id	sid	tid	token	lemma	pos
ejpam-782	1	1	10_782_kumar.dvi	10_782_kumar.dvi	NUM
ejpam-782	1	2	european	european	PROPN
ejpam-782	1	3	journal	journal	PROPN
ejpam-782	1	4	of	of	ADP
ejpam-782	1	5	pure	pure	ADJ
ejpam-782	1	6	and	and	CCONJ
ejpam-782	1	7	applied	apply	VERB
ejpam-782	1	8	mathematics	mathematic	NOUN
ejpam-782	1	9	vol	vol	NOUN
ejpam-782	1	10	.	.	PUNCT
ejpam-782	2	1	3	3	NUM
ejpam-782	2	2	,	,	PUNCT
ejpam-782	2	3	no	no	INTJ
ejpam-782	2	4	.	.	NOUN
ejpam-782	2	5	6	6	NUM
ejpam-782	2	6	,	,	PUNCT
ejpam-782	2	7	2010	2010	NUM
ejpam-782	2	8	,	,	PUNCT
ejpam-782	2	9	1062	1062	NUM
ejpam-782	2	10	-	-	SYM
ejpam-782	2	11	1069	1069	NUM
ejpam-782	2	12	issn	issn	PROPN
ejpam-782	2	13	1307	1307	NUM
ejpam-782	2	14	-	-	SYM
ejpam-782	2	15	5543	5543	NUM
ejpam-782	2	16	–	–	PUNCT
ejpam-782	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-782	2	18	special	special	ADJ
ejpam-782	2	19	issue	issue	NOUN
ejpam-782	2	20	on	on	ADP
ejpam-782	2	21	complex	complex	ADJ
ejpam-782	2	22	analysis	analysis	NOUN
ejpam-782	2	23	:	:	PUNCT
ejpam-782	2	24	theory	theory	NOUN
ejpam-782	2	25	and	and	CCONJ
ejpam-782	2	26	applications	application	NOUN
ejpam-782	2	27	dedicated	dedicate	VERB
ejpam-782	2	28	to	to	ADP
ejpam-782	2	29	professor	professor	PROPN
ejpam-782	2	30	hari	hari	PROPN
ejpam-782	2	31	m.	m.	PROPN
ejpam-782	2	32	srivastava	srivastava	PROPN
ejpam-782	2	33	,	,	PUNCT
ejpam-782	2	34	on	on	ADP
ejpam-782	2	35	the	the	DET
ejpam-782	2	36	occasion	occasion	NOUN
ejpam-782	2	37	of	of	ADP
ejpam-782	2	38	his	his	PRON
ejpam-782	2	39	70th	70th	ADJ
ejpam-782	2	40	birthday	birthday	NOUN
ejpam-782	2	41	growth	growth	NOUN
ejpam-782	2	42	and	and	CCONJ
ejpam-782	2	43	chebyshev	chebyshev	NOUN
ejpam-782	2	44	approximation	approximation	NOUN
ejpam-782	2	45	of	of	ADP
ejpam-782	2	46	entire	entire	ADJ
ejpam-782	2	47	function	function	NOUN
ejpam-782	2	48	solutions	solution	NOUN
ejpam-782	2	49	of	of	ADP
ejpam-782	2	50	helmholtz	helmholtz	NOUN
ejpam-782	2	51	equation	equation	NOUN
ejpam-782	2	52	in	in	ADP
ejpam-782	2	53	r2	r2	PROPN
ejpam-782	2	54	devendra	devendra	PROPN
ejpam-782	2	55	kumar	kumar	PROPN
ejpam-782	2	56	department	department	PROPN
ejpam-782	2	57	of	of	ADP
ejpam-782	2	58	mathematics	mathematics	PROPN
ejpam-782	3	1	[	[	X
ejpam-782	3	2	research	research	NOUN
ejpam-782	3	3	and	and	CCONJ
ejpam-782	3	4	postgraduate	postgraduate	NOUN
ejpam-782	3	5	studies	study	NOUN
ejpam-782	3	6	]	]	PUNCT
ejpam-782	3	7	,	,	PUNCT
ejpam-782	3	8	m.m.h.college	m.m.h.college	PROPN
ejpam-782	3	9	,	,	PUNCT
ejpam-782	3	10	model	model	NOUN
ejpam-782	3	11	town	town	NOUN
ejpam-782	3	12	,	,	PUNCT
ejpam-782	3	13	ghaziabad201001,u.p	ghaziabad201001,u.p	PROPN
ejpam-782	3	14	.	.	PUNCT
ejpam-782	3	15	india	india	PROPN
ejpam-782	3	16	abstract	abstract	PROPN
ejpam-782	3	17	.	.	PUNCT
ejpam-782	4	1	some	some	DET
ejpam-782	4	2	bounds	bound	NOUN
ejpam-782	4	3	on	on	ADP
ejpam-782	4	4	growth	growth	NOUN
ejpam-782	4	5	parameters	parameter	NOUN
ejpam-782	4	6	of	of	ADP
ejpam-782	4	7	entire	entire	ADJ
ejpam-782	4	8	function	function	NOUN
ejpam-782	4	9	solution	solution	NOUN
ejpam-782	4	10	of	of	ADP
ejpam-782	4	11	helmholtz	helmholtz	NOUN
ejpam-782	4	12	equation	equation	NOUN
ejpam-782	4	13	in	in	ADP
ejpam-782	4	14	r2	r2	PROPN
ejpam-782	4	15	have	have	AUX
ejpam-782	4	16	been	be	AUX
ejpam-782	4	17	studied	study	VERB
ejpam-782	4	18	in	in	ADP
ejpam-782	4	19	terms	term	NOUN
ejpam-782	4	20	of	of	ADP
ejpam-782	4	21	chebyshev	chebyshev	NOUN
ejpam-782	4	22	polynomial	polynomial	ADJ
ejpam-782	4	23	approximation	approximation	NOUN
ejpam-782	4	24	error	error	NOUN
ejpam-782	4	25	in	in	ADP
ejpam-782	4	26	sup	sup	PROPN
ejpam-782	4	27	norm	norm	NOUN
ejpam-782	4	28	.	.	PUNCT
ejpam-782	5	1	our	our	PRON
ejpam-782	5	2	results	result	NOUN
ejpam-782	5	3	extend	extend	VERB
ejpam-782	5	4	and	and	CCONJ
ejpam-782	5	5	improve	improve	VERB
ejpam-782	5	6	the	the	DET
ejpam-782	5	7	results	result	NOUN
ejpam-782	5	8	studied	study	VERB
ejpam-782	5	9	by	by	ADP
ejpam-782	5	10	mccoy	mccoy	PROPN
ejpam-782	6	1	[	[	X
ejpam-782	6	2	9	9	NUM
ejpam-782	6	3	]	]	SYM
ejpam-782	6	4	.	.	PUNCT
ejpam-782	6	5	2000	2000	NUM
ejpam-782	6	6	mathematics	mathematic	NOUN
ejpam-782	6	7	subject	subject	NOUN
ejpam-782	6	8	classifications	classification	NOUN
ejpam-782	6	9	:	:	PUNCT
ejpam-782	6	10	30a35,41a10	30a35,41a10	NUM
ejpam-782	6	11	key	key	ADJ
ejpam-782	6	12	words	word	NOUN
ejpam-782	6	13	and	and	CCONJ
ejpam-782	6	14	phrases	phrase	NOUN
ejpam-782	6	15	:	:	PUNCT
ejpam-782	6	16	chebyshev	chebyshev	NOUN
ejpam-782	6	17	approximation	approximation	NOUN
ejpam-782	6	18	,	,	PUNCT
ejpam-782	6	19	growth	growth	NOUN
ejpam-782	6	20	parameters	parameter	NOUN
ejpam-782	6	21	,	,	PUNCT
ejpam-782	6	22	bergman	bergman	PROPN
ejpam-782	6	23	integral	integral	ADJ
ejpam-782	6	24	operator	operator	NOUN
ejpam-782	6	25	,	,	PUNCT
ejpam-782	6	26	helmholtz	helmholtz	NOUN
ejpam-782	6	27	equation	equation	NOUN
ejpam-782	6	28	,	,	PUNCT
ejpam-782	6	29	entire	entire	ADJ
ejpam-782	6	30	function	function	NOUN
ejpam-782	6	31	1	1	NUM
ejpam-782	6	32	.	.	PUNCT
ejpam-782	6	33	introduction	introduction	NOUN
ejpam-782	6	34	for	for	ADP
ejpam-782	6	35	classifying	classify	VERB
ejpam-782	6	36	the	the	DET
ejpam-782	6	37	entire	entire	ADJ
ejpam-782	6	38	analytic	analytic	ADJ
ejpam-782	6	39	functions	function	NOUN
ejpam-782	6	40	by	by	ADP
ejpam-782	6	41	their	their	PRON
ejpam-782	6	42	growth	growth	NOUN
ejpam-782	6	43	in	in	ADP
ejpam-782	6	44	function	function	NOUN
ejpam-782	6	45	theory	theory	NOUN
ejpam-782	6	46	,	,	PUNCT
ejpam-782	6	47	the	the	DET
ejpam-782	6	48	growth	growth	NOUN
ejpam-782	6	49	parameters	parameter	NOUN
ejpam-782	6	50	order	order	NOUN
ejpam-782	6	51	and	and	CCONJ
ejpam-782	6	52	type	type	NOUN
ejpam-782	6	53	may	may	AUX
ejpam-782	6	54	be	be	AUX
ejpam-782	6	55	computed	compute	VERB
ejpam-782	6	56	from	from	ADP
ejpam-782	6	57	the	the	DET
ejpam-782	6	58	taylor	taylor	PROPN
ejpam-782	6	59	’s	’s	PART
ejpam-782	6	60	coefficients	coefficient	NOUN
ejpam-782	6	61	or	or	CCONJ
ejpam-782	6	62	chebyshev	chebyshev	NOUN
ejpam-782	6	63	polynomial	polynomial	ADJ
ejpam-782	6	64	approximations.mccoy[8,9	approximations.mccoy[8,9	NOUN
ejpam-782	6	65	]	]	PUNCT
ejpam-782	6	66	studied	study	VERB
ejpam-782	6	67	the	the	DET
ejpam-782	6	68	growth	growth	NOUN
ejpam-782	6	69	of	of	ADP
ejpam-782	6	70	entire	entire	ADJ
ejpam-782	6	71	analytic	analytic	ADJ
ejpam-782	6	72	function	function	NOUN
ejpam-782	6	73	solutions	solution	NOUN
ejpam-782	6	74	of	of	ADP
ejpam-782	6	75	helmholtz	helmholtz	NOUN
ejpam-782	6	76	equation	equation	NOUN
ejpam-782	6	77	in	in	ADP
ejpam-782	6	78	r2by	r2by	NOUN
ejpam-782	6	79	using	use	VERB
ejpam-782	6	80	function	function	NOUN
ejpam-782	6	81	theoretic	theoretic	NOUN
ejpam-782	6	82	methods	method	NOUN
ejpam-782	6	83	(	(	PUNCT
ejpam-782	6	84	see	see	VERB
ejpam-782	6	85	r.p.gilbert[2,3	r.p.gilbert[2,3	NOUN
ejpam-782	6	86	]	]	PUNCT
ejpam-782	6	87	and	and	CCONJ
ejpam-782	6	88	mccoy[8])and	mccoy[8])and	NOUN
ejpam-782	6	89	obtained	obtain	VERB
ejpam-782	6	90	some	some	DET
ejpam-782	6	91	bounds	bound	NOUN
ejpam-782	6	92	on	on	ADP
ejpam-782	6	93	growth	growth	NOUN
ejpam-782	6	94	parameters	parameter	NOUN
ejpam-782	6	95	in	in	ADP
ejpam-782	6	96	terms	term	NOUN
ejpam-782	6	97	of	of	ADP
ejpam-782	6	98	taylor‘s	taylor‘s	NOUN
ejpam-782	6	99	coefficients	coefficient	NOUN
ejpam-782	6	100	and	and	CCONJ
ejpam-782	6	101	chebyshev	chebyshev	NOUN
ejpam-782	6	102	polynomials	polynomial	NOUN
ejpam-782	6	103	approximation	approximation	NOUN
ejpam-782	6	104	errors	error	NOUN
ejpam-782	6	105	.	.	PUNCT
ejpam-782	7	1	the	the	DET
ejpam-782	7	2	helmholtz	helmholtz	NOUN
ejpam-782	7	3	equation	equation	NOUN
ejpam-782	7	4	be	be	AUX
ejpam-782	7	5	given	give	VERB
ejpam-782	7	6	in	in	ADP
ejpam-782	7	7	the	the	DET
ejpam-782	7	8	form	form	NOUN
ejpam-782	8	1	[	[	X
ejpam-782	8	2	∂r	∂r	VERB
ejpam-782	8	3	r	r	NOUN
ejpam-782	8	4	+	+	NOUN
ejpam-782	8	5	1	1	NUM
ejpam-782	8	6	r	r	NOUN
ejpam-782	9	1	∂r	∂r	NOUN
ejpam-782	9	2	+	+	CCONJ
ejpam-782	9	3	1	1	NUM
ejpam-782	9	4	r2	r2	NOUN
ejpam-782	9	5	∂θθ	∂θθ	NOUN
ejpam-782	9	6	+	+	CCONJ
ejpam-782	9	7	f(r2)]φ(r	f(r2)]φ(r	PROPN
ejpam-782	9	8	,	,	PUNCT
ejpam-782	9	9	θ	θ	NOUN
ejpam-782	9	10	)	)	PUNCT
ejpam-782	9	11	=	=	SYM
ejpam-782	9	12	0	0	PUNCT
ejpam-782	9	13	(	(	PUNCT
ejpam-782	9	14	1	1	X
ejpam-782	9	15	)	)	PUNCT
ejpam-782	9	16	email	email	NOUN
ejpam-782	9	17	address	address	NOUN
ejpam-782	9	18	:	:	PUNCT
ejpam-782	9	19	d_kumar001	d_kumar001	PROPN
ejpam-782	9	20	�	�	PROPN
ejpam-782	9	21	rediffmail	rediffmail	NOUN
ejpam-782	9	22	.	.	PUNCT
ejpam-782	10	1	om	om	PROPN
ejpam-782	10	2	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-782	10	3	1062	1062	NUM
ejpam-782	11	1	c	c	X
ejpam-782	11	2	©	©	PROPN
ejpam-782	11	3	2010	2010	NUM
ejpam-782	11	4	ejpam	ejpam	NOUN
ejpam-782	11	5	all	all	DET
ejpam-782	11	6	rights	right	NOUN
ejpam-782	11	7	reserved	reserve	VERB
ejpam-782	11	8	.	.	PUNCT
ejpam-782	12	1	d.	d.	PROPN
ejpam-782	12	2	kumar	kumar	PROPN
ejpam-782	12	3	/	/	SYM
ejpam-782	12	4	eur	eur	PROPN
ejpam-782	12	5	.	.	PUNCT
ejpam-782	13	1	j.	j.	PROPN
ejpam-782	13	2	pure	pure	PROPN
ejpam-782	13	3	appl	appl	PROPN
ejpam-782	13	4	.	.	PROPN
ejpam-782	13	5	math	math	PROPN
ejpam-782	13	6	,	,	PUNCT
ejpam-782	13	7	3	3	NUM
ejpam-782	13	8	(	(	PUNCT
ejpam-782	13	9	2010	2010	NUM
ejpam-782	13	10	)	)	PUNCT
ejpam-782	13	11	,	,	PUNCT
ejpam-782	13	12	1062	1062	NUM
ejpam-782	13	13	-	-	SYM
ejpam-782	13	14	1069	1069	NUM
ejpam-782	13	15	1063	1063	NUM
ejpam-782	13	16	where	where	SCONJ
ejpam-782	13	17	(	(	PUNCT
ejpam-782	13	18	r	r	NOUN
ejpam-782	13	19	,	,	PUNCT
ejpam-782	13	20	θ	θ	NOUN
ejpam-782	13	21	)	)	PUNCT
ejpam-782	13	22	are	be	AUX
ejpam-782	13	23	polar	polar	ADJ
ejpam-782	13	24	coordinates	coordinate	NOUN
ejpam-782	13	25	in	in	ADP
ejpam-782	13	26	r2	r2	PROPN
ejpam-782	13	27	and	and	CCONJ
ejpam-782	13	28	f(r2	f(r2	NOUN
ejpam-782	13	29	)	)	PUNCT
ejpam-782	13	30	6=	6=	ADP
ejpam-782	13	31	0	0	NUM
ejpam-782	13	32	is	be	AUX
ejpam-782	13	33	a	a	DET
ejpam-782	13	34	real	real	ADV
ejpam-782	13	35	valued	value	VERB
ejpam-782	13	36	entire	entire	ADJ
ejpam-782	13	37	functions	function	NOUN
ejpam-782	13	38	with	with	ADP
ejpam-782	13	39	analytic	analytic	ADJ
ejpam-782	13	40	continuation	continuation	NOUN
ejpam-782	13	41	as	as	ADP
ejpam-782	13	42	an	an	DET
ejpam-782	13	43	entire	entire	ADJ
ejpam-782	13	44	function	function	NOUN
ejpam-782	13	45	of	of	ADP
ejpam-782	13	46	z	z	PROPN
ejpam-782	13	47	∈	∈	PROPN
ejpam-782	13	48	c	c	NOUN
ejpam-782	13	49	.	.	PUNCT
ejpam-782	14	1	each	each	DET
ejpam-782	14	2	solution	solution	NOUN
ejpam-782	14	3	of	of	ADP
ejpam-782	14	4	(	(	PUNCT
ejpam-782	14	5	1	1	X
ejpam-782	14	6	)	)	PUNCT
ejpam-782	14	7	regular	regular	ADJ
ejpam-782	14	8	at	at	ADP
ejpam-782	14	9	the	the	DET
ejpam-782	14	10	origin	origin	NOUN
ejpam-782	14	11	has	have	VERB
ejpam-782	14	12	a	a	DET
ejpam-782	14	13	local	local	ADJ
ejpam-782	14	14	representation	representation	NOUN
ejpam-782	14	15	via	via	ADP
ejpam-782	14	16	the	the	DET
ejpam-782	14	17	bergman	bergman	PROPN
ejpam-782	14	18	operator[1,7	operator[1,7	PROPN
ejpam-782	14	19	]	]	PUNCT
ejpam-782	14	20	of	of	ADP
ejpam-782	14	21	the	the	DET
ejpam-782	14	22	first	first	ADJ
ejpam-782	14	23	kind	kind	NOUN
ejpam-782	14	24	φ(r	φ(r	ADJ
ejpam-782	14	25	,	,	PUNCT
ejpam-782	14	26	θ	θ	NOUN
ejpam-782	14	27	)	)	PUNCT
ejpam-782	15	1	=	=	SYM
ejpam-782	15	2	b	b	X
ejpam-782	15	3	(	(	PUNCT
ejpam-782	15	4	f	f	PROPN
ejpam-782	15	5	(	(	PUNCT
ejpam-782	15	6	z	z	NOUN
ejpam-782	15	7	)	)	PUNCT
ejpam-782	15	8	)	)	PUNCT
ejpam-782	16	1	=	=	SYM
ejpam-782	16	2	∫	∫	PROPN
ejpam-782	17	1	+1	+1	INTJ
ejpam-782	17	2	−1	−1	NOUN
ejpam-782	17	3	e(r2	e(r2	PROPN
ejpam-782	17	4	,	,	PUNCT
ejpam-782	17	5	t	t	PROPN
ejpam-782	17	6	)	)	PUNCT
ejpam-782	17	7	f	f	PROPN
ejpam-782	17	8	(	(	PUNCT
ejpam-782	17	9	z(1−	z(1−	PROPN
ejpam-782	17	10	t2/2)(1−	t2/2)(1−	PROPN
ejpam-782	17	11	t2)−1/2d	t2)−1/2d	ADP
ejpam-782	17	12	t	t	PROPN
ejpam-782	17	13	,	,	PUNCT
ejpam-782	17	14	(	(	PUNCT
ejpam-782	17	15	2	2	X
ejpam-782	17	16	)	)	PUNCT
ejpam-782	18	1	where	where	SCONJ
ejpam-782	18	2	e(r2	e(r2	PROPN
ejpam-782	18	3	,	,	PUNCT
ejpam-782	18	4	t	t	PROPN
ejpam-782	18	5	)	)	PUNCT
ejpam-782	18	6	=	=	PUNCT
ejpam-782	19	1	1	1	NUM
ejpam-782	19	2	+	+	NUM
ejpam-782	19	3	∞	∞	NUM
ejpam-782	19	4	∑	∑	PUNCT
ejpam-782	19	5	n=1	n=1	PROPN
ejpam-782	19	6	t2nq(2n)(r2	t2nq(2n)(r2	NOUN
ejpam-782	19	7	)	)	PUNCT
ejpam-782	19	8	is	be	AUX
ejpam-782	19	9	a	a	DET
ejpam-782	19	10	real	real	ADV
ejpam-782	19	11	valued	value	VERB
ejpam-782	19	12	analytic	analytic	ADJ
ejpam-782	19	13	function	function	NOUN
ejpam-782	19	14	for	for	ADP
ejpam-782	19	15	t	t	PROPN
ejpam-782	19	16	∈	∈	PROPN
ejpam-782	20	1	[	[	X
ejpam-782	20	2	−1,+1	−1,+1	X
ejpam-782	20	3	]	]	X
ejpam-782	20	4	that	that	PRON
ejpam-782	20	5	is	be	AUX
ejpam-782	20	6	entire	entire	ADJ
ejpam-782	20	7	for	for	ADP
ejpam-782	20	8	r	r	NOUN
ejpam-782	20	9	∈	∈	PROPN
ejpam-782	21	1	[	[	X
ejpam-782	21	2	0,∞	0,∞	NOUN
ejpam-782	21	3	)	)	PUNCT
ejpam-782	21	4	and	and	CCONJ
ejpam-782	21	5	is	be	AUX
ejpam-782	21	6	known	know	VERB
ejpam-782	21	7	as	as	ADP
ejpam-782	21	8	bergman	bergman	PROPN
ejpam-782	21	9	e	e	PROPN
ejpam-782	21	10	f	f	PROPN
ejpam-782	21	11	unction	unction	NOUN
ejpam-782	21	12	.	.	PUNCT
ejpam-782	22	1	in	in	ADP
ejpam-782	22	2	a	a	DET
ejpam-782	22	3	neighborhood	neighborhood	NOUN
ejpam-782	22	4	of	of	ADP
ejpam-782	22	5	the	the	DET
ejpam-782	22	6	origin	origin	NOUN
ejpam-782	22	7	the	the	DET
ejpam-782	22	8	solution	solution	NOUN
ejpam-782	22	9	of	of	ADP
ejpam-782	22	10	(	(	PUNCT
ejpam-782	22	11	1	1	X
ejpam-782	22	12	)	)	PUNCT
ejpam-782	22	13	has	have	VERB
ejpam-782	22	14	an	an	DET
ejpam-782	22	15	expansion	expansion	NOUN
ejpam-782	22	16	φ(r	φ(r	ADP
ejpam-782	22	17	,	,	PUNCT
ejpam-782	22	18	θ	θ	NOUN
ejpam-782	22	19	)	)	PUNCT
ejpam-782	22	20	=	=	SYM
ejpam-782	22	21	σ∞n=0anφn(r	σ∞n=0anφn(r	NOUN
ejpam-782	22	22	,	,	PUNCT
ejpam-782	22	23	θ	θ	NOUN
ejpam-782	22	24	)	)	PUNCT
ejpam-782	22	25	(	(	PUNCT
ejpam-782	22	26	3	3	X
ejpam-782	22	27	)	)	PUNCT
ejpam-782	22	28	where	where	SCONJ
ejpam-782	22	29	φn(r	φn(r	NOUN
ejpam-782	22	30	,	,	PUNCT
ejpam-782	22	31	θ	θ	NOUN
ejpam-782	22	32	)	)	PUNCT
ejpam-782	22	33	=	=	SYM
ejpam-782	22	34	(	(	PUNCT
ejpam-782	22	35	reiθ	reiθ	NOUN
ejpam-782	22	36	2	2	NUM
ejpam-782	22	37	)	)	PUNCT
ejpam-782	22	38	ngn(r	ngn(r	NOUN
ejpam-782	22	39	)	)	PUNCT
ejpam-782	22	40	and	and	CCONJ
ejpam-782	22	41	gn(r	gn(r	NOUN
ejpam-782	22	42	)	)	PUNCT
ejpam-782	23	1	=	=	SYM
ejpam-782	23	2	∫	∫	PROPN
ejpam-782	24	1	+1	+1	PROPN
ejpam-782	24	2	−1	−1	NOUN
ejpam-782	24	3	e(r2	e(r2	NOUN
ejpam-782	24	4	,	,	PUNCT
ejpam-782	24	5	t)(1−	t)(1−	PROPN
ejpam-782	24	6	t2)(n−1/2)d	t2)(n−1/2)d	PROPN
ejpam-782	24	7	t	t	PROPN
ejpam-782	24	8	,	,	PUNCT
ejpam-782	24	9	n	n	NOUN
ejpam-782	24	10	=	=	NUM
ejpam-782	24	11	0,1,2,3	0,1,2,3	NUM
ejpam-782	24	12	,	,	PUNCT
ejpam-782	24	13	.	.	PUNCT
ejpam-782	24	14	.	.	PUNCT
ejpam-782	24	15	.	.	PUNCT
ejpam-782	24	16	.	.	PUNCT
ejpam-782	25	1	the	the	DET
ejpam-782	25	2	b	b	PROPN
ejpam-782	25	3	associate	associate	NOUN
ejpam-782	25	4	of	of	ADP
ejpam-782	25	5	φ	φ	PROPN
ejpam-782	25	6	is	be	AUX
ejpam-782	25	7	given	give	VERB
ejpam-782	25	8	as	as	ADP
ejpam-782	25	9	f	f	PROPN
ejpam-782	25	10	(	(	PUNCT
ejpam-782	25	11	z	z	NOUN
ejpam-782	25	12	)	)	PUNCT
ejpam-782	25	13	=	=	SYM
ejpam-782	25	14	σ∞n=0anzn	σ∞n=0anzn	NOUN
ejpam-782	25	15	.	.	PUNCT
ejpam-782	26	1	(	(	PUNCT
ejpam-782	26	2	4	4	X
ejpam-782	26	3	)	)	PUNCT
ejpam-782	26	4	it	it	PRON
ejpam-782	26	5	is	be	AUX
ejpam-782	26	6	known	know	VERB
ejpam-782	26	7	from	from	ADP
ejpam-782	26	8	gilbert	gilbert	PROPN
ejpam-782	26	9	and	and	CCONJ
ejpam-782	26	10	colton	colton	PROPN
ejpam-782	27	1	[	[	X
ejpam-782	27	2	4	4	X
ejpam-782	27	3	]	]	PUNCT
ejpam-782	27	4	that	that	SCONJ
ejpam-782	27	5	φ(r	φ(r	ADJ
ejpam-782	27	6	,	,	PUNCT
ejpam-782	27	7	θ	θ	NOUN
ejpam-782	27	8	)	)	PUNCT
ejpam-782	27	9	is	be	AUX
ejpam-782	27	10	an	an	DET
ejpam-782	27	11	entire	entire	ADJ
ejpam-782	27	12	function	function	NOUN
ejpam-782	27	13	if	if	SCONJ
ejpam-782	27	14	and	and	CCONJ
ejpam-782	27	15	only	only	ADV
ejpam-782	27	16	if	if	SCONJ
ejpam-782	27	17	,	,	PUNCT
ejpam-782	27	18	the	the	DET
ejpam-782	27	19	associate	associate	NOUN
ejpam-782	27	20	f	f	PROPN
ejpam-782	27	21	(	(	PUNCT
ejpam-782	27	22	z	z	NOUN
ejpam-782	27	23	)	)	PUNCT
ejpam-782	27	24	is	be	AUX
ejpam-782	27	25	an	an	DET
ejpam-782	27	26	entire	entire	ADJ
ejpam-782	27	27	function	function	NOUN
ejpam-782	27	28	i.e.	i.e.	ADV
ejpam-782	27	29	,	,	PUNCT
ejpam-782	27	30	lim	lim	PROPN
ejpam-782	27	31	sup	sup	NOUN
ejpam-782	27	32	n→∞	n→∞	X
ejpam-782	27	33	|an|	|an|	NOUN
ejpam-782	27	34	1	1	NUM
ejpam-782	27	35	/	/	SYM
ejpam-782	27	36	n	n	NOUN
ejpam-782	27	37	=	=	SYM
ejpam-782	27	38	0	0	NUM
ejpam-782	27	39	.	.	PUNCT
ejpam-782	28	1	(	(	PUNCT
ejpam-782	28	2	5	5	X
ejpam-782	28	3	)	)	PUNCT
ejpam-782	28	4	the	the	DET
ejpam-782	28	5	sets	set	NOUN
ejpam-782	28	6	of	of	ADP
ejpam-782	28	7	polynomial	polynomial	ADJ
ejpam-782	28	8	solutions	solution	NOUN
ejpam-782	28	9	of	of	ADP
ejpam-782	28	10	helmholtz	helmholtz	NOUN
ejpam-782	28	11	equation	equation	NOUN
ejpam-782	28	12	are	be	AUX
ejpam-782	28	13	defined	define	VERB
ejpam-782	28	14	as	as	ADP
ejpam-782	28	15	πn	πn	INTJ
ejpam-782	28	16	=	=	PUNCT
ejpam-782	28	17	{	{	PUNCT
ejpam-782	28	18	p	p	X
ejpam-782	28	19	:	:	PUNCT
ejpam-782	28	20	p(r	p(r	PROPN
ejpam-782	28	21	,	,	PUNCT
ejpam-782	28	22	θ	θ	NOUN
ejpam-782	28	23	)	)	PUNCT
ejpam-782	28	24	=	=	NOUN
ejpam-782	28	25	σn	σn	NOUN
ejpam-782	28	26	κ=0aκφκ(r	κ=0aκφκ(r	NOUN
ejpam-782	28	27	,	,	PUNCT
ejpam-782	28	28	θ	θ	NOUN
ejpam-782	28	29	)	)	PUNCT
ejpam-782	28	30	,	,	PUNCT
ejpam-782	28	31	aκreal	aκreal	NOUN
ejpam-782	28	32	}	}	PUNCT
ejpam-782	28	33	the	the	DET
ejpam-782	28	34	best	good	ADJ
ejpam-782	28	35	chebyshev	chebyshev	NOUN
ejpam-782	28	36	approximation	approximation	NOUN
ejpam-782	28	37	error	error	NOUN
ejpam-782	28	38	in	in	ADP
ejpam-782	28	39	bernstein	bernstein	PROPN
ejpam-782	28	40	’s	’s	PART
ejpam-782	28	41	sense	sense	NOUN
ejpam-782	28	42	be	be	AUX
ejpam-782	28	43	given	give	VERB
ejpam-782	28	44	as	as	ADP
ejpam-782	28	45	en(φ	en(φ	NOUN
ejpam-782	28	46	)	)	PUNCT
ejpam-782	29	1	=	=	SYM
ejpam-782	29	2	inf‖	inf‖	PROPN
ejpam-782	29	3	φ	φ	NOUN
ejpam-782	29	4	−	−	PROPN
ejpam-782	30	1	p	p	PROPN
ejpam-782	30	2	‖ro	‖ro	PROPN
ejpam-782	30	3	:	:	PUNCT
ejpam-782	30	4	p	p	X
ejpam-782	30	5	∈	∈	PROPN
ejpam-782	30	6	πn	πn	INTJ
ejpam-782	30	7	,	,	PUNCT
ejpam-782	30	8	(	(	PUNCT
ejpam-782	30	9	6	6	NUM
ejpam-782	30	10	)	)	PUNCT
ejpam-782	30	11	‖	‖	PROPN
ejpam-782	31	1	φ	φ	PROPN
ejpam-782	31	2	−	−	PROPN
ejpam-782	31	3	p	p	PROPN
ejpam-782	31	4	‖r0	‖r0	PROPN
ejpam-782	31	5	=	=	PUNCT
ejpam-782	31	6	m(r0,φ	m(r0,φ	PROPN
ejpam-782	31	7	−	−	PROPN
ejpam-782	31	8	p	p	X
ejpam-782	31	9	)	)	PUNCT
ejpam-782	31	10	,	,	PUNCT
ejpam-782	31	11	p	p	PROPN
ejpam-782	31	12	∈	∈	PROPN
ejpam-782	31	13	πn	πn	INTJ
ejpam-782	31	14	where	where	SCONJ
ejpam-782	31	15	r0	r0	NOUN
ejpam-782	31	16	=	=	SYM
ejpam-782	31	17	r0(k	r0(k	VERB
ejpam-782	31	18	)	)	PUNCT
ejpam-782	32	1	=	=	NOUN
ejpam-782	32	2	min{1	min{1	NOUN
ejpam-782	32	3	,	,	PUNCT
ejpam-782	32	4	sup{r	sup{r	PRON
ejpam-782	32	5	:	:	PUNCT
ejpam-782	32	6	e(r2	e(r2	PROPN
ejpam-782	32	7	,	,	PUNCT
ejpam-782	32	8	t	t	PROPN
ejpam-782	32	9	)	)	PUNCT
ejpam-782	32	10	>	>	X
ejpam-782	32	11	0	0	NUM
ejpam-782	32	12	,	,	PUNCT
ejpam-782	32	13	t	t	PROPN
ejpam-782	32	14	∈	∈	PROPN
ejpam-782	33	1	[	[	X
ejpam-782	33	2	−1,+1	−1,+1	NOUN
ejpam-782	33	3	]	]	X
ejpam-782	33	4	}	}	PUNCT
ejpam-782	33	5	}	}	PUNCT
ejpam-782	33	6	>	>	X
ejpam-782	33	7	0	0	PROPN
ejpam-782	33	8	,	,	PUNCT
ejpam-782	33	9	d.	d.	PROPN
ejpam-782	33	10	kumar	kumar	PROPN
ejpam-782	33	11	/	/	SYM
ejpam-782	33	12	eur	eur	PROPN
ejpam-782	33	13	.	.	PUNCT
ejpam-782	34	1	j.	j.	PROPN
ejpam-782	34	2	pure	pure	PROPN
ejpam-782	34	3	appl	appl	PROPN
ejpam-782	34	4	.	.	PROPN
ejpam-782	34	5	math	math	PROPN
ejpam-782	34	6	,	,	PUNCT
ejpam-782	34	7	3	3	NUM
ejpam-782	34	8	(	(	PUNCT
ejpam-782	34	9	2010	2010	NUM
ejpam-782	34	10	)	)	PUNCT
ejpam-782	34	11	,	,	PUNCT
ejpam-782	34	12	1062	1062	NUM
ejpam-782	34	13	-	-	SYM
ejpam-782	34	14	1069	1069	NUM
ejpam-782	34	15	1064	1064	NUM
ejpam-782	34	16	and	and	CCONJ
ejpam-782	34	17	the	the	DET
ejpam-782	34	18	maximum	maximum	ADJ
ejpam-782	34	19	modulus	modulus	NOUN
ejpam-782	34	20	m(r0,φ	m(r0,φ	NOUN
ejpam-782	34	21	−	−	PROPN
ejpam-782	34	22	p	p	NOUN
ejpam-782	34	23	)	)	PUNCT
ejpam-782	35	1	=	=	PRON
ejpam-782	35	2	max{|(φ	max{|(φ	NOUN
ejpam-782	35	3	−	−	PROPN
ejpam-782	35	4	p)(z)|	p)(z)|	PROPN
ejpam-782	35	5	:	:	PUNCT
ejpam-782	35	6	|z|	|z|	VERB
ejpam-782	35	7	<	<	X
ejpam-782	35	8	r0	r0	NOUN
ejpam-782	35	9	}	}	PUNCT
ejpam-782	35	10	.	.	PUNCT
ejpam-782	36	1	mccoy[9	mccoy[9	NOUN
ejpam-782	36	2	]	]	PUNCT
ejpam-782	36	3	studied	study	VERB
ejpam-782	36	4	the	the	DET
ejpam-782	36	5	fast	fast	ADJ
ejpam-782	36	6	growth	growth	NOUN
ejpam-782	36	7	of	of	ADP
ejpam-782	36	8	entire	entire	ADJ
ejpam-782	36	9	function	function	NOUN
ejpam-782	36	10	solution	solution	NOUN
ejpam-782	36	11	φ(r	φ(r	NOUN
ejpam-782	36	12	,	,	PUNCT
ejpam-782	36	13	θ	θ	NOUN
ejpam-782	36	14	)	)	PUNCT
ejpam-782	36	15	in	in	ADP
ejpam-782	36	16	terms	term	NOUN
ejpam-782	36	17	of	of	ADP
ejpam-782	36	18	order	order	NOUN
ejpam-782	36	19	δ	δ	NOUN
ejpam-782	36	20	and	and	CCONJ
ejpam-782	36	21	type	type	NOUN
ejpam-782	36	22	τ	τ	PROPN
ejpam-782	36	23	using	use	VERB
ejpam-782	36	24	the	the	DET
ejpam-782	36	25	concept	concept	NOUN
ejpam-782	36	26	of	of	ADP
ejpam-782	36	27	index	index	NOUN
ejpam-782	36	28	k	k	PROPN
ejpam-782	36	29	i.e.	i.e.	X
ejpam-782	36	30	,	,	PUNCT
ejpam-782	36	31	δ(k−	δ(k−	NOUN
ejpam-782	36	32	1	1	NUM
ejpam-782	36	33	)	)	PUNCT
ejpam-782	36	34	=	=	NOUN
ejpam-782	36	35	∞	∞	NUM
ejpam-782	36	36	and	and	CCONJ
ejpam-782	36	37	δ(k	δ(k	NOUN
ejpam-782	36	38	)	)	PUNCT
ejpam-782	36	39	<	<	X
ejpam-782	36	40	∞.	∞.	PROPN
ejpam-782	36	41	due	due	ADP
ejpam-782	36	42	to	to	ADP
ejpam-782	36	43	lack	lack	NOUN
ejpam-782	36	44	of	of	ADP
ejpam-782	36	45	suitable	suitable	ADJ
ejpam-782	36	46	inverse	inverse	NOUN
ejpam-782	36	47	operator	operator	NOUN
ejpam-782	36	48	he	he	PRON
ejpam-782	36	49	obtained	obtain	VERB
ejpam-782	36	50	bounds	bound	NOUN
ejpam-782	36	51	on	on	ADP
ejpam-782	36	52	the	the	DET
ejpam-782	36	53	order	order	NOUN
ejpam-782	36	54	and	and	CCONJ
ejpam-782	36	55	type.it	type.it	PRON
ejpam-782	36	56	has	have	AUX
ejpam-782	36	57	been	be	AUX
ejpam-782	36	58	noticed	notice	VERB
ejpam-782	36	59	that	that	SCONJ
ejpam-782	36	60	his	his	PRON
ejpam-782	36	61	results	result	NOUN
ejpam-782	36	62	do	do	AUX
ejpam-782	36	63	not	not	PART
ejpam-782	36	64	give	give	VERB
ejpam-782	36	65	any	any	DET
ejpam-782	36	66	precise	precise	ADJ
ejpam-782	36	67	information	information	NOUN
ejpam-782	36	68	about	about	ADP
ejpam-782	36	69	the	the	DET
ejpam-782	36	70	growth	growth	NOUN
ejpam-782	36	71	of	of	ADP
ejpam-782	36	72	those	those	DET
ejpam-782	36	73	functions	function	NOUN
ejpam-782	36	74	for	for	ADP
ejpam-782	36	75	which	which	PRON
ejpam-782	36	76	δ(k−	δ(k−	NOUN
ejpam-782	36	77	1	1	NUM
ejpam-782	36	78	)	)	PUNCT
ejpam-782	36	79	=	=	NOUN
ejpam-782	36	80	∞	∞	NUM
ejpam-782	36	81	and	and	CCONJ
ejpam-782	36	82	δ(k	δ(k	NOUN
ejpam-782	36	83	)	)	PUNCT
ejpam-782	36	84	=	=	PUNCT
ejpam-782	36	85	0.to	0.to	NOUN
ejpam-782	36	86	overcome	overcome	VERB
ejpam-782	36	87	this	this	DET
ejpam-782	36	88	problem	problem	NOUN
ejpam-782	36	89	,	,	PUNCT
ejpam-782	36	90	in	in	ADP
ejpam-782	36	91	this	this	DET
ejpam-782	36	92	paper	paper	NOUN
ejpam-782	36	93	we	we	PRON
ejpam-782	36	94	pick	pick	VERB
ejpam-782	36	95	up	up	ADP
ejpam-782	36	96	a	a	DET
ejpam-782	36	97	concept	concept	NOUN
ejpam-782	36	98	of	of	ADP
ejpam-782	36	99	(	(	PUNCT
ejpam-782	36	100	p	p	NOUN
ejpam-782	36	101	,	,	PUNCT
ejpam-782	36	102	q)-order	q)-order	PUNCT
ejpam-782	36	103	and	and	CCONJ
ejpam-782	36	104	(	(	PUNCT
ejpam-782	36	105	p	p	X
ejpam-782	36	106	,	,	PUNCT
ejpam-782	36	107	q)-type	q)-type	PUNCT
ejpam-782	36	108	introduced	introduce	VERB
ejpam-782	36	109	by	by	ADP
ejpam-782	36	110	juneja	juneja	PROPN
ejpam-782	36	111	et	et	PROPN
ejpam-782	36	112	al.[5,6	al.[5,6	NOUN
ejpam-782	36	113	]	]	X
ejpam-782	36	114	.	.	PUNCT
ejpam-782	37	1	roughly	roughly	ADV
ejpam-782	37	2	speeking	speeking	ADJ
ejpam-782	37	3	,	,	PUNCT
ejpam-782	37	4	this	this	DET
ejpam-782	37	5	concept	concept	NOUN
ejpam-782	37	6	is	be	AUX
ejpam-782	37	7	a	a	DET
ejpam-782	37	8	modification	modification	NOUN
ejpam-782	37	9	of	of	ADP
ejpam-782	37	10	the	the	DET
ejpam-782	37	11	classical	classical	ADJ
ejpam-782	37	12	definition	definition	NOUN
ejpam-782	37	13	of	of	ADP
ejpam-782	37	14	order	order	NOUN
ejpam-782	37	15	and	and	CCONJ
ejpam-782	37	16	type	type	NOUN
ejpam-782	37	17	,	,	PUNCT
ejpam-782	37	18	obtained	obtain	VERB
ejpam-782	37	19	by	by	ADP
ejpam-782	37	20	replacing	replace	VERB
ejpam-782	37	21	logarithms	logarithm	NOUN
ejpam-782	37	22	by	by	ADP
ejpam-782	37	23	iterated	iterated	ADJ
ejpam-782	37	24	logarithms	logarithm	NOUN
ejpam-782	37	25	,	,	PUNCT
ejpam-782	37	26	where	where	SCONJ
ejpam-782	37	27	the	the	DET
ejpam-782	37	28	degrees	degree	NOUN
ejpam-782	37	29	of	of	ADP
ejpam-782	37	30	iteration	iteration	NOUN
ejpam-782	37	31	are	be	AUX
ejpam-782	37	32	determined	determine	VERB
ejpam-782	37	33	by	by	ADP
ejpam-782	37	34	p	p	PROPN
ejpam-782	37	35	and	and	CCONJ
ejpam-782	37	36	q	q	NOUN
ejpam-782	37	37	,	,	PUNCT
ejpam-782	37	38	p	p	NOUN
ejpam-782	37	39	≥	≥	NOUN
ejpam-782	37	40	q	q	NOUN
ejpam-782	37	41	≥	≥	PROPN
ejpam-782	37	42	0	0	NUM
ejpam-782	37	43	.	.	PUNCT
ejpam-782	38	1	our	our	PRON
ejpam-782	38	2	approach	approach	NOUN
ejpam-782	38	3	unifies	unify	VERB
ejpam-782	38	4	the	the	DET
ejpam-782	38	5	above	above	ADJ
ejpam-782	38	6	approach	approach	NOUN
ejpam-782	38	7	studied	study	VERB
ejpam-782	38	8	by	by	ADP
ejpam-782	38	9	those	those	PRON
ejpam-782	38	10	of	of	ADP
ejpam-782	38	11	mccoy[9	mccoy[9	NOUN
ejpam-782	38	12	]	]	PUNCT
ejpam-782	38	13	and	and	CCONJ
ejpam-782	38	14	at	at	ADP
ejpam-782	38	15	the	the	DET
ejpam-782	38	16	same	same	ADJ
ejpam-782	38	17	time	time	NOUN
ejpam-782	38	18	it	it	PRON
ejpam-782	38	19	is	be	AUX
ejpam-782	38	20	applicable	applicable	ADJ
ejpam-782	38	21	to	to	ADP
ejpam-782	38	22	every	every	DET
ejpam-782	38	23	entire	entire	ADJ
ejpam-782	38	24	function	function	NOUN
ejpam-782	38	25	,	,	PUNCT
ejpam-782	38	26	whether	whether	SCONJ
ejpam-782	38	27	of	of	ADP
ejpam-782	38	28	slow	slow	ADJ
ejpam-782	38	29	or	or	CCONJ
ejpam-782	38	30	fast	fast	ADJ
ejpam-782	38	31	growth	growth	NOUN
ejpam-782	38	32	.	.	PUNCT
ejpam-782	39	1	moreover	moreover	ADV
ejpam-782	39	2	,	,	PUNCT
ejpam-782	39	3	we	we	PRON
ejpam-782	39	4	make	make	VERB
ejpam-782	39	5	an	an	DET
ejpam-782	39	6	attempt	attempt	NOUN
ejpam-782	39	7	to	to	PART
ejpam-782	39	8	characterize	characterize	VERB
ejpam-782	39	9	(	(	PUNCT
ejpam-782	39	10	p	p	X
ejpam-782	39	11	,	,	PUNCT
ejpam-782	39	12	q	q	NOUN
ejpam-782	39	13	)	)	PUNCT
ejpam-782	39	14	growth	growth	NOUN
ejpam-782	39	15	of	of	ADP
ejpam-782	39	16	φ(r	φ(r	ADJ
ejpam-782	39	17	,	,	PUNCT
ejpam-782	39	18	θ	θ	NOUN
ejpam-782	39	19	)	)	PUNCT
ejpam-782	39	20	and	and	CCONJ
ejpam-782	39	21	obtained	obtain	VERB
ejpam-782	39	22	some	some	DET
ejpam-782	39	23	bounds	bound	NOUN
ejpam-782	39	24	on	on	ADP
ejpam-782	39	25	(	(	PUNCT
ejpam-782	39	26	p	p	X
ejpam-782	39	27	,	,	PUNCT
ejpam-782	39	28	q	q	NOUN
ejpam-782	39	29	)	)	PUNCT
ejpam-782	39	30	order	order	NOUN
ejpam-782	39	31	and	and	CCONJ
ejpam-782	39	32	(	(	PUNCT
ejpam-782	39	33	p	p	X
ejpam-782	39	34	,	,	PUNCT
ejpam-782	39	35	q	q	NOUN
ejpam-782	39	36	)	)	PUNCT
ejpam-782	39	37	type	type	NOUN
ejpam-782	39	38	in	in	ADP
ejpam-782	39	39	terms	term	NOUN
ejpam-782	39	40	of	of	ADP
ejpam-782	39	41	chebyshev	chebyshev	NOUN
ejpam-782	39	42	polynomial	polynomial	ADJ
ejpam-782	39	43	approximation	approximation	NOUN
ejpam-782	39	44	errors	error	NOUN
ejpam-782	39	45	defined	define	VERB
ejpam-782	39	46	by	by	ADP
ejpam-782	39	47	(	(	PUNCT
ejpam-782	39	48	6	6	NUM
ejpam-782	39	49	)	)	PUNCT
ejpam-782	39	50	.	.	PUNCT
ejpam-782	40	1	2	2	X
ejpam-782	40	2	.	.	NUM
ejpam-782	40	3	notations	notation	NOUN
ejpam-782	40	4	1	1	NUM
ejpam-782	40	5	.	.	PUNCT
ejpam-782	40	6	log[m	log[m	NOUN
ejpam-782	40	7	]	]	PUNCT
ejpam-782	40	8	x	x	X
ejpam-782	41	1	=	=	PUNCT
ejpam-782	41	2	exp[−m	exp[−m	ADJ
ejpam-782	41	3	]	]	PUNCT
ejpam-782	41	4	x	x	SYM
ejpam-782	41	5	=	=	SYM
ejpam-782	41	6	log(log[m−1	log(log[m−1	PROPN
ejpam-782	41	7	]	]	X
ejpam-782	41	8	x	x	X
ejpam-782	41	9	)	)	PUNCT
ejpam-782	41	10	=	=	SYM
ejpam-782	41	11	exp(exp[−m−1	exp(exp[−m−1	PROPN
ejpam-782	41	12	]	]	X
ejpam-782	41	13	x	x	X
ejpam-782	41	14	)	)	PUNCT
ejpam-782	41	15	,	,	PUNCT
ejpam-782	41	16	m	m	VERB
ejpam-782	41	17	=	=	SYM
ejpam-782	41	18	0	0	NUM
ejpam-782	41	19	,	,	PUNCT
ejpam-782	41	20	±1,±2	±1,±2	NOUN
ejpam-782	41	21	,	,	PUNCT
ejpam-782	41	22	.	.	PUNCT
ejpam-782	41	23	.	.	PUNCT
ejpam-782	42	1	.	.	PUNCT
ejpam-782	43	1	provided	provide	VERB
ejpam-782	43	2	that	that	SCONJ
ejpam-782	43	3	0	0	NUM
ejpam-782	43	4	<	<	X
ejpam-782	43	5	log[m−1	log[m−1	X
ejpam-782	43	6	]	]	PUNCT
ejpam-782	43	7	x	x	X
ejpam-782	43	8	<	<	X
ejpam-782	43	9	∞	∞	NOUN
ejpam-782	43	10	with	with	ADP
ejpam-782	43	11	log[0	log[0	NOUN
ejpam-782	43	12	]	]	PUNCT
ejpam-782	43	13	x	x	SYM
ejpam-782	43	14	=	=	SYM
ejpam-782	43	15	exp[0	exp[0	X
ejpam-782	43	16	]	]	PUNCT
ejpam-782	43	17	x	x	X
ejpam-782	43	18	=	=	PUNCT
ejpam-782	43	19	x	x	PROPN
ejpam-782	43	20	.	.	PUNCT
ejpam-782	44	1	2	2	NUM
ejpam-782	44	2	.	.	X
ejpam-782	44	3	ω(l(p	ω(l(p	NUM
ejpam-782	44	4	,	,	PUNCT
ejpam-782	44	5	q	q	NOUN
ejpam-782	44	6	)	)	PUNCT
ejpam-782	44	7	)	)	PUNCT
ejpam-782	45	1	=	=	PUNCT
ejpam-782	45	2			PROPN
ejpam-782	45	3			VERB
ejpam-782	45	4			PROPN
ejpam-782	45	5			NOUN
ejpam-782	45	6			PROPN
ejpam-782	45	7			PROPN
ejpam-782	45	8			PROPN
ejpam-782	45	9	ω(l(p	ω(l(p	NUM
ejpam-782	45	10	,	,	PUNCT
ejpam-782	45	11	q	q	NOUN
ejpam-782	45	12	)	)	PUNCT
ejpam-782	45	13	)	)	PUNCT
ejpam-782	46	1	=	=	SYM
ejpam-782	46	2	l(p	l(p	PROPN
ejpam-782	46	3	,	,	PUNCT
ejpam-782	46	4	q	q	NOUN
ejpam-782	46	5	)	)	PUNCT
ejpam-782	46	6	,	,	PUNCT
ejpam-782	46	7	if	if	SCONJ
ejpam-782	46	8	p	p	X
ejpam-782	46	9	>	>	X
ejpam-782	46	10	2	2	NUM
ejpam-782	46	11	;	;	PUNCT
ejpam-782	46	12	1	1	NUM
ejpam-782	46	13	+	+	NUM
ejpam-782	46	14	l(p	l(p	NOUN
ejpam-782	46	15	,	,	PUNCT
ejpam-782	46	16	q	q	NOUN
ejpam-782	46	17	)	)	PUNCT
ejpam-782	46	18	,	,	PUNCT
ejpam-782	46	19	if	if	SCONJ
ejpam-782	46	20	p	p	NOUN
ejpam-782	46	21	=	=	X
ejpam-782	46	22	q	q	NOUN
ejpam-782	46	23	=	=	SYM
ejpam-782	46	24	2	2	NUM
ejpam-782	46	25	;	;	PUNCT
ejpam-782	46	26	max(1	max(1	NOUN
ejpam-782	46	27	,	,	PUNCT
ejpam-782	46	28	l(p	l(p	PROPN
ejpam-782	46	29	,	,	PUNCT
ejpam-782	46	30	q	q	NOUN
ejpam-782	46	31	)	)	PUNCT
ejpam-782	46	32	)	)	PUNCT
ejpam-782	46	33	,	,	PUNCT
ejpam-782	46	34	if	if	SCONJ
ejpam-782	46	35	3≤	3≤	NUM
ejpam-782	46	36	p	p	X
ejpam-782	46	37	=	=	X
ejpam-782	46	38	q	q	X
ejpam-782	46	39	<	<	X
ejpam-782	46	40	∞	∞	NOUN
ejpam-782	46	41	;	;	PUNCT
ejpam-782	46	42	∞	∞	PROPN
ejpam-782	46	43	,	,	PUNCT
ejpam-782	46	44	if	if	SCONJ
ejpam-782	46	45	p	p	NOUN
ejpam-782	46	46	=	=	X
ejpam-782	46	47	q	q	X
ejpam-782	46	48	=	=	PRON
ejpam-782	46	49	∞.	∞.	PROPN
ejpam-782	46	50	where	where	SCONJ
ejpam-782	46	51	0≤	0≤	ADP
ejpam-782	46	52	ω(p	ω(p	NUM
ejpam-782	46	53	,	,	PUNCT
ejpam-782	46	54	q)≤∞.	q)≤∞.	NOUN
ejpam-782	46	55	3	3	NUM
ejpam-782	46	56	.	.	PUNCT
ejpam-782	47	1	(	(	PUNCT
ejpam-782	47	2	p	p	NOUN
ejpam-782	47	3	,	,	PUNCT
ejpam-782	47	4	q)-growth	q)-growth	NOUN
ejpam-782	47	5	of	of	ADP
ejpam-782	47	6	solutions	solution	NOUN
ejpam-782	47	7	and	and	CCONJ
ejpam-782	47	8	chebyshev	chebyshev	NOUN
ejpam-782	47	9	polynomial	polynomial	ADJ
ejpam-782	47	10	approximation	approximation	NOUN
ejpam-782	47	11	in	in	ADP
ejpam-782	47	12	this	this	DET
ejpam-782	47	13	section	section	NOUN
ejpam-782	47	14	we	we	PRON
ejpam-782	47	15	shall	shall	AUX
ejpam-782	47	16	prove	prove	VERB
ejpam-782	47	17	our	our	PRON
ejpam-782	47	18	main	main	ADJ
ejpam-782	47	19	results	result	NOUN
ejpam-782	47	20	.	.	PUNCT
ejpam-782	48	1	theorem	theorem	NOUN
ejpam-782	48	2	1	1	NUM
ejpam-782	48	3	.	.	PUNCT
ejpam-782	49	1	let	let	VERB
ejpam-782	49	2	φ(r	φ(r	ADJ
ejpam-782	49	3	,	,	PUNCT
ejpam-782	49	4	θ	θ	NOUN
ejpam-782	49	5	)	)	PUNCT
ejpam-782	49	6	be	be	VERB
ejpam-782	49	7	an	an	DET
ejpam-782	49	8	entire	entire	ADJ
ejpam-782	49	9	function	function	NOUN
ejpam-782	49	10	solution	solution	NOUN
ejpam-782	49	11	of	of	ADP
ejpam-782	49	12	the	the	DET
ejpam-782	49	13	helmholtz	helmholtz	NOUN
ejpam-782	49	14	equation	equation	NOUN
ejpam-782	49	15	with	with	ADP
ejpam-782	49	16	expansion	expansion	NOUN
ejpam-782	49	17	φ(r	φ(r	ADP
ejpam-782	49	18	,	,	PUNCT
ejpam-782	49	19	θ	θ	NOUN
ejpam-782	49	20	)	)	PUNCT
ejpam-782	49	21	=	=	SYM
ejpam-782	49	22	∞	∞	PROPN
ejpam-782	49	23	∑	∑	PROPN
ejpam-782	49	24	n=0	n=0	PROPN
ejpam-782	49	25	anφn(r	anφn(r	PROPN
ejpam-782	49	26	,	,	PUNCT
ejpam-782	49	27	θ	θ	NOUN
ejpam-782	49	28	)	)	PUNCT
ejpam-782	49	29	.	.	PUNCT
ejpam-782	50	1	let	let	VERB
ejpam-782	50	2	φ	φ	PROPN
ejpam-782	50	3	and	and	CCONJ
ejpam-782	50	4	b	b	PROPN
ejpam-782	50	5	associate	associate	NOUN
ejpam-782	50	6	f	f	AUX
ejpam-782	50	7	be	be	AUX
ejpam-782	50	8	entire	entire	ADJ
ejpam-782	50	9	functions	function	NOUN
ejpam-782	50	10	of	of	ADP
ejpam-782	50	11	(	(	PUNCT
ejpam-782	50	12	p	p	NOUN
ejpam-782	50	13	,	,	PUNCT
ejpam-782	50	14	q)-order	q)-order	NOUN
ejpam-782	50	15	δ(p	δ(p	PROPN
ejpam-782	50	16	,	,	PUNCT
ejpam-782	50	17	q	q	NOUN
ejpam-782	50	18	,	,	PUNCT
ejpam-782	50	19	φ	φ	NUM
ejpam-782	50	20	)	)	PUNCT
ejpam-782	50	21	and	and	CCONJ
ejpam-782	50	22	δ(p	δ(p	PROPN
ejpam-782	50	23	,	,	PUNCT
ejpam-782	50	24	q	q	NOUN
ejpam-782	50	25	,	,	PUNCT
ejpam-782	50	26	f	f	PROPN
ejpam-782	50	27	)	)	PUNCT
ejpam-782	50	28	for	for	ADP
ejpam-782	50	29	a	a	DET
ejpam-782	50	30	pair	pair	NOUN
ejpam-782	50	31	of	of	ADP
ejpam-782	50	32	integers	integer	NOUN
ejpam-782	50	33	(	(	PUNCT
ejpam-782	50	34	p	p	X
ejpam-782	50	35	,	,	PUNCT
ejpam-782	50	36	q	q	NOUN
ejpam-782	50	37	)	)	PUNCT
ejpam-782	50	38	,	,	PUNCT
ejpam-782	50	39	p≥2	p≥2	NOUN
ejpam-782	50	40	,	,	PUNCT
ejpam-782	50	41	q	q	X
ejpam-782	50	42	≥	≥	NUM
ejpam-782	50	43	1	1	NUM
ejpam-782	50	44	.	.	PUNCT
ejpam-782	51	1	then	then	ADV
ejpam-782	51	2	the	the	DET
ejpam-782	51	3	following	follow	VERB
ejpam-782	51	4	bounds	bound	NOUN
ejpam-782	51	5	are	be	AUX
ejpam-782	51	6	valid	valid	ADJ
ejpam-782	51	7	(	(	PUNCT
ejpam-782	51	8	i	i	NOUN
ejpam-782	51	9	)	)	PUNCT
ejpam-782	51	10	δ(p	δ(p	PROPN
ejpam-782	51	11	,	,	PUNCT
ejpam-782	51	12	q	q	NOUN
ejpam-782	51	13	,	,	PUNCT
ejpam-782	51	14	φ	φ	NUM
ejpam-782	51	15	)	)	PUNCT
ejpam-782	51	16	≥	≥	NOUN
ejpam-782	51	17	δ(p	δ(p	PROPN
ejpam-782	51	18	,	,	PUNCT
ejpam-782	51	19	q	q	NOUN
ejpam-782	51	20	,	,	PUNCT
ejpam-782	51	21	f	f	PROPN
ejpam-782	51	22	)	)	PUNCT
ejpam-782	51	23	(	(	PUNCT
ejpam-782	51	24	ii	ii	NOUN
ejpam-782	51	25	)	)	PUNCT
ejpam-782	51	26	δ(p	δ(p	PROPN
ejpam-782	51	27	,	,	PUNCT
ejpam-782	51	28	q	q	NOUN
ejpam-782	51	29	,	,	PUNCT
ejpam-782	51	30	e	e	NOUN
ejpam-782	51	31	)	)	PUNCT
ejpam-782	51	32	≤	≤	PROPN
ejpam-782	51	33	δ(p	δ(p	PROPN
ejpam-782	51	34	,	,	PUNCT
ejpam-782	51	35	q	q	NOUN
ejpam-782	51	36	,	,	PUNCT
ejpam-782	51	37	f	f	PROPN
ejpam-782	51	38	)	)	PUNCT
ejpam-782	51	39	d.	d.	PROPN
ejpam-782	51	40	kumar	kumar	PROPN
ejpam-782	51	41	/	/	SYM
ejpam-782	51	42	eur	eur	PROPN
ejpam-782	51	43	.	.	PUNCT
ejpam-782	52	1	j.	j.	PROPN
ejpam-782	52	2	pure	pure	PROPN
ejpam-782	52	3	appl	appl	PROPN
ejpam-782	52	4	.	.	PROPN
ejpam-782	52	5	math	math	PROPN
ejpam-782	52	6	,	,	PUNCT
ejpam-782	52	7	3	3	NUM
ejpam-782	52	8	(	(	PUNCT
ejpam-782	52	9	2010	2010	NUM
ejpam-782	52	10	)	)	PUNCT
ejpam-782	52	11	,	,	PUNCT
ejpam-782	52	12	1062	1062	NUM
ejpam-782	52	13	-	-	SYM
ejpam-782	52	14	1069	1069	NUM
ejpam-782	52	15	1065	1065	NUM
ejpam-782	52	16	where	where	SCONJ
ejpam-782	52	17	δ(p	δ(p	PROPN
ejpam-782	52	18	,	,	PUNCT
ejpam-782	52	19	q	q	NOUN
ejpam-782	52	20	,	,	PUNCT
ejpam-782	52	21	φ	φ	NUM
ejpam-782	52	22	)	)	PUNCT
ejpam-782	52	23	=	=	SYM
ejpam-782	52	24	ω(l(p	ω(l(p	NUM
ejpam-782	52	25	,	,	PUNCT
ejpam-782	52	26	q	q	NOUN
ejpam-782	52	27	,	,	PUNCT
ejpam-782	52	28	φ)),δ(p	φ)),δ(p	ADJ
ejpam-782	52	29	,	,	PUNCT
ejpam-782	52	30	q	q	NOUN
ejpam-782	52	31	,	,	PUNCT
ejpam-782	52	32	f	f	PROPN
ejpam-782	52	33	)	)	PUNCT
ejpam-782	52	34	=	=	SYM
ejpam-782	53	1	ω(l(p	ω(l(p	NUM
ejpam-782	53	2	,	,	PUNCT
ejpam-782	53	3	q	q	NOUN
ejpam-782	53	4	,	,	PUNCT
ejpam-782	53	5	f	f	PROPN
ejpam-782	53	6	)	)	PUNCT
ejpam-782	53	7	)	)	PUNCT
ejpam-782	53	8	,	,	PUNCT
ejpam-782	53	9	δ(p	δ(p	PROPN
ejpam-782	53	10	,	,	PUNCT
ejpam-782	53	11	q	q	NOUN
ejpam-782	53	12	,	,	PUNCT
ejpam-782	53	13	e	e	NOUN
ejpam-782	53	14	)	)	PUNCT
ejpam-782	53	15	=	=	SYM
ejpam-782	53	16	ω(l(p	ω(l(p	NUM
ejpam-782	53	17	,	,	PUNCT
ejpam-782	53	18	q	q	NOUN
ejpam-782	53	19	,	,	PUNCT
ejpam-782	53	20	e	e	NOUN
ejpam-782	53	21	)	)	PUNCT
ejpam-782	53	22	)	)	PUNCT
ejpam-782	53	23	and	and	CCONJ
ejpam-782	53	24	l(p	l(p	PROPN
ejpam-782	53	25	,	,	PUNCT
ejpam-782	53	26	q	q	NOUN
ejpam-782	53	27	,	,	PUNCT
ejpam-782	53	28	φ	φ	NUM
ejpam-782	53	29	)	)	PUNCT
ejpam-782	53	30	=	=	SYM
ejpam-782	53	31	lim	lim	PROPN
ejpam-782	53	32	sup	sup	VERB
ejpam-782	53	33	n→∞	n→∞	NUM
ejpam-782	53	34	log[p−1	log[p−1	NOUN
ejpam-782	53	35	]	]	PUNCT
ejpam-782	53	36	n	n	PRON
ejpam-782	53	37	log[q][en(φ)/µn(gn	log[q][en(φ)/µn(gn	NOUN
ejpam-782	53	38	)	)	PUNCT
ejpam-782	53	39	]	]	PUNCT
ejpam-782	53	40	−1	−1	NOUN
ejpam-782	53	41	/	/	SYM
ejpam-782	53	42	n	n	NOUN
ejpam-782	53	43	,	,	PUNCT
ejpam-782	53	44	l(p	l(p	PROPN
ejpam-782	53	45	,	,	PUNCT
ejpam-782	53	46	q	q	NOUN
ejpam-782	53	47	,	,	PUNCT
ejpam-782	53	48	f	f	PROPN
ejpam-782	53	49	)	)	PUNCT
ejpam-782	54	1	=	=	SYM
ejpam-782	54	2	lim	lim	PROPN
ejpam-782	54	3	sup	sup	VERB
ejpam-782	54	4	n→∞	n→∞	NUM
ejpam-782	54	5	log[p−1	log[p−1	NOUN
ejpam-782	54	6	]	]	PUNCT
ejpam-782	54	7	n	n	DET
ejpam-782	54	8	log[q	log[q	NOUN
ejpam-782	54	9	]	]	PUNCT
ejpam-782	54	10	|an|−1	|an|−1	NOUN
ejpam-782	54	11	/	/	SYM
ejpam-782	54	12	n	n	NOUN
ejpam-782	54	13	,	,	PUNCT
ejpam-782	54	14	l(p	l(p	PROPN
ejpam-782	54	15	,	,	PUNCT
ejpam-782	54	16	q	q	NOUN
ejpam-782	54	17	,	,	PUNCT
ejpam-782	54	18	e	e	NOUN
ejpam-782	54	19	)	)	PUNCT
ejpam-782	54	20	=	=	SYM
ejpam-782	54	21	lim	lim	PROPN
ejpam-782	54	22	sup	sup	VERB
ejpam-782	54	23	n→∞	n→∞	NUM
ejpam-782	54	24	log[p−1	log[p−1	NOUN
ejpam-782	54	25	]	]	X
ejpam-782	54	26	n	n	CCONJ
ejpam-782	54	27	log[q][en(φ	log[q][en(φ	NOUN
ejpam-782	54	28	)	)	PUNCT
ejpam-782	54	29	]	]	PUNCT
ejpam-782	55	1	−1	−1	NOUN
ejpam-782	55	2	/	/	SYM
ejpam-782	55	3	n	n	CCONJ
ejpam-782	55	4	,	,	PUNCT
ejpam-782	55	5	µ(gn	µ(gn	PROPN
ejpam-782	55	6	)	)	PUNCT
ejpam-782	55	7	=	=	SYM
ejpam-782	56	1	∫	∫	PROPN
ejpam-782	56	2	r0	r0	NOUN
ejpam-782	56	3	0	0	NUM
ejpam-782	56	4	gn(r	gn(r	NOUN
ejpam-782	56	5	2)rn+1dr	2)rn+1dr	NOUN
ejpam-782	56	6	>	>	SYM
ejpam-782	56	7	0	0	NUM
ejpam-782	56	8	,	,	PUNCT
ejpam-782	56	9	n=	n=	ADJ
ejpam-782	56	10	0,1,2,3	0,1,2,3	NUM
ejpam-782	56	11	.	.	PUNCT
ejpam-782	56	12	.	.	PUNCT
ejpam-782	56	13	.	.	PUNCT
ejpam-782	56	14	.	.	PUNCT
ejpam-782	57	1	proof	proof	NOUN
ejpam-782	57	2	.	.	PUNCT
ejpam-782	58	1	(	(	PUNCT
ejpam-782	58	2	i	i	NOUN
ejpam-782	58	3	)	)	PUNCT
ejpam-782	58	4	using	use	VERB
ejpam-782	58	5	the	the	DET
ejpam-782	58	6	orthogonality	orthogonality	NOUN
ejpam-782	58	7	argument	argument	NOUN
ejpam-782	58	8	in	in	ADP
ejpam-782	58	9	equation	equation	NOUN
ejpam-782	58	10	(	(	PUNCT
ejpam-782	58	11	4	4	NUM
ejpam-782	58	12	)	)	PUNCT
ejpam-782	58	13	.	.	PUNCT
ejpam-782	59	1	we	we	PRON
ejpam-782	59	2	get	get	VERB
ejpam-782	59	3	the	the	DET
ejpam-782	59	4	identity	identity	NOUN
ejpam-782	59	5	an	an	PRON
ejpam-782	59	6	(	(	PUNCT
ejpam-782	59	7	r	r	NOUN
ejpam-782	59	8	2	2	NUM
ejpam-782	59	9	)	)	PUNCT
ejpam-782	59	10	ngn(r	ngn(r	NUM
ejpam-782	59	11	2	2	NUM
ejpam-782	59	12	)	)	PUNCT
ejpam-782	59	13	=	=	SYM
ejpam-782	59	14	1	1	NUM
ejpam-782	59	15	2π	2π	NUM
ejpam-782	59	16	∫	∫	PROPN
ejpam-782	59	17	2π	2π	NOUN
ejpam-782	59	18	0	0	PUNCT
ejpam-782	60	1	[	[	X
ejpam-782	60	2	φ(r	φ(r	ADJ
ejpam-782	60	3	,	,	PUNCT
ejpam-782	60	4	θ)−	θ)−	PROPN
ejpam-782	60	5	p(r	p(r	PROPN
ejpam-782	60	6	,	,	PUNCT
ejpam-782	60	7	θ)]e−inφdφ	θ)]e−inφdφ	NOUN
ejpam-782	60	8	for	for	ADP
ejpam-782	60	9	p	p	PROPN
ejpam-782	60	10	∈	∈	PROPN
ejpam-782	60	11	πn−1	πn−1	PROPN
ejpam-782	60	12	,	,	PUNCT
ejpam-782	60	13	n=1,2,3	n=1,2,3	NUM
ejpam-782	60	14	.	.	PUNCT
ejpam-782	60	15	.	.	PUNCT
ejpam-782	60	16	.	.	PUNCT
ejpam-782	60	17	.	.	PUNCT
ejpam-782	61	1	integration	integration	NOUN
ejpam-782	61	2	above	above	ADP
ejpam-782	61	3	equation	equation	NOUN
ejpam-782	61	4	over	over	ADP
ejpam-782	61	5	the	the	DET
ejpam-782	61	6	disk	disk	NOUN
ejpam-782	61	7	we	we	PRON
ejpam-782	61	8	obtain	obtain	VERB
ejpam-782	61	9	anµn(gn)/2	anµn(gn)/2	PROPN
ejpam-782	61	10	n	n	NOUN
ejpam-782	61	11	=	=	SYM
ejpam-782	61	12	1	1	NUM
ejpam-782	61	13	2π	2π	NUM
ejpam-782	61	14	∫	∫	PROPN
ejpam-782	61	15	r0	r0	NOUN
ejpam-782	61	16	0	0	NUM
ejpam-782	62	1	∫	∫	PROPN
ejpam-782	62	2	2π	2π	PROPN
ejpam-782	62	3	0	0	PUNCT
ejpam-782	63	1	[	[	X
ejpam-782	63	2	φ(r	φ(r	ADJ
ejpam-782	63	3	,	,	PUNCT
ejpam-782	63	4	θ)−	θ)−	PROPN
ejpam-782	63	5	p(r	p(r	PROPN
ejpam-782	63	6	,	,	PUNCT
ejpam-782	63	7	θ)]e−inφ	θ)]e−inφ	ADP
ejpam-782	63	8	rd	rd	NOUN
ejpam-782	63	9	rdφ	rdφ	NOUN
ejpam-782	63	10	or	or	CCONJ
ejpam-782	63	11	|an|µn(gn)/2	|an|µn(gn)/2	PROPN
ejpam-782	63	12	n	n	CCONJ
ejpam-782	63	13	≤	≤	NUM
ejpam-782	63	14	1	1	NUM
ejpam-782	63	15	4π	4π	NUM
ejpam-782	63	16	r2	r2	PROPN
ejpam-782	63	17	0	0	NUM
ejpam-782	63	18	en(φ	en(φ	ADV
ejpam-782	63	19	)	)	PUNCT
ejpam-782	63	20	(	(	PUNCT
ejpam-782	63	21	7	7	X
ejpam-782	63	22	)	)	PUNCT
ejpam-782	63	23	leads	lead	VERB
ejpam-782	63	24	to	to	ADP
ejpam-782	63	25	lim	lim	PROPN
ejpam-782	63	26	sup	sup	VERB
ejpam-782	63	27	n→∞	n→∞	NUM
ejpam-782	63	28	log[p−1	log[p−1	NOUN
ejpam-782	63	29	]	]	PUNCT
ejpam-782	63	30	n	n	DET
ejpam-782	63	31	log[q	log[q	NOUN
ejpam-782	63	32	]	]	PUNCT
ejpam-782	63	33	|an|−1	|an|−1	NOUN
ejpam-782	63	34	/	/	SYM
ejpam-782	63	35	n	n	NOUN
ejpam-782	63	36	≤	≤	NOUN
ejpam-782	63	37	lim	lim	PROPN
ejpam-782	63	38	sup	sup	VERB
ejpam-782	63	39	n→∞	n→∞	NUM
ejpam-782	63	40	log[p−1	log[p−1	NOUN
ejpam-782	63	41	]	]	PUNCT
ejpam-782	63	42	n	n	PRON
ejpam-782	63	43	log[q][en(φ)/µn(gn	log[q][en(φ)/µn(gn	NOUN
ejpam-782	63	44	)	)	PUNCT
ejpam-782	63	45	]	]	PUNCT
ejpam-782	63	46	−1	−1	NOUN
ejpam-782	63	47	/	/	SYM
ejpam-782	63	48	n	n	NOUN
ejpam-782	63	49	.	.	PUNCT
ejpam-782	64	1	using	use	VERB
ejpam-782	64	2	the	the	DET
ejpam-782	64	3	(	(	PUNCT
ejpam-782	64	4	p	p	NOUN
ejpam-782	64	5	,	,	PUNCT
ejpam-782	64	6	q)-order	q)-order	PUNCT
ejpam-782	64	7	coefficient	coefficient	NOUN
ejpam-782	64	8	formula	formula	NOUN
ejpam-782	64	9	for	for	ADP
ejpam-782	64	10	the	the	DET
ejpam-782	64	11	associate	associate	NOUN
ejpam-782	64	12	[	[	X
ejpam-782	64	13	5	5	NUM
ejpam-782	64	14	,	,	PUNCT
ejpam-782	64	15	thm.1,pp.61	thm.1,pp.61	PROPN
ejpam-782	64	16	]	]	X
ejpam-782	64	17	we	we	PRON
ejpam-782	64	18	get	get	VERB
ejpam-782	64	19	δ(p	δ(p	NOUN
ejpam-782	64	20	,	,	PUNCT
ejpam-782	64	21	q	q	NOUN
ejpam-782	64	22	,	,	PUNCT
ejpam-782	64	23	f	f	PROPN
ejpam-782	64	24	)	)	PUNCT
ejpam-782	64	25	≤	≤	PROPN
ejpam-782	64	26	δ(p	δ(p	PROPN
ejpam-782	64	27	,	,	PUNCT
ejpam-782	64	28	q	q	NOUN
ejpam-782	64	29	,	,	PUNCT
ejpam-782	64	30	φ	φ	NUM
ejpam-782	64	31	)	)	PUNCT
ejpam-782	64	32	.	.	PUNCT
ejpam-782	65	1	(	(	PUNCT
ejpam-782	65	2	ii	ii	NOUN
ejpam-782	65	3	)	)	PUNCT
ejpam-782	65	4	let	let	VERB
ejpam-782	65	5	us	we	PRON
ejpam-782	65	6	consider	consider	VERB
ejpam-782	65	7	|φ(r	|φ(r	PROPN
ejpam-782	65	8	,	,	PUNCT
ejpam-782	65	9	θ)|	θ)|	PROPN
ejpam-782	65	10	≤	≤	NUM
ejpam-782	65	11	∫	∫	PROPN
ejpam-782	66	1	+1	+1	PROPN
ejpam-782	66	2	−1	−1	NOUN
ejpam-782	66	3	|e(r2	|e(r2	NOUN
ejpam-782	66	4	,	,	PUNCT
ejpam-782	66	5	t)||	t)||	NOUN
ejpam-782	66	6	f	f	PROPN
ejpam-782	67	1	(	(	PUNCT
ejpam-782	67	2	z	z	NOUN
ejpam-782	67	3	1−	1−	NUM
ejpam-782	67	4	t2	t2	PROPN
ejpam-782	67	5	2	2	NUM
ejpam-782	67	6	)	)	PUNCT
ejpam-782	67	7	−	−	PROPN
ejpam-782	68	1	p(z	p(z	NOUN
ejpam-782	68	2	1−	1−	NUM
ejpam-782	68	3	t2	t2	NOUN
ejpam-782	68	4	2	2	NUM
ejpam-782	68	5	)	)	PUNCT
ejpam-782	68	6	|(1−	|(1−	NOUN
ejpam-782	68	7	t2	t2	NOUN
ejpam-782	68	8	)	)	PUNCT
ejpam-782	68	9	−1	−1	NOUN
ejpam-782	68	10	2	2	NUM
ejpam-782	68	11	d	d	NOUN
ejpam-782	68	12	t	t	PROPN
ejpam-782	68	13	≤	≤	NUM
ejpam-782	68	14	k(r0)‖	k(r0)‖	PROPN
ejpam-782	68	15	f	f	PROPN
ejpam-782	68	16	−	−	PROPN
ejpam-782	68	17	p‖2	p‖2	PROPN
ejpam-782	68	18	/	/	SYM
ejpam-782	68	19	r0	r0	PROPN
ejpam-782	68	20	d.	d.	PROPN
ejpam-782	68	21	kumar	kumar	PROPN
ejpam-782	68	22	/	/	SYM
ejpam-782	68	23	eur	eur	PROPN
ejpam-782	68	24	.	.	PUNCT
ejpam-782	69	1	j.	j.	PROPN
ejpam-782	69	2	pure	pure	PROPN
ejpam-782	69	3	appl	appl	PROPN
ejpam-782	69	4	.	.	PROPN
ejpam-782	69	5	math	math	PROPN
ejpam-782	69	6	,	,	PUNCT
ejpam-782	69	7	3	3	NUM
ejpam-782	69	8	(	(	PUNCT
ejpam-782	69	9	2010	2010	NUM
ejpam-782	69	10	)	)	PUNCT
ejpam-782	69	11	,	,	PUNCT
ejpam-782	69	12	1062	1062	NUM
ejpam-782	69	13	-	-	SYM
ejpam-782	69	14	1069	1069	NUM
ejpam-782	69	15	1066	1066	NUM
ejpam-782	69	16	where	where	SCONJ
ejpam-782	69	17	k(r0	k(r0	ADV
ejpam-782	69	18	)	)	PUNCT
ejpam-782	69	19	=	=	NOUN
ejpam-782	69	20	max{k(r2	max{k(r2	NOUN
ejpam-782	69	21	)	)	PUNCT
ejpam-782	69	22	:	:	PUNCT
ejpam-782	69	23	0≤	0≤	NUM
ejpam-782	69	24	r	r	NOUN
ejpam-782	69	25	≤	≤	NUM
ejpam-782	69	26	r0	r0	NOUN
ejpam-782	69	27	}	}	PUNCT
ejpam-782	69	28	,	,	PUNCT
ejpam-782	69	29	k(r2	k(r2	NOUN
ejpam-782	69	30	)	)	PUNCT
ejpam-782	70	1	=	=	NOUN
ejpam-782	70	2	max{e(r2	max{e(r2	NOUN
ejpam-782	70	3	,	,	PUNCT
ejpam-782	70	4	t	t	PROPN
ejpam-782	70	5	)	)	PUNCT
ejpam-782	70	6	:	:	PUNCT
ejpam-782	71	1	t	t	PROPN
ejpam-782	71	2	∈	∈	PROPN
ejpam-782	72	1	[	[	X
ejpam-782	72	2	−1,+1	−1,+1	NOUN
ejpam-782	72	3	]	]	X
ejpam-782	72	4	}	}	PUNCT
ejpam-782	72	5	,	,	PUNCT
ejpam-782	72	6	f	f	PROPN
ejpam-782	72	7	(	(	PUNCT
ejpam-782	72	8	z)−	z)−	PROPN
ejpam-782	72	9	p(z	p(z	PROPN
ejpam-782	72	10	)	)	PUNCT
ejpam-782	72	11	=	=	SYM
ejpam-782	73	1	∞	∞	NUM
ejpam-782	73	2	∑	∑	PUNCT
ejpam-782	73	3	k	k	X
ejpam-782	73	4	=	=	PROPN
ejpam-782	73	5	n	n	PRON
ejpam-782	73	6	ak(r0/2	ak(r0/2	NOUN
ejpam-782	73	7	)	)	PUNCT
ejpam-782	73	8	kzk	kzk	PROPN
ejpam-782	73	9	.	.	PUNCT
ejpam-782	74	1	from	from	ADP
ejpam-782	74	2	this	this	PRON
ejpam-782	74	3	we	we	PRON
ejpam-782	74	4	get	get	VERB
ejpam-782	74	5	for	for	ADP
ejpam-782	74	6	p	p	PROPN
ejpam-782	74	7	∈	∈	PROPN
ejpam-782	74	8	∏	∏	PROPN
ejpam-782	74	9	n−1	n−1	PROPN
ejpam-782	74	10	en(φ	en(φ	PUNCT
ejpam-782	74	11	)	)	PUNCT
ejpam-782	74	12	≤‖	≤‖	PROPN
ejpam-782	74	13	φ	φ	NOUN
ejpam-782	74	14	−	−	PROPN
ejpam-782	74	15	p	p	PROPN
ejpam-782	74	16	‖r0	‖r0	PROPN
ejpam-782	74	17	≤	≤	NOUN
ejpam-782	74	18	k(r0	k(r0	NOUN
ejpam-782	74	19	)	)	PUNCT
ejpam-782	75	1	‖	‖	PROPN
ejpam-782	76	1	f	f	X
ejpam-782	77	1	−	−	PROPN
ejpam-782	77	2	p	p	NOUN
ejpam-782	77	3	‖2	‖2	NOUN
ejpam-782	77	4	/	/	SYM
ejpam-782	77	5	r0	r0	NOUN
ejpam-782	77	6	we	we	PRON
ejpam-782	77	7	have	have	VERB
ejpam-782	77	8	en	en	X
ejpam-782	77	9	(	(	PUNCT
ejpam-782	77	10	f	f	X
ejpam-782	77	11	)	)	PUNCT
ejpam-782	77	12	=	=	PUNCT
ejpam-782	78	1	inf{‖	inf{‖	PROPN
ejpam-782	78	2	f	f	X
ejpam-782	79	1	−	−	PROPN
ejpam-782	79	2	p	p	NOUN
ejpam-782	79	3	‖2	‖2	NOUN
ejpam-782	79	4	/	/	SYM
ejpam-782	79	5	r0	r0	NOUN
ejpam-782	79	6	:	:	PUNCT
ejpam-782	79	7	p	p	X
ejpam-782	79	8	∈	∈	PROPN
ejpam-782	79	9	πn−1	πn−1	PROPN
ejpam-782	79	10	}	}	PUNCT
ejpam-782	79	11	and	and	CCONJ
ejpam-782	79	12	πn	πn	X
ejpam-782	79	13	=	=	PUNCT
ejpam-782	79	14	{	{	PUNCT
ejpam-782	79	15	p	p	X
ejpam-782	79	16	:	:	PUNCT
ejpam-782	79	17	p(z	p(z	NOUN
ejpam-782	79	18	)	)	PUNCT
ejpam-782	79	19	=	=	SYM
ejpam-782	80	1	n	n	CCONJ
ejpam-782	80	2	∑	∑	ADP
ejpam-782	80	3	k=0	k=0	PROPN
ejpam-782	80	4	ak(r0/2	ak(r0/2	AUX
ejpam-782	80	5	)	)	PUNCT
ejpam-782	80	6	kzk	kzk	PROPN
ejpam-782	80	7	,	,	PUNCT
ejpam-782	80	8	akreal	akreal	NOUN
ejpam-782	80	9	}	}	PUNCT
ejpam-782	80	10	.	.	PUNCT
ejpam-782	81	1	by	by	ADP
ejpam-782	81	2	using	use	VERB
ejpam-782	81	3	to	to	ADP
ejpam-782	81	4	reddy	reddy	PROPN
ejpam-782	81	5	’s	’s	PART
ejpam-782	81	6	[	[	X
ejpam-782	81	7	10	10	NUM
ejpam-782	81	8	]	]	PUNCT
ejpam-782	81	9	extension	extension	NOUN
ejpam-782	81	10	of	of	ADP
ejpam-782	81	11	bernstein	bernstein	PROPN
ejpam-782	81	12	theorem	theorem	PROPN
ejpam-782	81	13	,	,	PUNCT
ejpam-782	81	14	for	for	ADP
ejpam-782	81	15	given	give	VERB
ejpam-782	81	16	ǫ	ǫ	PRON
ejpam-782	81	17	>	>	X
ejpam-782	81	18	0	0	PUNCT
ejpam-782	82	1	there	there	PRON
ejpam-782	82	2	is	be	VERB
ejpam-782	82	3	an	an	DET
ejpam-782	82	4	n(ǫ	n(ǫ	PROPN
ejpam-782	82	5	)	)	PUNCT
ejpam-782	82	6	>	>	X
ejpam-782	82	7	0	0	PUNCT
ejpam-782	82	8	such	such	ADJ
ejpam-782	82	9	that	that	SCONJ
ejpam-782	82	10	en	en	PROPN
ejpam-782	82	11	(	(	PUNCT
ejpam-782	82	12	f	f	PROPN
ejpam-782	82	13	)	)	PUNCT
ejpam-782	82	14	≤	≤	NOUN
ejpam-782	83	1	k(r0)[2	k(r0)[2	PROPN
ejpam-782	83	2	n|an|/(r0	n|an|/(r0	ADP
ejpam-782	83	3	+	+	NUM
ejpam-782	83	4	ǫ	ǫ	X
ejpam-782	83	5	)	)	PUNCT
ejpam-782	83	6	n	n	CCONJ
ejpam-782	83	7	]	]	PUNCT
ejpam-782	83	8	for	for	ADP
ejpam-782	83	9	all	all	PRON
ejpam-782	83	10	n	n	DET
ejpam-782	83	11	≥	≥	NOUN
ejpam-782	83	12	n(ǫ	n(ǫ	PROPN
ejpam-782	83	13	)	)	PUNCT
ejpam-782	83	14	or	or	CCONJ
ejpam-782	83	15	en(φ	en(φ	ADV
ejpam-782	83	16	)	)	PUNCT
ejpam-782	83	17	−1	−1	NOUN
ejpam-782	83	18	/	/	SYM
ejpam-782	83	19	n	n	PROPN
ejpam-782	83	20	≥|	≥|	NOUN
ejpam-782	83	21	an	an	DET
ejpam-782	83	22	|	|	NOUN
ejpam-782	83	23	−1	−1	NOUN
ejpam-782	83	24	/	/	SYM
ejpam-782	83	25	n	n	CCONJ
ejpam-782	83	26	(	(	PUNCT
ejpam-782	83	27	r0	r0	VERB
ejpam-782	83	28	+	+	CCONJ
ejpam-782	83	29	ǫ	ǫ	X
ejpam-782	83	30	)	)	PUNCT
ejpam-782	83	31	2	2	NUM
ejpam-782	83	32	k(r0	k(r0	NOUN
ejpam-782	83	33	)	)	PUNCT
ejpam-782	83	34	−1	−1	NOUN
ejpam-782	83	35	/	/	SYM
ejpam-782	83	36	n	n	CCONJ
ejpam-782	83	37	(	(	PUNCT
ejpam-782	83	38	8)	8)	NUM
ejpam-782	83	39	or	or	CCONJ
ejpam-782	83	40	log[q	log[q	NOUN
ejpam-782	83	41	]	]	X
ejpam-782	83	42	en(φ	en(φ	ADV
ejpam-782	83	43	)	)	PUNCT
ejpam-782	83	44	−1	−1	NOUN
ejpam-782	83	45	/	/	SYM
ejpam-782	83	46	n	n	CCONJ
ejpam-782	83	47	≥	≥	NOUN
ejpam-782	83	48	log[q	log[q	NOUN
ejpam-782	83	49	]	]	PUNCT
ejpam-782	83	50	|	|	ADV
ejpam-782	83	51	an	an	DET
ejpam-782	83	52	|	|	NOUN
ejpam-782	83	53	−1	−1	NOUN
ejpam-782	83	54	/	/	SYM
ejpam-782	83	55	n	n	PRON
ejpam-782	83	56	+0(1	+0(1	ADJ
ejpam-782	83	57	)	)	PUNCT
ejpam-782	83	58	or	or	CCONJ
ejpam-782	83	59	lim	lim	PROPN
ejpam-782	83	60	sup	sup	VERB
ejpam-782	83	61	n→∞	n→∞	NUM
ejpam-782	83	62	log[p−1	log[p−1	NOUN
ejpam-782	83	63	]	]	PUNCT
ejpam-782	83	64	n	n	DET
ejpam-782	83	65	log[q	log[q	NOUN
ejpam-782	83	66	]	]	X
ejpam-782	83	67	en(φ	en(φ	ADV
ejpam-782	83	68	)	)	PUNCT
ejpam-782	83	69	−1	−1	NOUN
ejpam-782	83	70	/	/	SYM
ejpam-782	83	71	n	n	CCONJ
ejpam-782	83	72	≤	≤	NOUN
ejpam-782	83	73	lim	lim	PROPN
ejpam-782	83	74	sup	sup	VERB
ejpam-782	83	75	n→∞	n→∞	NUM
ejpam-782	83	76	log[p−1	log[p−1	NOUN
ejpam-782	83	77	]	]	PUNCT
ejpam-782	83	78	n	n	DET
ejpam-782	83	79	log[q	log[q	NOUN
ejpam-782	83	80	]	]	PUNCT
ejpam-782	83	81	|	|	ADV
ejpam-782	83	82	an	an	DET
ejpam-782	83	83	|−1	|−1	NUM
ejpam-782	83	84	/	/	SYM
ejpam-782	83	85	n	n	NOUN
ejpam-782	83	86	.	.	PUNCT
ejpam-782	84	1	again	again	ADV
ejpam-782	84	2	using	use	VERB
ejpam-782	84	3	the	the	DET
ejpam-782	84	4	(	(	PUNCT
ejpam-782	84	5	p	p	NOUN
ejpam-782	84	6	,	,	PUNCT
ejpam-782	84	7	q)order	q)order	NOUN
ejpam-782	84	8	coefficient	coefficient	NOUN
ejpam-782	84	9	formula	formula	NOUN
ejpam-782	84	10	for	for	ADP
ejpam-782	84	11	the	the	DET
ejpam-782	84	12	associate	associate	NOUN
ejpam-782	84	13	[	[	X
ejpam-782	84	14	5	5	NUM
ejpam-782	84	15	,	,	PUNCT
ejpam-782	84	16	thm.1	thm.1	PROPN
ejpam-782	84	17	,	,	PUNCT
ejpam-782	84	18	pp	pp	ADP
ejpam-782	84	19	61	61	NUM
ejpam-782	84	20	]	]	PUNCT
ejpam-782	84	21	we	we	PRON
ejpam-782	84	22	obtain	obtain	VERB
ejpam-782	84	23	δ(p	δ(p	PROPN
ejpam-782	84	24	,	,	PUNCT
ejpam-782	84	25	q	q	NOUN
ejpam-782	84	26	,	,	PUNCT
ejpam-782	84	27	e	e	NOUN
ejpam-782	84	28	)	)	PUNCT
ejpam-782	84	29	≤	≤	PROPN
ejpam-782	84	30	δ(p	δ(p	PROPN
ejpam-782	84	31	,	,	PUNCT
ejpam-782	84	32	q	q	NOUN
ejpam-782	84	33	,	,	PUNCT
ejpam-782	84	34	f	f	PROPN
ejpam-782	84	35	)	)	PUNCT
ejpam-782	84	36	.	.	PUNCT
ejpam-782	85	1	hence	hence	ADV
ejpam-782	85	2	the	the	DET
ejpam-782	85	3	proof	proof	NOUN
ejpam-782	85	4	of	of	ADP
ejpam-782	85	5	(	(	PUNCT
ejpam-782	85	6	ii	ii	NOUN
ejpam-782	85	7	)	)	PUNCT
ejpam-782	85	8	is	be	AUX
ejpam-782	85	9	completed	complete	VERB
ejpam-782	85	10	.	.	PUNCT
ejpam-782	86	1	theorem	theorem	NOUN
ejpam-782	86	2	2	2	NUM
ejpam-782	86	3	.	.	PUNCT
ejpam-782	87	1	let	let	VERB
ejpam-782	87	2	φ(r	φ(r	ADJ
ejpam-782	87	3	,	,	PUNCT
ejpam-782	87	4	θ	θ	NOUN
ejpam-782	87	5	)	)	PUNCT
ejpam-782	87	6	be	be	VERB
ejpam-782	87	7	an	an	DET
ejpam-782	87	8	entire	entire	ADJ
ejpam-782	87	9	function	function	NOUN
ejpam-782	87	10	solution	solution	NOUN
ejpam-782	87	11	of	of	ADP
ejpam-782	87	12	the	the	DET
ejpam-782	87	13	helmholtz	helmholtz	NOUN
ejpam-782	87	14	equation	equation	NOUN
ejpam-782	87	15	with	with	ADP
ejpam-782	87	16	expansion	expansion	NOUN
ejpam-782	87	17	φ(r	φ(r	ADP
ejpam-782	87	18	,	,	PUNCT
ejpam-782	87	19	θ	θ	NOUN
ejpam-782	87	20	)	)	PUNCT
ejpam-782	87	21	and	and	CCONJ
ejpam-782	87	22	bassociate	bassociate	NOUN
ejpam-782	87	23	f(z	f(z	PROPN
ejpam-782	87	24	)	)	PUNCT
ejpam-782	87	25	have	have	VERB
ejpam-782	87	26	the	the	DET
ejpam-782	87	27	same	same	ADJ
ejpam-782	87	28	index	index	NOUN
ejpam-782	87	29	-	-	PUNCT
ejpam-782	87	30	pair	pair	NOUN
ejpam-782	87	31	(	(	PUNCT
ejpam-782	87	32	p	p	X
ejpam-782	87	33	,	,	PUNCT
ejpam-782	87	34	q	q	NOUN
ejpam-782	87	35	)	)	PUNCT
ejpam-782	87	36	.	.	PUNCT
ejpam-782	88	1	then	then	ADV
ejpam-782	88	2	the	the	DET
ejpam-782	88	3	(	(	PUNCT
ejpam-782	88	4	p	p	X
ejpam-782	88	5	,	,	PUNCT
ejpam-782	88	6	q	q	NOUN
ejpam-782	88	7	)	)	PUNCT
ejpam-782	88	8	types	type	NOUN
ejpam-782	88	9	satisfy	satisfy	VERB
ejpam-782	88	10	(	(	PUNCT
ejpam-782	88	11	i	i	NOUN
ejpam-782	88	12	)	)	PUNCT
ejpam-782	89	1	[	[	PUNCT
ejpam-782	89	2	t	t	X
ejpam-782	89	3	(	(	PUNCT
ejpam-782	89	4	p	p	X
ejpam-782	89	5	,	,	PUNCT
ejpam-782	89	6	q	q	X
ejpam-782	89	7	,	,	PUNCT
ejpam-782	89	8	φ	φ	NOUN
ejpam-782	89	9	)	)	PUNCT
ejpam-782	89	10	m(φ	m(φ	PROPN
ejpam-782	89	11	)	)	PUNCT
ejpam-782	89	12	]	]	PUNCT
ejpam-782	89	13	1	1	NUM
ejpam-782	89	14	(	(	PUNCT
ejpam-782	89	15	δ(p	δ(p	PROPN
ejpam-782	89	16	,	,	PUNCT
ejpam-782	89	17	q	q	NOUN
ejpam-782	89	18	,	,	PUNCT
ejpam-782	89	19	φ)−a	φ)−a	NUM
ejpam-782	89	20	)	)	PUNCT
ejpam-782	89	21	≥	≥	NOUN
ejpam-782	89	22	[	[	PUNCT
ejpam-782	89	23	t	t	X
ejpam-782	89	24	(	(	PUNCT
ejpam-782	89	25	p	p	X
ejpam-782	89	26	,	,	PUNCT
ejpam-782	89	27	q	q	NOUN
ejpam-782	89	28	,	,	PUNCT
ejpam-782	89	29	f	f	PROPN
ejpam-782	89	30	)	)	PUNCT
ejpam-782	89	31	m	m	PROPN
ejpam-782	89	32	(	(	PUNCT
ejpam-782	89	33	f	f	PROPN
ejpam-782	89	34	)	)	PUNCT
ejpam-782	89	35	]	]	PUNCT
ejpam-782	89	36	1	1	X
ejpam-782	89	37	(	(	PUNCT
ejpam-782	89	38	δ(p	δ(p	PROPN
ejpam-782	89	39	,	,	PUNCT
ejpam-782	89	40	q	q	NOUN
ejpam-782	89	41	,	,	PUNCT
ejpam-782	89	42	f	f	NOUN
ejpam-782	89	43	)	)	PUNCT
ejpam-782	89	44	−a	−a	NOUN
ejpam-782	89	45	)	)	PUNCT
ejpam-782	89	46	lim	lim	PROPN
ejpam-782	89	47	inf	inf	PROPN
ejpam-782	89	48	n→∞	n→∞	X
ejpam-782	89	49	(	(	PUNCT
ejpam-782	89	50	log[p−2	log[p−2	NOUN
ejpam-782	89	51	]	]	PUNCT
ejpam-782	89	52	n	n	CCONJ
ejpam-782	89	53	)	)	PUNCT
ejpam-782	89	54	1	1	NUM
ejpam-782	89	55	δ(p	δ(p	X
ejpam-782	89	56	,	,	PUNCT
ejpam-782	89	57	q	q	NOUN
ejpam-782	89	58	,	,	PUNCT
ejpam-782	89	59	φ)−a	φ)−a	AUX
ejpam-782	89	60	−	−	PROPN
ejpam-782	89	61	1	1	NUM
ejpam-782	89	62	δ(p	δ(p	X
ejpam-782	89	63	,	,	PUNCT
ejpam-782	89	64	q	q	NOUN
ejpam-782	89	65	,	,	PUNCT
ejpam-782	89	66	f	f	NOUN
ejpam-782	89	67	)	)	PUNCT
ejpam-782	89	68	−a	−a	ADV
ejpam-782	89	69	.	.	PUNCT
ejpam-782	90	1	d.	d.	PROPN
ejpam-782	90	2	kumar	kumar	PROPN
ejpam-782	90	3	/	/	SYM
ejpam-782	90	4	eur	eur	PROPN
ejpam-782	90	5	.	.	PUNCT
ejpam-782	91	1	j.	j.	PROPN
ejpam-782	91	2	pure	pure	PROPN
ejpam-782	91	3	appl	appl	PROPN
ejpam-782	91	4	.	.	PROPN
ejpam-782	91	5	math	math	PROPN
ejpam-782	91	6	,	,	PUNCT
ejpam-782	91	7	3	3	NUM
ejpam-782	91	8	(	(	PUNCT
ejpam-782	91	9	2010	2010	NUM
ejpam-782	91	10	)	)	PUNCT
ejpam-782	91	11	,	,	PUNCT
ejpam-782	91	12	1062	1062	NUM
ejpam-782	91	13	-	-	SYM
ejpam-782	91	14	1069	1069	NUM
ejpam-782	91	15	1067	1067	NUM
ejpam-782	91	16	(	(	PUNCT
ejpam-782	91	17	ii	ii	NOUN
ejpam-782	91	18	)	)	PUNCT
ejpam-782	91	19	[	[	PUNCT
ejpam-782	91	20	t	t	X
ejpam-782	91	21	(	(	PUNCT
ejpam-782	91	22	p	p	X
ejpam-782	91	23	,	,	PUNCT
ejpam-782	91	24	q	q	NOUN
ejpam-782	91	25	,	,	PUNCT
ejpam-782	91	26	f	f	PROPN
ejpam-782	91	27	)	)	PUNCT
ejpam-782	91	28	m	m	PROPN
ejpam-782	91	29	(	(	PUNCT
ejpam-782	91	30	f	f	PROPN
ejpam-782	91	31	)	)	PUNCT
ejpam-782	91	32	]	]	PUNCT
ejpam-782	92	1	1	1	X
ejpam-782	92	2	(	(	PUNCT
ejpam-782	92	3	δ(p	δ(p	PROPN
ejpam-782	92	4	,	,	PUNCT
ejpam-782	92	5	q	q	NOUN
ejpam-782	92	6	,	,	PUNCT
ejpam-782	92	7	f	f	NOUN
ejpam-782	92	8	)	)	PUNCT
ejpam-782	92	9	−a	−a	ADJ
ejpam-782	92	10	)	)	PUNCT
ejpam-782	92	11	≥	≥	NOUN
ejpam-782	92	12	[	[	PUNCT
ejpam-782	92	13	t	t	X
ejpam-782	92	14	(	(	PUNCT
ejpam-782	92	15	p	p	X
ejpam-782	92	16	,	,	PUNCT
ejpam-782	92	17	q	q	ADJ
ejpam-782	92	18	,	,	PUNCT
ejpam-782	92	19	e	e	NOUN
ejpam-782	92	20	)	)	PUNCT
ejpam-782	92	21	m(e	m(e	NUM
ejpam-782	92	22	)	)	PUNCT
ejpam-782	92	23	]	]	PUNCT
ejpam-782	92	24	1	1	NUM
ejpam-782	92	25	(	(	PUNCT
ejpam-782	92	26	δ(p	δ(p	PROPN
ejpam-782	92	27	,	,	PUNCT
ejpam-782	92	28	q	q	NOUN
ejpam-782	92	29	,	,	PUNCT
ejpam-782	92	30	e)−a	e)−a	NOUN
ejpam-782	92	31	)	)	PUNCT
ejpam-782	92	32	.β	.β	NOUN
ejpam-782	92	33	.	.	PUNCT
ejpam-782	93	1	lim	lim	PROPN
ejpam-782	93	2	inf	inf	PROPN
ejpam-782	93	3	n→∞	n→∞	X
ejpam-782	93	4	(	(	PUNCT
ejpam-782	93	5	log[p−2	log[p−2	NOUN
ejpam-782	93	6	]	]	PUNCT
ejpam-782	93	7	n	n	CCONJ
ejpam-782	93	8	)	)	PUNCT
ejpam-782	93	9	1	1	NUM
ejpam-782	93	10	δ(p	δ(p	X
ejpam-782	93	11	,	,	PUNCT
ejpam-782	93	12	q	q	NOUN
ejpam-782	93	13	,	,	PUNCT
ejpam-782	93	14	f	f	NOUN
ejpam-782	93	15	)	)	PUNCT
ejpam-782	93	16	−a	−a	ADV
ejpam-782	93	17	−	−	PROPN
ejpam-782	93	18	1	1	NUM
ejpam-782	93	19	δ(p	δ(p	PROPN
ejpam-782	93	20	,	,	PUNCT
ejpam-782	93	21	q.e)−a	q.e)−a	NOUN
ejpam-782	93	22	,	,	PUNCT
ejpam-782	93	23	where	where	SCONJ
ejpam-782	93	24	t	t	PROPN
ejpam-782	93	25	(	(	PUNCT
ejpam-782	93	26	p	p	X
ejpam-782	93	27	,	,	PUNCT
ejpam-782	93	28	q	q	X
ejpam-782	93	29	,	,	PUNCT
ejpam-782	93	30	φ	φ	NUM
ejpam-782	93	31	)	)	PUNCT
ejpam-782	93	32	=	=	SYM
ejpam-782	93	33	m(φ)υ(p	m(φ)υ(p	NOUN
ejpam-782	93	34	,	,	PUNCT
ejpam-782	93	35	q	q	NOUN
ejpam-782	93	36	,	,	PUNCT
ejpam-782	93	37	φ	φ	NOUN
ejpam-782	93	38	)	)	PUNCT
ejpam-782	93	39	,	,	PUNCT
ejpam-782	93	40	t	t	PROPN
ejpam-782	93	41	(	(	PUNCT
ejpam-782	93	42	p	p	X
ejpam-782	93	43	,	,	PUNCT
ejpam-782	93	44	q	q	ADJ
ejpam-782	93	45	,	,	PUNCT
ejpam-782	93	46	e	e	NOUN
ejpam-782	93	47	)	)	PUNCT
ejpam-782	93	48	=	=	SYM
ejpam-782	93	49	m(e)υ(p	m(e)υ(p	NOUN
ejpam-782	93	50	,	,	PUNCT
ejpam-782	93	51	q	q	NOUN
ejpam-782	93	52	,	,	PUNCT
ejpam-782	93	53	e	e	NOUN
ejpam-782	93	54	)	)	PUNCT
ejpam-782	93	55	,	,	PUNCT
ejpam-782	93	56	t	t	PROPN
ejpam-782	93	57	(	(	PUNCT
ejpam-782	93	58	p	p	X
ejpam-782	93	59	,	,	PUNCT
ejpam-782	93	60	q	q	NOUN
ejpam-782	93	61	,	,	PUNCT
ejpam-782	93	62	f	f	PROPN
ejpam-782	93	63	)	)	PUNCT
ejpam-782	94	1	=	=	SYM
ejpam-782	94	2	m(f)υ(p	m(f)υ(p	PROPN
ejpam-782	94	3	,	,	PUNCT
ejpam-782	94	4	q	q	NOUN
ejpam-782	94	5	,	,	PUNCT
ejpam-782	94	6	f	f	PROPN
ejpam-782	94	7	)	)	PUNCT
ejpam-782	94	8	and	and	CCONJ
ejpam-782	94	9	1	1	NUM
ejpam-782	94	10	υ(p	υ(p	PROPN
ejpam-782	94	11	,	,	PUNCT
ejpam-782	94	12	q	q	NOUN
ejpam-782	94	13	,	,	PUNCT
ejpam-782	94	14	φ	φ	NUM
ejpam-782	94	15	)	)	PUNCT
ejpam-782	94	16	=	=	PROPN
ejpam-782	94	17	lim	lim	PROPN
ejpam-782	94	18	inf	inf	PROPN
ejpam-782	94	19	n→∞	n→∞	X
ejpam-782	95	1	[	[	X
ejpam-782	95	2	log[q−1][en(φ)/µn(rn	log[q−1][en(φ)/µn(rn	PROPN
ejpam-782	95	3	)	)	PUNCT
ejpam-782	95	4	]	]	PUNCT
ejpam-782	95	5	−1	−1	NOUN
ejpam-782	95	6	/	/	SYM
ejpam-782	95	7	n](δ(p	n](δ(p	ADJ
ejpam-782	95	8	,	,	PUNCT
ejpam-782	95	9	q	q	NOUN
ejpam-782	95	10	,	,	PUNCT
ejpam-782	95	11	φ)−a	φ)−a	NUM
ejpam-782	95	12	)	)	PUNCT
ejpam-782	95	13	log[p−2	log[p−2	NOUN
ejpam-782	95	14	]	]	PUNCT
ejpam-782	96	1	n	n	X
ejpam-782	96	2	,	,	PUNCT
ejpam-782	96	3	1	1	NUM
ejpam-782	96	4	υ(p	υ(p	PROPN
ejpam-782	96	5	,	,	PUNCT
ejpam-782	96	6	q	q	NOUN
ejpam-782	96	7	,	,	PUNCT
ejpam-782	96	8	e	e	NOUN
ejpam-782	96	9	)	)	PUNCT
ejpam-782	96	10	=	=	SYM
ejpam-782	96	11	lim	lim	PROPN
ejpam-782	96	12	inf	inf	PROPN
ejpam-782	96	13	n→∞	n→∞	X
ejpam-782	97	1	[	[	X
ejpam-782	97	2	log[q−1	log[q−1	X
ejpam-782	97	3	]	]	PUNCT
ejpam-782	97	4	en(φ	en(φ	ADV
ejpam-782	97	5	)	)	PUNCT
ejpam-782	97	6	−1	−1	NOUN
ejpam-782	97	7	/	/	SYM
ejpam-782	97	8	n](δ(p	n](δ(p	ADJ
ejpam-782	97	9	,	,	PUNCT
ejpam-782	97	10	q	q	NOUN
ejpam-782	97	11	,	,	PUNCT
ejpam-782	97	12	e)−a	e)−a	NOUN
ejpam-782	97	13	)	)	PUNCT
ejpam-782	97	14	log[p−2	log[p−2	NOUN
ejpam-782	97	15	]	]	PUNCT
ejpam-782	97	16	n	n	X
ejpam-782	97	17	,	,	PUNCT
ejpam-782	97	18	1	1	NUM
ejpam-782	97	19	υ(p	υ(p	PROPN
ejpam-782	97	20	,	,	PUNCT
ejpam-782	97	21	q	q	NOUN
ejpam-782	97	22	,	,	PUNCT
ejpam-782	97	23	f	f	PROPN
ejpam-782	97	24	)	)	PUNCT
ejpam-782	98	1	=	=	PROPN
ejpam-782	98	2	lim	lim	PROPN
ejpam-782	98	3	inf	inf	PROPN
ejpam-782	98	4	n→∞	n→∞	X
ejpam-782	99	1	[	[	X
ejpam-782	99	2	log[q−1	log[q−1	X
ejpam-782	99	3	]	]	X
ejpam-782	99	4	|	|	ADV
ejpam-782	99	5	an	an	DET
ejpam-782	99	6	|	|	NOUN
ejpam-782	99	7	−1	−1	NOUN
ejpam-782	99	8	/	/	SYM
ejpam-782	99	9	n](δ(p	n](δ(p	ADJ
ejpam-782	99	10	,	,	PUNCT
ejpam-782	99	11	q	q	NOUN
ejpam-782	99	12	,	,	PUNCT
ejpam-782	99	13	f	f	NOUN
ejpam-782	99	14	)	)	PUNCT
ejpam-782	99	15	−a	−a	ADJ
ejpam-782	99	16	)	)	PUNCT
ejpam-782	99	17	log[p−2	log[p−2	NOUN
ejpam-782	99	18	]	]	PUNCT
ejpam-782	100	1	n	n	X
ejpam-782	100	2	.	.	PUNCT
ejpam-782	101	1	here	here	ADV
ejpam-782	101	2	a=	a=	PROPN
ejpam-782	101	3	1	1	NUM
ejpam-782	101	4	,	,	PUNCT
ejpam-782	101	5	if	if	SCONJ
ejpam-782	101	6	p	p	NOUN
ejpam-782	101	7	=	=	X
ejpam-782	101	8	q	q	X
ejpam-782	101	9	and	and	CCONJ
ejpam-782	101	10	a=	a=	PROPN
ejpam-782	101	11	0	0	PUNCT
ejpam-782	102	1	if	if	SCONJ
ejpam-782	102	2	p	p	X
ejpam-782	102	3	>	>	X
ejpam-782	102	4	q	q	PROPN
ejpam-782	102	5	and	and	CCONJ
ejpam-782	102	6	m(φ	m(φ	NOUN
ejpam-782	102	7	)	)	PUNCT
ejpam-782	102	8	=	=	PUNCT
ejpam-782	102	9			PROPN
ejpam-782	102	10			PROPN
ejpam-782	102	11			PROPN
ejpam-782	102	12	(	(	PUNCT
ejpam-782	102	13	δ(2,2,φ)−1)δ(2,2,φ)−1	δ(2,2,φ)−1)δ(2,2,φ)−1	NOUN
ejpam-782	102	14	(	(	PUNCT
ejpam-782	102	15	δ(2,2,φ))δ(2,2,φ	δ(2,2,φ))δ(2,2,φ	NOUN
ejpam-782	102	16	)	)	PUNCT
ejpam-782	102	17	,	,	PUNCT
ejpam-782	102	18	if	if	SCONJ
ejpam-782	102	19	(	(	PUNCT
ejpam-782	102	20	p	p	X
ejpam-782	102	21	,	,	PUNCT
ejpam-782	102	22	q	q	NOUN
ejpam-782	102	23	)	)	PUNCT
ejpam-782	102	24	=	=	SYM
ejpam-782	102	25	(	(	PUNCT
ejpam-782	102	26	2,2	2,2	NUM
ejpam-782	102	27	)	)	PUNCT
ejpam-782	102	28	,	,	PUNCT
ejpam-782	102	29	;	;	PUNCT
ejpam-782	102	30	1	1	NUM
ejpam-782	102	31	eδ(2,1,φ	eδ(2,1,φ	PROPN
ejpam-782	102	32	)	)	PUNCT
ejpam-782	102	33	,	,	PUNCT
ejpam-782	102	34	if	if	SCONJ
ejpam-782	102	35	(	(	PUNCT
ejpam-782	102	36	p	p	X
ejpam-782	102	37	,	,	PUNCT
ejpam-782	102	38	q	q	NOUN
ejpam-782	102	39	)	)	PUNCT
ejpam-782	102	40	=	=	SYM
ejpam-782	102	41	(	(	PUNCT
ejpam-782	102	42	2,1	2,1	NUM
ejpam-782	102	43	)	)	PUNCT
ejpam-782	102	44	,	,	PUNCT
ejpam-782	102	45	;	;	PUNCT
ejpam-782	102	46	1	1	X
ejpam-782	102	47	,	,	PUNCT
ejpam-782	102	48	if	if	SCONJ
ejpam-782	102	49	3≤	3≤	NUM
ejpam-782	102	50	p	p	X
ejpam-782	102	51	=	=	X
ejpam-782	102	52	q	q	X
ejpam-782	102	53	<	<	X
ejpam-782	102	54	∞.	∞.	PROPN
ejpam-782	102	55	m(f	m(f	PROPN
ejpam-782	102	56	)	)	PUNCT
ejpam-782	102	57	and	and	CCONJ
ejpam-782	102	58	m(e	m(e	NUM
ejpam-782	102	59	)	)	PUNCT
ejpam-782	102	60	are	be	AUX
ejpam-782	102	61	defined	define	VERB
ejpam-782	102	62	similarly.also	similarly.also	ADV
ejpam-782	102	63	β	β	X
ejpam-782	102	64	=	=	SYM
ejpam-782	102	65	(	(	PUNCT
ejpam-782	102	66	r0/2	r0/2	NUM
ejpam-782	102	67	)	)	PUNCT
ejpam-782	102	68	if	if	SCONJ
ejpam-782	102	69	(	(	PUNCT
ejpam-782	102	70	p	p	X
ejpam-782	102	71	,	,	PUNCT
ejpam-782	102	72	q	q	NOUN
ejpam-782	102	73	)	)	PUNCT
ejpam-782	102	74	=	=	SYM
ejpam-782	102	75	(	(	PUNCT
ejpam-782	102	76	2,1	2,1	NUM
ejpam-782	102	77	)	)	PUNCT
ejpam-782	102	78	and	and	CCONJ
ejpam-782	102	79	β=1	β=1	ADP
ejpam-782	102	80	;	;	PUNCT
ejpam-782	102	81	otherwise	otherwise	ADV
ejpam-782	102	82	.	.	PUNCT
ejpam-782	103	1	proof	proof	NOUN
ejpam-782	103	2	.	.	PUNCT
ejpam-782	104	1	(	(	PUNCT
ejpam-782	104	2	i	i	NOUN
ejpam-782	104	3	)	)	PUNCT
ejpam-782	104	4	from	from	ADP
ejpam-782	104	5	(	(	PUNCT
ejpam-782	104	6	7	7	X
ejpam-782	104	7	)	)	PUNCT
ejpam-782	104	8	we	we	PRON
ejpam-782	104	9	have	have	VERB
ejpam-782	104	10	[	[	X
ejpam-782	104	11	|an|	|an|	NOUN
ejpam-782	104	12	−1	−1	NOUN
ejpam-782	104	13	/	/	SYM
ejpam-782	104	14	n]δ(2,1	n]δ(2,1	PROPN
ejpam-782	104	15	,	,	PUNCT
ejpam-782	104	16	f	f	PROPN
ejpam-782	104	17	)	)	PUNCT
ejpam-782	105	1	n	n	PRON
ejpam-782	105	2	≥	≥	NOUN
ejpam-782	105	3	{	{	PUNCT
ejpam-782	105	4	{	{	PUNCT
ejpam-782	105	5	2[en(φ)/µn(gn	2[en(φ)/µn(gn	NUM
ejpam-782	105	6	)	)	PUNCT
ejpam-782	105	7	]	]	PUNCT
ejpam-782	105	8	−1	−1	NOUN
ejpam-782	105	9	/	/	SYM
ejpam-782	105	10	n}δ(2,1,φ	n}δ(2,1,φ	ADJ
ejpam-782	105	11	)	)	PUNCT
ejpam-782	105	12	n	n	CCONJ
ejpam-782	105	13	}	}	PUNCT
ejpam-782	105	14	δ(2,1	δ(2,1	PROPN
ejpam-782	105	15	,	,	PUNCT
ejpam-782	105	16	f	f	NOUN
ejpam-782	105	17	)	)	PUNCT
ejpam-782	105	18	δ(2,1,φ	δ(2,1,φ	NOUN
ejpam-782	105	19	)	)	PUNCT
ejpam-782	105	20	.n	.n	NOUN
ejpam-782	106	1	δ(2,1	δ(2,1	PROPN
ejpam-782	106	2	,	,	PUNCT
ejpam-782	106	3	f	f	NOUN
ejpam-782	106	4	)	)	PUNCT
ejpam-782	106	5	δ(2,1,φ	δ(2,1,φ	NOUN
ejpam-782	106	6	)	)	PUNCT
ejpam-782	106	7	−1	−1	NOUN
ejpam-782	106	8	.	.	PUNCT
ejpam-782	107	1	proceeding	proceed	VERB
ejpam-782	107	2	to	to	PART
ejpam-782	107	3	limit	limit	VERB
ejpam-782	107	4	infimum	infimum	ADV
ejpam-782	107	5	as	as	ADP
ejpam-782	107	6	n→∞	n→∞	NUM
ejpam-782	107	7	and	and	CCONJ
ejpam-782	107	8	using	use	VERB
ejpam-782	107	9	the	the	DET
ejpam-782	107	10	(	(	PUNCT
ejpam-782	107	11	2,1)-type	2,1)-type	NUM
ejpam-782	107	12	coefficient	coefficient	NOUN
ejpam-782	107	13	formula	formula	NOUN
ejpam-782	107	14	for	for	ADP
ejpam-782	107	15	the	the	DET
ejpam-782	107	16	associate	associate	NOUN
ejpam-782	107	17	[	[	X
ejpam-782	107	18	6,thm.1,pp.181	6,thm.1,pp.181	NUM
ejpam-782	107	19	]	]	X
ejpam-782	107	20	we	we	PRON
ejpam-782	107	21	get	get	VERB
ejpam-782	107	22	1	1	NUM
ejpam-782	107	23	eδ(2,1	eδ(2,1	NUM
ejpam-782	107	24	,	,	PUNCT
ejpam-782	107	25	f	f	PROPN
ejpam-782	107	26	)	)	PUNCT
ejpam-782	107	27	t	t	PROPN
ejpam-782	107	28	(	(	PUNCT
ejpam-782	107	29	2,1	2,1	NUM
ejpam-782	107	30	,	,	PUNCT
ejpam-782	107	31	f	f	PROPN
ejpam-782	107	32	)	)	PUNCT
ejpam-782	107	33	≥	≥	PROPN
ejpam-782	107	34	2δ	2δ	NUM
ejpam-782	107	35	(	(	PUNCT
ejpam-782	107	36	2,1	2,1	NUM
ejpam-782	107	37	,	,	PUNCT
ejpam-782	107	38	f	f	PROPN
ejpam-782	107	39	)	)	PUNCT
ejpam-782	107	40	(	(	PUNCT
ejpam-782	107	41	1	1	NUM
ejpam-782	107	42	eδ(2,1,φ)t	eδ(2,1,φ)t	NOUN
ejpam-782	107	43	(	(	PUNCT
ejpam-782	107	44	2,1,φ	2,1,φ	NUM
ejpam-782	107	45	)	)	PUNCT
ejpam-782	107	46	)	)	PUNCT
ejpam-782	108	1	δ(2,1	δ(2,1	PROPN
ejpam-782	108	2	,	,	PUNCT
ejpam-782	108	3	f	f	NOUN
ejpam-782	108	4	)	)	PUNCT
ejpam-782	108	5	/δ(2,1,φ	/δ(2,1,φ	SYM
ejpam-782	108	6	)	)	PUNCT
ejpam-782	109	1	lim	lim	PROPN
ejpam-782	109	2	inf	inf	PROPN
ejpam-782	109	3	n→∞	n→∞	X
ejpam-782	109	4	n	n	PRON
ejpam-782	109	5	δ(2,1	δ(2,1	PROPN
ejpam-782	109	6	,	,	PUNCT
ejpam-782	109	7	f	f	NOUN
ejpam-782	109	8	)	)	PUNCT
ejpam-782	109	9	δ(2,1,φ	δ(2,1,φ	NOUN
ejpam-782	109	10	)	)	PUNCT
ejpam-782	109	11	−1	−1	NOUN
ejpam-782	109	12	or	or	CCONJ
ejpam-782	109	13	(	(	PUNCT
ejpam-782	109	14	δ(2,1,φ)t	δ(2,1,φ)t	X
ejpam-782	109	15	(	(	PUNCT
ejpam-782	109	16	2,1,φ	2,1,φ	NUM
ejpam-782	109	17	)	)	PUNCT
ejpam-782	109	18	)	)	PUNCT
ejpam-782	109	19	1	1	NUM
ejpam-782	109	20	δ(2,1,φ	δ(2,1,φ	NOUN
ejpam-782	109	21	)	)	PUNCT
ejpam-782	109	22	≥	≥	NOUN
ejpam-782	109	23	2(δ(2,1	2(δ(2,1	NUM
ejpam-782	109	24	,	,	PUNCT
ejpam-782	109	25	f	f	PROPN
ejpam-782	109	26	)	)	PUNCT
ejpam-782	109	27	t	t	PROPN
ejpam-782	109	28	(	(	PUNCT
ejpam-782	109	29	2,1	2,1	NUM
ejpam-782	109	30	,	,	PUNCT
ejpam-782	109	31	f	f	NOUN
ejpam-782	109	32	)	)	PUNCT
ejpam-782	109	33	)	)	PUNCT
ejpam-782	109	34	1	1	NUM
ejpam-782	109	35	δ(2,1	δ(2,1	PROPN
ejpam-782	109	36	,	,	PUNCT
ejpam-782	109	37	f	f	PROPN
ejpam-782	109	38	)	)	PUNCT
ejpam-782	109	39	lim	lim	PROPN
ejpam-782	109	40	inf	inf	PROPN
ejpam-782	109	41	n→∞	n→∞	X
ejpam-782	109	42	{	{	PUNCT
ejpam-782	109	43	(	(	PUNCT
ejpam-782	109	44	n	n	CCONJ
ejpam-782	109	45	/	/	SYM
ejpam-782	109	46	e	e	NOUN
ejpam-782	109	47	)	)	PUNCT
ejpam-782	109	48	1	1	NUM
ejpam-782	109	49	δ(2,1,φ	δ(2,1,φ	NOUN
ejpam-782	109	50	)	)	PUNCT
ejpam-782	109	51	−	−	PROPN
ejpam-782	109	52	1	1	NUM
ejpam-782	109	53	δ(2,1	δ(2,1	PROPN
ejpam-782	109	54	,	,	PUNCT
ejpam-782	109	55	f	f	PROPN
ejpam-782	109	56	)	)	PUNCT
ejpam-782	109	57	}	}	PUNCT
ejpam-782	109	58	.	.	PUNCT
ejpam-782	110	1	(	(	PUNCT
ejpam-782	110	2	9	9	X
ejpam-782	110	3	)	)	PUNCT
ejpam-782	110	4	references	reference	NOUN
ejpam-782	110	5	1068	1068	NUM
ejpam-782	110	6	from	from	ADP
ejpam-782	110	7	(	(	PUNCT
ejpam-782	110	8	7	7	X
ejpam-782	110	9	)	)	PUNCT
ejpam-782	110	10	we	we	PRON
ejpam-782	110	11	can	can	AUX
ejpam-782	110	12	obtain	obtain	VERB
ejpam-782	110	13	that	that	DET
ejpam-782	110	14	[	[	X
ejpam-782	110	15	log	log	NOUN
ejpam-782	110	16	|an|	|an|	NOUN
ejpam-782	110	17	−1	−1	NOUN
ejpam-782	110	18	/	/	SYM
ejpam-782	110	19	n]δ(2,2	n]δ(2,2	PROPN
ejpam-782	110	20	,	,	PUNCT
ejpam-782	110	21	f	f	NOUN
ejpam-782	110	22	)	)	PUNCT
ejpam-782	110	23	−1	−1	NOUN
ejpam-782	110	24	n	n	PRON
ejpam-782	110	25	≥	≥	NOUN
ejpam-782	110	26	{	{	PUNCT
ejpam-782	111	1	[	[	X
ejpam-782	111	2	log	log	NOUN
ejpam-782	111	3	2[en(φ)/µn(gn	2[en(φ)/µn(gn	NUM
ejpam-782	111	4	)	)	PUNCT
ejpam-782	111	5	]	]	PUNCT
ejpam-782	111	6	−1	−1	NOUN
ejpam-782	111	7	/	/	SYM
ejpam-782	111	8	n]δ(2,2,φ)−1	n]δ(2,2,φ)−1	NOUN
ejpam-782	111	9	n	n	CCONJ
ejpam-782	111	10	}	}	PUNCT
ejpam-782	111	11	δ(2,2	δ(2,2	PROPN
ejpam-782	111	12	,	,	PUNCT
ejpam-782	111	13	f	f	NOUN
ejpam-782	111	14	)	)	PUNCT
ejpam-782	111	15	−1	−1	NOUN
ejpam-782	112	1	δ(2,2,φ)−1	δ(2,2,φ)−1	NOUN
ejpam-782	112	2	n	n	CCONJ
ejpam-782	112	3	(	(	PUNCT
ejpam-782	112	4	δ(2,2	δ(2,2	PROPN
ejpam-782	112	5	,	,	PUNCT
ejpam-782	112	6	f	f	NOUN
ejpam-782	112	7	)	)	PUNCT
ejpam-782	112	8	−1	−1	NOUN
ejpam-782	112	9	δ(2,2,φ)−1	δ(2,2,φ)−1	NOUN
ejpam-782	112	10	)	)	PUNCT
ejpam-782	112	11	−1	−1	NOUN
ejpam-782	112	12	.	.	PUNCT
ejpam-782	113	1	applying	apply	VERB
ejpam-782	113	2	the	the	DET
ejpam-782	113	3	limit	limit	NOUN
ejpam-782	113	4	infimum	infimum	ADV
ejpam-782	113	5	and	and	CCONJ
ejpam-782	113	6	taking	take	VERB
ejpam-782	113	7	into	into	ADP
ejpam-782	113	8	account	account	NOUN
ejpam-782	113	9	the	the	DET
ejpam-782	113	10	(	(	PUNCT
ejpam-782	113	11	2,2)-type	2,2)-type	NUM
ejpam-782	113	12	coefficient	coefficient	NOUN
ejpam-782	113	13	formula	formula	NOUN
ejpam-782	113	14	for	for	ADP
ejpam-782	113	15	associate	associate	NOUN
ejpam-782	113	16	[	[	X
ejpam-782	113	17	6,thm.1,pp.181	6,thm.1,pp.181	NUM
ejpam-782	113	18	]	]	X
ejpam-782	113	19	we	we	PRON
ejpam-782	113	20	obtain	obtain	VERB
ejpam-782	113	21	(	(	PUNCT
ejpam-782	113	22	δ(2,2	δ(2,2	PROPN
ejpam-782	113	23	,	,	PUNCT
ejpam-782	113	24	f	f	NOUN
ejpam-782	113	25	)	)	PUNCT
ejpam-782	113	26	−	−	PROPN
ejpam-782	113	27	1)δ(2,2	1)δ(2,2	NUM
ejpam-782	113	28	,	,	PUNCT
ejpam-782	113	29	f	f	NOUN
ejpam-782	113	30	)	)	PUNCT
ejpam-782	113	31	−1	−1	NOUN
ejpam-782	113	32	δ(2,2	δ(2,2	PROPN
ejpam-782	113	33	,	,	PUNCT
ejpam-782	113	34	f	f	NOUN
ejpam-782	113	35	)	)	PUNCT
ejpam-782	113	36	δ(2,2	δ(2,2	PROPN
ejpam-782	113	37	,	,	PUNCT
ejpam-782	113	38	f	f	PROPN
ejpam-782	113	39	)	)	PUNCT
ejpam-782	113	40	.	.	PUNCT
ejpam-782	114	1	1	1	NUM
ejpam-782	114	2	t	t	PROPN
ejpam-782	114	3	(	(	PUNCT
ejpam-782	114	4	2,2	2,2	NUM
ejpam-782	114	5	,	,	PUNCT
ejpam-782	114	6	f	f	PROPN
ejpam-782	114	7	)	)	PUNCT
ejpam-782	114	8	≥	≥	NOUN
ejpam-782	114	9	[	[	PUNCT
ejpam-782	114	10	(	(	PUNCT
ejpam-782	114	11	δ(2,2,φ)−	δ(2,2,φ)−	PROPN
ejpam-782	114	12	1)δ(2,2,φ)−1	1)δ(2,2,φ)−1	NUM
ejpam-782	114	13	δ(2,2,φ)δ(2,2,φ	δ(2,2,φ)δ(2,2,φ	PROPN
ejpam-782	114	14	)	)	PUNCT
ejpam-782	114	15	.	.	PUNCT
ejpam-782	115	1	1	1	NUM
ejpam-782	115	2	t	t	NOUN
ejpam-782	115	3	(	(	PUNCT
ejpam-782	115	4	2,2,φ	2,2,φ	NUM
ejpam-782	115	5	)	)	PUNCT
ejpam-782	115	6	]	]	PUNCT
ejpam-782	116	1	δ(2,2	δ(2,2	PROPN
ejpam-782	116	2	,	,	PUNCT
ejpam-782	116	3	f	f	NOUN
ejpam-782	116	4	)	)	PUNCT
ejpam-782	116	5	−1	−1	NOUN
ejpam-782	116	6	δ(2,2,φ)−1	δ(2,2,φ)−1	NOUN
ejpam-782	116	7	.	.	PUNCT
ejpam-782	117	1	lim	lim	PROPN
ejpam-782	117	2	inf	inf	PROPN
ejpam-782	117	3	n→∞	n→∞	X
ejpam-782	117	4	n	n	PROPN
ejpam-782	117	5	(	(	PUNCT
ejpam-782	117	6	δ(2,2	δ(2,2	PROPN
ejpam-782	117	7	,	,	PUNCT
ejpam-782	117	8	f	f	NOUN
ejpam-782	117	9	)	)	PUNCT
ejpam-782	117	10	−1	−1	NOUN
ejpam-782	117	11	δ(2,2,φ)−1	δ(2,2,φ)−1	NOUN
ejpam-782	117	12	−1	−1	NOUN
ejpam-782	117	13	)	)	PUNCT
ejpam-782	117	14	or	or	CCONJ
ejpam-782	117	15	(	(	PUNCT
ejpam-782	117	16	t	t	PROPN
ejpam-782	117	17	(	(	PUNCT
ejpam-782	117	18	2,2,φ	2,2,φ	NUM
ejpam-782	117	19	)	)	PUNCT
ejpam-782	117	20	)	)	PUNCT
ejpam-782	118	1	1	1	NUM
ejpam-782	118	2	δ(2,2,φ)−1	δ(2,2,φ)−1	NOUN
ejpam-782	118	3	≥	≥	NOUN
ejpam-782	118	4	(	(	PUNCT
ejpam-782	118	5	δ(2,2,φ)−	δ(2,2,φ)−	PROPN
ejpam-782	118	6	1	1	NUM
ejpam-782	118	7	δ(2,2	δ(2,2	PROPN
ejpam-782	118	8	,	,	PUNCT
ejpam-782	118	9	f	f	NOUN
ejpam-782	118	10	)	)	PUNCT
ejpam-782	118	11	−	−	PROPN
ejpam-782	118	12	1	1	NUM
ejpam-782	118	13	)	)	PUNCT
ejpam-782	118	14	(	(	PUNCT
ejpam-782	118	15	δ(2,2	δ(2,2	PROPN
ejpam-782	118	16	,	,	PUNCT
ejpam-782	118	17	f	f	NOUN
ejpam-782	118	18	)	)	PUNCT
ejpam-782	118	19	)	)	PUNCT
ejpam-782	118	20	δ(2,2	δ(2,2	PROPN
ejpam-782	118	21	,	,	PUNCT
ejpam-782	118	22	f	f	NOUN
ejpam-782	118	23	)	)	PUNCT
ejpam-782	118	24	/(δ(2,2	/(δ(2,2	PROPN
ejpam-782	118	25	,	,	PUNCT
ejpam-782	118	26	f	f	NOUN
ejpam-782	118	27	)	)	PUNCT
ejpam-782	118	28	−1	−1	NOUN
ejpam-782	118	29	)	)	PUNCT
ejpam-782	118	30	(	(	PUNCT
ejpam-782	118	31	δ(2,2,φ))δ(2,2,φ)/(δ(2,2,φ)−1	δ(2,2,φ))δ(2,2,φ)/(δ(2,2,φ)−1	NOUN
ejpam-782	118	32	)	)	PUNCT
ejpam-782	118	33	(	(	PUNCT
ejpam-782	118	34	t	t	PROPN
ejpam-782	118	35	(	(	PUNCT
ejpam-782	118	36	2,2	2,2	NUM
ejpam-782	118	37	,	,	PUNCT
ejpam-782	118	38	f	f	NOUN
ejpam-782	118	39	)	)	PUNCT
ejpam-782	118	40	)	)	PUNCT
ejpam-782	118	41	1	1	NUM
ejpam-782	118	42	δ(2,2	δ(2,2	PROPN
ejpam-782	118	43	,	,	PUNCT
ejpam-782	118	44	f	f	NOUN
ejpam-782	118	45	)	)	PUNCT
ejpam-782	118	46	−1	−1	NOUN
ejpam-782	118	47	.	.	PUNCT
ejpam-782	119	1	lim	lim	PROPN
ejpam-782	119	2	inf	inf	PROPN
ejpam-782	119	3	n→∞	n→∞	X
ejpam-782	119	4	n	n	CCONJ
ejpam-782	119	5	(	(	PUNCT
ejpam-782	119	6	1	1	NUM
ejpam-782	119	7	δ(2,2,φ)−1	δ(2,2,φ)−1	NOUN
ejpam-782	119	8	−	−	NOUN
ejpam-782	119	9	1	1	NUM
ejpam-782	119	10	δ(2,2	δ(2,2	PROPN
ejpam-782	119	11	,	,	PUNCT
ejpam-782	119	12	f	f	NOUN
ejpam-782	119	13	)	)	PUNCT
ejpam-782	119	14	−1	−1	NOUN
ejpam-782	119	15	)	)	PUNCT
ejpam-782	119	16	.	.	PUNCT
ejpam-782	120	1	(	(	PUNCT
ejpam-782	120	2	10	10	NUM
ejpam-782	120	3	)	)	PUNCT
ejpam-782	120	4	hence	hence	ADV
ejpam-782	120	5	for	for	ADP
ejpam-782	120	6	(	(	PUNCT
ejpam-782	120	7	p	p	X
ejpam-782	120	8	,	,	PUNCT
ejpam-782	120	9	q	q	NOUN
ejpam-782	120	10	)	)	PUNCT
ejpam-782	120	11	=	=	SYM
ejpam-782	120	12	(	(	PUNCT
ejpam-782	120	13	2,2	2,2	NUM
ejpam-782	120	14	)	)	PUNCT
ejpam-782	120	15	the	the	DET
ejpam-782	120	16	proof	proof	NOUN
ejpam-782	120	17	is	be	AUX
ejpam-782	120	18	completed	complete	VERB
ejpam-782	120	19	.	.	PUNCT
ejpam-782	121	1	now	now	ADV
ejpam-782	121	2	for	for	ADP
ejpam-782	121	3	3	3	NUM
ejpam-782	121	4	≤	≤	NOUN
ejpam-782	121	5	p	p	NOUN
ejpam-782	122	1	=	=	X
ejpam-782	122	2	q	q	X
ejpam-782	122	3	<	<	X
ejpam-782	122	4	0	0	NUM
ejpam-782	122	5	we	we	PRON
ejpam-782	122	6	can	can	AUX
ejpam-782	122	7	easily	easily	ADV
ejpam-782	122	8	obtain	obtain	VERB
ejpam-782	122	9	from	from	ADP
ejpam-782	122	10	(	(	PUNCT
ejpam-782	122	11	7	7	NUM
ejpam-782	122	12	)	)	PUNCT
ejpam-782	122	13	that	that	PRON
ejpam-782	123	1	[	[	X
ejpam-782	123	2	log[q−1	log[q−1	X
ejpam-782	123	3	]	]	X
ejpam-782	123	4	|	|	ADV
ejpam-782	123	5	an	an	DET
ejpam-782	123	6	|	|	NOUN
ejpam-782	123	7	−1	−1	NOUN
ejpam-782	123	8	/	/	SYM
ejpam-782	123	9	n]δ(p	n]δ(p	PROPN
ejpam-782	123	10	,	,	PUNCT
ejpam-782	123	11	q	q	NOUN
ejpam-782	123	12	,	,	PUNCT
ejpam-782	123	13	f	f	PROPN
ejpam-782	123	14	)	)	PUNCT
ejpam-782	123	15	log[p−2	log[p−2	NOUN
ejpam-782	123	16	]	]	PUNCT
ejpam-782	124	1	n	n	CCONJ
ejpam-782	124	2	≥	≥	PRON
ejpam-782	124	3	{	{	PUNCT
ejpam-782	124	4	[	[	X
ejpam-782	124	5	log[q−1][en(φ)/µ(rn	log[q−1][en(φ)/µ(rn	X
ejpam-782	124	6	)	)	PUNCT
ejpam-782	124	7	]	]	PUNCT
ejpam-782	124	8	−1	−1	NOUN
ejpam-782	124	9	/	/	SYM
ejpam-782	124	10	n	n	CCONJ
ejpam-782	124	11	]	]	X
ejpam-782	124	12	δ(p	δ(p	X
ejpam-782	124	13	,	,	PUNCT
ejpam-782	124	14	q	q	NOUN
ejpam-782	124	15	,	,	PUNCT
ejpam-782	124	16	φ	φ	NOUN
ejpam-782	124	17	)	)	PUNCT
ejpam-782	124	18	log[p−2	log[p−2	NOUN
ejpam-782	124	19	]	]	PUNCT
ejpam-782	124	20	n	n	CCONJ
ejpam-782	124	21	}	}	PUNCT
ejpam-782	124	22	δ(p	δ(p	PROPN
ejpam-782	124	23	,	,	PUNCT
ejpam-782	124	24	q	q	NOUN
ejpam-782	124	25	,	,	PUNCT
ejpam-782	124	26	f	f	PROPN
ejpam-782	124	27	)	)	PUNCT
ejpam-782	124	28	δ(p	δ(p	PROPN
ejpam-782	124	29	,	,	PUNCT
ejpam-782	124	30	q	q	NOUN
ejpam-782	124	31	,	,	PUNCT
ejpam-782	124	32	φ	φ	NUM
ejpam-782	124	33	)	)	PUNCT
ejpam-782	124	34	.(log[p−2	.(log[p−2	NUM
ejpam-782	124	35	]	]	PUNCT
ejpam-782	124	36	n	n	CCONJ
ejpam-782	124	37	)	)	PUNCT
ejpam-782	124	38	δ(p	δ(p	PROPN
ejpam-782	124	39	,	,	PUNCT
ejpam-782	124	40	q	q	NOUN
ejpam-782	124	41	,	,	PUNCT
ejpam-782	124	42	f	f	PROPN
ejpam-782	124	43	)	)	PUNCT
ejpam-782	124	44	δ(p	δ(p	PROPN
ejpam-782	124	45	,	,	PUNCT
ejpam-782	124	46	q	q	NOUN
ejpam-782	124	47	,	,	PUNCT
ejpam-782	124	48	φ	φ	NUM
ejpam-782	124	49	)	)	PUNCT
ejpam-782	124	50	−1	−1	NOUN
ejpam-782	124	51	.	.	PUNCT
ejpam-782	125	1	proceeding	proceed	VERB
ejpam-782	125	2	to	to	PART
ejpam-782	125	3	limit	limit	VERB
ejpam-782	125	4	infimum	infimum	ADV
ejpam-782	125	5	as	as	ADP
ejpam-782	125	6	n→∞	n→∞	NUM
ejpam-782	125	7	and	and	CCONJ
ejpam-782	125	8	the	the	DET
ejpam-782	125	9	(	(	PUNCT
ejpam-782	125	10	p	p	X
ejpam-782	125	11	,	,	PUNCT
ejpam-782	125	12	q	q	NOUN
ejpam-782	125	13	)	)	PUNCT
ejpam-782	125	14	type	type	NOUN
ejpam-782	125	15	coefficient	coefficient	NOUN
ejpam-782	125	16	formula	formula	NOUN
ejpam-782	125	17	for	for	ADP
ejpam-782	125	18	associate	associate	NOUN
ejpam-782	125	19	[	[	X
ejpam-782	125	20	6	6	NUM
ejpam-782	125	21	,	,	PUNCT
ejpam-782	125	22	thm.1,pp.181	thm.1,pp.181	PROPN
ejpam-782	125	23	]	]	PUNCT
ejpam-782	125	24	taking	take	VERB
ejpam-782	125	25	into	into	ADP
ejpam-782	125	26	account	account	NOUN
ejpam-782	125	27	we	we	PRON
ejpam-782	125	28	obtain	obtain	VERB
ejpam-782	125	29	(	(	PUNCT
ejpam-782	125	30	1	1	NUM
ejpam-782	125	31	t	t	NOUN
ejpam-782	125	32	(	(	PUNCT
ejpam-782	125	33	p	p	X
ejpam-782	125	34	,	,	PUNCT
ejpam-782	125	35	q	q	NOUN
ejpam-782	125	36	,	,	PUNCT
ejpam-782	125	37	f	f	PROPN
ejpam-782	125	38	)	)	PUNCT
ejpam-782	125	39	)	)	PUNCT
ejpam-782	125	40	1	1	NUM
ejpam-782	125	41	δ(p	δ(p	X
ejpam-782	125	42	,	,	PUNCT
ejpam-782	125	43	q	q	NOUN
ejpam-782	125	44	,	,	PUNCT
ejpam-782	125	45	f	f	PROPN
ejpam-782	125	46	)	)	PUNCT
ejpam-782	125	47	≥	≥	PROPN
ejpam-782	125	48	(	(	PUNCT
ejpam-782	125	49	1	1	NUM
ejpam-782	125	50	t	t	NOUN
ejpam-782	125	51	(	(	PUNCT
ejpam-782	125	52	p	p	X
ejpam-782	125	53	,	,	PUNCT
ejpam-782	125	54	q	q	X
ejpam-782	125	55	,	,	PUNCT
ejpam-782	125	56	φ	φ	NUM
ejpam-782	125	57	)	)	PUNCT
ejpam-782	125	58	)	)	PUNCT
ejpam-782	125	59	1	1	NUM
ejpam-782	125	60	δ(p	δ(p	X
ejpam-782	125	61	,	,	PUNCT
ejpam-782	125	62	q	q	NOUN
ejpam-782	125	63	,	,	PUNCT
ejpam-782	125	64	φ	φ	NUM
ejpam-782	125	65	)	)	PUNCT
ejpam-782	125	66	lim	lim	PROPN
ejpam-782	125	67	inf	inf	PROPN
ejpam-782	125	68	n→∞	n→∞	X
ejpam-782	125	69	(	(	PUNCT
ejpam-782	125	70	log[p−2	log[p−2	NOUN
ejpam-782	125	71	]	]	PUNCT
ejpam-782	125	72	n	n	CCONJ
ejpam-782	125	73	)	)	PUNCT
ejpam-782	125	74	(	(	PUNCT
ejpam-782	125	75	1	1	NUM
ejpam-782	125	76	δ(p	δ(p	X
ejpam-782	125	77	,	,	PUNCT
ejpam-782	125	78	q	q	NOUN
ejpam-782	125	79	,	,	PUNCT
ejpam-782	125	80	φ	φ	NUM
ejpam-782	125	81	)	)	PUNCT
ejpam-782	125	82	−	−	PROPN
ejpam-782	125	83	1	1	NUM
ejpam-782	125	84	δ(p	δ(p	PROPN
ejpam-782	125	85	,	,	PUNCT
ejpam-782	125	86	q	q	NOUN
ejpam-782	125	87	,	,	PUNCT
ejpam-782	125	88	f	f	PROPN
ejpam-782	125	89	)	)	PUNCT
ejpam-782	125	90	)	)	PUNCT
ejpam-782	125	91	or	or	CCONJ
ejpam-782	125	92	t	t	PROPN
ejpam-782	125	93	(	(	PUNCT
ejpam-782	125	94	p	p	X
ejpam-782	125	95	,	,	PUNCT
ejpam-782	125	96	q	q	X
ejpam-782	125	97	,	,	PUNCT
ejpam-782	125	98	φ	φ	NUM
ejpam-782	125	99	)	)	PUNCT
ejpam-782	125	100	1	1	NUM
ejpam-782	125	101	δ(p	δ(p	X
ejpam-782	125	102	,	,	PUNCT
ejpam-782	125	103	q	q	NOUN
ejpam-782	125	104	,	,	PUNCT
ejpam-782	125	105	φ	φ	NUM
ejpam-782	125	106	)	)	PUNCT
ejpam-782	125	107	≥	≥	PROPN
ejpam-782	125	108	t	t	PROPN
ejpam-782	125	109	(	(	PUNCT
ejpam-782	125	110	p	p	X
ejpam-782	125	111	,	,	PUNCT
ejpam-782	125	112	q	q	NOUN
ejpam-782	125	113	,	,	PUNCT
ejpam-782	125	114	f	f	PROPN
ejpam-782	125	115	)	)	PUNCT
ejpam-782	125	116	1	1	NUM
ejpam-782	125	117	δ(p	δ(p	X
ejpam-782	125	118	,	,	PUNCT
ejpam-782	125	119	q	q	NOUN
ejpam-782	125	120	,	,	PUNCT
ejpam-782	125	121	f	f	PROPN
ejpam-782	125	122	)	)	PUNCT
ejpam-782	126	1	lim	lim	PROPN
ejpam-782	126	2	inf	inf	PROPN
ejpam-782	126	3	n→∞	n→∞	X
ejpam-782	126	4	(	(	PUNCT
ejpam-782	126	5	log[p−2	log[p−2	NOUN
ejpam-782	126	6	]	]	PUNCT
ejpam-782	126	7	n	n	CCONJ
ejpam-782	126	8	)	)	PUNCT
ejpam-782	126	9	(	(	PUNCT
ejpam-782	126	10	1	1	NUM
ejpam-782	126	11	δ(p	δ(p	X
ejpam-782	126	12	,	,	PUNCT
ejpam-782	126	13	q	q	NOUN
ejpam-782	126	14	,	,	PUNCT
ejpam-782	126	15	φ	φ	NUM
ejpam-782	126	16	)	)	PUNCT
ejpam-782	126	17	−	−	PROPN
ejpam-782	126	18	1	1	NUM
ejpam-782	126	19	δ(p	δ(p	PROPN
ejpam-782	126	20	,	,	PUNCT
ejpam-782	126	21	q	q	NOUN
ejpam-782	126	22	,	,	PUNCT
ejpam-782	126	23	f	f	PROPN
ejpam-782	126	24	)	)	PUNCT
ejpam-782	126	25	)	)	PUNCT
ejpam-782	126	26	.	.	PUNCT
ejpam-782	127	1	(	(	PUNCT
ejpam-782	127	2	11	11	X
ejpam-782	127	3	)	)	PUNCT
ejpam-782	127	4	combining	combine	VERB
ejpam-782	127	5	(	(	PUNCT
ejpam-782	127	6	9),(10	9),(10	NUM
ejpam-782	127	7	)	)	PUNCT
ejpam-782	127	8	and	and	CCONJ
ejpam-782	127	9	(	(	PUNCT
ejpam-782	127	10	11	11	X
ejpam-782	127	11	)	)	PUNCT
ejpam-782	127	12	we	we	PRON
ejpam-782	127	13	get	get	VERB
ejpam-782	127	14	the	the	DET
ejpam-782	127	15	required	require	VERB
ejpam-782	127	16	result	result	NOUN
ejpam-782	127	17	i.e.	i.e.	X
ejpam-782	127	18	,	,	PUNCT
ejpam-782	127	19	(	(	PUNCT
ejpam-782	127	20	i	i	NOUN
ejpam-782	127	21	)	)	PUNCT
ejpam-782	127	22	.	.	PUNCT
ejpam-782	128	1	(	(	PUNCT
ejpam-782	128	2	ii	ii	NOUN
ejpam-782	128	3	)	)	PUNCT
ejpam-782	128	4	following	follow	VERB
ejpam-782	128	5	the	the	DET
ejpam-782	128	6	lines	line	NOUN
ejpam-782	128	7	of	of	ADP
ejpam-782	128	8	proof	proof	NOUN
ejpam-782	128	9	of	of	ADP
ejpam-782	128	10	(	(	PUNCT
ejpam-782	128	11	i	i	NOUN
ejpam-782	128	12	)	)	PUNCT
ejpam-782	128	13	with	with	ADP
ejpam-782	128	14	equation	equation	NOUN
ejpam-782	128	15	(	(	PUNCT
ejpam-782	128	16	8)	8)	NUM
ejpam-782	128	17	the	the	DET
ejpam-782	128	18	result	result	NOUN
ejpam-782	128	19	(	(	PUNCT
ejpam-782	128	20	ii	ii	NOUN
ejpam-782	128	21	)	)	PUNCT
ejpam-782	128	22	can	can	AUX
ejpam-782	128	23	be	be	AUX
ejpam-782	128	24	prove	prove	VERB
ejpam-782	128	25	easily	easily	ADV
ejpam-782	128	26	.	.	PUNCT
ejpam-782	129	1	hence	hence	ADV
ejpam-782	129	2	the	the	DET
ejpam-782	129	3	proof	proof	NOUN
ejpam-782	129	4	is	be	AUX
ejpam-782	129	5	left	leave	VERB
ejpam-782	129	6	for	for	ADP
ejpam-782	129	7	the	the	DET
ejpam-782	129	8	reader	reader	NOUN
ejpam-782	129	9	.	.	PUNCT
ejpam-782	130	1	references	reference	NOUN
ejpam-782	130	2	[	[	X
ejpam-782	130	3	1	1	X
ejpam-782	130	4	]	]	PUNCT
ejpam-782	130	5	s.	s.	PROPN
ejpam-782	130	6	bergman	bergman	PROPN
ejpam-782	130	7	,	,	PUNCT
ejpam-782	130	8	integral	integral	ADJ
ejpam-782	130	9	operators	operator	NOUN
ejpam-782	130	10	in	in	ADP
ejpam-782	130	11	the	the	DET
ejpam-782	130	12	theory	theory	NOUN
ejpam-782	130	13	of	of	ADP
ejpam-782	130	14	linear	linear	ADJ
ejpam-782	130	15	partial	partial	ADJ
ejpam-782	130	16	differential	differential	NOUN
ejpam-782	130	17	equations	equation	NOUN
ejpam-782	130	18	,	,	PUNCT
ejpam-782	130	19	ergebnisse	ergebnisse	PROPN
ejpam-782	130	20	der	der	PROPN
ejpam-782	130	21	mathematik	mathematik	PROPN
ejpam-782	130	22	und	und	VERB
ejpam-782	130	23	ihrer	ihrer	PROPN
ejpam-782	130	24	grenzgebiete	grenzgebiete	NOUN
ejpam-782	130	25	,	,	PUNCT
ejpam-782	130	26	band	band	NOUN
ejpam-782	130	27	23	23	NUM
ejpam-782	130	28	,	,	PUNCT
ejpam-782	130	29	springer	springer	NOUN
ejpam-782	130	30	-	-	PUNCT
ejpam-782	130	31	verlag	verlag	PROPN
ejpam-782	130	32	,	,	PUNCT
ejpam-782	130	33	new	new	ADJ
ejpam-782	130	34	yok	yok	PROPN
ejpam-782	130	35	,	,	PUNCT
ejpam-782	130	36	1969	1969	NUM
ejpam-782	130	37	.	.	PUNCT
ejpam-782	131	1	references	reference	NOUN
ejpam-782	131	2	1069	1069	NUM
ejpam-782	131	3	[	[	X
ejpam-782	131	4	2	2	NUM
ejpam-782	131	5	]	]	X
ejpam-782	131	6	r.p	r.p	PROPN
ejpam-782	131	7	.	.	PROPN
ejpam-782	131	8	gilbert	gilbert	PROPN
ejpam-782	131	9	,	,	PUNCT
ejpam-782	131	10	function	function	VERB
ejpam-782	131	11	theoretic	theoretic	ADJ
ejpam-782	131	12	methods	method	NOUN
ejpam-782	131	13	in	in	ADP
ejpam-782	131	14	partial	partial	ADJ
ejpam-782	131	15	differential	differential	NOUN
ejpam-782	131	16	equations	equation	NOUN
ejpam-782	131	17	,	,	PUNCT
ejpam-782	131	18	math	math	NOUN
ejpam-782	131	19	.	.	PUNCT
ejpam-782	132	1	in	in	ADP
ejpam-782	132	2	science	science	NOUN
ejpam-782	132	3	and	and	CCONJ
ejpam-782	132	4	engineering	engineering	NOUN
ejpam-782	132	5	vol.54	vol.54	PROPN
ejpam-782	132	6	,	,	PUNCT
ejpam-782	132	7	academic	academic	ADJ
ejpam-782	132	8	press	press	NOUN
ejpam-782	132	9	,	,	PUNCT
ejpam-782	132	10	new	new	PROPN
ejpam-782	132	11	york	york	PROPN
ejpam-782	132	12	,	,	PUNCT
ejpam-782	132	13	1969	1969	NUM
ejpam-782	132	14	.	.	PUNCT
ejpam-782	133	1	[	[	X
ejpam-782	133	2	3	3	X
ejpam-782	133	3	]	]	X
ejpam-782	133	4	r.p	r.p	PROPN
ejpam-782	133	5	.	.	PROPN
ejpam-782	133	6	gilbert	gilbert	PROPN
ejpam-782	133	7	and	and	CCONJ
ejpam-782	133	8	d.l	d.l	PROPN
ejpam-782	133	9	.	.	PROPN
ejpam-782	133	10	colton	colton	PROPN
ejpam-782	133	11	,	,	PUNCT
ejpam-782	133	12	integral	integral	ADJ
ejpam-782	133	13	operator	operator	NOUN
ejpam-782	133	14	methods	method	NOUN
ejpam-782	133	15	in	in	ADP
ejpam-782	133	16	biaxially	biaxially	ADV
ejpam-782	133	17	symmetric	symmetric	ADJ
ejpam-782	133	18	potential	potential	ADJ
ejpam-782	133	19	theory	theory	NOUN
ejpam-782	133	20	,	,	PUNCT
ejpam-782	133	21	contrib	contrib	PROPN
ejpam-782	133	22	.	.	PROPN
ejpam-782	133	23	differential	differential	PROPN
ejpam-782	133	24	equations	equation	NOUN
ejpam-782	133	25	2	2	NUM
ejpam-782	133	26	,	,	PUNCT
ejpam-782	133	27	441	441	NUM
ejpam-782	133	28	-	-	NUM
ejpam-782	133	29	456	456	NUM
ejpam-782	133	30	.	.	PUNCT
ejpam-782	134	1	1963	1963	NUM
ejpam-782	135	1	[	[	X
ejpam-782	135	2	4	4	X
ejpam-782	135	3	]	]	X
ejpam-782	135	4	r.p	r.p	PROPN
ejpam-782	135	5	.	.	PROPN
ejpam-782	135	6	gilbert	gilbert	PROPN
ejpam-782	135	7	and	and	CCONJ
ejpam-782	135	8	d.l	d.l	PROPN
ejpam-782	135	9	.	.	PROPN
ejpam-782	135	10	colton	colton	PROPN
ejpam-782	135	11	,	,	PUNCT
ejpam-782	135	12	singularities	singularity	NOUN
ejpam-782	135	13	of	of	ADP
ejpam-782	135	14	solutions	solution	NOUN
ejpam-782	135	15	to	to	ADP
ejpam-782	135	16	elliptic	elliptic	ADJ
ejpam-782	135	17	partial	partial	ADJ
ejpam-782	135	18	differential	differential	NOUN
ejpam-782	135	19	equations	equation	NOUN
ejpam-782	135	20	,	,	PUNCT
ejpam-782	135	21	quarterly	quarterly	PROPN
ejpam-782	135	22	j.	j.	PROPN
ejpam-782	135	23	math	math	PROPN
ejpam-782	135	24	.	.	PUNCT
ejpam-782	136	1	19	19	NUM
ejpam-782	136	2	,	,	PUNCT
ejpam-782	136	3	391	391	NUM
ejpam-782	136	4	-	-	SYM
ejpam-782	136	5	396	396	NUM
ejpam-782	136	6	.	.	PUNCT
ejpam-782	137	1	1968	1968	NUM
ejpam-782	138	1	[	[	X
ejpam-782	138	2	5	5	NUM
ejpam-782	138	3	]	]	X
ejpam-782	138	4	o.p	o.p	PROPN
ejpam-782	138	5	.	.	PROPN
ejpam-782	138	6	juneja	juneja	PROPN
ejpam-782	138	7	,	,	PUNCT
ejpam-782	138	8	g.p.kapoor	g.p.kapoor	NOUN
ejpam-782	138	9	and	and	CCONJ
ejpam-782	138	10	s.k	s.k	PROPN
ejpam-782	138	11	.	.	PROPN
ejpam-782	138	12	bajpai	bajpai	PROPN
ejpam-782	138	13	,	,	PUNCT
ejpam-782	138	14	on	on	ADP
ejpam-782	138	15	the	the	DET
ejpam-782	138	16	(	(	PUNCT
ejpam-782	138	17	p	p	NOUN
ejpam-782	138	18	,	,	PUNCT
ejpam-782	138	19	q)-order	q)-order	PUNCT
ejpam-782	138	20	and	and	CCONJ
ejpam-782	138	21	lower	low	ADJ
ejpam-782	138	22	(	(	PUNCT
ejpam-782	138	23	p	p	NOUN
ejpam-782	138	24	,	,	PUNCT
ejpam-782	138	25	q)-order	q)-order	NOUN
ejpam-782	138	26	of	of	ADP
ejpam-782	138	27	an	an	DET
ejpam-782	138	28	entire	entire	ADJ
ejpam-782	138	29	function	function	NOUN
ejpam-782	138	30	,	,	PUNCT
ejpam-782	138	31	j.reine	j.reine	PROPN
ejpam-782	138	32	angew	angew	PROPN
ejpam-782	138	33	.	.	PUNCT
ejpam-782	138	34	math	math	NOUN
ejpam-782	138	35	.	.	PUNCT
ejpam-782	139	1	282	282	NUM
ejpam-782	139	2	,	,	PUNCT
ejpam-782	139	3	53	53	NUM
ejpam-782	139	4	-	-	SYM
ejpam-782	139	5	67	67	NUM
ejpam-782	139	6	.	.	PUNCT
ejpam-782	139	7	1976	1976	NUM
ejpam-782	139	8	.	.	PUNCT
ejpam-782	140	1	[	[	X
ejpam-782	140	2	6	6	NUM
ejpam-782	140	3	]	]	X
ejpam-782	140	4	o.p.juneja	o.p.juneja	NOUN
ejpam-782	140	5	,	,	PUNCT
ejpam-782	140	6	g.p.kapoor	g.p.kapoor	NOUN
ejpam-782	140	7	and	and	CCONJ
ejpam-782	140	8	s.k.bajpai	s.k.bajpai	NOUN
ejpam-782	140	9	,	,	PUNCT
ejpam-782	140	10	on	on	ADP
ejpam-782	140	11	the	the	DET
ejpam-782	140	12	(	(	PUNCT
ejpam-782	140	13	p	p	X
ejpam-782	140	14	,	,	PUNCT
ejpam-782	140	15	q	q	NOUN
ejpam-782	140	16	)	)	PUNCT
ejpam-782	140	17	type	type	NOUN
ejpam-782	140	18	and	and	CCONJ
ejpam-782	140	19	lower(p	lower(p	VERB
ejpam-782	140	20	,	,	PUNCT
ejpam-782	140	21	q)-type	q)-type	PUNCT
ejpam-782	140	22	of	of	ADP
ejpam-782	140	23	an	an	DET
ejpam-782	140	24	entire	entire	ADJ
ejpam-782	140	25	function	function	NOUN
ejpam-782	140	26	,	,	PUNCT
ejpam-782	140	27	j.reine	j.reine	PROPN
ejpam-782	140	28	angrew	angrew	PROPN
ejpam-782	140	29	.	.	PUNCT
ejpam-782	141	1	math	math	NOUN
ejpam-782	141	2	.	.	PUNCT
ejpam-782	142	1	290	290	NUM
ejpam-782	142	2	,	,	PUNCT
ejpam-782	142	3	180	180	NUM
ejpam-782	142	4	-	-	SYM
ejpam-782	142	5	190	190	NUM
ejpam-782	142	6	.	.	PUNCT
ejpam-782	142	7	1977	1977	NUM
ejpam-782	142	8	.	.	PUNCT
ejpam-782	143	1	[	[	X
ejpam-782	143	2	7	7	X
ejpam-782	143	3	]	]	X
ejpam-782	143	4	e.o.kreyszig	e.o.kreyszig	NOUN
ejpam-782	143	5	and	and	CCONJ
ejpam-782	143	6	m.kracht	m.kracht	NOUN
ejpam-782	143	7	,	,	PUNCT
ejpam-782	143	8	methods	method	NOUN
ejpam-782	143	9	of	of	ADP
ejpam-782	143	10	complex	complex	ADJ
ejpam-782	143	11	analysis	analysis	NOUN
ejpam-782	143	12	in	in	ADP
ejpam-782	143	13	partial	partial	ADJ
ejpam-782	143	14	differential	differential	ADJ
ejpam-782	143	15	equations	equation	NOUN
ejpam-782	143	16	with	with	ADP
ejpam-782	143	17	applications	application	NOUN
ejpam-782	143	18	,	,	PUNCT
ejpam-782	143	19	canadian	canadian	ADJ
ejpam-782	143	20	math	math	NOUN
ejpam-782	143	21	.	.	PUNCT
ejpam-782	144	1	soc	soc	PROPN
ejpam-782	144	2	.	.	PUNCT
ejpam-782	145	1	series	series	PROPN
ejpam-782	145	2	of	of	ADP
ejpam-782	145	3	monographs	monographs	PROPN
ejpam-782	145	4	adv	adv	PROPN
ejpam-782	145	5	.	.	PUNCT
ejpam-782	146	1	texts	texts	PROPN
ejpam-782	146	2	john	john	PROPN
ejpam-782	146	3	wiley	wiley	PROPN
ejpam-782	146	4	and	and	CCONJ
ejpam-782	146	5	sons	son	NOUN
ejpam-782	146	6	,	,	PUNCT
ejpam-782	146	7	new	new	PROPN
ejpam-782	146	8	york	york	PROPN
ejpam-782	146	9	,	,	PUNCT
ejpam-782	146	10	1988	1988	NUM
ejpam-782	146	11	.	.	PUNCT
ejpam-782	147	1	[	[	X
ejpam-782	147	2	8	8	NUM
ejpam-782	147	3	]	]	X
ejpam-782	147	4	p.a	p.a	PROPN
ejpam-782	147	5	.	.	PROPN
ejpam-782	147	6	mccoy	mccoy	PROPN
ejpam-782	147	7	,	,	PUNCT
ejpam-782	147	8	polynomial	polynomial	ADJ
ejpam-782	147	9	approximation	approximation	NOUN
ejpam-782	147	10	and	and	CCONJ
ejpam-782	147	11	growth	growth	NOUN
ejpam-782	147	12	of	of	ADP
ejpam-782	147	13	generalized	generalized	ADJ
ejpam-782	147	14	axisymmetric	axisymmetric	ADJ
ejpam-782	147	15	potentials	potential	NOUN
ejpam-782	147	16	,	,	PUNCT
ejpam-782	147	17	canadian	canadian	PROPN
ejpam-782	147	18	j.	j.	PROPN
ejpam-782	147	19	math	math	PROPN
ejpam-782	147	20	.	.	PUNCT
ejpam-782	148	1	xxxi	xxxi	PROPN
ejpam-782	148	2	,	,	PUNCT
ejpam-782	148	3	1	1	NUM
ejpam-782	148	4	(	(	PUNCT
ejpam-782	148	5	1579	1579	NUM
ejpam-782	148	6	)	)	PUNCT
ejpam-782	148	7	,	,	PUNCT
ejpam-782	148	8	49	49	NUM
ejpam-782	148	9	-	-	SYM
ejpam-782	148	10	59	59	NUM
ejpam-782	148	11	.	.	PUNCT
ejpam-782	149	1	[	[	X
ejpam-782	149	2	9	9	NUM
ejpam-782	149	3	]	]	X
ejpam-782	149	4	p.a.mccoy	p.a.mccoy	ADJ
ejpam-782	149	5	,	,	PUNCT
ejpam-782	149	6	solutions	solution	NOUN
ejpam-782	149	7	of	of	ADP
ejpam-782	149	8	the	the	DET
ejpam-782	149	9	helmholtz	helmholtz	NOUN
ejpam-782	149	10	equation	equation	NOUN
ejpam-782	149	11	having	have	VERB
ejpam-782	149	12	rapid	rapid	ADJ
ejpam-782	149	13	growth	growth	NOUN
ejpam-782	149	14	,	,	PUNCT
ejpam-782	149	15	complex	complex	ADJ
ejpam-782	149	16	variables	variable	NOUN
ejpam-782	149	17	and	and	CCONJ
ejpam-782	149	18	elliptic	elliptic	ADJ
ejpam-782	149	19	equations	equation	NOUN
ejpam-782	149	20	,	,	PUNCT
ejpam-782	149	21	18,1	18,1	NUM
ejpam-782	149	22	,	,	PUNCT
ejpam-782	149	23	91	91	NUM
ejpam-782	149	24	-	-	SYM
ejpam-782	149	25	101	101	NUM
ejpam-782	149	26	.	.	NOUN
ejpam-782	149	27	1992	1992	NUM
ejpam-782	149	28	.	.	PUNCT
ejpam-782	150	1	[	[	X
ejpam-782	150	2	10	10	NUM
ejpam-782	150	3	]	]	PUNCT
ejpam-782	150	4	a.r.reddy	a.r.reddy	NOUN
ejpam-782	150	5	,	,	PUNCT
ejpam-782	150	6	best	good	ADJ
ejpam-782	150	7	apporoximation	apporoximation	NOUN
ejpam-782	150	8	of	of	ADP
ejpam-782	150	9	certain	certain	ADJ
ejpam-782	150	10	entire	entire	ADJ
ejpam-782	150	11	functions	function	NOUN
ejpam-782	150	12	,	,	PUNCT
ejpam-782	150	13	j.approx	j.approx	PROPN
ejpam-782	150	14	.	.	PUNCT
ejpam-782	150	15	theory	theory	NOUN
ejpam-782	150	16	5	5	NUM
ejpam-782	150	17	,	,	PUNCT
ejpam-782	150	18	97	97	NUM
ejpam-782	150	19	-	-	SYM
ejpam-782	150	20	112	112	NUM
ejpam-782	150	21	.	.	PUNCT
ejpam-782	150	22	1972	1972	NUM
ejpam-782	150	23	.	.	PUNCT