	111	22	→	→	SYM
ejpam-4815	111	23	∞.	∞.	PROPN
ejpam-4815	111	24	hence	hence	ADV
ejpam-4815	111	25	γ(k	γ(k	PROPN
ejpam-4815	111	26	+	+	CCONJ
ejpam-4815	111	27	α+	α+	PUNCT
ejpam-4815	111	28	1	1	X
ejpam-4815	111	29	)	)	PUNCT
ejpam-4815	111	30	γ(k	γ(k	NOUN
ejpam-4815	111	31	+	+	CCONJ
ejpam-4815	111	32	1	1	X
ejpam-4815	111	33	)	)	PUNCT
ejpam-4815	112	1	[	[	X
ejpam-4815	112	2	(	(	PUNCT
ejpam-4815	112	3	2k	2k	NUM
ejpam-4815	112	4	+	+	CCONJ
ejpam-4815	112	5	µ+	µ+	X
ejpam-4815	112	6	ν)c(k	ν)c(k	PROPN
ejpam-4815	112	7	,	,	PUNCT
ejpam-4815	112	8	µ	µ	NOUN
ejpam-4815	112	9	,	,	PUNCT
ejpam-4815	112	10	ν	ν	NOUN
ejpam-4815	112	11	)	)	PUNCT
ejpam-4815	112	12	]	]	PUNCT
ejpam-4815	112	13	1	1	NUM
ejpam-4815	112	14	2	2	NUM
ejpam-4815	112	15	<	<	SYM
ejpam-4815	112	16	2	2	NUM
ejpam-4815	112	17	√	√	NUM
ejpam-4815	112	18	2kα+	2kα+	NUM
ejpam-4815	112	19	1	1	NUM
ejpam-4815	112	20	2	2	NUM
ejpam-4815	112	21	for	for	ADP
ejpam-4815	112	22	all	all	DET
ejpam-4815	112	23	k	k	PROPN
ejpam-4815	112	24	>	>	X
ejpam-4815	112	25	k0	k0	PROPN
ejpam-4815	112	26	.	.	PUNCT
ejpam-4815	113	1	thus	thus	ADV
ejpam-4815	113	2	,	,	PUNCT
ejpam-4815	113	3	for	for	ADP
ejpam-4815	113	4	n	n	PROPN
ejpam-4815	113	5	>	>	X
ejpam-4815	113	6	k0	k0	PROPN
ejpam-4815	113	7	and	and	CCONJ
ejpam-4815	113	8	r	r	X
ejpam-4815	113	9	>	>	X
ejpam-4815	113	10	2r′r	2r′r	NUM
ejpam-4815	113	11	,	,	PUNCT
ejpam-4815	113	12	using	use	VERB
ejpam-4815	113	13	(	(	PUNCT
ejpam-4815	113	14	2.8	2.8	NUM
ejpam-4815	113	15	)	)	PUNCT
ejpam-4815	113	16	with	with	ADP
ejpam-4815	113	17	above	above	ADP
ejpam-4815	113	18	inequality	inequality	NOUN
ejpam-4815	113	19	,	,	PUNCT
ejpam-4815	113	20	we	we	PRON
ejpam-4815	113	21	obtain	obtain	VERB
ejpam-4815	113	22	eβ	eβ	ADP
ejpam-4815	113	23	n(f	n(f	PROPN
ejpam-4815	113	24	,	,	PUNCT
ejpam-4815	113	25	r	r	NOUN
ejpam-4815	113	26	)	)	PUNCT
ejpam-4815	113	27	≤	≤	PROPN
ejpam-4815	113	28	m(r	m(r	PROPN
ejpam-4815	113	29	,	,	PUNCT
ejpam-4815	113	30	f	f	PROPN
ejpam-4815	113	31	)	)	PUNCT
ejpam-4815	114	1	γ(α+	γ(α+	DET
ejpam-4815	114	2	1	1	NUM
ejpam-4815	114	3	)	)	PUNCT
ejpam-4815	114	4	2(2c(µ	2(2c(µ	NUM
ejpam-4815	114	5	,	,	PUNCT
ejpam-4815	114	6	ν	ν	NOUN
ejpam-4815	114	7	)	)	PUNCT
ejpam-4815	114	8	)	)	PUNCT
ejpam-4815	114	9	1	1	NUM
ejpam-4815	114	10	2	2	NUM
ejpam-4815	114	11	∞∑	∞∑	NUM
ejpam-4815	114	12	k	k	X
ejpam-4815	114	13	=	=	X
ejpam-4815	114	14	n+1	n+1	PROPN
ejpam-4815	114	15	kα+	kα+	NOUN
ejpam-4815	114	16	1	1	NUM
ejpam-4815	114	17	2	2	NUM
ejpam-4815	114	18	(	(	PUNCT
ejpam-4815	114	19	r′r	r′r	NOUN
ejpam-4815	114	20	r	r	NOUN
ejpam-4815	114	21	)	)	PUNCT
ejpam-4815	114	22	2k	2k	PROPN
ejpam-4815	114	23	≤	≤	PROPN
ejpam-4815	114	24	m(r	m(r	PROPN
ejpam-4815	114	25	,	,	PUNCT
ejpam-4815	114	26	f	f	PROPN
ejpam-4815	114	27	)	)	PUNCT
ejpam-4815	115	1	γ(α+	γ(α+	DET
ejpam-4815	115	2	1	1	NUM
ejpam-4815	115	3	)	)	PUNCT
ejpam-4815	115	4	2(2c(µ	2(2c(µ	NUM
ejpam-4815	115	5	,	,	PUNCT
ejpam-4815	115	6	ν	ν	NOUN
ejpam-4815	115	7	)	)	PUNCT
ejpam-4815	115	8	)	)	PUNCT
ejpam-4815	115	9	1	1	NUM
ejpam-4815	115	10	2	2	NUM
ejpam-4815	115	11	(	(	PUNCT
ejpam-4815	115	12	n+)α+	n+)α+	NUM
ejpam-4815	115	13	1	1	NUM
ejpam-4815	115	14	2	2	NUM
ejpam-4815	115	15	(	(	PUNCT
ejpam-4815	115	16	r′r	r′r	NOUN
ejpam-4815	115	17	r	r	NOUN
ejpam-4815	115	18	)	)	PUNCT
ejpam-4815	115	19	2(n+1	2(n+1	NUM
ejpam-4815	115	20	)	)	PUNCT
ejpam-4815	116	1	∞∑	∞∑	DET
ejpam-4815	116	2	k=0	k=0	PROPN
ejpam-4815	116	3	(	(	PUNCT
ejpam-4815	116	4	1	1	NUM
ejpam-4815	116	5	+	+	CCONJ
ejpam-4815	116	6	k	k	PROPN
ejpam-4815	116	7	k0	k0	PROPN
ejpam-4815	116	8	+	+	CCONJ
ejpam-4815	116	9	1	1	NUM
ejpam-4815	116	10	)	)	PUNCT
ejpam-4815	116	11	α+	α+	PUNCT
ejpam-4815	116	12	1	1	NUM
ejpam-4815	116	13	2	2	NUM
ejpam-4815	116	14	(	(	PUNCT
ejpam-4815	116	15	r′r	r′r	NOUN
ejpam-4815	116	16	r	r	NOUN
ejpam-4815	116	17	)	)	PUNCT
ejpam-4815	116	18	2k	2k	NOUN
ejpam-4815	116	19	.	.	PUNCT
ejpam-4815	117	1	hence	hence	ADV
ejpam-4815	117	2	the	the	DET
ejpam-4815	117	3	proof	proof	NOUN
ejpam-4815	117	4	is	be	AUX
ejpam-4815	117	5	completed	complete	VERB
ejpam-4815	117	6	from	from	ADP
ejpam-4815	117	7	the	the	DET
ejpam-4815	117	8	above	above	ADJ
ejpam-4815	117	9	inequality	inequality	NOUN
ejpam-4815	117	10	.	.	PUNCT
ejpam-4815	118	1	lemma	lemma	PROPN
ejpam-4815	118	2	2.4	2.4	NUM
ejpam-4815	118	3	.	.	PUNCT
ejpam-4815	119	1	let	let	VERB
ejpam-4815	119	2	f	f	PROPN
ejpam-4815	119	3	∈	∈	PROPN
ejpam-4815	119	4	aβ(sr	aβ(sr	PROPN
ejpam-4815	119	5	)	)	PUNCT
ejpam-4815	119	6	,	,	PUNCT
ejpam-4815	119	7	r	r	NOUN
ejpam-4815	119	8	>	>	X
ejpam-4815	119	9	r∗	r∗	PROPN
ejpam-4815	119	10	,	,	PUNCT
ejpam-4815	119	11	be	be	AUX
ejpam-4815	119	12	an	an	DET
ejpam-4815	119	13	entire	entire	ADJ
ejpam-4815	119	14	gbasp	gbasp	NOUN
ejpam-4815	119	15	function	function	NOUN
ejpam-4815	119	16	.	.	PUNCT
ejpam-4815	120	1	then	then	ADV
ejpam-4815	120	2	h(z	h(z	NOUN
ejpam-4815	120	3	)	)	PUNCT
ejpam-4815	120	4	=	=	PUNCT
ejpam-4815	121	1	∞∑	∞∑	NUM
ejpam-4815	121	2	n=1	n=1	PUNCT
ejpam-4815	121	3	[	[	PUNCT
ejpam-4815	121	4	2(n+	2(n+	NUM
ejpam-4815	121	5	1)(2n+	1)(2n+	PROPN
ejpam-4815	121	6	µ+	µ+	X
ejpam-4815	121	7	ν)c(n	ν)c(n	PROPN
ejpam-4815	121	8	,	,	PUNCT
ejpam-4815	121	9	µ	µ	X
ejpam-4815	121	10	,	,	PUNCT
ejpam-4815	121	11	ν)(n+	ν)(n+	PROPN
ejpam-4815	121	12	1)α	1)α	NUM
ejpam-4815	121	13	γ(n+	γ(n+	NUM
ejpam-4815	121	14	1	1	NUM
ejpam-4815	121	15	)	)	PUNCT
ejpam-4815	121	16	]	]	PUNCT
ejpam-4815	121	17	2eβ	2eβ	PROPN
ejpam-4815	121	18	n−1(f	n−1(f	PROPN
ejpam-4815	121	19	,	,	PUNCT
ejpam-4815	121	20	r	r	NOUN
ejpam-4815	121	21	)	)	PUNCT
ejpam-4815	121	22	(	(	PUNCT
ejpam-4815	121	23	z	z	NOUN
ejpam-4815	121	24	r∗	r∗	PROPN
ejpam-4815	121	25	)	)	PUNCT
ejpam-4815	121	26	2n	2n	NUM
ejpam-4815	121	27	(	(	PUNCT
ejpam-4815	121	28	2.9	2.9	NUM
ejpam-4815	121	29	)	)	PUNCT
ejpam-4815	121	30	is	be	AUX
ejpam-4815	121	31	entire	entire	ADJ
ejpam-4815	121	32	.	.	PUNCT
ejpam-4815	122	1	further	far	ADV
ejpam-4815	122	2	,	,	PUNCT
ejpam-4815	122	3	ρ(f	ρ(f	NOUN
ejpam-4815	122	4	)	)	PUNCT
ejpam-4815	122	5	=	=	SYM
ejpam-4815	123	1	ρ(h	ρ(h	X
ejpam-4815	123	2	)	)	PUNCT
ejpam-4815	123	3	and	and	CCONJ
ejpam-4815	123	4	for	for	ADP
ejpam-4815	123	5	b	b	PROPN
ejpam-4815	123	6	<	<	X
ejpam-4815	123	7	ρ(f	ρ(f	PROPN
ejpam-4815	123	8	)	)	PUNCT
ejpam-4815	123	9	=	=	SYM
ejpam-4815	123	10	ρ(h	ρ(h	X
ejpam-4815	123	11	)	)	PUNCT
ejpam-4815	123	12	<	<	X
ejpam-4815	123	13	∞	∞	PROPN
ejpam-4815	123	14	,	,	PUNCT
ejpam-4815	123	15	t	t	PROPN
ejpam-4815	123	16	∗(f	∗(f	PROPN
ejpam-4815	123	17	)	)	PUNCT
ejpam-4815	124	1	=	=	PUNCT
ejpam-4815	124	2	γt	γt	PROPN
ejpam-4815	124	3	∗(h	∗(h	PROPN
ejpam-4815	124	4	)	)	PUNCT
ejpam-4815	124	5	.	.	PUNCT
ejpam-4815	125	1	proof	proof	NOUN
ejpam-4815	125	2	.	.	PUNCT
ejpam-4815	126	1	since	since	SCONJ
ejpam-4815	126	2	[	[	PUNCT
ejpam-4815	126	3	2(n+	2(n+	NUM
ejpam-4815	126	4	1)(2n+	1)(2n+	PROPN
ejpam-4815	126	5	µ+	µ+	X
ejpam-4815	126	6	ν)c(n	ν)c(n	PROPN
ejpam-4815	126	7	,	,	PUNCT
ejpam-4815	126	8	µ	µ	X
ejpam-4815	126	9	,	,	PUNCT
ejpam-4815	126	10	ν)(n+	ν)(n+	PROPN
ejpam-4815	126	11	1)α	1)α	NUM
ejpam-4815	126	12	γ(n+	γ(n+	NUM
ejpam-4815	126	13	1	1	NUM
ejpam-4815	126	14	)	)	PUNCT
ejpam-4815	126	15	]	]	PUNCT
ejpam-4815	126	16	1	1	NUM
ejpam-4815	126	17	2n	2n	NUM
ejpam-4815	126	18	∼	∼	NOUN
ejpam-4815	126	19	(	(	PUNCT
ejpam-4815	126	20	√	√	NUM
ejpam-4815	126	21	2(n+	2(n+	NUM
ejpam-4815	126	22	1	1	NUM
ejpam-4815	126	23	)	)	PUNCT
ejpam-4815	126	24	√	√	NOUN
ejpam-4815	126	25	2nα+	2nα+	NUM
ejpam-4815	126	26	1	1	NUM
ejpam-4815	126	27	2	2	NUM
ejpam-4815	126	28	)	)	PUNCT
ejpam-4815	126	29	1	1	NUM
ejpam-4815	126	30	n	n	PROPN
ejpam-4815	126	31	→	→	SYM
ejpam-4815	126	32	1	1	NUM
ejpam-4815	126	33	as	as	ADP
ejpam-4815	126	34	n→	n→	ADV
ejpam-4815	126	35	∞	∞	PROPN
ejpam-4815	126	36	,	,	PUNCT
ejpam-4815	126	37	it	it	PRON
ejpam-4815	126	38	follows	follow	VERB
ejpam-4815	126	39	from	from	ADP
ejpam-4815	126	40	lemma	lemma	PROPN
ejpam-4815	126	41	2.2	2.2	NUM
ejpam-4815	126	42	that	that	SCONJ
ejpam-4815	126	43	h(z	h(z	NOUN
ejpam-4815	126	44	)	)	PUNCT
ejpam-4815	126	45	is	be	AUX
ejpam-4815	126	46	entire	entire	ADJ
ejpam-4815	126	47	and	and	CCONJ
ejpam-4815	126	48	eβ	eβ	NOUN
ejpam-4815	126	49	n(f	n(f	PROPN
ejpam-4815	126	50	,	,	PUNCT
ejpam-4815	126	51	r	r	NOUN
ejpam-4815	126	52	)	)	PUNCT
ejpam-4815	126	53	≤	≤	NOUN
ejpam-4815	126	54	km(r	km(r	NOUN
ejpam-4815	127	1	+	+	CCONJ
ejpam-4815	127	2	1	1	NUM
ejpam-4815	127	3	,	,	PUNCT
ejpam-4815	127	4	f	f	NOUN
ejpam-4815	127	5	)	)	PUNCT
ejpam-4815	127	6	(	(	PUNCT
ejpam-4815	127	7	r′r	r′r	NOUN
ejpam-4815	127	8	r	r	NOUN
ejpam-4815	127	9	+	+	CCONJ
ejpam-4815	127	10	1	1	NUM
ejpam-4815	127	11	)	)	PUNCT
ejpam-4815	127	12	2n	2n	NUM
ejpam-4815	127	13	,	,	PUNCT
ejpam-4815	127	14	we	we	PRON
ejpam-4815	127	15	have	have	VERB
ejpam-4815	127	16	h(z	h(z	NOUN
ejpam-4815	127	17	)	)	PUNCT
ejpam-4815	127	18	=	=	SYM
ejpam-4815	128	1	∞∑	∞∑	NUM
ejpam-4815	128	2	n=1	n=1	PUNCT
ejpam-4815	128	3	[	[	PUNCT
ejpam-4815	128	4	2(n+	2(n+	NUM
ejpam-4815	128	5	1)(2n+	1)(2n+	PROPN
ejpam-4815	128	6	µ+	µ+	X
ejpam-4815	128	7	ν)c(n	ν)c(n	PROPN
ejpam-4815	128	8	,	,	PUNCT
ejpam-4815	128	9	µ	µ	X
ejpam-4815	128	10	,	,	PUNCT
ejpam-4815	128	11	ν)(n+	ν)(n+	PROPN
ejpam-4815	128	12	1)α	1)α	NUM
ejpam-4815	128	13	γ(n+	γ(n+	NUM
ejpam-4815	128	14	1	1	NUM
ejpam-4815	128	15	)	)	PUNCT
ejpam-4815	128	16	]	]	PUNCT
ejpam-4815	128	17	2eβ	2eβ	PROPN
ejpam-4815	128	18	n−1(f	n−1(f	PROPN
ejpam-4815	128	19	,	,	PUNCT
ejpam-4815	128	20	r	r	NOUN
ejpam-4815	128	21	)	)	PUNCT
ejpam-4815	128	22	(	(	PUNCT
ejpam-4815	128	23	z	z	NOUN
ejpam-4815	128	24	r∗	r∗	PROPN
ejpam-4815	128	25	)	)	PUNCT
ejpam-4815	128	26	2n	2n	NUM
ejpam-4815	128	27	,	,	PUNCT
ejpam-4815	128	28	d.	d.	PROPN
ejpam-4815	128	29	kumar	kumar	PROPN
ejpam-4815	128	30	/	/	SYM
ejpam-4815	128	31	eur	eur	PROPN
ejpam-4815	128	32	.	.	PUNCT
ejpam-4815	129	1	j.	j.	PROPN
ejpam-4815	129	2	pure	pure	PROPN
ejpam-4815	129	3	appl	appl	PROPN
ejpam-4815	129	4	.	.	PROPN
ejpam-4815	129	5	math	math	PROPN
ejpam-4815	129	6	,	,	PUNCT
ejpam-4815	129	7	16	16	NUM
ejpam-4815	129	8	(	(	PUNCT
ejpam-4815	129	9	3	3	NUM
ejpam-4815	129	10	)	)	PUNCT
ejpam-4815	129	11	(	(	PUNCT
ejpam-4815	129	12	2023	2023	NUM
ejpam-4815	129	13	)	)	PUNCT
ejpam-4815	129	14	,	,	PUNCT
ejpam-4815	129	15	1508	1508	NUM
ejpam-4815	129	16	-	-	SYM
ejpam-4815	129	17	1517	1517	NUM
ejpam-4815	129	18	1514	1514	NUM
ejpam-4815	129	19	so	so	SCONJ
ejpam-4815	129	20	we	we	PRON
ejpam-4815	129	21	get	get	VERB
ejpam-4815	129	22	m	m	VERB
ejpam-4815	129	23	(	(	PUNCT
ejpam-4815	129	24	r	r	NOUN
ejpam-4815	129	25	rr′	rr′	PROPN
ejpam-4815	129	26	,	,	PUNCT
ejpam-4815	129	27	h	h	NOUN
ejpam-4815	129	28	)	)	PUNCT
ejpam-4815	129	29	≤q(r	≤q(r	NOUN
ejpam-4815	129	30	)	)	PUNCT
ejpam-4815	130	1	+	+	NOUN
ejpam-4815	130	2	km(r	km(r	X
ejpam-4815	130	3	+	+	X
ejpam-4815	130	4	1	1	NUM
ejpam-4815	130	5	,	,	PUNCT
ejpam-4815	130	6	f	f	NOUN
ejpam-4815	130	7	)	)	PUNCT
ejpam-4815	131	1	∞∑	∞∑	PRON
ejpam-4815	131	2	n=0	n=0	NUM
ejpam-4815	131	3	[	[	PUNCT
ejpam-4815	131	4	r	r	NOUN
ejpam-4815	131	5	r∗(r	r∗(r	NOUN
ejpam-4815	131	6	+	+	CCONJ
ejpam-4815	131	7	1	1	NUM
ejpam-4815	131	8	)	)	PUNCT
ejpam-4815	131	9	]	]	PUNCT
ejpam-4815	131	10	2n	2n	X
ejpam-4815	131	11	=	=	SYM
ejpam-4815	131	12	q(r	q(r	PROPN
ejpam-4815	131	13	)	)	PUNCT
ejpam-4815	132	1	+	+	PROPN
ejpam-4815	132	2	k	k	PROPN
ejpam-4815	132	3	r∗	r∗	VERB
ejpam-4815	132	4	2(r	2(r	NUM
ejpam-4815	133	1	+	+	NUM
ejpam-4815	133	2	1)2m(r	1)2m(r	NUM
ejpam-4815	133	3	+	+	CCONJ
ejpam-4815	133	4	1	1	NUM
ejpam-4815	133	5	,	,	PUNCT
ejpam-4815	133	6	f	f	NOUN
ejpam-4815	133	7	)	)	PUNCT
ejpam-4815	133	8	(	(	PUNCT
ejpam-4815	133	9	r	r	NOUN
ejpam-4815	133	10	+	+	SYM
ejpam-4815	133	11	1)2r∗	1)2r∗	NUM
ejpam-4815	133	12	2	2	NUM
ejpam-4815	133	13	−	−	NOUN
ejpam-4815	133	14	r2	r2	PROPN
ejpam-4815	133	15	,	,	PUNCT
ejpam-4815	133	16	r′	r′	PROPN
ejpam-4815	133	17	>	>	X
ejpam-4815	133	18	1	1	NUM
ejpam-4815	133	19	,	,	PUNCT
ejpam-4815	133	20	(	(	PUNCT
ejpam-4815	133	21	2.10	2.10	NUM
ejpam-4815	133	22	)	)	PUNCT
ejpam-4815	133	23	where	where	SCONJ
ejpam-4815	133	24	q(r	q(r	PROPN
ejpam-4815	133	25	)	)	PUNCT
ejpam-4815	133	26	is	be	AUX
ejpam-4815	133	27	a	a	DET
ejpam-4815	133	28	polynomial	polynomial	NOUN
ejpam-4815	133	29	for	for	ADP
ejpam-4815	133	30	all	all	DET
ejpam-4815	133	31	sufficiently	sufficiently	ADV
ejpam-4815	133	32	large	large	ADJ
ejpam-4815	133	33	value	value	NOUN
ejpam-4815	133	34	of	of	ADP
ejpam-4815	133	35	r.	r.	PROPN
ejpam-4815	133	36	on	on	ADP
ejpam-4815	133	37	the	the	DET
ejpam-4815	133	38	other	other	ADJ
ejpam-4815	133	39	hand	hand	NOUN
ejpam-4815	133	40	,	,	PUNCT
ejpam-4815	133	41	using	use	VERB
ejpam-4815	133	42	(	(	PUNCT
ejpam-4815	133	43	1.2	1.2	NUM
ejpam-4815	133	44	)	)	PUNCT
ejpam-4815	133	45	,	,	PUNCT
ejpam-4815	133	46	(	(	PUNCT
ejpam-4815	133	47	2.2	2.2	NUM
ejpam-4815	133	48	)	)	PUNCT
ejpam-4815	133	49	and	and	CCONJ
ejpam-4815	133	50	lemma	lemma	PROPN
ejpam-4815	133	51	2.1	2.1	NUM
ejpam-4815	133	52	,	,	PUNCT
ejpam-4815	133	53	we	we	PRON
ejpam-4815	133	54	get	get	VERB
ejpam-4815	133	55	|	|	ADV
ejpam-4815	133	56	∞∑	∞∑	NUM
ejpam-4815	133	57	n=0	n=0	NUM
ejpam-4815	133	58	anr	anr	NOUN
ejpam-4815	133	59	2np	2np	NOUN
ejpam-4815	133	60	(	(	PUNCT
ejpam-4815	133	61	µ−	µ−	PROPN
ejpam-4815	133	62	1	1	NUM
ejpam-4815	133	63	2	2	NUM
ejpam-4815	133	64	,	,	PUNCT
ejpam-4815	133	65	ν−	ν−	PROPN
ejpam-4815	133	66	1	1	NUM
ejpam-4815	133	67	2	2	NUM
ejpam-4815	133	68	)	)	PUNCT
ejpam-4815	133	69	n	n	CCONJ
ejpam-4815	133	70	(	(	PUNCT
ejpam-4815	133	71	cos	cos	PROPN
ejpam-4815	133	72	2θ)|	2θ)|	NOUN
ejpam-4815	133	73	≤	≤	NUM
ejpam-4815	133	74	|a0|+	|a0|+	X
ejpam-4815	133	75	1	1	NUM
ejpam-4815	133	76	γ(α+	γ(α+	DET
ejpam-4815	133	77	1	1	NUM
ejpam-4815	133	78	)	)	PUNCT
ejpam-4815	133	79	∞∑	∞∑	NUM
ejpam-4815	133	80	n=1	n=1	PROPN
ejpam-4815	133	81	|ak|r2nγ(n+	|ak|r2nγ(n+	PROPN
ejpam-4815	133	82	α+	α+	PUNCT
ejpam-4815	133	83	1	1	NUM
ejpam-4815	133	84	)	)	PUNCT
ejpam-4815	133	85	γ(n+	γ(n+	PRON
ejpam-4815	133	86	1	1	NUM
ejpam-4815	133	87	)	)	PUNCT
ejpam-4815	133	88	≤	≤	NOUN
ejpam-4815	133	89	|a0|+	|a0|+	X
ejpam-4815	134	1	+	+	NOUN
ejpam-4815	134	2	kk0	kk0	NOUN
ejpam-4815	134	3	∞∑	∞∑	NUM
ejpam-4815	134	4	n=1	n=1	PROPN
ejpam-4815	134	5	[	[	PUNCT
ejpam-4815	134	6	2(n+	2(n+	NUM
ejpam-4815	134	7	1)(2n+	1)(2n+	PROPN
ejpam-4815	134	8	µ+	µ+	X
ejpam-4815	134	9	ν)c(n	ν)c(n	PROPN
ejpam-4815	134	10	,	,	PUNCT
ejpam-4815	134	11	µ	µ	X
ejpam-4815	134	12	,	,	PUNCT
ejpam-4815	134	13	ν)(n+	ν)(n+	PROPN
ejpam-4815	134	14	1)α	1)α	NUM
ejpam-4815	134	15	γ(n+	γ(n+	NUM
ejpam-4815	134	16	1	1	NUM
ejpam-4815	134	17	)	)	PUNCT
ejpam-4815	134	18	]	]	PUNCT
ejpam-4815	134	19	2×	2×	NUM
ejpam-4815	134	20	×	×	PROPN
ejpam-4815	134	21	eβ	eβ	PROPN
ejpam-4815	134	22	n−1(f	n−1(f	PROPN
ejpam-4815	134	23	,	,	PUNCT
ejpam-4815	134	24	r	r	NOUN
ejpam-4815	134	25	)	)	PUNCT
ejpam-4815	134	26	(	(	PUNCT
ejpam-4815	134	27	r	r	NOUN
ejpam-4815	134	28	r0	r0	NOUN
ejpam-4815	134	29	)	)	PUNCT
ejpam-4815	134	30	2n+2	2n+2	PROPN
ejpam-4815	134	31	,	,	PUNCT
ejpam-4815	134	32	z	z	PROPN
ejpam-4815	134	33	∈	∈	PROPN
ejpam-4815	134	34	sr	sr	PROPN
ejpam-4815	134	35	,	,	PUNCT
ejpam-4815	134	36	r0	r0	NOUN
ejpam-4815	134	37	<	<	X
ejpam-4815	134	38	r.	r.	PROPN
ejpam-4815	134	39	or	or	CCONJ
ejpam-4815	134	40	m(r	m(r	PROPN
ejpam-4815	134	41	,	,	PUNCT
ejpam-4815	134	42	f	f	PROPN
ejpam-4815	134	43	)	)	PUNCT
ejpam-4815	134	44	≤m	≤m	PROPN
ejpam-4815	134	45	(	(	PUNCT
ejpam-4815	134	46	r	r	NOUN
ejpam-4815	134	47	r0	r0	NOUN
ejpam-4815	134	48	,	,	PUNCT
ejpam-4815	134	49	|a0|+kk0h(z	|a0|+kk0h(z	NOUN
ejpam-4815	134	50	)	)	PUNCT
ejpam-4815	134	51	)	)	PUNCT
ejpam-4815	134	52	.	.	PUNCT
ejpam-4815	135	1	(	(	PUNCT
ejpam-4815	135	2	2.11	2.11	NUM
ejpam-4815	135	3	)	)	PUNCT
ejpam-4815	135	4	now	now	ADV
ejpam-4815	135	5	the	the	DET
ejpam-4815	135	6	proof	proof	NOUN
ejpam-4815	135	7	follows	follow	VERB
ejpam-4815	135	8	from	from	ADP
ejpam-4815	135	9	(	(	PUNCT
ejpam-4815	135	10	2.10	2.10	NUM
ejpam-4815	135	11	)	)	PUNCT
ejpam-4815	135	12	and	and	CCONJ
ejpam-4815	135	13	(	(	PUNCT
ejpam-4815	135	14	2.11	2.11	NUM
ejpam-4815	135	15	)	)	PUNCT
ejpam-4815	135	16	.	.	PUNCT
ejpam-4815	136	1	3	3	X
ejpam-4815	136	2	.	.	X
ejpam-4815	136	3	main	main	ADJ
ejpam-4815	136	4	results	result	NOUN
ejpam-4815	136	5	in	in	ADP
ejpam-4815	136	6	this	this	DET
ejpam-4815	136	7	section	section	NOUN
ejpam-4815	136	8	we	we	PRON
ejpam-4815	136	9	will	will	AUX
ejpam-4815	136	10	prove	prove	VERB
ejpam-4815	136	11	our	our	PRON
ejpam-4815	136	12	main	main	ADJ
ejpam-4815	136	13	results	result	NOUN
ejpam-4815	136	14	.	.	PUNCT
ejpam-4815	137	1	theorem	theorem	VERB
ejpam-4815	137	2	3.1	3.1	NUM
ejpam-4815	137	3	.	.	PUNCT
ejpam-4815	138	1	let	let	VERB
ejpam-4815	138	2	the	the	DET
ejpam-4815	138	3	gbasp	gbasp	NOUN
ejpam-4815	138	4	f	f	PROPN
ejpam-4815	138	5	∈	∈	PROPN
ejpam-4815	138	6	aβ(s1	aβ(s1	NOUN
ejpam-4815	138	7	)	)	PUNCT
ejpam-4815	138	8	,	,	PUNCT
ejpam-4815	138	9	β	β	X
ejpam-4815	138	10	≥	≥	NUM
ejpam-4815	138	11	1	1	NUM
ejpam-4815	138	12	.	.	PUNCT
ejpam-4815	139	1	then	then	ADV
ejpam-4815	139	2	f	f	PROPN
ejpam-4815	139	3	harmonically	harmonically	ADV
ejpam-4815	139	4	continues	continue	VERB
ejpam-4815	139	5	as	as	ADP
ejpam-4815	139	6	an	an	DET
ejpam-4815	139	7	entire	entire	ADJ
ejpam-4815	139	8	function	function	NOUN
ejpam-4815	139	9	gbasp	gbasp	NOUN
ejpam-4815	139	10	if	if	SCONJ
ejpam-4815	139	11	and	and	CCONJ
ejpam-4815	139	12	only	only	ADV
ejpam-4815	140	1	if	if	SCONJ
ejpam-4815	140	2	lim	lim	PROPN
ejpam-4815	140	3	n→∞	n→∞	X
ejpam-4815	141	1	[	[	X
ejpam-4815	141	2	eβ	eβ	X
ejpam-4815	141	3	n(f	n(f	PROPN
ejpam-4815	141	4	,	,	PUNCT
ejpam-4815	141	5	r	r	NOUN
ejpam-4815	141	6	)	)	PUNCT
ejpam-4815	141	7	]	]	PUNCT
ejpam-4815	141	8	1	1	NUM
ejpam-4815	141	9	n	n	NOUN
ejpam-4815	141	10	=	=	SYM
ejpam-4815	141	11	0	0	PROPN
ejpam-4815	141	12	.	.	PUNCT
ejpam-4815	141	13	(	(	PUNCT
ejpam-4815	141	14	3.1	3.1	NUM
ejpam-4815	141	15	)	)	PUNCT
ejpam-4815	141	16	proof	proof	NOUN
ejpam-4815	141	17	.	.	PUNCT
ejpam-4815	142	1	let	let	VERB
ejpam-4815	142	2	f	f	PROPN
ejpam-4815	142	3	∈	∈	PROPN
ejpam-4815	142	4	aβ(s1	aβ(s1	NOUN
ejpam-4815	142	5	)	)	PUNCT
ejpam-4815	142	6	,	,	PUNCT
ejpam-4815	142	7	then	then	ADV
ejpam-4815	142	8	for	for	ADP
ejpam-4815	142	9	0	0	NUM
ejpam-4815	142	10	<	<	X
ejpam-4815	142	11	r	r	X
ejpam-4815	142	12	<	<	X
ejpam-4815	142	13	1	1	NUM
ejpam-4815	142	14	,	,	PUNCT
ejpam-4815	142	15	f	f	PROPN
ejpam-4815	142	16	∈	∈	PROPN
ejpam-4815	142	17	aβ(sr	aβ(sr	NOUN
ejpam-4815	142	18	)	)	PUNCT
ejpam-4815	142	19	.	.	PUNCT
ejpam-4815	143	1	first	first	ADV
ejpam-4815	143	2	suppose	suppose	VERB
ejpam-4815	143	3	that	that	SCONJ
ejpam-4815	143	4	f	f	PROPN
ejpam-4815	143	5	is	be	AUX
ejpam-4815	143	6	entire	entire	ADJ
ejpam-4815	143	7	.	.	PUNCT
ejpam-4815	144	1	then	then	ADV
ejpam-4815	144	2	it	it	PRON
ejpam-4815	144	3	follows	follow	VERB
ejpam-4815	144	4	from	from	ADP
ejpam-4815	144	5	lemma	lemma	PROPN
ejpam-4815	144	6	2.3	2.3	NUM
ejpam-4815	144	7	that	that	PRON
ejpam-4815	144	8	lim	lim	PROPN
ejpam-4815	144	9	sup	sup	VERB
ejpam-4815	144	10	n→∞	n→∞	NUM
ejpam-4815	145	1	[	[	X
ejpam-4815	145	2	eβ	eβ	X
ejpam-4815	145	3	n(f	n(f	PROPN
ejpam-4815	145	4	,	,	PUNCT
ejpam-4815	145	5	r	r	NOUN
ejpam-4815	145	6	)	)	PUNCT
ejpam-4815	145	7	]	]	PUNCT
ejpam-4815	145	8	1	1	NUM
ejpam-4815	145	9	n	n	X
ejpam-4815	145	10	≤	≤	NUM
ejpam-4815	145	11	(	(	PUNCT
ejpam-4815	145	12	r′r	r′r	NOUN
ejpam-4815	145	13	r	r	NOUN
ejpam-4815	145	14	)	)	PUNCT
ejpam-4815	145	15	,	,	PUNCT
ejpam-4815	145	16	r	r	NOUN
ejpam-4815	145	17	>	>	X
ejpam-4815	145	18	2r′r	2r′r	NUM
ejpam-4815	145	19	.	.	PUNCT
ejpam-4815	146	1	thus	thus	ADV
ejpam-4815	146	2	,	,	PUNCT
ejpam-4815	146	3	for	for	ADP
ejpam-4815	146	4	all	all	DET
ejpam-4815	146	5	sufficiently	sufficiently	ADV
ejpam-4815	146	6	large	large	ADJ
ejpam-4815	146	7	r	r	NOUN
ejpam-4815	146	8	,	,	PUNCT
ejpam-4815	146	9	we	we	PRON
ejpam-4815	146	10	have	have	VERB
ejpam-4815	146	11	lim	lim	PROPN
ejpam-4815	146	12	sup	sup	PROPN
ejpam-4815	146	13	n→∞	n→∞	PRON
ejpam-4815	147	1	[	[	X
ejpam-4815	147	2	eβ	eβ	X
ejpam-4815	147	3	n(f	n(f	PROPN
ejpam-4815	147	4	,	,	PUNCT
ejpam-4815	147	5	r	r	NOUN
ejpam-4815	147	6	)	)	PUNCT
ejpam-4815	147	7	]	]	PUNCT
ejpam-4815	147	8	1	1	NUM
ejpam-4815	147	9	n	n	NOUN
ejpam-4815	147	10	=	=	SYM
ejpam-4815	147	11	0	0	NUM
ejpam-4815	147	12	.	.	PUNCT
ejpam-4815	147	13	to	to	PART
ejpam-4815	147	14	prove	prove	VERB
ejpam-4815	147	15	only	only	ADV
ejpam-4815	147	16	if	if	SCONJ
ejpam-4815	147	17	part	part	NOUN
ejpam-4815	147	18	,	,	PUNCT
ejpam-4815	147	19	suppose	suppose	VERB
ejpam-4815	147	20	that	that	SCONJ
ejpam-4815	147	21	(	(	PUNCT
ejpam-4815	147	22	3.1	3.1	NUM
ejpam-4815	147	23	)	)	PUNCT
ejpam-4815	147	24	holds	hold	VERB
ejpam-4815	147	25	,	,	PUNCT
ejpam-4815	147	26	then	then	ADV
ejpam-4815	147	27	it	it	PRON
ejpam-4815	147	28	follows	follow	VERB
ejpam-4815	147	29	from	from	ADP
ejpam-4815	147	30	(	(	PUNCT
ejpam-4815	147	31	2.11	2.11	NUM
ejpam-4815	147	32	)	)	PUNCT
ejpam-4815	147	33	that	that	DET
ejpam-4815	147	34	series	series	NOUN
ejpam-4815	147	35	on	on	ADP
ejpam-4815	147	36	the	the	DET
ejpam-4815	147	37	right	right	ADJ
ejpam-4815	147	38	hand	hand	NOUN
ejpam-4815	147	39	side	side	NOUN
ejpam-4815	147	40	of	of	ADP
ejpam-4815	147	41	(	(	PUNCT
ejpam-4815	147	42	1.2	1.2	NUM
ejpam-4815	147	43	)	)	PUNCT
ejpam-4815	147	44	converges	converge	VERB
ejpam-4815	147	45	uniformly	uniformly	ADV
ejpam-4815	147	46	on	on	ADP
ejpam-4815	147	47	every	every	DET
ejpam-4815	147	48	compact	compact	ADJ
ejpam-4815	147	49	subset	subset	NOUN
ejpam-4815	147	50	of	of	ADP
ejpam-4815	147	51	s∞	s∞	PROPN
ejpam-4815	147	52	and	and	CCONJ
ejpam-4815	147	53	gbasp	gbasp	NOUN
ejpam-4815	147	54	f	f	PROPN
ejpam-4815	147	55	is	be	AUX
ejpam-4815	147	56	entire	entire	ADJ
ejpam-4815	147	57	.	.	PUNCT
ejpam-4815	148	1	d.	d.	PROPN
ejpam-4815	148	2	kumar	kumar	PROPN
ejpam-4815	148	3	/	/	SYM
ejpam-4815	148	4	eur	eur	PROPN
ejpam-4815	148	5	.	.	PUNCT
ejpam-4815	149	1	j.	j.	PROPN
ejpam-4815	149	2	pure	pure	PROPN
ejpam-4815	149	3	appl	appl	PROPN
ejpam-4815	149	4	.	.	PROPN
ejpam-4815	149	5	math	math	PROPN
ejpam-4815	149	6	,	,	PUNCT
ejpam-4815	149	7	16	16	NUM
ejpam-4815	149	8	(	(	PUNCT
ejpam-4815	149	9	3	3	NUM
ejpam-4815	149	10	)	)	PUNCT
ejpam-4815	149	11	(	(	PUNCT
ejpam-4815	149	12	2023	2023	NUM
ejpam-4815	149	13	)	)	PUNCT
ejpam-4815	149	14	,	,	PUNCT
ejpam-4815	149	15	1508	1508	NUM
ejpam-4815	149	16	-	-	SYM
ejpam-4815	149	17	1517	1517	NUM
ejpam-4815	149	18	1515	1515	NUM
ejpam-4815	149	19	theorem	theorem	VERB
ejpam-4815	149	20	3.2	3.2	NUM
ejpam-4815	149	21	.	.	PUNCT
ejpam-4815	150	1	let	let	VERB
ejpam-4815	150	2	the	the	DET
ejpam-4815	150	3	gbasp	gbasp	NOUN
ejpam-4815	150	4	f	f	PROPN
ejpam-4815	150	5	∈	∈	PROPN
ejpam-4815	150	6	aβ(sr	aβ(sr	PROPN
ejpam-4815	150	7	)	)	PUNCT
ejpam-4815	150	8	,	,	PUNCT
ejpam-4815	150	9	r	r	NOUN
ejpam-4815	150	10	>	>	X
ejpam-4815	150	11	2r′r	2r′r	NUM
ejpam-4815	150	12	.	.	PUNCT
ejpam-4815	151	1	then	then	ADV
ejpam-4815	151	2	f	f	PROPN
ejpam-4815	151	3	harmonically	harmonically	ADV
ejpam-4815	151	4	continues	continue	VERB
ejpam-4815	151	5	as	as	ADP
ejpam-4815	151	6	an	an	DET
ejpam-4815	151	7	entire	entire	ADJ
ejpam-4815	151	8	function	function	NOUN
ejpam-4815	151	9	gbasp	gbasp	NOUN
ejpam-4815	151	10	of	of	ADP
ejpam-4815	151	11	finite	finite	NOUN
ejpam-4815	151	12	(	(	PUNCT
ejpam-4815	151	13	p	p	NOUN
ejpam-4815	151	14	,	,	PUNCT
ejpam-4815	151	15	q)-order	q)-order	PUNCT
ejpam-4815	151	16	ρ	ρ	NOUN
ejpam-4815	151	17	if	if	SCONJ
ejpam-4815	151	18	and	and	CCONJ
ejpam-4815	151	19	only	only	ADV
ejpam-4815	151	20	if	if	SCONJ
ejpam-4815	151	21	ρ(p	ρ(p	NUM
ejpam-4815	151	22	,	,	PUNCT
ejpam-4815	151	23	q	q	NOUN
ejpam-4815	151	24	)	)	PUNCT
ejpam-4815	151	25	=	=	SYM
ejpam-4815	152	1	p	p	X
ejpam-4815	152	2	(	(	PUNCT
ejpam-4815	152	3	l∗(p	l∗(p	PROPN
ejpam-4815	152	4	,	,	PUNCT
ejpam-4815	152	5	q	q	NOUN
ejpam-4815	152	6	)	)	PUNCT
ejpam-4815	152	7	)	)	PUNCT
ejpam-4815	152	8	,	,	PUNCT
ejpam-4815	152	9	where	where	SCONJ
ejpam-4815	152	10	l∗(p	l∗(p	PROPN
ejpam-4815	152	11	,	,	PUNCT
ejpam-4815	152	12	q	q	NOUN
ejpam-4815	152	13	)	)	PUNCT
ejpam-4815	152	14	=	=	SYM
ejpam-4815	152	15	lim	lim	PROPN
ejpam-4815	152	16	sup	sup	VERB
ejpam-4815	152	17	n→∞	n→∞	NUM
ejpam-4815	152	18	log[p−1	log[p−1	NOUN
ejpam-4815	152	19	]	]	PUNCT
ejpam-4815	152	20	n	n	CCONJ
ejpam-4815	152	21	log[q][eβ	log[q][eβ	NOUN
ejpam-4815	152	22	n(f	n(f	PROPN
ejpam-4815	152	23	,	,	PUNCT
ejpam-4815	152	24	r	r	NOUN
ejpam-4815	152	25	)	)	PUNCT
ejpam-4815	152	26	]	]	PUNCT
ejpam-4815	153	1	−	−	PROPN
ejpam-4815	153	2	1	1	NUM
ejpam-4815	153	3	n	n	NOUN
ejpam-4815	153	4	,	,	PUNCT
ejpam-4815	153	5	and	and	CCONJ
ejpam-4815	153	6	p	p	X
ejpam-4815	153	7	(	(	PUNCT
ejpam-4815	153	8	l∗(p	l∗(p	PROPN
ejpam-4815	153	9	,	,	PUNCT
ejpam-4815	153	10	q	q	NOUN
ejpam-4815	153	11	)	)	PUNCT
ejpam-4815	153	12	)	)	PUNCT
ejpam-4815	154	1	=	=	PRON
ejpam-4815	154	2	{	{	PUNCT
ejpam-4815	154	3	l∗(p	l∗(p	PROPN
ejpam-4815	154	4	,	,	PUNCT
ejpam-4815	154	5	q	q	NOUN
ejpam-4815	154	6	)	)	PUNCT
ejpam-4815	154	7	if	if	SCONJ
ejpam-4815	154	8	q	q	X
ejpam-4815	154	9	<	<	X
ejpam-4815	154	10	p	p	X
ejpam-4815	154	11	<	<	X
ejpam-4815	154	12	∞	∞	PROPN
ejpam-4815	154	13	,	,	PUNCT
ejpam-4815	154	14	1	1	NUM
ejpam-4815	154	15	+	+	X
ejpam-4815	154	16	l∗(p	l∗(p	PROPN
ejpam-4815	154	17	,	,	PUNCT
ejpam-4815	154	18	q	q	NOUN
ejpam-4815	154	19	)	)	PUNCT
ejpam-4815	154	20	if	if	SCONJ
ejpam-4815	154	21	p	p	NOUN
ejpam-4815	154	22	=	=	X
ejpam-4815	154	23	q	q	NOUN
ejpam-4815	154	24	=	=	SYM
ejpam-4815	154	25	2	2	NUM
ejpam-4815	154	26	,	,	PUNCT
ejpam-4815	154	27	max(1	max(1	NOUN
ejpam-4815	154	28	+	+	CCONJ
ejpam-4815	154	29	l∗(p	l∗(p	PROPN
ejpam-4815	154	30	,	,	PUNCT
ejpam-4815	154	31	q	q	NOUN
ejpam-4815	154	32	)	)	PUNCT
ejpam-4815	154	33	)	)	PUNCT
ejpam-4815	155	1	if	if	SCONJ
ejpam-4815	155	2	3	3	NUM
ejpam-4815	155	3	≤	≤	NOUN
ejpam-4815	155	4	p	p	NOUN
ejpam-4815	155	5	=	=	NOUN
ejpam-4815	155	6	q	q	NOUN
ejpam-4815	155	7	,	,	PUNCT
ejpam-4815	155	8	∞	∞	PROPN
ejpam-4815	155	9	if	if	SCONJ
ejpam-4815	155	10	p	p	NOUN
ejpam-4815	155	11	=	=	X
ejpam-4815	155	12	q	q	X
ejpam-4815	155	13	=	=	SYM
ejpam-4815	155	14	∞	∞	NOUN
ejpam-4815	155	15	}	}	PUNCT
ejpam-4815	155	16	.	.	PUNCT
ejpam-4815	156	1	proof	proof	NOUN
ejpam-4815	156	2	.	.	PUNCT
ejpam-4815	157	1	using	use	VERB
ejpam-4815	157	2	theorem	theorem	NOUN
ejpam-4815	157	3	3.1	3.1	NUM
ejpam-4815	157	4	,	,	PUNCT
ejpam-4815	157	5	we	we	PRON
ejpam-4815	157	6	have	have	VERB
ejpam-4815	157	7	f	f	PROPN
ejpam-4815	157	8	∈	∈	PROPN
ejpam-4815	157	9	aβ(sr	aβ(sr	NOUN
ejpam-4815	157	10	)	)	PUNCT
ejpam-4815	157	11	is	be	AUX
ejpam-4815	157	12	harmonically	harmonically	ADV
ejpam-4815	157	13	continues	continue	VERB
ejpam-4815	157	14	as	as	ADP
ejpam-4815	157	15	an	an	DET
ejpam-4815	157	16	entire	entire	ADJ
ejpam-4815	157	17	function	function	NOUN
ejpam-4815	157	18	gbasp	gbasp	NOUN
ejpam-4815	157	19	if	if	SCONJ
ejpam-4815	157	20	and	and	CCONJ
ejpam-4815	157	21	only	only	ADV
ejpam-4815	157	22	if	if	SCONJ
ejpam-4815	157	23	h(z	h(z	NOUN
ejpam-4815	157	24	)	)	PUNCT
ejpam-4815	157	25	is	be	AUX
ejpam-4815	157	26	an	an	DET
ejpam-4815	157	27	entire	entire	ADJ
ejpam-4815	157	28	function	function	NOUN
ejpam-4815	157	29	.	.	PUNCT
ejpam-4815	158	1	using	use	VERB
ejpam-4815	158	2	lemma	lemma	PROPN
ejpam-4815	158	3	2.4	2.4	NUM
ejpam-4815	158	4	,	,	PUNCT
ejpam-4815	158	5	f	f	PROPN
ejpam-4815	158	6	and	and	CCONJ
ejpam-4815	158	7	h(z	h(z	NOUN
ejpam-4815	158	8	)	)	PUNCT
ejpam-4815	158	9	have	have	VERB
ejpam-4815	158	10	same	same	ADJ
ejpam-4815	158	11	(	(	PUNCT
ejpam-4815	158	12	p	p	X
ejpam-4815	158	13	,	,	PUNCT
ejpam-4815	158	14	q)-order	q)-order	NOUN
ejpam-4815	158	15	.	.	PUNCT
ejpam-4815	159	1	the	the	DET
ejpam-4815	159	2	remaining	remain	VERB
ejpam-4815	159	3	part	part	NOUN
ejpam-4815	159	4	of	of	ADP
ejpam-4815	159	5	the	the	DET
ejpam-4815	159	6	proof	proof	NOUN
ejpam-4815	159	7	can	can	AUX
ejpam-4815	159	8	be	be	AUX
ejpam-4815	159	9	obtain	obtain	VERB
ejpam-4815	159	10	easily	easily	ADV
ejpam-4815	159	11	.	.	PUNCT
ejpam-4815	160	1	theorem	theorem	VERB
ejpam-4815	160	2	3.3	3.3	NUM
ejpam-4815	160	3	.	.	PUNCT
ejpam-4815	161	1	let	let	VERB
ejpam-4815	161	2	the	the	DET
ejpam-4815	161	3	gbasp	gbasp	NOUN
ejpam-4815	161	4	f	f	PROPN
ejpam-4815	161	5	∈	∈	PROPN
ejpam-4815	161	6	aβ(sr	aβ(sr	PROPN
ejpam-4815	161	7	)	)	PUNCT
ejpam-4815	161	8	,	,	PUNCT
ejpam-4815	161	9	r	r	NOUN
ejpam-4815	161	10	>	>	X
ejpam-4815	161	11	2r′r	2r′r	NUM
ejpam-4815	161	12	.	.	PUNCT
ejpam-4815	162	1	then	then	ADV
ejpam-4815	162	2	f	f	PROPN
ejpam-4815	162	3	harmonically	harmonically	ADV
ejpam-4815	162	4	continues	continue	VERB
ejpam-4815	162	5	as	as	ADP
ejpam-4815	162	6	an	an	DET
ejpam-4815	162	7	entire	entire	ADJ
ejpam-4815	162	8	function	function	NOUN
ejpam-4815	162	9	gbasp	gbasp	NOUN
ejpam-4815	162	10	of	of	ADP
ejpam-4815	162	11	finite	finite	NOUN
ejpam-4815	162	12	(	(	PUNCT
ejpam-4815	162	13	p	p	NOUN
ejpam-4815	162	14	,	,	PUNCT
ejpam-4815	162	15	q)-order	q)-order	PUNCT
ejpam-4815	162	16	ρ(b	ρ(b	PROPN
ejpam-4815	162	17	<	<	X
ejpam-4815	162	18	ρ	ρ	X
ejpam-4815	162	19	<	<	X
ejpam-4815	162	20	∞	∞	PROPN
ejpam-4815	162	21	)	)	PUNCT
ejpam-4815	162	22	and	and	CCONJ
ejpam-4815	162	23	generalized	generalize	VERB
ejpam-4815	162	24	(	(	PUNCT
ejpam-4815	162	25	p	p	NOUN
ejpam-4815	162	26	,	,	PUNCT
ejpam-4815	162	27	q)-type	q)-type	PUNCT
ejpam-4815	162	28	t	t	PROPN
ejpam-4815	162	29	∗	∗	NOUN
ejpam-4815	162	30	of	of	ADP
ejpam-4815	162	31	f	f	PROPN
ejpam-4815	162	32	with	with	ADP
ejpam-4815	162	33	respect	respect	NOUN
ejpam-4815	162	34	to	to	ADP
ejpam-4815	162	35	a	a	DET
ejpam-4815	162	36	proximate	proximate	NOUN
ejpam-4815	162	37	order	order	NOUN
ejpam-4815	162	38	ρ(r	ρ(r	NOUN
ejpam-4815	162	39	)	)	PUNCT
ejpam-4815	163	1	if	if	SCONJ
ejpam-4815	163	2	and	and	CCONJ
ejpam-4815	163	3	only	only	ADV
ejpam-4815	163	4	if	if	SCONJ
ejpam-4815	163	5	t	t	PROPN
ejpam-4815	163	6	∗(p	∗(p	PROPN
ejpam-4815	163	7	,	,	PUNCT
ejpam-4815	163	8	q	q	X
ejpam-4815	163	9	)	)	PUNCT
ejpam-4815	163	10	mγ	mγ	PROPN
ejpam-4815	163	11	=	=	NOUN
ejpam-4815	163	12	lim	lim	PROPN
ejpam-4815	163	13	sup	sup	VERB
ejpam-4815	163	14	n→∞	n→∞	X
ejpam-4815	163	15	[	[	PUNCT
ejpam-4815	163	16	ϕ(log[p−2	ϕ(log[p−2	X
ejpam-4815	163	17	]	]	PUNCT
ejpam-4815	163	18	n	n	CCONJ
ejpam-4815	163	19	)	)	PUNCT
ejpam-4815	163	20	log[q−1][eβ	log[q−1][eβ	VERB
ejpam-4815	164	1	n(f	n(f	PROPN
ejpam-4815	164	2	,	,	PUNCT
ejpam-4815	164	3	r	r	NOUN
ejpam-4815	164	4	)	)	PUNCT
ejpam-4815	164	5	]	]	PUNCT
ejpam-4815	165	1	−	−	PROPN
ejpam-4815	165	2	1	1	NUM
ejpam-4815	165	3	n	n	NOUN
ejpam-4815	165	4	]	]	SYM
ejpam-4815	165	5	ρ−a	ρ−a	NOUN
ejpam-4815	165	6	,	,	PUNCT
ejpam-4815	165	7	where	where	SCONJ
ejpam-4815	165	8	a	a	DET
ejpam-4815	165	9	=	=	SYM
ejpam-4815	165	10	1	1	NUM
ejpam-4815	165	11	if	if	SCONJ
ejpam-4815	165	12	q	q	NOUN
ejpam-4815	165	13	=	=	SYM
ejpam-4815	165	14	2	2	NUM
ejpam-4815	165	15	,	,	PUNCT
ejpam-4815	165	16	a	a	DET
ejpam-4815	165	17	=	=	SYM
ejpam-4815	165	18	0	0	PUNCT
ejpam-4815	165	19	if	if	SCONJ
ejpam-4815	165	20	q	q	PRON
ejpam-4815	165	21	̸=	̸=	PROPN
ejpam-4815	165	22	2	2	NUM
ejpam-4815	165	23	and	and	CCONJ
ejpam-4815	165	24	m	m	PROPN
ejpam-4815	165	25	≡	≡	PROPN
ejpam-4815	165	26	m(p	m(p	PROPN
ejpam-4815	165	27	,	,	PUNCT
ejpam-4815	165	28	q	q	NOUN
ejpam-4815	165	29	)	)	PUNCT
ejpam-4815	165	30	=	=	SYM
ejpam-4815	165	31	{	{	PUNCT
ejpam-4815	165	32	(	(	PUNCT
ejpam-4815	165	33	ρ−1)(ρ−1	ρ−1)(ρ−1	PROPN
ejpam-4815	165	34	)	)	PUNCT
ejpam-4815	165	35	ρρ	ρρ	NOUN
ejpam-4815	166	1	if	if	SCONJ
ejpam-4815	166	2	(	(	PUNCT
ejpam-4815	166	3	p	p	X
ejpam-4815	166	4	,	,	PUNCT
ejpam-4815	166	5	q	q	NOUN
ejpam-4815	166	6	)	)	PUNCT
ejpam-4815	166	7	=	=	SYM
ejpam-4815	166	8	(	(	PUNCT
ejpam-4815	166	9	2	2	NUM
ejpam-4815	166	10	,	,	PUNCT
ejpam-4815	166	11	2	2	NUM
ejpam-4815	166	12	)	)	PUNCT
ejpam-4815	166	13	,	,	PUNCT
ejpam-4815	166	14	1	1	NUM
ejpam-4815	166	15	eρ	eρ	VERB
ejpam-4815	166	16	if	if	SCONJ
ejpam-4815	166	17	(	(	PUNCT
ejpam-4815	166	18	p	p	X
ejpam-4815	166	19	,	,	PUNCT
ejpam-4815	166	20	q	q	NOUN
ejpam-4815	166	21	)	)	PUNCT
ejpam-4815	166	22	=	=	SYM
ejpam-4815	166	23	(	(	PUNCT
ejpam-4815	166	24	2	2	NUM
ejpam-4815	166	25	,	,	PUNCT
ejpam-4815	166	26	1	1	NUM
ejpam-4815	166	27	)	)	PUNCT
ejpam-4815	166	28	,	,	PUNCT
ejpam-4815	166	29	1	1	NUM
ejpam-4815	166	30	otherwise	otherwise	ADV
ejpam-4815	166	31	}	}	PUNCT
ejpam-4815	166	32	.	.	PUNCT
ejpam-4815	167	1	the	the	DET
ejpam-4815	167	2	function	function	NOUN
ejpam-4815	167	3	ϕ(x	ϕ(x	PROPN
ejpam-4815	167	4	)	)	PUNCT
ejpam-4815	167	5	be	be	VERB
ejpam-4815	167	6	the	the	DET
ejpam-4815	167	7	unique	unique	ADJ
ejpam-4815	167	8	solution	solution	NOUN
ejpam-4815	167	9	of	of	ADP
ejpam-4815	167	10	the	the	DET
ejpam-4815	167	11	equation	equation	NOUN
ejpam-4815	167	12	x	x	PUNCT
ejpam-4815	167	13	=	=	PUNCT
ejpam-4815	168	1	(	(	PUNCT
ejpam-4815	168	2	log[q−1	log[q−1	X
ejpam-4815	168	3	]	]	X
ejpam-4815	168	4	r)ρ(r)−a	r)ρ(r)−a	VERB
ejpam-4815	168	5	⇔	⇔	PROPN
ejpam-4815	168	6	ϕ(x	ϕ(x	PROPN
ejpam-4815	168	7	)	)	PUNCT
ejpam-4815	168	8	=	=	SYM
ejpam-4815	169	1	log[q−1	log[q−1	X
ejpam-4815	169	2	]	]	PUNCT
ejpam-4815	169	3	r.	r.	PROPN
ejpam-4815	169	4	proof	proof	NOUN
ejpam-4815	169	5	.	.	PUNCT
ejpam-4815	170	1	applying	apply	VERB
ejpam-4815	170	2	theorem	theorem	NOUN
ejpam-4815	170	3	3	3	NUM
ejpam-4815	170	4	of	of	ADP
ejpam-4815	170	5	nandan	nandan	PROPN
ejpam-4815	170	6	et	et	PROPN
ejpam-4815	170	7	al	al	PROPN
ejpam-4815	170	8	.	.	PUNCT
ejpam-4815	171	1	[	[	X
ejpam-4815	171	2	9	9	NUM
ejpam-4815	171	3	]	]	PUNCT
ejpam-4815	171	4	to	to	ADP
ejpam-4815	171	5	the	the	DET
ejpam-4815	171	6	function	function	NOUN
ejpam-4815	171	7	h(z	h(z	NOUN
ejpam-4815	171	8	)	)	PUNCT
ejpam-4815	171	9	and	and	CCONJ
ejpam-4815	171	10	resulting	result	VERB
ejpam-4815	171	11	characterization	characterization	NOUN
ejpam-4815	171	12	of	of	ADP
ejpam-4815	171	13	t	t	NOUN
ejpam-4815	171	14	∗	∗	NOUN
ejpam-4815	171	15	=	=	SYM
ejpam-4815	171	16	γt	γt	PROPN
ejpam-4815	171	17	∗(h	∗(h	PROPN
ejpam-4815	171	18	)	)	PUNCT
ejpam-4815	171	19	,	,	PUNCT
ejpam-4815	171	20	with	with	ADP
ejpam-4815	171	21	lemma	lemma	PROPN
ejpam-4815	171	22	2.4	2.4	NUM
ejpam-4815	171	23	,	,	PUNCT
ejpam-4815	171	24	taking	take	VERB
ejpam-4815	171	25	together	together	ADV
ejpam-4815	171	26	completes	complete	VERB
ejpam-4815	171	27	the	the	DET
ejpam-4815	171	28	proof	proof	NOUN
ejpam-4815	171	29	.	.	PUNCT
ejpam-4815	172	1	remark	remark	PROPN
ejpam-4815	172	2	3.1	3.1	NUM
ejpam-4815	172	3	.	.	PUNCT
ejpam-4815	173	1	for	for	ADP
ejpam-4815	173	2	(	(	PUNCT
ejpam-4815	173	3	p	p	X
ejpam-4815	173	4	,	,	PUNCT
ejpam-4815	173	5	q	q	NOUN
ejpam-4815	173	6	)	)	PUNCT
ejpam-4815	173	7	=	=	SYM
ejpam-4815	173	8	(	(	PUNCT
ejpam-4815	173	9	2	2	NUM
ejpam-4815	173	10	,	,	PUNCT
ejpam-4815	173	11	1	1	NUM
ejpam-4815	173	12	)	)	PUNCT
ejpam-4815	173	13	,	,	PUNCT
ejpam-4815	173	14	theorem	theorem	VERB
ejpam-4815	173	15	3.2	3.2	NUM
ejpam-4815	173	16	gives	give	VERB
ejpam-4815	173	17	the	the	DET
ejpam-4815	173	18	theorem	theorem	NOUN
ejpam-4815	173	19	2	2	NUM
ejpam-4815	173	20	of	of	ADP
ejpam-4815	173	21	p.a	p.a	PROPN
ejpam-4815	173	22	.	.	PUNCT
ejpam-4815	173	23	mccoy	mccoy	PROPN
ejpam-4815	174	1	[	[	X
ejpam-4815	174	2	14	14	NUM
ejpam-4815	174	3	]	]	PUNCT
ejpam-4815	174	4	.	.	PUNCT
ejpam-4815	175	1	remark	remark	PROPN
ejpam-4815	175	2	3.2	3.2	NUM
ejpam-4815	175	3	.	.	PUNCT
ejpam-4815	176	1	for	for	ADP
ejpam-4815	176	2	(	(	PUNCT
ejpam-4815	176	3	p	p	X
ejpam-4815	176	4	,	,	PUNCT
ejpam-4815	176	5	q	q	NOUN
ejpam-4815	176	6	)	)	PUNCT
ejpam-4815	176	7	=	=	SYM
ejpam-4815	176	8	(	(	PUNCT
ejpam-4815	176	9	2	2	NUM
ejpam-4815	176	10	,	,	PUNCT
ejpam-4815	176	11	1	1	NUM
ejpam-4815	176	12	)	)	PUNCT
ejpam-4815	176	13	and	and	CCONJ
ejpam-4815	176	14	x	x	X
ejpam-4815	176	15	=	=	SYM
ejpam-4815	176	16	ϕ(n	ϕ(n	X
ejpam-4815	176	17	)	)	PUNCT
ejpam-4815	176	18	is	be	AUX
ejpam-4815	176	19	the	the	DET
ejpam-4815	176	20	function	function	NOUN
ejpam-4815	176	21	inverse	inverse	NOUN
ejpam-4815	176	22	to	to	ADP
ejpam-4815	176	23	n	n	PROPN
ejpam-4815	176	24	=	=	SYM
ejpam-4815	176	25	xρ(r	xρ(r	NUM
ejpam-4815	176	26	)	)	PUNCT
ejpam-4815	176	27	,	,	PUNCT
ejpam-4815	176	28	theorem	theorem	VERB
ejpam-4815	176	29	3.3	3.3	NUM
ejpam-4815	176	30	gives	give	VERB
ejpam-4815	176	31	the	the	DET
ejpam-4815	176	32	theorem	theorem	NOUN
ejpam-4815	176	33	3	3	NUM
ejpam-4815	176	34	of	of	ADP
ejpam-4815	176	35	p.a	p.a	PROPN
ejpam-4815	176	36	.	.	PUNCT
ejpam-4815	176	37	mccoy	mccoy	PROPN
ejpam-4815	177	1	[	[	X
ejpam-4815	177	2	14	14	NUM
ejpam-4815	177	3	]	]	PUNCT
ejpam-4815	177	4	.	.	PUNCT
ejpam-4815	178	1	4	4	X
ejpam-4815	178	2	.	.	X
ejpam-4815	178	3	conclusions	conclusion	NOUN
ejpam-4815	178	4	we	we	PRON
ejpam-4815	178	5	estimate	estimate	VERB
ejpam-4815	178	6	formulae	formulae	ADJ
ejpam-4815	178	7	for	for	ADP
ejpam-4815	178	8	the	the	DET
ejpam-4815	178	9	(	(	PUNCT
ejpam-4815	178	10	p	p	NOUN
ejpam-4815	178	11	,	,	PUNCT
ejpam-4815	178	12	q)-order	q)-order	PUNCT
ejpam-4815	178	13	and	and	CCONJ
ejpam-4815	178	14	generalized	generalize	VERB
ejpam-4815	178	15	(	(	PUNCT
ejpam-4815	178	16	p	p	NOUN
ejpam-4815	178	17	,	,	PUNCT
ejpam-4815	178	18	q)-type	q)-type	PUNCT
ejpam-4815	178	19	with	with	ADP
ejpam-4815	178	20	respect	respect	NOUN
ejpam-4815	178	21	to	to	ADP
ejpam-4815	178	22	a	a	DET
ejpam-4815	178	23	proximate	proximate	NOUN
ejpam-4815	178	24	order	order	NOUN
ejpam-4815	178	25	of	of	ADP
ejpam-4815	178	26	entire	entire	ADJ
ejpam-4815	178	27	gbasp	gbasp	NOUN
ejpam-4815	178	28	functions	function	NOUN
ejpam-4815	178	29	in	in	ADP
ejpam-4815	178	30	terms	term	NOUN
ejpam-4815	178	31	of	of	ADP
ejpam-4815	178	32	gbasp	gbasp	ADJ
ejpam-4815	178	33	polynomial	polynomial	ADJ
ejpam-4815	178	34	approximation	approximation	NOUN
ejpam-4815	178	35	errors	error	NOUN
ejpam-4815	178	36	in	in	ADP
ejpam-4815	178	37	lβ	lβ	ADJ
ejpam-4815	178	38	-	-	NOUN
ejpam-4815	178	39	norm	norm	NOUN
ejpam-4815	178	40	,	,	PUNCT
ejpam-4815	178	41	which	which	PRON
ejpam-4815	178	42	made	make	VERB
ejpam-4815	178	43	it	it	PRON
ejpam-4815	178	44	possible	possible	ADJ
ejpam-4815	178	45	to	to	PART
ejpam-4815	178	46	obtain	obtain	VERB
ejpam-4815	178	47	the	the	DET
ejpam-4815	178	48	necessary	necessary	ADJ
ejpam-4815	178	49	and	and	CCONJ
ejpam-4815	178	50	sufficient	sufficient	ADJ
ejpam-4815	178	51	conditions	condition	NOUN
ejpam-4815	178	52	under	under	ADP
ejpam-4815	178	53	which	which	PRON
ejpam-4815	178	54	a	a	DET
ejpam-4815	178	55	gbasp	gbasp	NOUN
ejpam-4815	178	56	function	function	NOUN
ejpam-4815	178	57	harmonically	harmonically	ADV
ejpam-4815	178	58	continues	continue	VERB
ejpam-4815	178	59	to	to	PART
ejpam-4815	178	60	entire	entire	VERB
ejpam-4815	178	61	gbasp	gbasp	NOUN
ejpam-4815	178	62	.	.	PUNCT
ejpam-4815	179	1	our	our	PRON
ejpam-4815	179	2	results	result	NOUN
ejpam-4815	179	3	references	reference	VERB
ejpam-4815	179	4	1516	1516	NUM
ejpam-4815	179	5	improve	improve	VERB
ejpam-4815	179	6	and	and	CCONJ
ejpam-4815	179	7	extends	extend	VERB
ejpam-4815	179	8	the	the	DET
ejpam-4815	179	9	results	result	NOUN
ejpam-4815	179	10	of	of	ADP
ejpam-4815	179	11	mccoy	mccoy	PROPN
ejpam-4815	180	1	[	[	X
ejpam-4815	180	2	14	14	NUM
ejpam-4815	180	3	]	]	PUNCT
ejpam-4815	180	4	.	.	PUNCT
ejpam-4815	181	1	the	the	DET
ejpam-4815	181	2	relevance	relevance	NOUN
ejpam-4815	181	3	of	of	ADP
ejpam-4815	181	4	our	our	PRON
ejpam-4815	181	5	study	study	NOUN
ejpam-4815	181	6	is	be	AUX
ejpam-4815	181	7	due	due	ADJ
ejpam-4815	181	8	to	to	ADP
ejpam-4815	181	9	the	the	DET
ejpam-4815	181	10	fact	fact	NOUN
ejpam-4815	181	11	that	that	SCONJ
ejpam-4815	181	12	gbasp	gbasp	NOUN
ejpam-4815	181	13	play	play	VERB
ejpam-4815	181	14	and	and	CCONJ
ejpam-4815	181	15	important	important	ADJ
ejpam-4815	181	16	role	role	NOUN
ejpam-4815	181	17	not	not	PART
ejpam-4815	181	18	only	only	ADV
ejpam-4815	181	19	in	in	ADP
ejpam-4815	181	20	theoretical	theoretical	ADJ
ejpam-4815	181	21	mathematical	mathematical	ADJ
ejpam-4815	181	22	research	research	NOUN
ejpam-4815	181	23	,	,	PUNCT
ejpam-4815	181	24	but	but	CCONJ
ejpam-4815	181	25	are	be	AUX
ejpam-4815	181	26	used	use	VERB
ejpam-4815	181	27	in	in	ADP
ejpam-4815	181	28	gas	gas	NOUN
ejpam-4815	181	29	dynamics	dynamic	NOUN
ejpam-4815	181	30	in	in	ADP
ejpam-4815	181	31	order	order	NOUN
ejpam-4815	181	32	to	to	PART
ejpam-4815	181	33	describe	describe	VERB
ejpam-4815	181	34	different	different	ADJ
ejpam-4815	181	35	stationary	stationary	ADJ
ejpam-4815	181	36	processes	process	NOUN
ejpam-4815	181	37	.	.	PUNCT
ejpam-4815	182	1	thus	thus	ADV
ejpam-4815	182	2	,	,	PUNCT
ejpam-4815	182	3	the	the	DET
ejpam-4815	182	4	special	special	ADJ
ejpam-4815	182	5	interest	interest	NOUN
ejpam-4815	182	6	are	be	AUX
ejpam-4815	182	7	global	global	ADJ
ejpam-4815	182	8	properties	property	NOUN
ejpam-4815	182	9	characterising	characterise	VERB
ejpam-4815	182	10	solutions	solution	NOUN
ejpam-4815	182	11	to	to	ADP
ejpam-4815	182	12	the	the	DET
ejpam-4815	182	13	partial	partial	ADJ
ejpam-4815	182	14	differential	differential	NOUN
ejpam-4815	182	15	equation	equation	NOUN
ejpam-4815	182	16	that	that	PRON
ejpam-4815	182	17	are	be	AUX
ejpam-4815	182	18	determined	determine	VERB
ejpam-4815	182	19	from	from	ADP
ejpam-4815	182	20	local	local	ADJ
ejpam-4815	182	21	properties	property	NOUN
ejpam-4815	182	22	.	.	PUNCT
ejpam-4815	183	1	acknowledgements	acknowledgement	NOUN
ejpam-4815	183	2	the	the	DET
ejpam-4815	183	3	authors	author	NOUN
ejpam-4815	183	4	are	be	AUX
ejpam-4815	183	5	thankful	thankful	ADJ
ejpam-4815	183	6	to	to	ADP
ejpam-4815	183	7	the	the	DET
ejpam-4815	183	8	editor	editor	NOUN
ejpam-4815	183	9	for	for	ADP
ejpam-4815	183	10	his	his	PRON
ejpam-4815	183	11	useful	useful	ADJ
ejpam-4815	183	12	comments	comment	NOUN
ejpam-4815	183	13	,	,	PUNCT
ejpam-4815	183	14	and	and	CCONJ
ejpam-4815	183	15	the	the	DET
ejpam-4815	183	16	referees	referee	NOUN
ejpam-4815	183	17	for	for	ADP
ejpam-4815	183	18	their	their	PRON
ejpam-4815	183	19	valuable	valuable	ADJ
ejpam-4815	183	20	suggestions	suggestion	NOUN
ejpam-4815	183	21	which	which	PRON
ejpam-4815	183	22	improved	improve	VERB
ejpam-4815	183	23	the	the	DET
ejpam-4815	183	24	paper	paper	NOUN
ejpam-4815	183	25	.	.	PUNCT
ejpam-4815	184	1	references	reference	NOUN
ejpam-4815	184	2	[	[	X
ejpam-4815	184	3	1	1	NUM
ejpam-4815	184	4	]	]	X
ejpam-4815	184	5	r	r	NOUN
ejpam-4815	184	6	askey	askey	NOUN
ejpam-4815	184	7	.	.	PUNCT
ejpam-4815	185	1	orthogonal	orthogonal	ADJ
ejpam-4815	185	2	polynomials	polynomial	NOUN
ejpam-4815	185	3	and	and	CCONJ
ejpam-4815	185	4	special	special	ADJ
ejpam-4815	185	5	functions	function	NOUN
ejpam-4815	185	6	.	.	PUNCT
ejpam-4815	186	1	in	in	ADP
ejpam-4815	186	2	regional	regional	ADJ
ejpam-4815	186	3	conference	conference	NOUN
ejpam-4815	186	4	series	series	NOUN
ejpam-4815	186	5	in	in	ADP
ejpam-4815	186	6	applied	applied	ADJ
ejpam-4815	186	7	math	math	NOUN
ejpam-4815	186	8	.	.	PUNCT
ejpam-4815	186	9	,	,	PUNCT
ejpam-4815	186	10	philadelphia	philadelphia	PROPN
ejpam-4815	186	11	,	,	PUNCT
ejpam-4815	186	12	pa	pa	PROPN
ejpam-4815	186	13	.	.	PROPN
ejpam-4815	186	14	,	,	PUNCT
ejpam-4815	186	15	1975	1975	NUM
ejpam-4815	186	16	.	.	PUNCT
ejpam-4815	187	1	siam	siam	PROPN
ejpam-4815	187	2	.	.	PUNCT
ejpam-4815	188	1	[	[	X
ejpam-4815	188	2	2	2	X
ejpam-4815	188	3	]	]	PUNCT
ejpam-4815	188	4	s.	s.	PROPN
ejpam-4815	188	5	bergman	bergman	PROPN
ejpam-4815	188	6	.	.	PUNCT
ejpam-4815	188	7	integral	integral	ADJ
ejpam-4815	188	8	operators	operator	NOUN
ejpam-4815	188	9	in	in	ADP
ejpam-4815	188	10	the	the	DET
ejpam-4815	188	11	theory	theory	NOUN
ejpam-4815	188	12	of	of	ADP
ejpam-4815	188	13	linear	linear	ADJ
ejpam-4815	188	14	partial	partial	ADJ
ejpam-4815	188	15	differential	differential	NOUN
ejpam-4815	188	16	equations	equation	NOUN
ejpam-4815	188	17	.	.	PUNCT
ejpam-4815	189	1	ergebnisse	ergebnisse	PROPN
ejpam-4815	189	2	der	der	ADJ
ejpam-4815	189	3	math	math	NOUN
ejpam-4815	189	4	.	.	PUNCT
ejpam-4815	190	1	und	und	PROPN
ejpam-4815	190	2	ihrer	ihrer	PROPN
ejpam-4815	190	3	grenzebiete	grenzebiete	NOUN
ejpam-4815	190	4	,	,	PUNCT
ejpam-4815	190	5	heft	heft	ADJ
ejpam-4815	190	6	23	23	NUM
ejpam-4815	190	7	,	,	PUNCT
ejpam-4815	190	8	springer	springer	NOUN
ejpam-4815	190	9	-	-	PUNCT
ejpam-4815	190	10	verlag	verlag	PROPN
ejpam-4815	190	11	,	,	PUNCT
ejpam-4815	190	12	berlin	berlin	PROPN
ejpam-4815	190	13	and	and	CCONJ
ejpam-4815	190	14	new	new	PROPN
ejpam-4815	190	15	york	york	PROPN
ejpam-4815	190	16	,	,	PUNCT
ejpam-4815	190	17	1961	1961	NUM
ejpam-4815	190	18	.	.	PUNCT
ejpam-4815	191	1	[	[	X
ejpam-4815	191	2	3	3	X
ejpam-4815	191	3	]	]	X
ejpam-4815	191	4	d.	d.	PROPN
ejpam-4815	191	5	l.	l.	PROPN
ejpam-4815	191	6	colton	colton	PROPN
ejpam-4815	191	7	.	.	PUNCT
ejpam-4815	192	1	partial	partial	ADJ
ejpam-4815	192	2	differential	differential	ADJ
ejpam-4815	192	3	equations	equation	NOUN
ejpam-4815	192	4	in	in	ADP
ejpam-4815	192	5	the	the	DET
ejpam-4815	192	6	complex	complex	ADJ
ejpam-4815	192	7	domain	domain	NOUN
ejpam-4815	192	8	.	.	PUNCT
ejpam-4815	193	1	research	research	NOUN
ejpam-4815	193	2	notes	note	NOUN
ejpam-4815	193	3	in	in	ADP
ejpam-4815	193	4	mathematics	mathematic	NOUN
ejpam-4815	193	5	vol	vol	NOUN
ejpam-4815	193	6	.	.	PROPN
ejpam-4815	194	1	4	4	NUM
ejpam-4815	194	2	,	,	PUNCT
ejpam-4815	194	3	pitman	pitman	NOUN
ejpam-4815	194	4	,	,	PUNCT
ejpam-4815	194	5	san	san	PROPN
ejpam-4815	194	6	francisco	francisco	PROPN
ejpam-4815	194	7	,	,	PUNCT
ejpam-4815	194	8	calif	calif	PROPN
ejpam-4815	194	9	,	,	PUNCT
ejpam-4815	194	10	1976	1976	NUM
ejpam-4815	194	11	.	.	PUNCT
ejpam-4815	195	1	[	[	X
ejpam-4815	195	2	4	4	NUM
ejpam-4815	195	3	]	]	X
ejpam-4815	195	4	s.m	s.m	PROPN
ejpam-4815	195	5	.	.	PROPN
ejpam-4815	195	6	einstein	einstein	PROPN
ejpam-4815	195	7	-	-	PUNCT
ejpam-4815	195	8	matthews	matthews	PROPN
ejpam-4815	195	9	and	and	CCONJ
ejpam-4815	195	10	h.s	h.s	PROPN
ejpam-4815	195	11	.	.	PROPN
ejpam-4815	195	12	kasana	kasana	PROPN
ejpam-4815	195	13	.	.	PUNCT
ejpam-4815	196	1	proximate	proximate	VERB
ejpam-4815	196	2	order	order	NOUN
ejpam-4815	196	3	and	and	CCONJ
ejpam-4815	196	4	type	type	NOUN
ejpam-4815	196	5	of	of	ADP
ejpam-4815	196	6	entire	entire	ADJ
ejpam-4815	196	7	functions	function	NOUN
ejpam-4815	196	8	of	of	ADP
ejpam-4815	196	9	several	several	ADJ
ejpam-4815	196	10	complex	complex	ADJ
ejpam-4815	196	11	variables	variable	NOUN
ejpam-4815	196	12	.	.	PUNCT
ejpam-4815	197	1	israel	israel	PROPN
ejpam-4815	197	2	j.	j.	PROPN
ejpam-4815	197	3	math	math	PROPN
ejpam-4815	197	4	.	.	PUNCT
ejpam-4815	197	5	,	,	PUNCT
ejpam-4815	197	6	92(1	92(1	NOUN
ejpam-4815	197	7	-	-	SYM
ejpam-4815	197	8	3):273–284	3):273–284	NUM
ejpam-4815	197	9	,	,	PUNCT
ejpam-4815	197	10	1995	1995	NUM
ejpam-4815	197	11	.	.	PUNCT
ejpam-4815	198	1	[	[	X
ejpam-4815	198	2	5	5	NUM
ejpam-4815	198	3	]	]	X
ejpam-4815	198	4	a.j	a.j	PROPN
ejpam-4815	198	5	.	.	PROPN
ejpam-4815	198	6	fryant	fryant	PROPN
ejpam-4815	198	7	.	.	PUNCT
ejpam-4815	199	1	growth	growth	NOUN
ejpam-4815	199	2	and	and	CCONJ
ejpam-4815	199	3	complete	complete	ADJ
ejpam-4815	199	4	sequences	sequence	NOUN
ejpam-4815	199	5	of	of	ADP
ejpam-4815	199	6	generalized	generalized	ADJ
ejpam-4815	199	7	bi	bi	NOUN
ejpam-4815	199	8	-	-	ADJ
ejpam-4815	199	9	axially	axially	ADV
ejpam-4815	199	10	symmetric	symmetric	ADJ
ejpam-4815	199	11	potentials	potential	NOUN
ejpam-4815	199	12	.	.	PUNCT
ejpam-4815	200	1	j.	j.	PROPN
ejpam-4815	200	2	differential	differential	PROPN
ejpam-4815	200	3	equations	equation	NOUN
ejpam-4815	200	4	,	,	PUNCT
ejpam-4815	200	5	31:155–164	31:155–164	NOUN
ejpam-4815	200	6	,	,	PUNCT
ejpam-4815	200	7	1979	1979	NUM
ejpam-4815	200	8	.	.	PUNCT
ejpam-4815	201	1	[	[	X
ejpam-4815	201	2	6	6	NUM
ejpam-4815	201	3	]	]	PUNCT
ejpam-4815	201	4	r.	r.	PROPN
ejpam-4815	201	5	p.	p.	PROPN
ejpam-4815	201	6	gilbert	gilbert	PROPN
ejpam-4815	201	7	.	.	PUNCT
ejpam-4815	202	1	integral	integral	ADJ
ejpam-4815	202	2	operator	operator	NOUN
ejpam-4815	202	3	methods	method	NOUN
ejpam-4815	202	4	in	in	ADP
ejpam-4815	202	5	bi	bi	ADJ
ejpam-4815	202	6	-	-	ADJ
ejpam-4815	202	7	axially	axially	ADV
ejpam-4815	202	8	symmetric	symmetric	ADJ
ejpam-4815	202	9	potential	potential	ADJ
ejpam-4815	202	10	theory	theory	NOUN
ejpam-4815	202	11	.	.	PUNCT
ejpam-4815	203	1	contrib	contrib	PROPN
ejpam-4815	203	2	.	.	PROPN
ejpam-4815	203	3	differential	differential	PROPN
ejpam-4815	203	4	equations	equation	NOUN
ejpam-4815	203	5	,	,	PUNCT
ejpam-4815	203	6	2:441–456	2:441–456	PROPN
ejpam-4815	203	7	,	,	PUNCT
ejpam-4815	203	8	1963	1963	NUM
ejpam-4815	203	9	.	.	PUNCT
ejpam-4815	204	1	[	[	X
ejpam-4815	204	2	7	7	X
ejpam-4815	204	3	]	]	X
ejpam-4815	204	4	r.p	r.p	PROPN
ejpam-4815	204	5	.	.	PROPN
ejpam-4815	204	6	gilbert	gilbert	PROPN
ejpam-4815	204	7	.	.	PUNCT
ejpam-4815	205	1	function	function	VERB
ejpam-4815	205	2	theoretic	theoretic	ADJ
ejpam-4815	205	3	methods	method	NOUN
ejpam-4815	205	4	in	in	ADP
ejpam-4815	205	5	partial	partial	ADJ
ejpam-4815	205	6	differential	differential	NOUN
ejpam-4815	205	7	equations	equation	NOUN
ejpam-4815	205	8	,	,	PUNCT
ejpam-4815	205	9	math	math	NOUN
ejpam-4815	205	10	.	.	PUNCT
ejpam-4815	206	1	in	in	ADP
ejpam-4815	206	2	sci	sci	PROPN
ejpam-4815	206	3	.	.	PROPN
ejpam-4815	207	1	and	and	CCONJ
ejpam-4815	207	2	engineering	engineering	NOUN
ejpam-4815	207	3	,	,	PUNCT
ejpam-4815	207	4	vol	vol	NOUN
ejpam-4815	207	5	.	.	PROPN
ejpam-4815	207	6	54	54	NUM
ejpam-4815	207	7	.	.	PUNCT
ejpam-4815	208	1	academic	academic	ADJ
ejpam-4815	208	2	press	press	NOUN
ejpam-4815	208	3	,	,	PUNCT
ejpam-4815	208	4	new	new	PROPN
ejpam-4815	208	5	york	york	PROPN
ejpam-4815	208	6	,	,	PUNCT
ejpam-4815	208	7	1969	1969	NUM
ejpam-4815	208	8	.	.	PUNCT
ejpam-4815	209	1	[	[	X
ejpam-4815	209	2	8	8	NUM
ejpam-4815	209	3	]	]	X
ejpam-4815	209	4	r.p	r.p	PROPN
ejpam-4815	209	5	.	.	PROPN
ejpam-4815	209	6	gilbert	gilbert	PROPN
ejpam-4815	209	7	.	.	PUNCT
ejpam-4815	210	1	constructive	constructive	ADJ
ejpam-4815	210	2	methods	method	NOUN
ejpam-4815	210	3	for	for	ADP
ejpam-4815	210	4	elliptic	elliptic	ADJ
ejpam-4815	210	5	equations	equation	NOUN
ejpam-4815	210	6	,	,	PUNCT
ejpam-4815	210	7	lecture	lecture	NOUN
ejpam-4815	210	8	notes	note	NOUN
ejpam-4815	210	9	in	in	ADP
ejpam-4815	210	10	math	math	NOUN
ejpam-4815	210	11	.	.	PUNCT
ejpam-4815	211	1	vol	vol	NOUN
ejpam-4815	211	2	.	.	PROPN
ejpam-4815	211	3	365	365	NUM
ejpam-4815	211	4	.	.	PUNCT
ejpam-4815	212	1	springer	springer	NOUN
ejpam-4815	212	2	-	-	PUNCT
ejpam-4815	212	3	verlag	verlag	PROPN
ejpam-4815	212	4	,	,	PUNCT
ejpam-4815	212	5	berlin	berlin	PROPN
ejpam-4815	212	6	and	and	CCONJ
ejpam-4815	212	7	new	new	PROPN
ejpam-4815	212	8	york	york	PROPN
ejpam-4815	212	9	,	,	PUNCT
ejpam-4815	212	10	1970	1970	NUM
ejpam-4815	212	11	.	.	PUNCT
ejpam-4815	213	1	[	[	X
ejpam-4815	213	2	9	9	NUM
ejpam-4815	213	3	]	]	X
ejpam-4815	213	4	r.p	r.p	PROPN
ejpam-4815	213	5	.	.	PROPN
ejpam-4815	213	6	doherey	doherey	PROPN
ejpam-4815	213	7	k.	k.	PROPN
ejpam-4815	213	8	nandan	nandan	PROPN
ejpam-4815	213	9	and	and	CCONJ
ejpam-4815	213	10	r.s.l	r.s.l	NOUN
ejpam-4815	213	11	.	.	PUNCT
ejpam-4815	214	1	srivastava	srivastava	PROPN
ejpam-4815	214	2	.	.	PUNCT
ejpam-4815	215	1	on	on	ADP
ejpam-4815	215	2	the	the	DET
ejpam-4815	215	3	generalized	generalized	ADJ
ejpam-4815	215	4	type	type	NOUN
ejpam-4815	215	5	and	and	CCONJ
ejpam-4815	215	6	lower	low	ADJ
ejpam-4815	215	7	generalized	generalized	ADJ
ejpam-4815	215	8	type	type	NOUN
ejpam-4815	215	9	of	of	ADP
ejpam-4815	215	10	an	an	DET
ejpam-4815	215	11	entire	entire	ADJ
ejpam-4815	215	12	function	function	NOUN
ejpam-4815	215	13	with	with	ADP
ejpam-4815	215	14	index	index	NOUN
ejpam-4815	215	15	-	-	PUNCT
ejpam-4815	215	16	pair	pair	NOUN
ejpam-4815	215	17	(	(	PUNCT
ejpam-4815	215	18	p	p	X
ejpam-4815	215	19	,	,	PUNCT
ejpam-4815	215	20	q	q	NOUN
ejpam-4815	215	21	)	)	PUNCT
ejpam-4815	215	22	.	.	PUNCT
ejpam-4815	216	1	indian	indian	PROPN
ejpam-4815	216	2	j.	j.	PROPN
ejpam-4815	216	3	pure	pure	PROPN
ejpam-4815	216	4	appl	appl	PROPN
ejpam-4815	216	5	.	.	PUNCT
ejpam-4815	216	6	math	math	PROPN
ejpam-4815	216	7	.	.	PUNCT
ejpam-4815	216	8	,	,	PUNCT
ejpam-4815	216	9	11:1424–1433	11:1424–1433	NUM
ejpam-4815	216	10	,	,	PUNCT
ejpam-4815	216	11	1980	1980	NUM
ejpam-4815	216	12	.	.	PUNCT
ejpam-4815	217	1	[	[	X
ejpam-4815	217	2	10	10	NUM
ejpam-4815	217	3	]	]	X
ejpam-4815	217	4	h.s	h.s	PROPN
ejpam-4815	217	5	.	.	PROPN
ejpam-4815	217	6	kasana	kasana	PROPN
ejpam-4815	217	7	and	and	CCONJ
ejpam-4815	217	8	d.	d.	PROPN
ejpam-4815	217	9	kumar	kumar	PROPN
ejpam-4815	217	10	.	.	PUNCT
ejpam-4815	218	1	the	the	DET
ejpam-4815	218	2	lp	lp	NOUN
ejpam-4815	218	3	-	-	PUNCT
ejpam-4815	218	4	approximation	approximation	NOUN
ejpam-4815	218	5	of	of	ADP
ejpam-4815	218	6	generalized	generalized	ADJ
ejpam-4815	218	7	bi	bi	NOUN
ejpam-4815	218	8	-	-	ADJ
ejpam-4815	218	9	axially	axially	ADV
ejpam-4815	218	10	symmetric	symmetric	ADJ
ejpam-4815	218	11	potentials	potential	NOUN
ejpam-4815	218	12	.	.	PUNCT
ejpam-4815	219	1	int	int	NOUN
ejpam-4815	219	2	.	.	PUNCT
ejpam-4815	220	1	j.	j.	PROPN
ejpam-4815	220	2	diff.eqs	diff.eqs	PROPN
ejpam-4815	220	3	.	.	PUNCT
ejpam-4815	220	4	appl	appl	PROPN
ejpam-4815	220	5	.	.	PROPN
ejpam-4815	220	6	,	,	PUNCT
ejpam-4815	220	7	9(2):127–142	9(2):127–142	NUM
ejpam-4815	220	8	,	,	PUNCT
ejpam-4815	220	9	2004	2004	NUM
ejpam-4815	220	10	.	.	PUNCT
ejpam-4815	221	1	[	[	X
ejpam-4815	221	2	11	11	NUM
ejpam-4815	221	3	]	]	X
ejpam-4815	221	4	h.s	h.s	PROPN
ejpam-4815	221	5	.	.	PROPN
ejpam-4815	221	6	kasana	kasana	PROPN
ejpam-4815	221	7	and	and	CCONJ
ejpam-4815	221	8	a.	a.	PROPN
ejpam-4815	221	9	shai	shai	PROPN
ejpam-4815	221	10	.	.	PUNCT
ejpam-4815	222	1	the	the	DET
ejpam-4815	222	2	proximate	proximate	NOUN
ejpam-4815	222	3	order	order	NOUN
ejpam-4815	222	4	of	of	ADP
ejpam-4815	222	5	entire	entire	ADJ
ejpam-4815	222	6	dirichlet	dirichlet	PROPN
ejpam-4815	222	7	series	series	NOUN
ejpam-4815	222	8	,	,	PUNCT
ejpam-4815	222	9	complex	complex	ADJ
ejpam-4815	222	10	variables	variable	NOUN
ejpam-4815	222	11	.	.	PUNCT
ejpam-4815	223	1	complex	complex	ADJ
ejpam-4815	223	2	variables;theory	variables;theory	NOUN
ejpam-4815	223	3	and	and	CCONJ
ejpam-4815	223	4	applications	application	NOUN
ejpam-4815	223	5	,	,	PUNCT
ejpam-4815	223	6	9(1):49–62	9(1):49–62	NUM
ejpam-4815	223	7	,	,	PUNCT
ejpam-4815	223	8	1987	1987	NUM
ejpam-4815	223	9	.	.	PUNCT
ejpam-4815	224	1	references	reference	NOUN
ejpam-4815	224	2	1517	1517	NUM
ejpam-4815	224	3	[	[	X
ejpam-4815	224	4	12	12	NUM
ejpam-4815	224	5	]	]	X
ejpam-4815	224	6	d.	d.	PROPN
ejpam-4815	224	7	kumar	kumar	PROPN
ejpam-4815	224	8	.	.	PUNCT
ejpam-4815	225	1	ultra	ultra	ADJ
ejpam-4815	225	2	-	-	ADJ
ejpam-4815	225	3	spherical	spherical	ADJ
ejpam-4815	225	4	expansions	expansion	NOUN
ejpam-4815	225	5	of	of	ADP
ejpam-4815	225	6	generalized	generalized	ADJ
ejpam-4815	225	7	bi	bi	NOUN
ejpam-4815	225	8	-	-	ADJ
ejpam-4815	225	9	axially	axially	ADV
ejpam-4815	225	10	symmetric	symmetric	ADJ
ejpam-4815	225	11	potentials	potential	NOUN
ejpam-4815	225	12	and	and	CCONJ
ejpam-4815	225	13	pseudoanalytic	pseudoanalytic	ADJ
ejpam-4815	225	14	functions	function	NOUN
ejpam-4815	225	15	.	.	PUNCT
ejpam-4815	226	1	complex	complex	ADJ
ejpam-4815	226	2	variables	variable	NOUN
ejpam-4815	226	3	and	and	CCONJ
ejpam-4815	226	4	elliptic	elliptic	ADJ
ejpam-4815	226	5	equations	equation	NOUN
ejpam-4815	226	6	,	,	PUNCT
ejpam-4815	226	7	53(1):53	53(1):53	NUM
ejpam-4815	226	8	–	–	PUNCT
ejpam-4815	226	9	64	64	NUM
ejpam-4815	226	10	,	,	PUNCT
ejpam-4815	226	11	2008	2008	NUM
ejpam-4815	226	12	.	.	PUNCT
ejpam-4815	227	1	[	[	X
ejpam-4815	227	2	13	13	NUM
ejpam-4815	227	3	]	]	X
ejpam-4815	227	4	d.	d.	PROPN
ejpam-4815	227	5	kumar	kumar	PROPN
ejpam-4815	227	6	.	.	PUNCT
ejpam-4815	228	1	growth	growth	NOUN
ejpam-4815	228	2	and	and	CCONJ
ejpam-4815	228	3	approximation	approximation	NOUN
ejpam-4815	228	4	of	of	ADP
ejpam-4815	228	5	solutions	solution	NOUN
ejpam-4815	228	6	to	to	ADP
ejpam-4815	228	7	a	a	DET
ejpam-4815	228	8	class	class	NOUN
ejpam-4815	228	9	of	of	ADP
ejpam-4815	228	10	certain	certain	ADJ
ejpam-4815	228	11	linear	linear	ADJ
ejpam-4815	228	12	partial	partial	ADJ
ejpam-4815	228	13	differential	differential	NOUN
ejpam-4815	228	14	equations	equation	NOUN
ejpam-4815	228	15	in	in	ADP
ejpam-4815	228	16	rn	rn	PROPN
ejpam-4815	228	17	.	.	PUNCT
ejpam-4815	229	1	mathematica	mathematica	PROPN
ejpam-4815	229	2	slovaca	slovaca	PROPN
ejpam-4815	229	3	,	,	PUNCT
ejpam-4815	229	4	64(1):139–154	64(1):139–154	PROPN
ejpam-4815	229	5	,	,	PUNCT
ejpam-4815	229	6	2014	2014	NUM
ejpam-4815	229	7	.	.	PUNCT
ejpam-4815	230	1	[	[	X
ejpam-4815	230	2	14	14	NUM
ejpam-4815	230	3	]	]	X
ejpam-4815	230	4	p.a	p.a	PROPN
ejpam-4815	230	5	.	.	PROPN
ejpam-4815	230	6	mccoy	mccoy	PROPN
ejpam-4815	230	7	.	.	PUNCT
ejpam-4815	231	1	best	good	ADJ
ejpam-4815	232	1	lp	lp	ADJ
ejpam-4815	232	2	-	-	NOUN
ejpam-4815	232	3	approximation	approximation	NOUN
ejpam-4815	232	4	of	of	ADP
ejpam-4815	232	5	generalized	generalized	ADJ
ejpam-4815	232	6	biaxisymmetric	biaxisymmetric	ADJ
ejpam-4815	232	7	potentials	potential	NOUN
ejpam-4815	232	8	.	.	PUNCT
ejpam-4815	233	1	proc	proc	NOUN
ejpam-4815	233	2	.	.	PUNCT
ejpam-4815	234	1	amer	amer	PROPN
ejpam-4815	234	2	.	.	PUNCT
ejpam-4815	234	3	math	math	PROPN
ejpam-4815	234	4	.	.	PUNCT
ejpam-4815	235	1	soc	soc	PROPN
ejpam-4815	235	2	.	.	PUNCT
ejpam-4815	235	3	,	,	PUNCT
ejpam-4815	236	1	79(3):435–440	79(3):435–440	PROPN
ejpam-4815	236	2	,	,	PUNCT
ejpam-4815	236	3	1980	1980	NUM
ejpam-4815	236	4	.	.	PUNCT
ejpam-4815	237	1	[	[	X
ejpam-4815	237	2	15	15	NUM
ejpam-4815	237	3	]	]	X
ejpam-4815	237	4	g.p	g.p	PROPN
ejpam-4815	237	5	.	.	PROPN
ejpam-4815	237	6	kapoor	kapoor	PROPN
ejpam-4815	237	7	o.p	o.p	PROPN
ejpam-4815	237	8	.	.	PROPN
ejpam-4815	237	9	juneja	juneja	PROPN
ejpam-4815	237	10	and	and	CCONJ
ejpam-4815	237	11	s.k	s.k	PROPN
ejpam-4815	237	12	.	.	PROPN
ejpam-4815	237	13	bajpai	bajpai	PROPN
ejpam-4815	237	14	.	.	PUNCT
ejpam-4815	238	1	on	on	ADP
ejpam-4815	238	2	the	the	DET
ejpam-4815	238	3	(	(	PUNCT
ejpam-4815	238	4	p	p	NOUN
ejpam-4815	238	5	,	,	PUNCT
ejpam-4815	238	6	q)-order	q)-order	NOUN
ejpam-4815	238	7	and	and	CCONJ
ejpam-4815	238	8	lower	low	ADJ
ejpam-4815	238	9	(	(	PUNCT
ejpam-4815	238	10	p	p	NOUN
ejpam-4815	238	11	,	,	PUNCT
ejpam-4815	238	12	q)-order	q)-order	NOUN
ejpam-4815	238	13	of	of	ADP
ejpam-4815	238	14	an	an	DET
ejpam-4815	238	15	entire	entire	ADJ
ejpam-4815	238	16	function	function	NOUN
ejpam-4815	238	17	.	.	PUNCT
ejpam-4815	239	1	j.	j.	PROPN
ejpam-4815	239	2	reine	reine	PROPN
ejpam-4815	239	3	angew	angew	PROPN
ejpam-4815	239	4	.	.	PUNCT
ejpam-4815	240	1	math	math	NOUN
ejpam-4815	240	2	.	.	PUNCT
ejpam-4815	240	3	,	,	PUNCT
ejpam-4815	241	1	282:53–67	282:53–67	NUM
ejpam-4815	241	2	,	,	PUNCT
ejpam-4815	241	3	1976	1976	NUM
ejpam-4815	241	4	.	.	PUNCT
ejpam-4815	242	1	[	[	X
ejpam-4815	242	2	16	16	NUM
ejpam-4815	242	3	]	]	X
ejpam-4815	242	4	g.p	g.p	PROPN
ejpam-4815	242	5	.	.	PROPN
ejpam-4815	242	6	kapoor	kapoor	PROPN
ejpam-4815	242	7	o.p	o.p	PROPN
ejpam-4815	242	8	.	.	PROPN
ejpam-4815	242	9	juneja	juneja	PROPN
ejpam-4815	242	10	and	and	CCONJ
ejpam-4815	242	11	s.k	s.k	PROPN
ejpam-4815	242	12	.	.	PROPN
ejpam-4815	242	13	bajpai	bajpai	PROPN
ejpam-4815	242	14	.	.	PUNCT
ejpam-4815	243	1	on	on	ADP
ejpam-4815	243	2	the	the	DET
ejpam-4815	243	3	(	(	PUNCT
ejpam-4815	243	4	p	p	NOUN
ejpam-4815	243	5	,	,	PUNCT
ejpam-4815	243	6	q)-type	q)-type	PUNCT
ejpam-4815	243	7	and	and	CCONJ
ejpam-4815	243	8	lower	low	ADJ
ejpam-4815	243	9	(	(	PUNCT
ejpam-4815	243	10	p	p	NOUN
ejpam-4815	243	11	,	,	PUNCT
ejpam-4815	243	12	q)-type	q)-type	ADV
ejpam-4815	243	13	of	of	ADP
ejpam-4815	243	14	an	an	DET
ejpam-4815	243	15	entire	entire	ADJ
ejpam-4815	243	16	function	function	NOUN
ejpam-4815	243	17	.	.	PUNCT
ejpam-4815	244	1	j.	j.	PROPN
ejpam-4815	244	2	reine	reine	PROPN
ejpam-4815	244	3	angew	angew	PROPN
ejpam-4815	244	4	.	.	PUNCT
ejpam-4815	245	1	math	math	PROPN
ejpam-4815	245	2	.	.	PUNCT
ejpam-4815	245	3	,	,	PUNCT
ejpam-4815	245	4	290:180–190	290:180–190	NUM
ejpam-4815	245	5	,	,	PUNCT
ejpam-4815	245	6	1977	1977	NUM
ejpam-4815	245	7	.	.	PUNCT
ejpam-4815	246	1	[	[	X
ejpam-4815	246	2	17	17	NUM
ejpam-4815	246	3	]	]	X
ejpam-4815	246	4	g.	g.	PROPN
ejpam-4815	246	5	szegö.	szegö.	PROPN
ejpam-4815	246	6	orthogonal	orthogonal	ADJ
ejpam-4815	246	7	polynomials	polynomial	NOUN
ejpam-4815	246	8	,	,	PUNCT
ejpam-4815	246	9	vol	vol	NOUN
ejpam-4815	246	10	.	.	PROPN
ejpam-4815	246	11	23	23	NUM
ejpam-4815	246	12	.	.	PUNCT
ejpam-4815	247	1	colloquim	colloquim	PROPN
ejpam-4815	247	2	publications	publication	NOUN
ejpam-4815	247	3	,	,	PUNCT
ejpam-4815	247	4	amer	amer	PROPN
ejpam-4815	247	5	.	.	PROPN
ejpam-4815	247	6	math	math	PROPN
ejpam-4815	247	7	.	.	PUNCT
ejpam-4815	248	1	soc	soc	PROPN
ejpam-4815	248	2	.	.	PUNCT
ejpam-4815	249	1	providence	providence	NOUN
ejpam-4815	249	2	,	,	PUNCT
ejpam-4815	249	3	r.i	r.i	PROPN
ejpam-4815	249	4	.	.	PROPN
ejpam-4815	249	5	,	,	PUNCT
ejpam-4815	249	6	1967	1967	NUM
ejpam-4815	249	7	.	.	PUNCT
ejpam-4815	250	1	[	[	X
ejpam-4815	250	2	18	18	NUM
ejpam-4815	250	3	]	]	PUNCT
ejpam-4815	250	4	t.	t.	PROPN
ejpam-4815	250	5	winiarski	winiarski	PROPN
ejpam-4815	250	6	.	.	PUNCT
ejpam-4815	251	1	approximation	approximation	NOUN
ejpam-4815	251	2	and	and	CCONJ
ejpam-4815	251	3	interpolation	interpolation	NOUN
ejpam-4815	251	4	of	of	ADP
ejpam-4815	251	5	entire	entire	ADJ
ejpam-4815	251	6	functions	function	NOUN
ejpam-4815	251	7	.	.	PUNCT
ejpam-4815	252	1	ann	ann	PROPN
ejpam-4815	252	2	.	.	PUNCT
ejpam-4815	252	3	polon	polon	PROPN
ejpam-4815	252	4	.	.	PUNCT
ejpam-4815	253	1	math	math	NOUN
ejpam-4815	253	2	.	.	PUNCT
ejpam-4815	253	3	,	,	PUNCT
ejpam-4815	254	1	23:259–273	23:259–273	NUM
ejpam-4815	254	2	,	,	PUNCT
ejpam-4815	254	3	1973	1973	NUM
ejpam-4815	254	4	.	.	PUNCT