id	sid	tid	token	lemma	pos
ejpam-365	1	1	4_365_srivastava.dvi	4_365_srivastava.dvi	NUM
ejpam-365	1	2	european	european	PROPN
ejpam-365	1	3	journal	journal	PROPN
ejpam-365	1	4	of	of	ADP
ejpam-365	1	5	pure	pure	ADJ
ejpam-365	1	6	and	and	CCONJ
ejpam-365	1	7	applied	apply	VERB
ejpam-365	1	8	mathematics	mathematic	NOUN
ejpam-365	1	9	vol	vol	NOUN
ejpam-365	1	10	.	.	PROPN
ejpam-365	2	1	2	2	NUM
ejpam-365	2	2	,	,	PUNCT
ejpam-365	2	3	no	no	INTJ
ejpam-365	2	4	.	.	NOUN
ejpam-365	2	5	4	4	NUM
ejpam-365	2	6	,	,	PUNCT
ejpam-365	2	7	2009	2009	NUM
ejpam-365	2	8	,	,	PUNCT
ejpam-365	2	9	(	(	PUNCT
ejpam-365	2	10	520	520	NUM
ejpam-365	2	11	-	-	SYM
ejpam-365	2	12	531	531	NUM
ejpam-365	2	13	)	)	PUNCT
ejpam-365	2	14	issn	issn	PROPN
ejpam-365	2	15	1307	1307	NUM
ejpam-365	2	16	-	-	SYM
ejpam-365	2	17	5543	5543	NUM
ejpam-365	2	18	–	–	PUNCT
ejpam-365	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-365	2	20	on	on	ADP
ejpam-365	2	21	approximation	approximation	NOUN
ejpam-365	2	22	and	and	CCONJ
ejpam-365	2	23	generalized	generalized	ADJ
ejpam-365	2	24	type	type	NOUN
ejpam-365	2	25	of	of	ADP
ejpam-365	2	26	entire	entire	ADJ
ejpam-365	2	27	functions	function	NOUN
ejpam-365	2	28	of	of	ADP
ejpam-365	2	29	several	several	ADJ
ejpam-365	2	30	complex	complex	ADJ
ejpam-365	2	31	variables	variable	NOUN
ejpam-365	3	1	g.	g.	PROPN
ejpam-365	3	2	s.	s.	PROPN
ejpam-365	3	3	srivastava∗	srivastava∗	PROPN
ejpam-365	3	4	and	and	CCONJ
ejpam-365	3	5	susheel	susheel	PROPN
ejpam-365	3	6	kumar	kumar	PROPN
ejpam-365	3	7	department	department	PROPN
ejpam-365	3	8	of	of	ADP
ejpam-365	3	9	mathematics	mathematics	PROPN
ejpam-365	3	10	,	,	PUNCT
ejpam-365	3	11	indian	indian	PROPN
ejpam-365	3	12	institute	institute	PROPN
ejpam-365	3	13	of	of	ADP
ejpam-365	3	14	technology	technology	PROPN
ejpam-365	3	15	roorkee	roorkee	NOUN
ejpam-365	3	16	,	,	PUNCT
ejpam-365	3	17	roorkee-247667	roorkee-247667	NOUN
ejpam-365	3	18	,	,	PUNCT
ejpam-365	3	19	india	india	PROPN
ejpam-365	3	20	.	.	PUNCT
ejpam-365	4	1	abstract	abstract	PROPN
ejpam-365	4	2	.	.	PUNCT
ejpam-365	5	1	in	in	ADP
ejpam-365	5	2	the	the	DET
ejpam-365	5	3	present	present	ADJ
ejpam-365	5	4	paper	paper	NOUN
ejpam-365	5	5	,	,	PUNCT
ejpam-365	5	6	we	we	PRON
ejpam-365	5	7	study	study	VERB
ejpam-365	5	8	the	the	DET
ejpam-365	5	9	polynomial	polynomial	ADJ
ejpam-365	5	10	approximation	approximation	NOUN
ejpam-365	5	11	of	of	ADP
ejpam-365	5	12	entire	entire	ADJ
ejpam-365	5	13	functions	function	NOUN
ejpam-365	5	14	of	of	ADP
ejpam-365	5	15	several	several	ADJ
ejpam-365	5	16	complex	complex	ADJ
ejpam-365	5	17	variables	variable	NOUN
ejpam-365	5	18	.	.	PUNCT
ejpam-365	6	1	the	the	DET
ejpam-365	6	2	characterizations	characterization	NOUN
ejpam-365	6	3	of	of	ADP
ejpam-365	6	4	generalized	generalized	ADJ
ejpam-365	6	5	type	type	NOUN
ejpam-365	6	6	of	of	ADP
ejpam-365	6	7	entire	entire	ADJ
ejpam-365	6	8	functions	function	NOUN
ejpam-365	6	9	of	of	ADP
ejpam-365	6	10	several	several	ADJ
ejpam-365	6	11	complex	complex	ADJ
ejpam-365	6	12	variables	variable	NOUN
ejpam-365	6	13	have	have	AUX
ejpam-365	6	14	been	be	AUX
ejpam-365	6	15	obtained	obtain	VERB
ejpam-365	6	16	in	in	ADP
ejpam-365	6	17	terms	term	NOUN
ejpam-365	6	18	of	of	ADP
ejpam-365	6	19	approximation	approximation	NOUN
ejpam-365	6	20	and	and	CCONJ
ejpam-365	6	21	interpolation	interpolation	NOUN
ejpam-365	6	22	errors	error	NOUN
ejpam-365	6	23	.	.	PUNCT
ejpam-365	7	1	2000	2000	NUM
ejpam-365	7	2	mathematics	mathematic	NOUN
ejpam-365	7	3	subject	subject	NOUN
ejpam-365	7	4	classifications	classification	NOUN
ejpam-365	7	5	:	:	PUNCT
ejpam-365	7	6	30b10	30b10	NUM
ejpam-365	7	7	,	,	PUNCT
ejpam-365	7	8	30d20	30d20	NUM
ejpam-365	7	9	,	,	PUNCT
ejpam-365	7	10	32k05	32k05	PRON
ejpam-365	7	11	key	key	ADJ
ejpam-365	7	12	words	word	NOUN
ejpam-365	7	13	and	and	CCONJ
ejpam-365	7	14	phrases	phrase	NOUN
ejpam-365	7	15	:	:	PUNCT
ejpam-365	7	16	entire	entire	ADJ
ejpam-365	7	17	function	function	NOUN
ejpam-365	7	18	,	,	PUNCT
ejpam-365	7	19	siciak	siciak	PROPN
ejpam-365	7	20	extremal	extremal	ADJ
ejpam-365	7	21	function	function	NOUN
ejpam-365	7	22	,	,	PUNCT
ejpam-365	7	23	generalized	generalized	ADJ
ejpam-365	7	24	type	type	NOUN
ejpam-365	7	25	,	,	PUNCT
ejpam-365	7	26	approximation	approximation	NOUN
ejpam-365	7	27	errors	error	NOUN
ejpam-365	7	28	,	,	PUNCT
ejpam-365	7	29	interpolation	interpolation	NOUN
ejpam-365	7	30	errors	error	NOUN
ejpam-365	7	31	.	.	PUNCT
ejpam-365	8	1	1	1	X
ejpam-365	8	2	.	.	X
ejpam-365	8	3	introduction	introduction	NOUN
ejpam-365	8	4	the	the	DET
ejpam-365	8	5	concept	concept	NOUN
ejpam-365	8	6	of	of	ADP
ejpam-365	8	7	generalized	generalized	ADJ
ejpam-365	8	8	order	order	NOUN
ejpam-365	8	9	and	and	CCONJ
ejpam-365	8	10	generalized	generalized	ADJ
ejpam-365	8	11	type	type	NOUN
ejpam-365	8	12	for	for	ADP
ejpam-365	8	13	entire	entire	ADJ
ejpam-365	8	14	transcendental	transcendental	ADJ
ejpam-365	8	15	functions	function	NOUN
ejpam-365	8	16	was	be	AUX
ejpam-365	8	17	given	give	VERB
ejpam-365	8	18	by	by	ADP
ejpam-365	8	19	seremeta	seremeta	NOUN
ejpam-365	9	1	[	[	X
ejpam-365	9	2	4	4	NUM
ejpam-365	9	3	]	]	PUNCT
ejpam-365	9	4	and	and	CCONJ
ejpam-365	9	5	shah	shah	NOUN
ejpam-365	9	6	[	[	X
ejpam-365	9	7	5	5	NUM
ejpam-365	9	8	]	]	PUNCT
ejpam-365	9	9	.	.	PUNCT
ejpam-365	10	1	hence	hence	ADV
ejpam-365	10	2	,	,	PUNCT
ejpam-365	10	3	let	let	VERB
ejpam-365	10	4	l0	l0	NOUN
ejpam-365	10	5	denote	denote	VERB
ejpam-365	10	6	the	the	DET
ejpam-365	10	7	class	class	NOUN
ejpam-365	10	8	of	of	ADP
ejpam-365	10	9	∗corresponding	∗corresponde	VERB
ejpam-365	10	10	author	author	NOUN
ejpam-365	10	11	.	.	PUNCT
ejpam-365	11	1	email	email	NOUN
ejpam-365	11	2	address	address	NOUN
ejpam-365	11	3	:	:	PUNCT
ejpam-365	11	4	girssfma�iitr.ernet.in	girssfma�iitr.ernet.in	INTJ
ejpam-365	11	5	(	(	PUNCT
ejpam-365	11	6	g.	g.	PROPN
ejpam-365	11	7	srivastava	srivastava	PROPN
ejpam-365	11	8	)	)	PUNCT
ejpam-365	11	9	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-365	12	1	520	520	NUM
ejpam-365	12	2	c	c	X
ejpam-365	12	3	©	©	PROPN
ejpam-365	12	4	2009	2009	NUM
ejpam-365	12	5	ejpam	ejpam	NOUN
ejpam-365	12	6	all	all	DET
ejpam-365	12	7	rights	right	NOUN
ejpam-365	12	8	reserved	reserve	VERB
ejpam-365	12	9	.	.	PUNCT
ejpam-365	13	1	g.	g.	PROPN
ejpam-365	13	2	srivastava	srivastava	PROPN
ejpam-365	13	3	and	and	CCONJ
ejpam-365	13	4	s.	s.	PROPN
ejpam-365	13	5	kumar	kumar	PROPN
ejpam-365	13	6	/	/	SYM
ejpam-365	13	7	eur	eur	PROPN
ejpam-365	13	8	.	.	PUNCT
ejpam-365	14	1	j.	j.	PROPN
ejpam-365	14	2	pure	pure	PROPN
ejpam-365	14	3	appl	appl	PROPN
ejpam-365	14	4	.	.	PROPN
ejpam-365	14	5	math	math	PROPN
ejpam-365	14	6	,	,	PUNCT
ejpam-365	14	7	2	2	NUM
ejpam-365	14	8	(	(	PUNCT
ejpam-365	14	9	2009	2009	NUM
ejpam-365	14	10	)	)	PUNCT
ejpam-365	14	11	,	,	PUNCT
ejpam-365	14	12	(	(	PUNCT
ejpam-365	14	13	520	520	NUM
ejpam-365	14	14	-	-	SYM
ejpam-365	14	15	531	531	NUM
ejpam-365	14	16	)	)	PUNCT
ejpam-365	14	17	521	521	NUM
ejpam-365	14	18	functions	function	NOUN
ejpam-365	14	19	h(x	h(x	PROPN
ejpam-365	14	20	)	)	PUNCT
ejpam-365	14	21	satisfying	satisfy	VERB
ejpam-365	14	22	the	the	DET
ejpam-365	14	23	following	follow	VERB
ejpam-365	14	24	conditions	condition	NOUN
ejpam-365	14	25	:	:	PUNCT
ejpam-365	14	26	(	(	PUNCT
ejpam-365	14	27	i	i	NOUN
ejpam-365	14	28	)	)	PUNCT
ejpam-365	14	29	h(x	h(x	PROPN
ejpam-365	14	30	)	)	PUNCT
ejpam-365	14	31	is	be	AUX
ejpam-365	14	32	defined	define	VERB
ejpam-365	14	33	on	on	ADP
ejpam-365	14	34	[	[	X
ejpam-365	14	35	a,∞	a,∞	PROPN
ejpam-365	14	36	)	)	PUNCT
ejpam-365	14	37	and	and	CCONJ
ejpam-365	14	38	is	be	AUX
ejpam-365	14	39	positive	positive	ADJ
ejpam-365	14	40	,	,	PUNCT
ejpam-365	14	41	strictly	strictly	ADV
ejpam-365	14	42	increasing	increase	VERB
ejpam-365	14	43	,	,	PUNCT
ejpam-365	14	44	differentiable	differentiable	ADJ
ejpam-365	14	45	and	and	CCONJ
ejpam-365	14	46	tends	tend	VERB
ejpam-365	14	47	to∞	to∞	PROPN
ejpam-365	14	48	as	as	ADP
ejpam-365	14	49	x	x	X
ejpam-365	14	50	→∞	→∞	PROPN
ejpam-365	14	51	,	,	PUNCT
ejpam-365	14	52	(	(	PUNCT
ejpam-365	14	53	ii	ii	NOUN
ejpam-365	14	54	)	)	PUNCT
ejpam-365	14	55	lim	lim	PROPN
ejpam-365	14	56	x→∞	x→∞	NUM
ejpam-365	15	1	h[{1	h[{1	PROPN
ejpam-365	15	2	+	+	CCONJ
ejpam-365	15	3	1	1	NUM
ejpam-365	15	4	/	/	SYM
ejpam-365	15	5	ψ(x)}x	ψ(x)}x	NOUN
ejpam-365	15	6	]	]	PUNCT
ejpam-365	15	7	h(x	h(x	PROPN
ejpam-365	15	8	)	)	PUNCT
ejpam-365	15	9	=	=	PUNCT
ejpam-365	15	10	1	1	NUM
ejpam-365	15	11	for	for	ADP
ejpam-365	15	12	every	every	DET
ejpam-365	15	13	function	function	NOUN
ejpam-365	15	14	ψ(x	ψ(x	NOUN
ejpam-365	15	15	)	)	PUNCT
ejpam-365	15	16	such	such	ADJ
ejpam-365	15	17	that	that	DET
ejpam-365	15	18	ψ(x)→∞	ψ(x)→∞	NOUN
ejpam-365	15	19	as	as	SCONJ
ejpam-365	15	20	x	x	X
ejpam-365	15	21	→∞.	→∞.	X
ejpam-365	15	22	let	let	VERB
ejpam-365	15	23	λ	λ	PART
ejpam-365	15	24	denote	denote	VERB
ejpam-365	15	25	the	the	DET
ejpam-365	15	26	class	class	NOUN
ejpam-365	15	27	of	of	ADP
ejpam-365	15	28	functions	function	NOUN
ejpam-365	15	29	h(x	h(x	PROPN
ejpam-365	15	30	)	)	PUNCT
ejpam-365	16	1	satisfying	satisfy	VERB
ejpam-365	16	2	conditions	condition	NOUN
ejpam-365	16	3	(	(	PUNCT
ejpam-365	16	4	i	i	NOUN
ejpam-365	16	5	)	)	PUNCT
ejpam-365	16	6	and	and	CCONJ
ejpam-365	16	7	(	(	PUNCT
ejpam-365	16	8	iii	iii	X
ejpam-365	16	9	)	)	PUNCT
ejpam-365	16	10	lim	lim	NOUN
ejpam-365	16	11	x→∞	x→∞	NUM
ejpam-365	16	12	h(cx	h(cx	PROPN
ejpam-365	16	13	)	)	PUNCT
ejpam-365	16	14	h(x	h(x	PROPN
ejpam-365	16	15	)	)	PUNCT
ejpam-365	17	1	=	=	NOUN
ejpam-365	17	2	1	1	NUM
ejpam-365	17	3	for	for	ADP
ejpam-365	17	4	every	every	DET
ejpam-365	17	5	c	c	PROPN
ejpam-365	17	6	>	>	X
ejpam-365	17	7	0	0	PROPN
ejpam-365	17	8	,	,	PUNCT
ejpam-365	17	9	that	that	PRON
ejpam-365	17	10	is	be	AUX
ejpam-365	17	11	h(x	h(x	PROPN
ejpam-365	17	12	)	)	PUNCT
ejpam-365	17	13	is	be	AUX
ejpam-365	17	14	slowly	slowly	ADV
ejpam-365	17	15	increasing	increase	VERB
ejpam-365	17	16	.	.	PUNCT
ejpam-365	18	1	for	for	ADP
ejpam-365	18	2	an	an	DET
ejpam-365	18	3	entire	entire	ADJ
ejpam-365	18	4	transcendental	transcendental	ADJ
ejpam-365	18	5	function	function	NOUN
ejpam-365	18	6	f	f	PROPN
ejpam-365	18	7	(	(	PUNCT
ejpam-365	18	8	z	z	NOUN
ejpam-365	18	9	)	)	PUNCT
ejpam-365	18	10	=	=	NOUN
ejpam-365	18	11	∑∞	∑∞	NOUN
ejpam-365	18	12	n=1	n=1	PROPN
ejpam-365	18	13	bnzn	bnzn	NOUN
ejpam-365	18	14	,	,	PUNCT
ejpam-365	18	15	define	define	VERB
ejpam-365	18	16	m(r	m(r	NOUN
ejpam-365	18	17	)	)	PUNCT
ejpam-365	19	1	=	=	NOUN
ejpam-365	19	2	max	max	PROPN
ejpam-365	19	3	|z|=r	|z|=r	PROPN
ejpam-365	19	4	|	|	NOUN
ejpam-365	19	5	f	f	PROPN
ejpam-365	19	6	(	(	PUNCT
ejpam-365	19	7	z)|	z)|	PROPN
ejpam-365	19	8	.	.	PUNCT
ejpam-365	20	1	for	for	ADP
ejpam-365	20	2	functions	function	NOUN
ejpam-365	20	3	α(x	α(x	NOUN
ejpam-365	20	4	)	)	PUNCT
ejpam-365	20	5	∈	∈	PROPN
ejpam-365	20	6	λ	λ	PROPN
ejpam-365	20	7	,	,	PUNCT
ejpam-365	20	8	β(x	β(x	PROPN
ejpam-365	20	9	)	)	PUNCT
ejpam-365	20	10	∈	∈	PROPN
ejpam-365	20	11	l0	l0	PROPN
ejpam-365	20	12	,	,	PUNCT
ejpam-365	20	13	the	the	DET
ejpam-365	20	14	generalized	generalized	ADJ
ejpam-365	20	15	order	order	NOUN
ejpam-365	20	16	of	of	ADP
ejpam-365	20	17	f	f	PROPN
ejpam-365	20	18	(	(	PUNCT
ejpam-365	20	19	z	z	NOUN
ejpam-365	20	20	)	)	PUNCT
ejpam-365	20	21	is	be	AUX
ejpam-365	20	22	given	give	VERB
ejpam-365	20	23	by	by	ADP
ejpam-365	20	24	ρ(α	ρ(α	NOUN
ejpam-365	20	25	,	,	PUNCT
ejpam-365	20	26	β	β	X
ejpam-365	20	27	,	,	PUNCT
ejpam-365	20	28	f	f	PROPN
ejpam-365	20	29	)	)	PUNCT
ejpam-365	21	1	=	=	SYM
ejpam-365	21	2	lim	lim	PROPN
ejpam-365	21	3	r→∞	r→∞	NUM
ejpam-365	21	4	sup	sup	PROPN
ejpam-365	21	5	α[log	α[log	PROPN
ejpam-365	21	6	m(r	m(r	PROPN
ejpam-365	21	7	)	)	PUNCT
ejpam-365	21	8	]	]	PUNCT
ejpam-365	21	9	β(log	β(log	NOUN
ejpam-365	21	10	r	r	NOUN
ejpam-365	21	11	)	)	PUNCT
ejpam-365	21	12	.	.	PUNCT
ejpam-365	22	1	further	far	ADV
ejpam-365	22	2	,	,	PUNCT
ejpam-365	22	3	for	for	ADP
ejpam-365	22	4	α(x	α(x	NOUN
ejpam-365	22	5	)	)	PUNCT
ejpam-365	22	6	,	,	PUNCT
ejpam-365	22	7	β−1(x	β−1(x	PROPN
ejpam-365	22	8	)	)	PUNCT
ejpam-365	22	9	and	and	CCONJ
ejpam-365	22	10	γ(x	γ(x	NOUN
ejpam-365	22	11	)	)	PUNCT
ejpam-365	22	12	∈	∈	PROPN
ejpam-365	22	13	l0	l0	PROPN
ejpam-365	22	14	,	,	PUNCT
ejpam-365	22	15	generalized	generalized	ADJ
ejpam-365	22	16	type	type	NOUN
ejpam-365	22	17	of	of	ADP
ejpam-365	22	18	an	an	DET
ejpam-365	22	19	entire	entire	ADJ
ejpam-365	22	20	transcendental	transcendental	ADJ
ejpam-365	22	21	function	function	NOUN
ejpam-365	22	22	f	f	PROPN
ejpam-365	22	23	(	(	PUNCT
ejpam-365	22	24	z	z	NOUN
ejpam-365	22	25	)	)	PUNCT
ejpam-365	22	26	is	be	AUX
ejpam-365	22	27	given	give	VERB
ejpam-365	22	28	as	as	ADP
ejpam-365	22	29	σ(α	σ(α	PROPN
ejpam-365	22	30	,	,	PUNCT
ejpam-365	22	31	β	β	X
ejpam-365	22	32	,	,	PUNCT
ejpam-365	22	33	ρ	ρ	PROPN
ejpam-365	22	34	,	,	PUNCT
ejpam-365	22	35	f	f	NOUN
ejpam-365	22	36	)	)	PUNCT
ejpam-365	23	1	=	=	SYM
ejpam-365	23	2	lim	lim	PROPN
ejpam-365	23	3	r→∞	r→∞	NUM
ejpam-365	23	4	sup	sup	PROPN
ejpam-365	23	5	α[log	α[log	PROPN
ejpam-365	23	6	m(r	m(r	PROPN
ejpam-365	23	7	)	)	PUNCT
ejpam-365	23	8	]	]	PUNCT
ejpam-365	24	1	β[{γ(r)}ρ	β[{γ(r)}ρ	PROPN
ejpam-365	24	2	]	]	PUNCT
ejpam-365	24	3	where	where	SCONJ
ejpam-365	24	4	0	0	NUM
ejpam-365	24	5	<	<	X
ejpam-365	24	6	ρ	ρ	X
ejpam-365	24	7	<	<	X
ejpam-365	24	8	∞	∞	PROPN
ejpam-365	24	9	is	be	AUX
ejpam-365	24	10	a	a	DET
ejpam-365	24	11	fixed	fix	VERB
ejpam-365	24	12	number	number	NOUN
ejpam-365	24	13	.	.	PUNCT
ejpam-365	25	1	let	let	VERB
ejpam-365	25	2	g	g	NOUN
ejpam-365	25	3	:	:	PUNCT
ejpam-365	25	4	c	c	PROPN
ejpam-365	25	5	n	n	PROPN
ejpam-365	25	6	→	→	SYM
ejpam-365	25	7	c	c	X
ejpam-365	25	8	,	,	PUNCT
ejpam-365	25	9	n	n	X
ejpam-365	25	10	≥	≥	NOUN
ejpam-365	25	11	1	1	NUM
ejpam-365	25	12	,	,	PUNCT
ejpam-365	25	13	be	be	AUX
ejpam-365	25	14	an	an	DET
ejpam-365	25	15	entire	entire	ADJ
ejpam-365	25	16	transcendental	transcendental	ADJ
ejpam-365	25	17	function	function	NOUN
ejpam-365	25	18	.	.	PUNCT
ejpam-365	26	1	for	for	ADP
ejpam-365	26	2	z	z	NOUN
ejpam-365	26	3	=	=	SYM
ejpam-365	26	4	(	(	PUNCT
ejpam-365	26	5	z1	z1	PROPN
ejpam-365	26	6	,	,	PUNCT
ejpam-365	26	7	z2	z2	PROPN
ejpam-365	26	8	,	,	PUNCT
ejpam-365	26	9	...	...	PUNCT
ejpam-365	26	10	,	,	PUNCT
ejpam-365	26	11	zn	zn	X
ejpam-365	26	12	)	)	PUNCT
ejpam-365	26	13	∈	∈	PROPN
ejpam-365	26	14	c	c	NOUN
ejpam-365	26	15	n	n	NOUN
ejpam-365	26	16	,	,	PUNCT
ejpam-365	26	17	we	we	PRON
ejpam-365	26	18	put	put	VERB
ejpam-365	26	19	s(r	s(r	PROPN
ejpam-365	26	20	,	,	PUNCT
ejpam-365	26	21	g	g	NOUN
ejpam-365	26	22	)	)	PUNCT
ejpam-365	27	1	=	=	PRON
ejpam-365	27	2	sup{|g(z)|	sup{|g(z)|	ADJ
ejpam-365	27	3	:	:	PUNCT
ejpam-365	27	4	|z1|2	|z1|2	X
ejpam-365	27	5	+	+	NUM
ejpam-365	27	6	|z2|2	|z2|2	PUNCT
ejpam-365	27	7	+	+	NUM
ejpam-365	27	8	...	...	PUNCT
ejpam-365	28	1	+	+	CCONJ
ejpam-365	28	2	|zn	|zn	X
ejpam-365	28	3	|2	|2	X
ejpam-365	28	4	=	=	SYM
ejpam-365	28	5	r2	r2	PROPN
ejpam-365	28	6	}	}	PUNCT
ejpam-365	28	7	,	,	PUNCT
ejpam-365	28	8	r	r	NOUN
ejpam-365	28	9	>	>	X
ejpam-365	28	10	0	0	NUM
ejpam-365	28	11	.	.	PUNCT
ejpam-365	29	1	then	then	ADV
ejpam-365	29	2	we	we	PRON
ejpam-365	29	3	define	define	VERB
ejpam-365	29	4	the	the	DET
ejpam-365	29	5	generalized	generalized	ADJ
ejpam-365	29	6	order	order	NOUN
ejpam-365	29	7	and	and	CCONJ
ejpam-365	29	8	generalized	generalized	ADJ
ejpam-365	29	9	type	type	NOUN
ejpam-365	29	10	of	of	ADP
ejpam-365	29	11	g(z	g(z	PROPN
ejpam-365	29	12	)	)	PUNCT
ejpam-365	29	13	as	as	ADP
ejpam-365	29	14	ρ(α	ρ(α	NOUN
ejpam-365	29	15	,	,	PUNCT
ejpam-365	29	16	β	β	X
ejpam-365	29	17	,	,	PUNCT
ejpam-365	29	18	g	g	NOUN
ejpam-365	29	19	)	)	PUNCT
ejpam-365	29	20	=	=	SYM
ejpam-365	29	21	lim	lim	PROPN
ejpam-365	29	22	r→∞	r→∞	PRON
ejpam-365	29	23	sup	sup	PROPN
ejpam-365	29	24	α	α	X
ejpam-365	30	1	[	[	X
ejpam-365	30	2	logs(r	logs(r	ADJ
ejpam-365	30	3	,	,	PUNCT
ejpam-365	30	4	g	g	NOUN
ejpam-365	30	5	)	)	PUNCT
ejpam-365	30	6	]	]	PUNCT
ejpam-365	31	1	β	β	X
ejpam-365	31	2	(	(	PUNCT
ejpam-365	31	3	log	log	PROPN
ejpam-365	31	4	r	r	NOUN
ejpam-365	31	5	)	)	PUNCT
ejpam-365	31	6	g.	g.	PROPN
ejpam-365	31	7	srivastava	srivastava	PROPN
ejpam-365	31	8	and	and	CCONJ
ejpam-365	31	9	s.	s.	PROPN
ejpam-365	31	10	kumar	kumar	PROPN
ejpam-365	31	11	/	/	SYM
ejpam-365	31	12	eur	eur	PROPN
ejpam-365	31	13	.	.	PUNCT
ejpam-365	32	1	j.	j.	PROPN
ejpam-365	32	2	pure	pure	PROPN
ejpam-365	32	3	appl	appl	PROPN
ejpam-365	32	4	.	.	PROPN
ejpam-365	32	5	math	math	PROPN
ejpam-365	32	6	,	,	PUNCT
ejpam-365	32	7	2	2	NUM
ejpam-365	32	8	(	(	PUNCT
ejpam-365	32	9	2009	2009	NUM
ejpam-365	32	10	)	)	PUNCT
ejpam-365	32	11	,	,	PUNCT
ejpam-365	32	12	(	(	PUNCT
ejpam-365	32	13	520	520	NUM
ejpam-365	32	14	-	-	SYM
ejpam-365	32	15	531	531	NUM
ejpam-365	32	16	)	)	PUNCT
ejpam-365	32	17	522	522	NUM
ejpam-365	32	18	and	and	CCONJ
ejpam-365	32	19	σ(α	σ(α	PROPN
ejpam-365	32	20	,	,	PUNCT
ejpam-365	32	21	β	β	X
ejpam-365	32	22	,	,	PUNCT
ejpam-365	32	23	ρ	ρ	PROPN
ejpam-365	32	24	,	,	PUNCT
ejpam-365	32	25	g	g	NOUN
ejpam-365	32	26	)	)	PUNCT
ejpam-365	32	27	=	=	SYM
ejpam-365	32	28	lim	lim	PROPN
ejpam-365	32	29	r→∞	r→∞	PRON
ejpam-365	32	30	sup	sup	PROPN
ejpam-365	32	31	α	α	X
ejpam-365	33	1	[	[	X
ejpam-365	33	2	logs(r	logs(r	ADJ
ejpam-365	33	3	,	,	PUNCT
ejpam-365	33	4	g	g	NOUN
ejpam-365	33	5	)	)	PUNCT
ejpam-365	33	6	]	]	PUNCT
ejpam-365	34	1	β	β	X
ejpam-365	35	1	[	[	X
ejpam-365	35	2	{	{	PUNCT
ejpam-365	35	3	γ(r)}ρ	γ(r)}ρ	NOUN
ejpam-365	35	4	]	]	PUNCT
ejpam-365	35	5	.	.	PUNCT
ejpam-365	36	1	let	let	VERB
ejpam-365	36	2	k	k	PRON
ejpam-365	36	3	be	be	AUX
ejpam-365	36	4	a	a	DET
ejpam-365	36	5	compact	compact	ADJ
ejpam-365	36	6	set	set	NOUN
ejpam-365	36	7	in	in	ADP
ejpam-365	36	8	c	c	PROPN
ejpam-365	36	9	n	n	NOUN
ejpam-365	36	10	and	and	CCONJ
ejpam-365	36	11	let	let	VERB
ejpam-365	36	12	||.||k	||.||k	PRON
ejpam-365	36	13	denote	denote	VERB
ejpam-365	36	14	the	the	DET
ejpam-365	36	15	sup	sup	NOUN
ejpam-365	36	16	norm	norm	NOUN
ejpam-365	36	17	on	on	ADP
ejpam-365	36	18	k	k	PROPN
ejpam-365	36	19	.	.	PUNCT
ejpam-365	37	1	the	the	DET
ejpam-365	37	2	function	function	NOUN
ejpam-365	37	3	φk(z)=	φk(z)=	PROPN
ejpam-365	37	4	sup	sup	PROPN
ejpam-365	37	5	�	�	PROPN
ejpam-365	37	6	|p(z)|1	|p(z)|1	NUM
ejpam-365	37	7	/	/	SYM
ejpam-365	37	8	n	n	CCONJ
ejpam-365	37	9	:	:	PUNCT
ejpam-365	37	10	p−polynomial	p−polynomial	ADJ
ejpam-365	37	11	,	,	PUNCT
ejpam-365	37	12	deg	deg	NOUN
ejpam-365	37	13	p	p	NOUN
ejpam-365	37	14	≤	≤	PROPN
ejpam-365	37	15	n	n	CCONJ
ejpam-365	37	16	,	,	PUNCT
ejpam-365	37	17	||p||k	||p||k	PROPN
ejpam-365	37	18	≤	≤	PROPN
ejpam-365	37	19	1	1	NUM
ejpam-365	37	20	,	,	PUNCT
ejpam-365	37	21	n	n	NOUN
ejpam-365	37	22	=	=	SYM
ejpam-365	37	23	1	1	NUM
ejpam-365	37	24	,	,	PUNCT
ejpam-365	37	25	2	2	NUM
ejpam-365	37	26	,	,	PUNCT
ejpam-365	37	27	..	..	PUNCT
ejpam-365	37	28	and	and	CCONJ
ejpam-365	37	29	z	z	NOUN
ejpam-365	37	30	∈	∈	PROPN
ejpam-365	37	31	c	c	PROPN
ejpam-365	37	32	n	n	PRON
ejpam-365	37	33	�	�	PROPN
ejpam-365	37	34	,	,	PUNCT
ejpam-365	37	35	is	be	AUX
ejpam-365	37	36	called	call	VERB
ejpam-365	37	37	the	the	DET
ejpam-365	37	38	siciak	siciak	NOUN
ejpam-365	37	39	extremal	extremal	ADJ
ejpam-365	37	40	function	function	NOUN
ejpam-365	37	41	of	of	ADP
ejpam-365	37	42	the	the	DET
ejpam-365	37	43	compact	compact	ADJ
ejpam-365	37	44	set	set	NOUN
ejpam-365	37	45	k	k	PROPN
ejpam-365	37	46	(	(	PUNCT
ejpam-365	37	47	see	see	VERB
ejpam-365	37	48	[	[	X
ejpam-365	37	49	2	2	NUM
ejpam-365	37	50	]	]	PUNCT
ejpam-365	37	51	and	and	CCONJ
ejpam-365	37	52	[	[	X
ejpam-365	37	53	3	3	NUM
ejpam-365	37	54	]	]	NUM
ejpam-365	37	55	)	)	PUNCT
ejpam-365	37	56	.	.	PUNCT
ejpam-365	38	1	given	give	VERB
ejpam-365	38	2	a	a	DET
ejpam-365	38	3	function	function	NOUN
ejpam-365	38	4	f	f	NOUN
ejpam-365	38	5	defined	define	VERB
ejpam-365	38	6	and	and	CCONJ
ejpam-365	38	7	bounded	bound	VERB
ejpam-365	38	8	on	on	ADP
ejpam-365	38	9	k	k	PROPN
ejpam-365	38	10	,	,	PUNCT
ejpam-365	38	11	we	we	PRON
ejpam-365	38	12	put	put	VERB
ejpam-365	38	13	for	for	ADP
ejpam-365	38	14	n	n	NOUN
ejpam-365	38	15	=	=	SYM
ejpam-365	38	16	1	1	NUM
ejpam-365	38	17	,	,	PUNCT
ejpam-365	38	18	2	2	NUM
ejpam-365	38	19	,	,	PUNCT
ejpam-365	38	20	...	...	PUNCT
ejpam-365	39	1	e1	e1	PROPN
ejpam-365	39	2	n	n	CCONJ
ejpam-365	39	3	(	(	PUNCT
ejpam-365	39	4	f	f	PROPN
ejpam-365	39	5	,	,	PUNCT
ejpam-365	39	6	k	k	PROPN
ejpam-365	39	7	)	)	PUNCT
ejpam-365	39	8	=	=	PUNCT
ejpam-365	40	1	||	||	NOUN
ejpam-365	41	1	f	f	NOUN
ejpam-365	42	1	−	−	ADP
ejpam-365	42	2	tn||k	tn||k	NOUN
ejpam-365	42	3	;	;	PUNCT
ejpam-365	43	1	e2	e2	PROPN
ejpam-365	43	2	n	n	PRON
ejpam-365	43	3	(	(	PUNCT
ejpam-365	43	4	f	f	PROPN
ejpam-365	43	5	,	,	PUNCT
ejpam-365	43	6	k	k	PROPN
ejpam-365	43	7	)	)	PUNCT
ejpam-365	43	8	=	=	PUNCT
ejpam-365	44	1	||	||	NOUN
ejpam-365	45	1	f	f	X
ejpam-365	45	2	−	−	PROPN
ejpam-365	45	3	ln||k	ln||k	NOUN
ejpam-365	45	4	;	;	PUNCT
ejpam-365	45	5	e3	e3	VERB
ejpam-365	45	6	n+1	n+1	PROPN
ejpam-365	45	7	(	(	PUNCT
ejpam-365	45	8	f	f	PROPN
ejpam-365	45	9	,	,	PUNCT
ejpam-365	45	10	k	k	PROPN
ejpam-365	45	11	)	)	PUNCT
ejpam-365	45	12	=	=	SYM
ejpam-365	45	13	||ln+1	||ln+1	PROPN
ejpam-365	45	14	−	−	PROPN
ejpam-365	46	1	ln||k	ln||k	NOUN
ejpam-365	46	2	;	;	PUNCT
ejpam-365	46	3	where	where	SCONJ
ejpam-365	46	4	tn	tn	PROPN
ejpam-365	46	5	denotes	denote	VERB
ejpam-365	46	6	the	the	DET
ejpam-365	46	7	nth	nth	NOUN
ejpam-365	46	8	chebyshev	chebyshev	PROPN
ejpam-365	46	9	polynomial	polynomial	NOUN
ejpam-365	46	10	of	of	ADP
ejpam-365	46	11	the	the	DET
ejpam-365	46	12	best	good	ADJ
ejpam-365	46	13	approximation	approximation	NOUN
ejpam-365	46	14	to	to	ADP
ejpam-365	46	15	f	f	PROPN
ejpam-365	46	16	on	on	ADP
ejpam-365	46	17	k	k	PROPN
ejpam-365	46	18	and	and	CCONJ
ejpam-365	46	19	ln	ln	ADJ
ejpam-365	46	20	denotes	denote	NOUN
ejpam-365	46	21	the	the	DET
ejpam-365	46	22	nth	nth	NOUN
ejpam-365	46	23	lagrange	lagrange	PROPN
ejpam-365	46	24	interpolation	interpolation	NOUN
ejpam-365	46	25	polynomial	polynomial	NOUN
ejpam-365	46	26	for	for	ADP
ejpam-365	46	27	f	f	PROPN
ejpam-365	46	28	with	with	ADP
ejpam-365	46	29	nodes	node	NOUN
ejpam-365	46	30	at	at	ADP
ejpam-365	46	31	extremal	extremal	ADJ
ejpam-365	46	32	points	point	NOUN
ejpam-365	46	33	of	of	ADP
ejpam-365	46	34	k	k	PROPN
ejpam-365	46	35	(	(	PUNCT
ejpam-365	46	36	see	see	VERB
ejpam-365	46	37	[	[	X
ejpam-365	46	38	2	2	NUM
ejpam-365	46	39	]	]	PUNCT
ejpam-365	46	40	and	and	CCONJ
ejpam-365	46	41	[	[	X
ejpam-365	46	42	3	3	NUM
ejpam-365	46	43	]	]	PUNCT
ejpam-365	46	44	)	)	PUNCT
ejpam-365	46	45	.	.	PUNCT
ejpam-365	47	1	janik	janik	X
ejpam-365	48	1	[	[	X
ejpam-365	48	2	1	1	NUM
ejpam-365	48	3	]	]	PUNCT
ejpam-365	48	4	obtained	obtain	VERB
ejpam-365	48	5	the	the	DET
ejpam-365	48	6	characterizations	characterization	NOUN
ejpam-365	48	7	of	of	ADP
ejpam-365	48	8	order	order	NOUN
ejpam-365	48	9	of	of	ADP
ejpam-365	48	10	entire	entire	ADJ
ejpam-365	48	11	functions	function	NOUN
ejpam-365	48	12	in	in	ADP
ejpam-365	48	13	terms	term	NOUN
ejpam-365	48	14	of	of	ADP
ejpam-365	48	15	the	the	DET
ejpam-365	48	16	approximation	approximation	NOUN
ejpam-365	48	17	errors	error	NOUN
ejpam-365	48	18	defined	define	VERB
ejpam-365	48	19	above	above	ADV
ejpam-365	48	20	.	.	PUNCT
ejpam-365	49	1	later	later	ADV
ejpam-365	49	2	he	he	PRON
ejpam-365	49	3	obtained	obtain	VERB
ejpam-365	49	4	the	the	DET
ejpam-365	49	5	characterizations	characterization	NOUN
ejpam-365	49	6	of	of	ADP
ejpam-365	49	7	the	the	DET
ejpam-365	49	8	generalized	generalized	ADJ
ejpam-365	49	9	order	order	NOUN
ejpam-365	49	10	[	[	X
ejpam-365	49	11	3	3	NUM
ejpam-365	49	12	]	]	PUNCT
ejpam-365	49	13	.	.	PUNCT
ejpam-365	50	1	in	in	ADP
ejpam-365	50	2	this	this	DET
ejpam-365	50	3	note	note	NOUN
ejpam-365	50	4	we	we	PRON
ejpam-365	50	5	obtained	obtain	VERB
ejpam-365	50	6	the	the	DET
ejpam-365	50	7	characterizations	characterization	NOUN
ejpam-365	50	8	of	of	ADP
ejpam-365	50	9	the	the	DET
ejpam-365	50	10	generalized	generalized	ADJ
ejpam-365	50	11	type	type	NOUN
ejpam-365	50	12	.	.	PUNCT
ejpam-365	51	1	for	for	ADP
ejpam-365	51	2	the	the	DET
ejpam-365	51	3	case	case	NOUN
ejpam-365	51	4	n	n	NOUN
ejpam-365	51	5	=	=	SYM
ejpam-365	51	6	1	1	NUM
ejpam-365	51	7	this	this	DET
ejpam-365	51	8	result	result	NOUN
ejpam-365	51	9	was	be	AUX
ejpam-365	51	10	obtained	obtain	VERB
ejpam-365	51	11	by	by	ADP
ejpam-365	51	12	shah	shah	NOUN
ejpam-365	51	13	[	[	X
ejpam-365	51	14	5	5	NUM
ejpam-365	51	15	]	]	PUNCT
ejpam-365	51	16	.	.	PUNCT
ejpam-365	52	1	2	2	X
ejpam-365	52	2	.	.	X
ejpam-365	52	3	results	result	NOUN
ejpam-365	52	4	we	we	PRON
ejpam-365	52	5	first	first	ADV
ejpam-365	52	6	prove	prove	VERB
ejpam-365	52	7	a	a	DET
ejpam-365	52	8	lemma	lemma	PROPN
ejpam-365	52	9	.	.	PUNCT
ejpam-365	53	1	lemma	lemma	PROPN
ejpam-365	53	2	1	1	X
ejpam-365	53	3	.	.	PUNCT
ejpam-365	54	1	let	let	VERB
ejpam-365	54	2	k	k	PRON
ejpam-365	54	3	be	be	AUX
ejpam-365	54	4	a	a	DET
ejpam-365	54	5	compact	compact	ADJ
ejpam-365	54	6	set	set	NOUN
ejpam-365	54	7	in	in	ADP
ejpam-365	54	8	c	c	PROPN
ejpam-365	54	9	n	n	PRON
ejpam-365	54	10	such	such	ADJ
ejpam-365	54	11	that	that	SCONJ
ejpam-365	54	12	φk	φk	NOUN
ejpam-365	54	13	is	be	AUX
ejpam-365	54	14	locally	locally	ADV
ejpam-365	54	15	bounded	bound	VERB
ejpam-365	54	16	in	in	ADP
ejpam-365	54	17	c	c	PROPN
ejpam-365	54	18	n	n	PROPN
ejpam-365	54	19	.	.	PUNCT
ejpam-365	55	1	set	set	VERB
ejpam-365	55	2	g(x	g(x	PROPN
ejpam-365	55	3	,	,	PUNCT
ejpam-365	55	4	t	t	PROPN
ejpam-365	55	5	,	,	PUNCT
ejpam-365	55	6	ρ	ρ	PROPN
ejpam-365	55	7	)	)	PUNCT
ejpam-365	55	8	=	=	SYM
ejpam-365	55	9	γ−1{[β−1{tα(x)}]1	γ−1{[β−1{tα(x)}]1	PROPN
ejpam-365	55	10	/	/	SYM
ejpam-365	55	11	ρ	ρ	NOUN
ejpam-365	55	12	}	}	PUNCT
ejpam-365	55	13	.	.	PUNCT
ejpam-365	56	1	suppose	suppose	VERB
ejpam-365	56	2	that	that	SCONJ
ejpam-365	56	3	for	for	ADP
ejpam-365	56	4	all	all	DET
ejpam-365	56	5	t	t	NOUN
ejpam-365	56	6	,	,	PUNCT
ejpam-365	56	7	0	0	NUM
ejpam-365	56	8	<	<	X
ejpam-365	56	9	t	t	X
ejpam-365	56	10	<	<	X
ejpam-365	56	11	∞	∞	PROPN
ejpam-365	56	12	,	,	PUNCT
ejpam-365	56	13	(	(	PUNCT
ejpam-365	56	14	a	a	X
ejpam-365	56	15	)	)	PUNCT
ejpam-365	56	16	if	if	SCONJ
ejpam-365	56	17	γ(x	γ(x	NOUN
ejpam-365	56	18	)	)	PUNCT
ejpam-365	56	19	∈	∈	PROPN
ejpam-365	56	20	λ	λ	PROPN
ejpam-365	56	21	and	and	CCONJ
ejpam-365	56	22	α(x	α(x	PROPN
ejpam-365	56	23	)	)	PUNCT
ejpam-365	56	24	∈	∈	PROPN
ejpam-365	56	25	λ	λ	PROPN
ejpam-365	56	26	,	,	PUNCT
ejpam-365	56	27	then	then	ADV
ejpam-365	56	28	d[log{g(x	d[log{g(x	ADJ
ejpam-365	56	29	,	,	PUNCT
ejpam-365	56	30	t	t	PROPN
ejpam-365	56	31	,	,	PUNCT
ejpam-365	56	32	ρ	ρ	PROPN
ejpam-365	56	33	)	)	PUNCT
ejpam-365	56	34	}	}	PUNCT
ejpam-365	56	35	]	]	PUNCT
ejpam-365	56	36	d(log	d(log	PROPN
ejpam-365	56	37	x	x	X
ejpam-365	56	38	)	)	PUNCT
ejpam-365	56	39	=	=	SYM
ejpam-365	56	40	o(1	o(1	PROPN
ejpam-365	56	41	)	)	PUNCT
ejpam-365	56	42	g.	g.	PROPN
ejpam-365	56	43	srivastava	srivastava	PROPN
ejpam-365	56	44	and	and	CCONJ
ejpam-365	56	45	s.	s.	PROPN
ejpam-365	56	46	kumar	kumar	PROPN
ejpam-365	56	47	/	/	SYM
ejpam-365	56	48	eur	eur	PROPN
ejpam-365	56	49	.	.	PUNCT
ejpam-365	57	1	j.	j.	PROPN
ejpam-365	57	2	pure	pure	PROPN
ejpam-365	57	3	appl	appl	PROPN
ejpam-365	57	4	.	.	PROPN
ejpam-365	57	5	math	math	PROPN
ejpam-365	57	6	,	,	PUNCT
ejpam-365	57	7	2	2	NUM
ejpam-365	57	8	(	(	PUNCT
ejpam-365	57	9	2009	2009	NUM
ejpam-365	57	10	)	)	PUNCT
ejpam-365	57	11	,	,	PUNCT
ejpam-365	57	12	(	(	PUNCT
ejpam-365	57	13	520	520	NUM
ejpam-365	57	14	-	-	SYM
ejpam-365	57	15	531	531	NUM
ejpam-365	57	16	)	)	PUNCT
ejpam-365	57	17	523	523	NUM
ejpam-365	57	18	as	as	ADP
ejpam-365	57	19	x	x	X
ejpam-365	57	20	→∞.	→∞.	X
ejpam-365	57	21	(	(	PUNCT
ejpam-365	57	22	b	b	NOUN
ejpam-365	57	23	)	)	PUNCT
ejpam-365	57	24	if	if	SCONJ
ejpam-365	57	25	γ(x	γ(x	NOUN
ejpam-365	57	26	)	)	PUNCT
ejpam-365	57	27	∈	∈	PROPN
ejpam-365	57	28	(	(	PUNCT
ejpam-365	57	29	l0	l0	NOUN
ejpam-365	57	30	−λ	−λ	NOUN
ejpam-365	57	31	)	)	PUNCT
ejpam-365	57	32	or	or	CCONJ
ejpam-365	57	33	α(x	α(x	NOUN
ejpam-365	57	34	)	)	PUNCT
ejpam-365	57	35	∈	∈	PROPN
ejpam-365	57	36	(	(	PUNCT
ejpam-365	57	37	l0	l0	NOUN
ejpam-365	57	38	−λ	−λ	NOUN
ejpam-365	57	39	)	)	PUNCT
ejpam-365	57	40	,	,	PUNCT
ejpam-365	57	41	then	then	ADV
ejpam-365	57	42	lim	lim	PROPN
ejpam-365	57	43	x→∞	x→∞	NUM
ejpam-365	58	1	d[log{g(x	d[log{g(x	X
ejpam-365	58	2	,	,	PUNCT
ejpam-365	58	3	t	t	PROPN
ejpam-365	58	4	,	,	PUNCT
ejpam-365	58	5	ρ	ρ	PROPN
ejpam-365	58	6	)	)	PUNCT
ejpam-365	58	7	}	}	PUNCT
ejpam-365	58	8	]	]	PUNCT
ejpam-365	59	1	d(log	d(log	PROPN
ejpam-365	59	2	x	x	X
ejpam-365	59	3	)	)	PUNCT
ejpam-365	59	4	=	=	SYM
ejpam-365	59	5	1	1	NUM
ejpam-365	59	6	ρ	ρ	NOUN
ejpam-365	59	7	.	.	PUNCT
ejpam-365	60	1	let	let	VERB
ejpam-365	60	2	(	(	PUNCT
ejpam-365	60	3	pn)n∈n	pn)n∈n	X
ejpam-365	60	4	be	be	AUX
ejpam-365	60	5	a	a	DET
ejpam-365	60	6	sequence	sequence	NOUN
ejpam-365	60	7	of	of	ADP
ejpam-365	60	8	polynomials	polynomial	NOUN
ejpam-365	60	9	in	in	ADP
ejpam-365	60	10	c	c	NOUN
ejpam-365	60	11	n	n	PRON
ejpam-365	60	12	such	such	ADJ
ejpam-365	60	13	that	that	SCONJ
ejpam-365	60	14	(	(	PUNCT
ejpam-365	60	15	i	i	NOUN
ejpam-365	60	16	)	)	PUNCT
ejpam-365	60	17	deg	deg	PROPN
ejpam-365	60	18	pn	pn	PROPN
ejpam-365	60	19	≤	≤	PROPN
ejpam-365	60	20	n	n	CCONJ
ejpam-365	60	21	,	,	PUNCT
ejpam-365	60	22	n	n	CCONJ
ejpam-365	60	23	∈	∈	PROPN
ejpam-365	60	24	n	n	X
ejpam-365	60	25	.	.	PUNCT
ejpam-365	61	1	(	(	PUNCT
ejpam-365	61	2	ii	ii	NOUN
ejpam-365	61	3	)	)	PUNCT
ejpam-365	61	4	there	there	PRON
ejpam-365	61	5	exists	exist	VERB
ejpam-365	61	6	n0	n0	PROPN
ejpam-365	61	7	∈	∈	PROPN
ejpam-365	61	8	n	n	PRON
ejpam-365	61	9	such	such	ADJ
ejpam-365	61	10	that	that	DET
ejpam-365	61	11	||pn||k	||pn||k	NOUN
ejpam-365	61	12	≤	≤	X
ejpam-365	61	13	en	en	PROPN
ejpam-365	61	14	/	/	SYM
ejpam-365	61	15	ρ	ρ	PROPN
ejpam-365	61	16	�	�	PROPN
ejpam-365	61	17	γ−1	γ−1	PROPN
ejpam-365	61	18	¨	¨	ADJ
ejpam-365	61	19	�	�	PROPN
ejpam-365	61	20	β−1	β−1	SYM
ejpam-365	61	21	�	�	PROPN
ejpam-365	61	22	1	1	NUM
ejpam-365	61	23	t	t	PROPN
ejpam-365	61	24	α(n	α(n	PROPN
ejpam-365	61	25	/	/	SYM
ejpam-365	61	26	ρ	ρ	PROPN
ejpam-365	61	27	)	)	PUNCT
ejpam-365	61	28	�	�	PROPN
ejpam-365	61	29	�	�	PROPN
ejpam-365	61	30	1	1	NUM
ejpam-365	61	31	/	/	SYM
ejpam-365	61	32	ρ	ρ	PRON
ejpam-365	61	33	«	«	PUNCT
ejpam-365	61	34	�	�	X
ejpam-365	61	35	−n	−n	NOUN
ejpam-365	61	36	,	,	PUNCT
ejpam-365	61	37	where	where	SCONJ
ejpam-365	61	38	t	t	NOUN
ejpam-365	61	39	=	=	SYM
ejpam-365	61	40	t	t	PROPN
ejpam-365	61	41	+	+	CCONJ
ejpam-365	61	42	ǫ	ǫ	X
ejpam-365	61	43	,	,	PUNCT
ejpam-365	61	44	for	for	ADP
ejpam-365	61	45	small	small	ADJ
ejpam-365	61	46	ǫ	ǫ	NOUN
ejpam-365	61	47	>	>	X
ejpam-365	61	48	0	0	X
ejpam-365	61	49	.	.	PUNCT
ejpam-365	62	1	then	then	ADV
ejpam-365	62	2	∑∞	∑∞	NOUN
ejpam-365	62	3	n=0	n=0	NUM
ejpam-365	62	4	pn	pn	NOUN
ejpam-365	62	5	is	be	AUX
ejpam-365	62	6	an	an	DET
ejpam-365	62	7	entire	entire	ADJ
ejpam-365	62	8	function	function	NOUN
ejpam-365	62	9	and	and	CCONJ
ejpam-365	62	10	the	the	DET
ejpam-365	62	11	generalized	generalized	ADJ
ejpam-365	62	12	type	type	NOUN
ejpam-365	62	13	σ(α	σ(α	PROPN
ejpam-365	62	14	,	,	PUNCT
ejpam-365	62	15	β	β	X
ejpam-365	62	16	,	,	PUNCT
ejpam-365	62	17	ρ	ρ	PROPN
ejpam-365	62	18	,	,	PUNCT
ejpam-365	62	19	∑∞	∑∞	NOUN
ejpam-365	62	20	n=0	n=0	NUM
ejpam-365	62	21	pn	pn	NOUN
ejpam-365	62	22	)	)	PUNCT
ejpam-365	62	23	of	of	ADP
ejpam-365	62	24	this	this	DET
ejpam-365	62	25	entire	entire	ADJ
ejpam-365	62	26	function	function	NOUN
ejpam-365	62	27	satisfies	satisfie	NOUN
ejpam-365	62	28	σ(α	σ(α	PROPN
ejpam-365	62	29	,	,	PUNCT
ejpam-365	62	30	β	β	X
ejpam-365	62	31	,	,	PUNCT
ejpam-365	62	32	ρ	ρ	PROPN
ejpam-365	62	33	,	,	PUNCT
ejpam-365	62	34	∞	∞	PROPN
ejpam-365	62	35	∑	∑	ADP
ejpam-365	62	36	n=0	n=0	NUM
ejpam-365	62	37	pn)≤	pn)≤	NOUN
ejpam-365	62	38	t	t	NOUN
ejpam-365	62	39	provided	provide	VERB
ejpam-365	62	40	∑∞	∑∞	NOUN
ejpam-365	62	41	n=0	n=0	NUM
ejpam-365	62	42	pn	pn	NOUN
ejpam-365	62	43	is	be	AUX
ejpam-365	62	44	not	not	PART
ejpam-365	62	45	a	a	DET
ejpam-365	62	46	polynomial	polynomial	ADJ
ejpam-365	62	47	.	.	PUNCT
ejpam-365	63	1	proof	proof	NOUN
ejpam-365	63	2	.	.	PUNCT
ejpam-365	64	1	by	by	ADP
ejpam-365	64	2	assumption	assumption	NOUN
ejpam-365	64	3	,	,	PUNCT
ejpam-365	64	4	we	we	PRON
ejpam-365	64	5	have	have	VERB
ejpam-365	64	6	||pn||k	||pn||k	PROPN
ejpam-365	64	7	rn	rn	PROPN
ejpam-365	64	8	≤	≤	PROPN
ejpam-365	64	9	rnen	rnen	PROPN
ejpam-365	64	10	/	/	SYM
ejpam-365	64	11	ρ	ρ	PROPN
ejpam-365	64	12	�	�	PROPN
ejpam-365	65	1	γ−1	γ−1	PROPN
ejpam-365	65	2	¨	¨	ADJ
ejpam-365	65	3	�	�	PROPN
ejpam-365	65	4	β−1	β−1	SYM
ejpam-365	65	5	�	�	PROPN
ejpam-365	65	6	1	1	NUM
ejpam-365	65	7	t	t	PROPN
ejpam-365	65	8	α(n	α(n	PROPN
ejpam-365	65	9	/	/	SYM
ejpam-365	65	10	ρ	ρ	PROPN
ejpam-365	65	11	)	)	PUNCT
ejpam-365	65	12	�	�	PROPN
ejpam-365	65	13	�	�	PROPN
ejpam-365	65	14	1	1	NUM
ejpam-365	65	15	/	/	SYM
ejpam-365	65	16	ρ	ρ	PRON
ejpam-365	65	17	«	«	PUNCT
ejpam-365	65	18	�	�	X
ejpam-365	65	19	−n	−n	NUM
ejpam-365	65	20	,	,	PUNCT
ejpam-365	65	21	n	n	CCONJ
ejpam-365	65	22	≥	≥	NOUN
ejpam-365	65	23	n0	n0	NUM
ejpam-365	65	24	,	,	PUNCT
ejpam-365	65	25	r	r	NOUN
ejpam-365	65	26	>	>	X
ejpam-365	65	27	0	0	NUM
ejpam-365	65	28	.	.	PUNCT
ejpam-365	66	1	if	if	SCONJ
ejpam-365	66	2	γ(x	γ(x	NOUN
ejpam-365	66	3	)	)	PUNCT
ejpam-365	66	4	∈	∈	PROPN
ejpam-365	66	5	λ	λ	PROPN
ejpam-365	66	6	and	and	CCONJ
ejpam-365	66	7	α(x	α(x	PROPN
ejpam-365	66	8	)	)	PUNCT
ejpam-365	66	9	∈	∈	PROPN
ejpam-365	66	10	λ	λ	PROPN
ejpam-365	66	11	,	,	PUNCT
ejpam-365	66	12	then	then	ADV
ejpam-365	66	13	by	by	ADP
ejpam-365	66	14	assumptions	assumption	NOUN
ejpam-365	66	15	of	of	ADP
ejpam-365	66	16	lemma	lemma	PROPN
ejpam-365	66	17	,	,	PUNCT
ejpam-365	66	18	there	there	PRON
ejpam-365	66	19	exists	exist	VERB
ejpam-365	66	20	a	a	DET
ejpam-365	66	21	number	number	NOUN
ejpam-365	66	22	b	b	NOUN
ejpam-365	66	23	>	>	X
ejpam-365	66	24	0	0	NUM
ejpam-365	66	25	such	such	ADJ
ejpam-365	66	26	that	that	PRON
ejpam-365	66	27	for	for	ADP
ejpam-365	66	28	x	x	SYM
ejpam-365	66	29	>	>	X
ejpam-365	66	30	a	a	X
ejpam-365	66	31	,	,	PUNCT
ejpam-365	66	32	we	we	PRON
ejpam-365	66	33	have	have	VERB
ejpam-365	66	34	�	�	PROPN
ejpam-365	66	35	�	�	PROPN
ejpam-365	66	36	�	�	PROPN
ejpam-365	66	37	�	�	PROPN
ejpam-365	66	38	d[log{g(x	d[log{g(x	ADP
ejpam-365	66	39	,	,	PUNCT
ejpam-365	66	40	t	t	PROPN
ejpam-365	66	41	,	,	PUNCT
ejpam-365	66	42	ρ	ρ	PROPN
ejpam-365	66	43	)	)	PUNCT
ejpam-365	66	44	}	}	PUNCT
ejpam-365	66	45	]	]	PUNCT
ejpam-365	66	46	d(log	d(log	PROPN
ejpam-365	66	47	x	x	SYM
ejpam-365	66	48	)	)	PUNCT
ejpam-365	66	49	�	�	PROPN
ejpam-365	66	50	�	�	PROPN
ejpam-365	66	51	�	�	PROPN
ejpam-365	66	52	�	�	PROPN
ejpam-365	66	53	<	<	X
ejpam-365	66	54	b.	b.	PROPN
ejpam-365	66	55	let	let	VERB
ejpam-365	66	56	us	we	PRON
ejpam-365	66	57	consider	consider	VERB
ejpam-365	66	58	the	the	DET
ejpam-365	66	59	function	function	NOUN
ejpam-365	66	60	φ(x	φ(x	NOUN
ejpam-365	66	61	)	)	PUNCT
ejpam-365	67	1	=	=	SYM
ejpam-365	67	2	r	r	NOUN
ejpam-365	67	3	x	x	PUNCT
ejpam-365	67	4	ex	ex	NOUN
ejpam-365	67	5	/	/	SYM
ejpam-365	67	6	ρ	ρ	PROPN
ejpam-365	67	7	�	�	PROPN
ejpam-365	67	8	γ−1	γ−1	PROPN
ejpam-365	67	9	¨	¨	ADJ
ejpam-365	67	10	�	�	PROPN
ejpam-365	67	11	β−1	β−1	SYM
ejpam-365	67	12	�	�	PROPN
ejpam-365	67	13	1	1	NUM
ejpam-365	67	14	t	t	PROPN
ejpam-365	67	15	α(x	α(x	PROPN
ejpam-365	67	16	/	/	SYM
ejpam-365	67	17	ρ	ρ	PROPN
ejpam-365	67	18	)	)	PUNCT
ejpam-365	67	19	�	�	PROPN
ejpam-365	67	20	�	�	PROPN
ejpam-365	67	21	1	1	NUM
ejpam-365	67	22	/	/	SYM
ejpam-365	67	23	ρ	ρ	PRON
ejpam-365	67	24	«	«	PUNCT
ejpam-365	67	25	�	�	NOUN
ejpam-365	67	26	−x	−x	NOUN
ejpam-365	67	27	.	.	PUNCT
ejpam-365	68	1	g.	g.	PROPN
ejpam-365	68	2	srivastava	srivastava	PROPN
ejpam-365	68	3	and	and	CCONJ
ejpam-365	68	4	s.	s.	PROPN
ejpam-365	68	5	kumar	kumar	PROPN
ejpam-365	68	6	/	/	SYM
ejpam-365	68	7	eur	eur	PROPN
ejpam-365	68	8	.	.	PUNCT
ejpam-365	69	1	j.	j.	PROPN
ejpam-365	69	2	pure	pure	PROPN
ejpam-365	69	3	appl	appl	PROPN
ejpam-365	69	4	.	.	PROPN
ejpam-365	69	5	math	math	PROPN
ejpam-365	69	6	,	,	PUNCT
ejpam-365	69	7	2	2	NUM
ejpam-365	69	8	(	(	PUNCT
ejpam-365	69	9	2009	2009	NUM
ejpam-365	69	10	)	)	PUNCT
ejpam-365	69	11	,	,	PUNCT
ejpam-365	69	12	(	(	PUNCT
ejpam-365	69	13	520	520	NUM
ejpam-365	69	14	-	-	SYM
ejpam-365	69	15	531	531	NUM
ejpam-365	69	16	)	)	PUNCT
ejpam-365	69	17	524	524	NUM
ejpam-365	69	18	the	the	DET
ejpam-365	69	19	maximum	maximum	NOUN
ejpam-365	69	20	of	of	ADP
ejpam-365	69	21	φ(x	φ(x	NOUN
ejpam-365	69	22	)	)	PUNCT
ejpam-365	69	23	is	be	AUX
ejpam-365	69	24	attained	attain	VERB
ejpam-365	69	25	for	for	ADP
ejpam-365	69	26	a	a	DET
ejpam-365	69	27	value	value	NOUN
ejpam-365	69	28	of	of	ADP
ejpam-365	69	29	x	x	PUNCT
ejpam-365	69	30	given	give	VERB
ejpam-365	69	31	by	by	ADP
ejpam-365	69	32	(	(	PUNCT
ejpam-365	69	33	see	see	VERB
ejpam-365	69	34	e.g.	e.g.	ADV
ejpam-365	69	35	[	[	X
ejpam-365	69	36	4	4	NUM
ejpam-365	69	37	]	]	SYM
ejpam-365	69	38	)	)	PUNCT
ejpam-365	69	39	x∗(r	x∗(r	PROPN
ejpam-365	69	40	)	)	PUNCT
ejpam-365	70	1	=	=	PUNCT
ejpam-365	71	1	ρα−1[tβ{(γ{re1	ρα−1[tβ{(γ{re1	ADJ
ejpam-365	71	2	/	/	SYM
ejpam-365	71	3	ρ−a(r)})ρ	ρ−a(r)})ρ	NOUN
ejpam-365	71	4	}	}	PUNCT
ejpam-365	71	5	]	]	PUNCT
ejpam-365	71	6	,	,	PUNCT
ejpam-365	71	7	where	where	SCONJ
ejpam-365	71	8	a(r	a(r	NOUN
ejpam-365	71	9	)	)	PUNCT
ejpam-365	71	10	=	=	PUNCT
ejpam-365	72	1	d[log{g(x	d[log{g(x	PROPN
ejpam-365	72	2	/	/	SYM
ejpam-365	72	3	ρ	ρ	PROPN
ejpam-365	72	4	,	,	PUNCT
ejpam-365	72	5	1	1	NUM
ejpam-365	72	6	/	/	SYM
ejpam-365	72	7	t	t	PROPN
ejpam-365	72	8	,	,	PUNCT
ejpam-365	72	9	ρ	ρ	NOUN
ejpam-365	72	10	)	)	PUNCT
ejpam-365	72	11	}	}	PUNCT
ejpam-365	72	12	]	]	PUNCT
ejpam-365	72	13	d(log	d(log	PROPN
ejpam-365	72	14	x	x	X
ejpam-365	72	15	)	)	PUNCT
ejpam-365	72	16	.	.	PUNCT
ejpam-365	73	1	thus	thus	ADV
ejpam-365	73	2	,	,	PUNCT
ejpam-365	73	3	||pn||k	||pn||k	PROPN
ejpam-365	73	4	rn	rn	PROPN
ejpam-365	73	5	≤	≤	PROPN
ejpam-365	73	6	exp(bρα−1[tβ({γ(re	exp(bρα−1[tβ({γ(re	VERB
ejpam-365	73	7	1	1	NUM
ejpam-365	73	8	/	/	SYM
ejpam-365	73	9	ρ+b	ρ+b	NUM
ejpam-365	73	10	)	)	PUNCT
ejpam-365	73	11	}	}	PUNCT
ejpam-365	73	12	ρ	ρ	PROPN
ejpam-365	73	13	)	)	PUNCT
ejpam-365	73	14	]	]	PUNCT
ejpam-365	73	15	)	)	PUNCT
ejpam-365	73	16	,	,	PUNCT
ejpam-365	73	17	n≥	n≥	PROPN
ejpam-365	73	18	n0	n0	NUM
ejpam-365	73	19	,	,	PUNCT
ejpam-365	73	20	r	r	NOUN
ejpam-365	73	21	>	>	X
ejpam-365	73	22	0	0	NUM
ejpam-365	73	23	.	.	PUNCT
ejpam-365	74	1	(	(	PUNCT
ejpam-365	74	2	1	1	X
ejpam-365	74	3	)	)	PUNCT
ejpam-365	74	4	let	let	VERB
ejpam-365	74	5	us	we	PRON
ejpam-365	74	6	write	write	VERB
ejpam-365	74	7	kr	kr	PROPN
ejpam-365	74	8	=	=	PUNCT
ejpam-365	74	9	{	{	PUNCT
ejpam-365	74	10	z	z	NOUN
ejpam-365	74	11	∈	∈	PROPN
ejpam-365	74	12	c	c	NOUN
ejpam-365	74	13	n	n	NOUN
ejpam-365	74	14	:	:	PUNCT
ejpam-365	75	1	φk(z	φk(z	NUM
ejpam-365	75	2	)	)	PUNCT
ejpam-365	75	3	<	<	X
ejpam-365	76	1	r	r	X
ejpam-365	76	2	,	,	PUNCT
ejpam-365	76	3	r	r	NOUN
ejpam-365	76	4	>	>	X
ejpam-365	76	5	1	1	NUM
ejpam-365	76	6	}	}	PUNCT
ejpam-365	76	7	,	,	PUNCT
ejpam-365	76	8	then	then	ADV
ejpam-365	76	9	for	for	ADP
ejpam-365	76	10	every	every	DET
ejpam-365	76	11	polynomial	polynomial	ADJ
ejpam-365	76	12	p	p	NOUN
ejpam-365	76	13	of	of	ADP
ejpam-365	76	14	degree	degree	NOUN
ejpam-365	76	15	≤	≤	NUM
ejpam-365	76	16	n	n	CCONJ
ejpam-365	76	17	,	,	PUNCT
ejpam-365	76	18	we	we	PRON
ejpam-365	76	19	have	have	AUX
ejpam-365	76	20	(	(	PUNCT
ejpam-365	76	21	see	see	VERB
ejpam-365	76	22	e.g.	e.g.	ADV
ejpam-365	76	23	[	[	X
ejpam-365	76	24	3	3	NUM
ejpam-365	76	25	]	]	SYM
ejpam-365	76	26	p.323	p.323	X
ejpam-365	76	27	)	)	PUNCT
ejpam-365	76	28	|pn(z)|	|pn(z)|	VERB
ejpam-365	76	29	≤	≤	NOUN
ejpam-365	76	30	||pn||kφn	||pn||kφn	ADJ
ejpam-365	76	31	k	k	PROPN
ejpam-365	76	32	(	(	PUNCT
ejpam-365	76	33	z	z	NOUN
ejpam-365	76	34	)	)	PUNCT
ejpam-365	76	35	,	,	PUNCT
ejpam-365	76	36	z	z	PROPN
ejpam-365	76	37	∈	∈	PROPN
ejpam-365	76	38	c	c	NOUN
ejpam-365	76	39	n	n	NOUN
ejpam-365	76	40	.	.	PUNCT
ejpam-365	77	1	(	(	PUNCT
ejpam-365	77	2	2	2	X
ejpam-365	77	3	)	)	PUNCT
ejpam-365	77	4	so	so	SCONJ
ejpam-365	77	5	the	the	DET
ejpam-365	77	6	series	series	NOUN
ejpam-365	77	7	∑∞	∑∞	PROPN
ejpam-365	77	8	n=0	n=0	NUM
ejpam-365	77	9	pn	pn	NOUN
ejpam-365	77	10	is	be	AUX
ejpam-365	77	11	convergent	convergent	ADJ
ejpam-365	77	12	in	in	ADP
ejpam-365	77	13	every	every	DET
ejpam-365	77	14	kr	kr	PROPN
ejpam-365	77	15	,	,	PUNCT
ejpam-365	77	16	r	r	NOUN
ejpam-365	77	17	>	>	X
ejpam-365	77	18	1	1	NUM
ejpam-365	77	19	,	,	PUNCT
ejpam-365	77	20	whence	whence	NOUN
ejpam-365	77	21	∑∞	∑∞	NOUN
ejpam-365	77	22	n=0	n=0	NUM
ejpam-365	77	23	pn	pn	NOUN
ejpam-365	77	24	is	be	AUX
ejpam-365	77	25	an	an	DET
ejpam-365	77	26	entire	entire	ADJ
ejpam-365	77	27	function	function	NOUN
ejpam-365	77	28	.	.	PUNCT
ejpam-365	78	1	put	put	VERB
ejpam-365	78	2	m	m	PROPN
ejpam-365	78	3	∗(r	∗(r	PROPN
ejpam-365	78	4	)	)	PUNCT
ejpam-365	78	5	=	=	PUNCT
ejpam-365	79	1	sup{||pn||k	sup{||pn||k	PROPN
ejpam-365	79	2	rn	rn	PROPN
ejpam-365	79	3	:	:	PUNCT
ejpam-365	79	4	n	n	PROPN
ejpam-365	79	5	∈	∈	PROPN
ejpam-365	79	6	n	n	NOUN
ejpam-365	79	7	,	,	PUNCT
ejpam-365	79	8	r	r	NOUN
ejpam-365	79	9	>	>	X
ejpam-365	79	10	0	0	NUM
ejpam-365	79	11	}	}	PUNCT
ejpam-365	79	12	.	.	PUNCT
ejpam-365	80	1	on	on	ADP
ejpam-365	80	2	account	account	NOUN
ejpam-365	80	3	of	of	ADP
ejpam-365	80	4	1	1	NUM
ejpam-365	80	5	,	,	PUNCT
ejpam-365	80	6	for	for	ADP
ejpam-365	80	7	every	every	DET
ejpam-365	80	8	r	r	NOUN
ejpam-365	80	9	>	>	X
ejpam-365	80	10	0	0	NUM
ejpam-365	80	11	,	,	PUNCT
ejpam-365	80	12	there	there	PRON
ejpam-365	80	13	exists	exist	VERB
ejpam-365	80	14	a	a	DET
ejpam-365	80	15	positive	positive	ADJ
ejpam-365	80	16	integer	integer	NOUN
ejpam-365	80	17	ν(r	ν(r	VERB
ejpam-365	80	18	)	)	PUNCT
ejpam-365	80	19	such	such	ADJ
ejpam-365	80	20	that	that	SCONJ
ejpam-365	80	21	m	m	VERB
ejpam-365	80	22	∗(r	∗(r	PROPN
ejpam-365	80	23	)	)	PUNCT
ejpam-365	80	24	=	=	SYM
ejpam-365	80	25	||pν(r)||k	||pν(r)||k	NOUN
ejpam-365	80	26	rν(r	rν(r	NUM
ejpam-365	80	27	)	)	PUNCT
ejpam-365	80	28	and	and	CCONJ
ejpam-365	80	29	m	m	PROPN
ejpam-365	80	30	∗(r)>||pn||k	∗(r)>||pn||k	PROPN
ejpam-365	80	31	rn	rn	PROPN
ejpam-365	80	32	,	,	PUNCT
ejpam-365	80	33	n	n	PROPN
ejpam-365	80	34	>	>	PUNCT
ejpam-365	80	35	ν(r	ν(r	PROPN
ejpam-365	80	36	)	)	PUNCT
ejpam-365	80	37	.	.	PUNCT
ejpam-365	81	1	it	it	PRON
ejpam-365	81	2	is	be	AUX
ejpam-365	81	3	evident	evident	ADJ
ejpam-365	81	4	that	that	SCONJ
ejpam-365	81	5	ν(r	ν(r	VERB
ejpam-365	81	6	)	)	PUNCT
ejpam-365	81	7	increases	increase	VERB
ejpam-365	81	8	with	with	ADP
ejpam-365	81	9	r.	r.	PROPN
ejpam-365	81	10	first	first	ADV
ejpam-365	81	11	suppose	suppose	VERB
ejpam-365	81	12	that	that	SCONJ
ejpam-365	81	13	ν(r)→∞	ν(r)→∞	NOUN
ejpam-365	81	14	as	as	ADP
ejpam-365	81	15	r	r	NOUN
ejpam-365	81	16	→∞.	→∞.	PUNCT
ejpam-365	81	17	then	then	ADV
ejpam-365	81	18	putting	put	VERB
ejpam-365	81	19	n	n	X
ejpam-365	81	20	=	=	SYM
ejpam-365	81	21	ν(r	ν(r	VERB
ejpam-365	81	22	)	)	PUNCT
ejpam-365	81	23	in	in	ADP
ejpam-365	81	24	1	1	NUM
ejpam-365	81	25	we	we	PRON
ejpam-365	81	26	get	get	VERB
ejpam-365	81	27	for	for	ADP
ejpam-365	81	28	sufficiently	sufficiently	ADV
ejpam-365	81	29	large	large	ADJ
ejpam-365	81	30	r	r	NOUN
ejpam-365	81	31	m	m	NOUN
ejpam-365	81	32	∗(r)≤	∗(r)≤	PROPN
ejpam-365	81	33	exp(bρα−1[tβ({γ(re	exp(bρα−1[tβ({γ(re	NOUN
ejpam-365	81	34	1	1	NUM
ejpam-365	81	35	/	/	SYM
ejpam-365	81	36	ρ+b	ρ+b	NUM
ejpam-365	81	37	)	)	PUNCT
ejpam-365	81	38	}	}	PUNCT
ejpam-365	81	39	ρ	ρ	PROPN
ejpam-365	81	40	)	)	PUNCT
ejpam-365	81	41	]	]	PUNCT
ejpam-365	81	42	)	)	PUNCT
ejpam-365	81	43	.	.	PUNCT
ejpam-365	82	1	(	(	PUNCT
ejpam-365	82	2	3	3	X
ejpam-365	82	3	)	)	PUNCT
ejpam-365	82	4	put	put	VERB
ejpam-365	82	5	fr	fr	NOUN
ejpam-365	82	6	=	=	PUNCT
ejpam-365	82	7	{	{	PUNCT
ejpam-365	82	8	z	z	NOUN
ejpam-365	82	9	∈	∈	PROPN
ejpam-365	82	10	c	c	NOUN
ejpam-365	82	11	n	n	NOUN
ejpam-365	82	12	:	:	PUNCT
ejpam-365	82	13	φk(z	φk(z	NOUN
ejpam-365	82	14	)	)	PUNCT
ejpam-365	82	15	=	=	SYM
ejpam-365	83	1	r	r	X
ejpam-365	83	2	}	}	PUNCT
ejpam-365	83	3	,	,	PUNCT
ejpam-365	83	4	r	r	NOUN
ejpam-365	83	5	>	>	X
ejpam-365	83	6	1	1	NUM
ejpam-365	83	7	g.	g.	PROPN
ejpam-365	83	8	srivastava	srivastava	PROPN
ejpam-365	83	9	and	and	CCONJ
ejpam-365	83	10	s.	s.	PROPN
ejpam-365	83	11	kumar	kumar	PROPN
ejpam-365	83	12	/	/	SYM
ejpam-365	83	13	eur	eur	PROPN
ejpam-365	83	14	.	.	PUNCT
ejpam-365	84	1	j.	j.	PROPN
ejpam-365	84	2	pure	pure	PROPN
ejpam-365	84	3	appl	appl	PROPN
ejpam-365	84	4	.	.	PROPN
ejpam-365	84	5	math	math	PROPN
ejpam-365	84	6	,	,	PUNCT
ejpam-365	84	7	2	2	NUM
ejpam-365	84	8	(	(	PUNCT
ejpam-365	84	9	2009	2009	NUM
ejpam-365	84	10	)	)	PUNCT
ejpam-365	84	11	,	,	PUNCT
ejpam-365	84	12	(	(	PUNCT
ejpam-365	84	13	520	520	NUM
ejpam-365	84	14	-	-	SYM
ejpam-365	84	15	531	531	NUM
ejpam-365	84	16	)	)	PUNCT
ejpam-365	84	17	525	525	NUM
ejpam-365	84	18	and	and	CCONJ
ejpam-365	84	19	m(r	m(r	PROPN
ejpam-365	84	20	)	)	PUNCT
ejpam-365	85	1	=	=	PUNCT
ejpam-365	85	2	sup{|	sup{|	NOUN
ejpam-365	85	3	∞	∞	PROPN
ejpam-365	85	4	∑	∑	PROPN
ejpam-365	85	5	n=0	n=0	X
ejpam-365	85	6	pn(z)|	pn(z)|	NOUN
ejpam-365	85	7	:	:	PUNCT
ejpam-365	85	8	z	z	PROPN
ejpam-365	85	9	∈	∈	PROPN
ejpam-365	85	10	fr	fr	NOUN
ejpam-365	85	11	}	}	PUNCT
ejpam-365	85	12	,	,	PUNCT
ejpam-365	85	13	r	r	NOUN
ejpam-365	85	14	>	>	X
ejpam-365	85	15	1	1	NUM
ejpam-365	85	16	.	.	PUNCT
ejpam-365	85	17	now	now	ADV
ejpam-365	85	18	following	follow	VERB
ejpam-365	85	19	janik	janik	X
ejpam-365	85	20	(	(	PUNCT
ejpam-365	85	21	[	[	X
ejpam-365	85	22	3	3	NUM
ejpam-365	85	23	]	]	SYM
ejpam-365	85	24	p.323	p.323	NUM
ejpam-365	85	25	)	)	PUNCT
ejpam-365	85	26	,	,	PUNCT
ejpam-365	85	27	we	we	PRON
ejpam-365	85	28	have	have	VERB
ejpam-365	85	29	for	for	ADP
ejpam-365	85	30	some	some	DET
ejpam-365	85	31	positive	positive	ADJ
ejpam-365	85	32	constant	constant	ADJ
ejpam-365	85	33	k	k	NOUN
ejpam-365	85	34	,	,	PUNCT
ejpam-365	85	35	s	s	NOUN
ejpam-365	85	36	r	r	NOUN
ejpam-365	85	37	,	,	PUNCT
ejpam-365	85	38	∞	∞	NUM
ejpam-365	85	39	∑	∑	PROPN
ejpam-365	85	40	n=0	n=0	PROPN
ejpam-365	85	41	pn	pn	NOUN
ejpam-365	85	42	!	!	PUNCT
ejpam-365	86	1	≤	≤	NOUN
ejpam-365	87	1	m(kr	m(kr	ADJ
ejpam-365	87	2	)	)	PUNCT
ejpam-365	87	3	≤	≤	NUM
ejpam-365	87	4	2	2	NUM
ejpam-365	87	5	m	m	NOUN
ejpam-365	87	6	∗(2kr	∗(2kr	VERB
ejpam-365	87	7	)	)	PUNCT
ejpam-365	87	8	.	.	PUNCT
ejpam-365	88	1	(	(	PUNCT
ejpam-365	88	2	4	4	X
ejpam-365	88	3	)	)	PUNCT
ejpam-365	88	4	combining	combine	VERB
ejpam-365	88	5	3	3	NUM
ejpam-365	88	6	and	and	CCONJ
ejpam-365	88	7	4	4	NUM
ejpam-365	88	8	,	,	PUNCT
ejpam-365	88	9	we	we	PRON
ejpam-365	88	10	get	get	VERB
ejpam-365	88	11	s	s	NOUN
ejpam-365	88	12	r	r	NOUN
ejpam-365	88	13	,	,	PUNCT
ejpam-365	88	14	∞	∞	NUM
ejpam-365	88	15	∑	∑	PROPN
ejpam-365	88	16	n=0	n=0	PROPN
ejpam-365	88	17	pn	pn	NOUN
ejpam-365	88	18	!	!	PUNCT
ejpam-365	89	1	≤	≤	NUM
ejpam-365	89	2	2exp(bρα−1[tβ({γ(2kre	2exp(bρα−1[tβ({γ(2kre	NUM
ejpam-365	89	3	1	1	NUM
ejpam-365	89	4	/	/	SYM
ejpam-365	89	5	ρ+b	ρ+b	NUM
ejpam-365	89	6	)	)	PUNCT
ejpam-365	89	7	}	}	PUNCT
ejpam-365	89	8	ρ	ρ	PROPN
ejpam-365	89	9	)	)	PUNCT
ejpam-365	89	10	]	]	PUNCT
ejpam-365	89	11	)	)	PUNCT
ejpam-365	89	12	or	or	CCONJ
ejpam-365	89	13	α	α	DET
ejpam-365	89	14	�	�	PROPN
ejpam-365	89	15	1	1	NUM
ejpam-365	89	16	bρ	bρ	VERB
ejpam-365	89	17	log	log	NOUN
ejpam-365	89	18	¦	¦	NOUN
ejpam-365	89	19	1	1	NUM
ejpam-365	89	20	2	2	NUM
ejpam-365	89	21	s(r	s(r	NOUN
ejpam-365	89	22	,	,	PUNCT
ejpam-365	89	23	∑∞	∑∞	NOUN
ejpam-365	89	24	n=0	n=0	NUM
ejpam-365	89	25	pn	pn	NOUN
ejpam-365	89	26	)	)	PUNCT
ejpam-365	89	27	©	©	PROPN
ejpam-365	89	28	�	�	PROPN
ejpam-365	89	29	β({γ(2kre	β({γ(2kre	ADP
ejpam-365	89	30	1	1	NUM
ejpam-365	89	31	/	/	SYM
ejpam-365	89	32	ρ+b	ρ+b	NUM
ejpam-365	89	33	)	)	PUNCT
ejpam-365	89	34	}	}	PUNCT
ejpam-365	89	35	ρ	ρ	PROPN
ejpam-365	89	36	)	)	PUNCT
ejpam-365	89	37	≤	≤	NOUN
ejpam-365	89	38	t.	t.	NOUN
ejpam-365	89	39	since	since	SCONJ
ejpam-365	89	40	α(x	α(x	PROPN
ejpam-365	89	41	)	)	PUNCT
ejpam-365	89	42	and	and	CCONJ
ejpam-365	89	43	γ(x	γ(x	NOUN
ejpam-365	89	44	)	)	PUNCT
ejpam-365	89	45	∈	∈	PROPN
ejpam-365	89	46	λ	λ	PROPN
ejpam-365	89	47	,	,	PUNCT
ejpam-365	89	48	we	we	PRON
ejpam-365	89	49	get	get	VERB
ejpam-365	89	50	on	on	ADP
ejpam-365	89	51	using	use	VERB
ejpam-365	89	52	(	(	PUNCT
ejpam-365	89	53	iii	iii	NOUN
ejpam-365	89	54	)	)	PUNCT
ejpam-365	89	55	,	,	PUNCT
ejpam-365	89	56	lim	lim	PROPN
ejpam-365	89	57	sup	sup	PROPN
ejpam-365	89	58	r→∞	r→∞	VERB
ejpam-365	89	59	α	α	PROPN
ejpam-365	89	60	�	�	PROPN
ejpam-365	89	61	logs(r	logs(r	PROPN
ejpam-365	89	62	,	,	PUNCT
ejpam-365	89	63	∑∞	∑∞	NOUN
ejpam-365	89	64	n=0	n=0	NUM
ejpam-365	89	65	pn	pn	NOUN
ejpam-365	89	66	)	)	PUNCT
ejpam-365	89	67	�	�	PROPN
ejpam-365	89	68	β({γ(r)}ρ	β({γ(r)}ρ	NOUN
ejpam-365	89	69	)	)	PUNCT
ejpam-365	89	70	≤	≤	NUM
ejpam-365	90	1	t.	t.	NOUN
ejpam-365	90	2	(	(	PUNCT
ejpam-365	90	3	5	5	NUM
ejpam-365	90	4	)	)	PUNCT
ejpam-365	90	5	now	now	ADV
ejpam-365	90	6	let	let	VERB
ejpam-365	90	7	α(x	α(x	NUM
ejpam-365	90	8	)	)	PUNCT
ejpam-365	90	9	∈	∈	PROPN
ejpam-365	90	10	(	(	PUNCT
ejpam-365	90	11	l0−λ	l0−λ	PROPN
ejpam-365	90	12	)	)	PUNCT
ejpam-365	90	13	or	or	CCONJ
ejpam-365	90	14	γ(x	γ(x	NOUN
ejpam-365	90	15	)	)	PUNCT
ejpam-365	90	16	∈	∈	PROPN
ejpam-365	90	17	(	(	PUNCT
ejpam-365	90	18	l0−λ	l0−λ	PROPN
ejpam-365	90	19	)	)	PUNCT
ejpam-365	90	20	,	,	PUNCT
ejpam-365	90	21	then	then	ADV
ejpam-365	90	22	by	by	ADP
ejpam-365	90	23	the	the	DET
ejpam-365	90	24	assumption	assumption	NOUN
ejpam-365	90	25	of	of	ADP
ejpam-365	90	26	the	the	DET
ejpam-365	90	27	lemma	lemma	PROPN
ejpam-365	90	28	and	and	CCONJ
ejpam-365	90	29	as	as	ADP
ejpam-365	90	30	in	in	ADP
ejpam-365	90	31	[	[	X
ejpam-365	90	32	4	4	NUM
ejpam-365	90	33	]	]	PUNCT
ejpam-365	90	34	,	,	PUNCT
ejpam-365	90	35	we	we	PRON
ejpam-365	90	36	have	have	VERB
ejpam-365	90	37	log	log	NOUN
ejpam-365	90	38	r	r	NOUN
ejpam-365	90	39	+	+	CCONJ
ejpam-365	90	40	o(1	o(1	NOUN
ejpam-365	90	41	)	)	PUNCT
ejpam-365	90	42	=	=	PUNCT
ejpam-365	91	1	log	log	VERB
ejpam-365	91	2	f(x	f(x	PROPN
ejpam-365	91	3	/	/	SYM
ejpam-365	91	4	ρ	ρ	PROPN
ejpam-365	91	5	,	,	PUNCT
ejpam-365	91	6	1	1	NUM
ejpam-365	91	7	/	/	SYM
ejpam-365	91	8	t	t	PROPN
ejpam-365	91	9	,	,	PUNCT
ejpam-365	91	10	ρ	ρ	PROPN
ejpam-365	91	11	)	)	PUNCT
ejpam-365	91	12	.	.	PUNCT
ejpam-365	92	1	hence	hence	ADV
ejpam-365	92	2	we	we	PRON
ejpam-365	92	3	obtain	obtain	VERB
ejpam-365	92	4	r{1	r{1	NOUN
ejpam-365	92	5	+	+	SYM
ejpam-365	92	6	o(1	o(1	NOUN
ejpam-365	92	7	)	)	PUNCT
ejpam-365	92	8	}	}	PUNCT
ejpam-365	92	9	=	=	SYM
ejpam-365	92	10	f(x	f(x	PROPN
ejpam-365	92	11	/	/	SYM
ejpam-365	92	12	ρ	ρ	PROPN
ejpam-365	92	13	,	,	PUNCT
ejpam-365	92	14	1	1	NUM
ejpam-365	92	15	/	/	SYM
ejpam-365	92	16	t	t	PROPN
ejpam-365	92	17	,	,	PUNCT
ejpam-365	92	18	ρ	ρ	PROPN
ejpam-365	92	19	)	)	PUNCT
ejpam-365	92	20	.	.	PUNCT
ejpam-365	93	1	as	as	ADP
ejpam-365	93	2	in	in	ADP
ejpam-365	93	3	[	[	X
ejpam-365	93	4	4	4	NUM
ejpam-365	93	5	]	]	PUNCT
ejpam-365	93	6	,	,	PUNCT
ejpam-365	93	7	the	the	DET
ejpam-365	93	8	maximum	maximum	NOUN
ejpam-365	93	9	of	of	ADP
ejpam-365	93	10	the	the	DET
ejpam-365	93	11	function	function	NOUN
ejpam-365	93	12	φ(x	φ(x	PROPN
ejpam-365	93	13	)	)	PUNCT
ejpam-365	93	14	in	in	ADP
ejpam-365	93	15	this	this	DET
ejpam-365	93	16	case	case	NOUN
ejpam-365	93	17	is	be	AUX
ejpam-365	93	18	attained	attain	VERB
ejpam-365	93	19	for	for	ADP
ejpam-365	93	20	x∗(r	x∗(r	PROPN
ejpam-365	93	21	)	)	PUNCT
ejpam-365	94	1	=	=	PUNCT
ejpam-365	94	2	ρα−1[tβ([γ(r{1	ρα−1[tβ([γ(r{1	PROPN
ejpam-365	94	3	+	+	ADJ
ejpam-365	94	4	o(1)})]ρ	o(1)})]ρ	PROPN
ejpam-365	94	5	)	)	PUNCT
ejpam-365	94	6	]	]	PUNCT
ejpam-365	94	7	.	.	PUNCT
ejpam-365	95	1	further	far	ADV
ejpam-365	95	2	,	,	PUNCT
ejpam-365	95	3	||pn||k	||pn||k	PROPN
ejpam-365	95	4	rn	rn	PROPN
ejpam-365	95	5	≤	≤	PROPN
ejpam-365	95	6	exp({1	exp({1	PROPN
ejpam-365	95	7	+	+	NUM
ejpam-365	95	8	o(1)}α−1[tβ([γ(r{1	o(1)}α−1[tβ([γ(r{1	NOUN
ejpam-365	95	9	+	+	ADJ
ejpam-365	95	10	o(1)})]ρ	o(1)})]ρ	PROPN
ejpam-365	95	11	)	)	PUNCT
ejpam-365	95	12	]	]	PUNCT
ejpam-365	95	13	)	)	PUNCT
ejpam-365	95	14	,	,	PUNCT
ejpam-365	95	15	n	n	PRON
ejpam-365	95	16	≥	≥	NOUN
ejpam-365	95	17	n0	n0	NUM
ejpam-365	95	18	,	,	PUNCT
ejpam-365	95	19	r	r	NOUN
ejpam-365	95	20	>	>	X
ejpam-365	95	21	0	0	NUM
ejpam-365	95	22	g.	g.	PROPN
ejpam-365	95	23	srivastava	srivastava	PROPN
ejpam-365	95	24	and	and	CCONJ
ejpam-365	95	25	s.	s.	PROPN
ejpam-365	95	26	kumar	kumar	PROPN
ejpam-365	95	27	/	/	SYM
ejpam-365	95	28	eur	eur	PROPN
ejpam-365	95	29	.	.	PUNCT
ejpam-365	96	1	j.	j.	PROPN
ejpam-365	96	2	pure	pure	PROPN
ejpam-365	96	3	appl	appl	PROPN
ejpam-365	96	4	.	.	PROPN
ejpam-365	96	5	math	math	PROPN
ejpam-365	96	6	,	,	PUNCT
ejpam-365	96	7	2	2	NUM
ejpam-365	96	8	(	(	PUNCT
ejpam-365	96	9	2009	2009	NUM
ejpam-365	96	10	)	)	PUNCT
ejpam-365	96	11	,	,	PUNCT
ejpam-365	96	12	(	(	PUNCT
ejpam-365	96	13	520	520	NUM
ejpam-365	96	14	-	-	NUM
ejpam-365	96	15	531	531	NUM
ejpam-365	96	16	)	)	PUNCT
ejpam-365	96	17	526	526	NUM
ejpam-365	96	18	and	and	CCONJ
ejpam-365	96	19	in	in	ADP
ejpam-365	96	20	this	this	DET
ejpam-365	96	21	case	case	NOUN
ejpam-365	96	22	we	we	PRON
ejpam-365	96	23	have	have	VERB
ejpam-365	96	24	s	s	NOUN
ejpam-365	96	25	r	r	NOUN
ejpam-365	96	26	,	,	PUNCT
ejpam-365	96	27	∞	∞	PROPN
ejpam-365	96	28	∑	∑	PROPN
ejpam-365	96	29	n=0	n=0	PROPN
ejpam-365	96	30	pn	pn	NOUN
ejpam-365	96	31	!	!	PUNCT
ejpam-365	96	32	≤	≤	NUM
ejpam-365	97	1	2exp	2exp	PROPN
ejpam-365	97	2	�	�	PROPN
ejpam-365	97	3	{	{	PUNCT
ejpam-365	97	4	1	1	NUM
ejpam-365	97	5	+	+	NUM
ejpam-365	97	6	o(1)}α−1[tβ({γ(2kr{1	o(1)}α−1[tβ({γ(2kr{1	NOUN
ejpam-365	97	7	+	+	CCONJ
ejpam-365	97	8	o(1)})}ρ	o(1)})}ρ	ADJ
ejpam-365	97	9	)	)	PUNCT
ejpam-365	97	10	]	]	PUNCT
ejpam-365	97	11	�	�	PROPN
ejpam-365	97	12	or	or	CCONJ
ejpam-365	97	13	α	α	DET
ejpam-365	97	14	�	�	PROPN
ejpam-365	97	15	{	{	PUNCT
ejpam-365	97	16	1	1	NUM
ejpam-365	97	17	+	+	NUM
ejpam-365	97	18	o(1)}−1	o(1)}−1	ADJ
ejpam-365	97	19	log	log	NOUN
ejpam-365	97	20	¦	¦	NOUN
ejpam-365	97	21	1	1	NUM
ejpam-365	97	22	2	2	NUM
ejpam-365	97	23	s(r	s(r	NOUN
ejpam-365	97	24	,	,	PUNCT
ejpam-365	97	25	∑∞	∑∞	NOUN
ejpam-365	97	26	n=0	n=0	NUM
ejpam-365	97	27	pn	pn	NOUN
ejpam-365	97	28	)	)	PUNCT
ejpam-365	97	29	©	©	PROPN
ejpam-365	97	30	�	�	PROPN
ejpam-365	97	31	β({γ(2kr{1	β({γ(2kr{1	NUM
ejpam-365	97	32	+	+	CCONJ
ejpam-365	97	33	o(1)})}ρ	o(1)})}ρ	ADJ
ejpam-365	97	34	)	)	PUNCT
ejpam-365	97	35	≤	≤	NOUN
ejpam-365	97	36	t.	t.	NOUN
ejpam-365	97	37	using	use	VERB
ejpam-365	97	38	the	the	DET
ejpam-365	97	39	properties	property	NOUN
ejpam-365	97	40	of	of	ADP
ejpam-365	97	41	the	the	DET
ejpam-365	97	42	functions	function	NOUN
ejpam-365	97	43	α	α	NOUN
ejpam-365	97	44	,	,	PUNCT
ejpam-365	97	45	β	β	X
ejpam-365	97	46	and	and	CCONJ
ejpam-365	97	47	γ	γ	PROPN
ejpam-365	97	48	and	and	CCONJ
ejpam-365	97	49	proceeding	proceed	VERB
ejpam-365	97	50	to	to	ADP
ejpam-365	97	51	limits	limit	NOUN
ejpam-365	97	52	we	we	PRON
ejpam-365	97	53	again	again	ADV
ejpam-365	97	54	obtain	obtain	VERB
ejpam-365	97	55	5	5	NUM
ejpam-365	97	56	.	.	PUNCT
ejpam-365	97	57	since	since	SCONJ
ejpam-365	97	58	t	t	PROPN
ejpam-365	97	59	=	=	SYM
ejpam-365	97	60	t	t	PROPN
ejpam-365	97	61	+	+	CCONJ
ejpam-365	97	62	ǫ	ǫ	X
ejpam-365	97	63	,	,	PUNCT
ejpam-365	97	64	ǫ	ǫ	PRON
ejpam-365	97	65	>	>	X
ejpam-365	97	66	0	0	PUNCT
ejpam-365	97	67	being	be	AUX
ejpam-365	97	68	arbitrarily	arbitrarily	ADV
ejpam-365	97	69	,	,	PUNCT
ejpam-365	97	70	we	we	PRON
ejpam-365	97	71	finally	finally	ADV
ejpam-365	97	72	get	get	VERB
ejpam-365	97	73	σ(α	σ(α	PROPN
ejpam-365	97	74	,	,	PUNCT
ejpam-365	97	75	β	β	X
ejpam-365	97	76	,	,	PUNCT
ejpam-365	97	77	ρ	ρ	PROPN
ejpam-365	97	78	,	,	PUNCT
ejpam-365	97	79	∞	∞	PROPN
ejpam-365	97	80	∑	∑	PROPN
ejpam-365	97	81	n=0	n=0	PROPN
ejpam-365	97	82	pn	pn	NOUN
ejpam-365	97	83	)	)	PUNCT
ejpam-365	97	84	≤	≤	NOUN
ejpam-365	97	85	t	t	NOUN
ejpam-365	97	86	.	.	PUNCT
ejpam-365	98	1	in	in	ADP
ejpam-365	98	2	the	the	DET
ejpam-365	98	3	case	case	NOUN
ejpam-365	98	4	when	when	SCONJ
ejpam-365	98	5	ν(r	ν(r	VERB
ejpam-365	98	6	)	)	PUNCT
ejpam-365	98	7	is	be	AUX
ejpam-365	98	8	bounded	bound	VERB
ejpam-365	98	9	then	then	ADV
ejpam-365	98	10	m	m	VERB
ejpam-365	98	11	∗(r	∗(r	PROPN
ejpam-365	98	12	)	)	PUNCT
ejpam-365	98	13	is	be	AUX
ejpam-365	98	14	also	also	ADV
ejpam-365	98	15	bounded	bound	VERB
ejpam-365	98	16	,	,	PUNCT
ejpam-365	98	17	whence	whence	NOUN
ejpam-365	98	18	∑∞	∑∞	NOUN
ejpam-365	98	19	n=0	n=0	NUM
ejpam-365	98	20	pn	pn	NOUN
ejpam-365	98	21	reduces	reduce	VERB
ejpam-365	98	22	to	to	ADP
ejpam-365	98	23	a	a	DET
ejpam-365	98	24	polynomial	polynomial	NOUN
ejpam-365	98	25	.	.	PUNCT
ejpam-365	99	1	hence	hence	ADV
ejpam-365	99	2	the	the	DET
ejpam-365	99	3	lemma	lemma	PROPN
ejpam-365	99	4	is	be	AUX
ejpam-365	99	5	proved	prove	VERB
ejpam-365	99	6	.	.	PUNCT
ejpam-365	100	1	now	now	ADV
ejpam-365	100	2	we	we	PRON
ejpam-365	100	3	give	give	VERB
ejpam-365	100	4	our	our	PRON
ejpam-365	100	5	main	main	ADJ
ejpam-365	100	6	result	result	NOUN
ejpam-365	100	7	.	.	PUNCT
ejpam-365	101	1	theorem	theorem	NOUN
ejpam-365	101	2	1	1	NUM
ejpam-365	101	3	.	.	PUNCT
ejpam-365	102	1	let	let	VERB
ejpam-365	102	2	k	k	PRON
ejpam-365	102	3	be	be	AUX
ejpam-365	102	4	a	a	DET
ejpam-365	102	5	compact	compact	ADJ
ejpam-365	102	6	set	set	NOUN
ejpam-365	102	7	in	in	ADP
ejpam-365	102	8	c	c	PROPN
ejpam-365	102	9	n	n	PRON
ejpam-365	102	10	such	such	ADJ
ejpam-365	102	11	that	that	SCONJ
ejpam-365	102	12	φk	φk	NOUN
ejpam-365	102	13	is	be	AUX
ejpam-365	102	14	locally	locally	ADV
ejpam-365	102	15	bounded	bound	VERB
ejpam-365	102	16	in	in	ADP
ejpam-365	102	17	c	c	PROPN
ejpam-365	102	18	n	n	PROPN
ejpam-365	102	19	.	.	PUNCT
ejpam-365	103	1	set	set	VERB
ejpam-365	103	2	f(x	f(x	PROPN
ejpam-365	103	3	,	,	PUNCT
ejpam-365	103	4	t	t	PROPN
ejpam-365	103	5	,	,	PUNCT
ejpam-365	103	6	ρ	ρ	PROPN
ejpam-365	103	7	)	)	PUNCT
ejpam-365	103	8	=	=	SYM
ejpam-365	103	9	γ−1{[β−1{tα(x)}]1	γ−1{[β−1{tα(x)}]1	PROPN
ejpam-365	103	10	/	/	SYM
ejpam-365	103	11	ρ	ρ	NOUN
ejpam-365	103	12	}	}	PUNCT
ejpam-365	103	13	.	.	PUNCT
ejpam-365	104	1	suppose	suppose	VERB
ejpam-365	104	2	that	that	SCONJ
ejpam-365	104	3	for	for	ADP
ejpam-365	104	4	all	all	DET
ejpam-365	104	5	t	t	NOUN
ejpam-365	104	6	,	,	PUNCT
ejpam-365	104	7	0	0	NUM
ejpam-365	104	8	<	<	X
ejpam-365	104	9	t	t	X
ejpam-365	104	10	<	<	X
ejpam-365	104	11	∞	∞	PROPN
ejpam-365	104	12	,	,	PUNCT
ejpam-365	104	13	(	(	PUNCT
ejpam-365	104	14	a	a	X
ejpam-365	104	15	)	)	PUNCT
ejpam-365	104	16	if	if	SCONJ
ejpam-365	104	17	γ(x	γ(x	NOUN
ejpam-365	104	18	)	)	PUNCT
ejpam-365	104	19	∈	∈	PROPN
ejpam-365	104	20	λ	λ	PROPN
ejpam-365	104	21	and	and	CCONJ
ejpam-365	104	22	α(x	α(x	PROPN
ejpam-365	104	23	)	)	PUNCT
ejpam-365	104	24	∈	∈	PROPN
ejpam-365	104	25	λ	λ	PROPN
ejpam-365	104	26	,	,	PUNCT
ejpam-365	104	27	then	then	ADV
ejpam-365	104	28	d[log(f(x	d[log(f(x	PROPN
ejpam-365	104	29	,	,	PUNCT
ejpam-365	104	30	t	t	PROPN
ejpam-365	104	31	,	,	PUNCT
ejpam-365	104	32	ρ	ρ	PROPN
ejpam-365	104	33	)	)	PUNCT
ejpam-365	104	34	)	)	PUNCT
ejpam-365	104	35	d(log	d(log	PROPN
ejpam-365	104	36	x	x	X
ejpam-365	104	37	)	)	PUNCT
ejpam-365	104	38	=	=	SYM
ejpam-365	104	39	o(1	o(1	NOUN
ejpam-365	104	40	)	)	PUNCT
ejpam-365	104	41	as	as	ADP
ejpam-365	104	42	x	x	X
ejpam-365	104	43	→∞.	→∞.	PROPN
ejpam-365	104	44	(	(	PUNCT
ejpam-365	104	45	b	b	NOUN
ejpam-365	104	46	)	)	PUNCT
ejpam-365	104	47	if	if	SCONJ
ejpam-365	104	48	γ(x	γ(x	NOUN
ejpam-365	104	49	)	)	PUNCT
ejpam-365	104	50	∈	∈	PROPN
ejpam-365	104	51	(	(	PUNCT
ejpam-365	104	52	l0	l0	NOUN
ejpam-365	104	53	−λ	−λ	NOUN
ejpam-365	104	54	)	)	PUNCT
ejpam-365	104	55	or	or	CCONJ
ejpam-365	104	56	α(x	α(x	NOUN
ejpam-365	104	57	)	)	PUNCT
ejpam-365	104	58	∈	∈	PROPN
ejpam-365	104	59	(	(	PUNCT
ejpam-365	104	60	l0	l0	NOUN
ejpam-365	104	61	−λ	−λ	NOUN
ejpam-365	104	62	)	)	PUNCT
ejpam-365	104	63	,	,	PUNCT
ejpam-365	104	64	then	then	ADV
ejpam-365	104	65	lim	lim	PROPN
ejpam-365	104	66	x→∞	x→∞	PROPN
ejpam-365	104	67	d[log(f(x	d[log(f(x	PROPN
ejpam-365	104	68	,	,	PUNCT
ejpam-365	104	69	t	t	PROPN
ejpam-365	104	70	,	,	PUNCT
ejpam-365	104	71	ρ	ρ	PROPN
ejpam-365	104	72	)	)	PUNCT
ejpam-365	104	73	)	)	PUNCT
ejpam-365	104	74	d(log	d(log	PROPN
ejpam-365	104	75	x	x	X
ejpam-365	104	76	)	)	PUNCT
ejpam-365	104	77	=	=	SYM
ejpam-365	104	78	1	1	NUM
ejpam-365	104	79	ρ	ρ	NOUN
ejpam-365	104	80	.	.	PUNCT
ejpam-365	105	1	then	then	ADV
ejpam-365	105	2	the	the	DET
ejpam-365	105	3	function	function	NOUN
ejpam-365	105	4	f	f	PROPN
ejpam-365	105	5	,	,	PUNCT
ejpam-365	105	6	defined	define	VERB
ejpam-365	105	7	and	and	CCONJ
ejpam-365	105	8	bounded	bound	VERB
ejpam-365	105	9	on	on	ADP
ejpam-365	105	10	k	k	PROPN
ejpam-365	105	11	,	,	PUNCT
ejpam-365	105	12	is	be	AUX
ejpam-365	105	13	the	the	DET
ejpam-365	105	14	restriction	restriction	NOUN
ejpam-365	105	15	of	of	ADP
ejpam-365	105	16	an	an	DET
ejpam-365	105	17	entire	entire	ADJ
ejpam-365	105	18	function	function	NOUN
ejpam-365	105	19	g	g	NOUN
ejpam-365	105	20	of	of	ADP
ejpam-365	105	21	the	the	DET
ejpam-365	105	22	generalized	generalized	ADJ
ejpam-365	105	23	type	type	NOUN
ejpam-365	105	24	σ(α	σ(α	PROPN
ejpam-365	105	25	,	,	PUNCT
ejpam-365	105	26	β	β	X
ejpam-365	105	27	,	,	PUNCT
ejpam-365	105	28	ρ	ρ	PROPN
ejpam-365	105	29	,	,	PUNCT
ejpam-365	105	30	g	g	NOUN
ejpam-365	105	31	)	)	PUNCT
ejpam-365	105	32	if	if	SCONJ
ejpam-365	105	33	and	and	CCONJ
ejpam-365	105	34	only	only	ADV
ejpam-365	105	35	if	if	SCONJ
ejpam-365	105	36	σ(α	σ(α	PROPN
ejpam-365	105	37	,	,	PUNCT
ejpam-365	105	38	β	β	X
ejpam-365	105	39	,	,	PUNCT
ejpam-365	105	40	ρ	ρ	PROPN
ejpam-365	105	41	,	,	PUNCT
ejpam-365	105	42	g	g	NOUN
ejpam-365	105	43	)	)	PUNCT
ejpam-365	106	1	=	=	VERB
ejpam-365	106	2	lim	lim	PROPN
ejpam-365	106	3	n→∞	n→∞	NUM
ejpam-365	106	4	sup	sup	NOUN
ejpam-365	106	5	α(n	α(n	NOUN
ejpam-365	106	6	/	/	SYM
ejpam-365	106	7	ρ	ρ	NOUN
ejpam-365	106	8	)	)	PUNCT
ejpam-365	106	9	β{[γ(e1	β{[γ(e1	NOUN
ejpam-365	106	10	/	/	SYM
ejpam-365	106	11	ρ[es	ρ[es	PROPN
ejpam-365	106	12	n	n	PROPN
ejpam-365	106	13	(	(	PUNCT
ejpam-365	106	14	f	f	PROPN
ejpam-365	106	15	,	,	PUNCT
ejpam-365	106	16	k)]−1	k)]−1	NOUN
ejpam-365	106	17	/	/	SYM
ejpam-365	106	18	n)]ρ	n)]ρ	NOUN
ejpam-365	106	19	}	}	PUNCT
ejpam-365	106	20	;	;	PUNCT
ejpam-365	106	21	s	s	X
ejpam-365	106	22	=	=	SYM
ejpam-365	106	23	1	1	NUM
ejpam-365	106	24	,	,	PUNCT
ejpam-365	106	25	2	2	NUM
ejpam-365	106	26	,	,	PUNCT
ejpam-365	106	27	3	3	NUM
ejpam-365	106	28	.	.	PUNCT
ejpam-365	106	29	g.	g.	PROPN
ejpam-365	106	30	srivastava	srivastava	PROPN
ejpam-365	106	31	and	and	CCONJ
ejpam-365	106	32	s.	s.	PROPN
ejpam-365	106	33	kumar	kumar	PROPN
ejpam-365	106	34	/	/	SYM
ejpam-365	106	35	eur	eur	PROPN
ejpam-365	106	36	.	.	PUNCT
ejpam-365	107	1	j.	j.	PROPN
ejpam-365	107	2	pure	pure	PROPN
ejpam-365	107	3	appl	appl	PROPN
ejpam-365	107	4	.	.	PROPN
ejpam-365	107	5	math	math	PROPN
ejpam-365	107	6	,	,	PUNCT
ejpam-365	107	7	2	2	NUM
ejpam-365	107	8	(	(	PUNCT
ejpam-365	107	9	2009	2009	NUM
ejpam-365	107	10	)	)	PUNCT
ejpam-365	107	11	,	,	PUNCT
ejpam-365	107	12	(	(	PUNCT
ejpam-365	107	13	520	520	NUM
ejpam-365	107	14	-	-	SYM
ejpam-365	107	15	531	531	NUM
ejpam-365	107	16	)	)	PUNCT
ejpam-365	107	17	527	527	NUM
ejpam-365	107	18	proof	proof	NOUN
ejpam-365	107	19	.	.	PUNCT
ejpam-365	108	1	first	first	ADV
ejpam-365	108	2	we	we	PRON
ejpam-365	108	3	assume	assume	VERB
ejpam-365	108	4	that	that	SCONJ
ejpam-365	108	5	f	f	PROPN
ejpam-365	108	6	has	have	VERB
ejpam-365	108	7	an	an	DET
ejpam-365	108	8	entire	entire	ADJ
ejpam-365	108	9	function	function	NOUN
ejpam-365	108	10	extension	extension	NOUN
ejpam-365	108	11	g	g	NOUN
ejpam-365	108	12	which	which	PRON
ejpam-365	108	13	is	be	AUX
ejpam-365	108	14	of	of	ADP
ejpam-365	108	15	generalized	generalized	ADJ
ejpam-365	108	16	type	type	NOUN
ejpam-365	108	17	σ	σ	NOUN
ejpam-365	108	18	=	=	SYM
ejpam-365	108	19	σ(α	σ(α	PROPN
ejpam-365	108	20	,	,	PUNCT
ejpam-365	108	21	β	β	X
ejpam-365	108	22	,	,	PUNCT
ejpam-365	108	23	ρ	ρ	PROPN
ejpam-365	108	24	,	,	PUNCT
ejpam-365	108	25	g	g	NOUN
ejpam-365	108	26	)	)	PUNCT
ejpam-365	108	27	.	.	PUNCT
ejpam-365	109	1	we	we	PRON
ejpam-365	109	2	write	write	VERB
ejpam-365	109	3	ηs	ηs	ADP
ejpam-365	109	4	=	=	PROPN
ejpam-365	109	5	lim	lim	PROPN
ejpam-365	109	6	n→∞	n→∞	NUM
ejpam-365	109	7	sup	sup	NOUN
ejpam-365	109	8	α(n	α(n	NOUN
ejpam-365	109	9	/	/	SYM
ejpam-365	109	10	ρ	ρ	NOUN
ejpam-365	109	11	)	)	PUNCT
ejpam-365	109	12	β{[γ(e1	β{[γ(e1	NOUN
ejpam-365	109	13	/	/	SYM
ejpam-365	109	14	ρ[es	ρ[es	PROPN
ejpam-365	109	15	n	n	PROPN
ejpam-365	109	16	]	]	SYM
ejpam-365	109	17	−1	−1	NOUN
ejpam-365	109	18	/	/	SYM
ejpam-365	109	19	n)]ρ	n)]ρ	NOUN
ejpam-365	109	20	}	}	PUNCT
ejpam-365	109	21	;	;	PUNCT
ejpam-365	109	22	s	s	X
ejpam-365	109	23	=	=	SYM
ejpam-365	109	24	1	1	NUM
ejpam-365	109	25	,	,	PUNCT
ejpam-365	109	26	2	2	NUM
ejpam-365	109	27	,	,	PUNCT
ejpam-365	109	28	3	3	NUM
ejpam-365	109	29	.	.	X
ejpam-365	109	30	here	here	ADV
ejpam-365	109	31	es	es	X
ejpam-365	109	32	n	n	ADV
ejpam-365	109	33	stands	stand	VERB
ejpam-365	109	34	for	for	ADP
ejpam-365	109	35	es	es	ADP
ejpam-365	109	36	n	n	PRON
ejpam-365	109	37	�	�	PROPN
ejpam-365	109	38	g|k	g|k	X
ejpam-365	109	39	,	,	PUNCT
ejpam-365	109	40	k	k	PROPN
ejpam-365	109	41	�	�	PROPN
ejpam-365	109	42	,	,	PUNCT
ejpam-365	109	43	s	s	PART
ejpam-365	109	44	=	=	SYM
ejpam-365	109	45	1	1	NUM
ejpam-365	109	46	,	,	PUNCT
ejpam-365	109	47	2	2	NUM
ejpam-365	109	48	,	,	PUNCT
ejpam-365	109	49	3	3	NUM
ejpam-365	109	50	.	.	X
ejpam-365	110	1	we	we	PRON
ejpam-365	110	2	show	show	VERB
ejpam-365	110	3	that	that	SCONJ
ejpam-365	110	4	σ	σ	NOUN
ejpam-365	110	5	=	=	SYM
ejpam-365	110	6	ηs	ηs	PROPN
ejpam-365	110	7	,	,	PUNCT
ejpam-365	110	8	s	s	NOUN
ejpam-365	110	9	=	=	SYM
ejpam-365	110	10	1	1	NUM
ejpam-365	110	11	,	,	PUNCT
ejpam-365	110	12	2	2	NUM
ejpam-365	110	13	,	,	PUNCT
ejpam-365	110	14	3	3	NUM
ejpam-365	110	15	.	.	X
ejpam-365	111	1	it	it	PRON
ejpam-365	111	2	is	be	AUX
ejpam-365	111	3	known	know	VERB
ejpam-365	111	4	(	(	PUNCT
ejpam-365	111	5	see	see	VERB
ejpam-365	111	6	e.g.	e.g.	ADV
ejpam-365	111	7	[	[	X
ejpam-365	111	8	6	6	NUM
ejpam-365	111	9	]	]	PUNCT
ejpam-365	111	10	)	)	PUNCT
ejpam-365	111	11	that	that	PRON
ejpam-365	111	12	e1	e1	VERB
ejpam-365	111	13	n	n	PRON
ejpam-365	111	14	≤	≤	NOUN
ejpam-365	111	15	e2	e2	PROPN
ejpam-365	111	16	n	n	CCONJ
ejpam-365	111	17	≤	≤	NUM
ejpam-365	111	18	(	(	PUNCT
ejpam-365	111	19	n∗	n∗	X
ejpam-365	111	20	+	+	CCONJ
ejpam-365	111	21	2)e1	2)e1	NUM
ejpam-365	111	22	n	n	NOUN
ejpam-365	111	23	,	,	PUNCT
ejpam-365	111	24	n	n	PRON
ejpam-365	111	25	≥	≥	NOUN
ejpam-365	111	26	0	0	NUM
ejpam-365	111	27	,	,	PUNCT
ejpam-365	111	28	(	(	PUNCT
ejpam-365	111	29	6	6	X
ejpam-365	111	30	)	)	PUNCT
ejpam-365	111	31	e3	e3	VERB
ejpam-365	111	32	n	n	PRON
ejpam-365	111	33	≤	≤	NOUN
ejpam-365	111	34	2(n∗	2(n∗	NUM
ejpam-365	112	1	+	+	CCONJ
ejpam-365	112	2	2)e1	2)e1	NUM
ejpam-365	112	3	n−1	n−1	PROPN
ejpam-365	112	4	,	,	PUNCT
ejpam-365	112	5	n≥	n≥	PROPN
ejpam-365	112	6	1	1	NUM
ejpam-365	112	7	,	,	PUNCT
ejpam-365	112	8	(	(	PUNCT
ejpam-365	112	9	7	7	X
ejpam-365	112	10	)	)	PUNCT
ejpam-365	112	11	where	where	SCONJ
ejpam-365	112	12	n∗	n∗	PROPN
ejpam-365	112	13	=	=	SYM
ejpam-365	112	14			PROPN
ejpam-365	112	15			NOUN
ejpam-365	112	16			NOUN
ejpam-365	112	17	n+	n+	NUM
ejpam-365	112	18	n	n	CCONJ
ejpam-365	112	19	n	n	CCONJ
ejpam-365	112	20			NOUN
ejpam-365	112	21			NOUN
ejpam-365	112	22			PUNCT
ejpam-365	112	23	.	.	PUNCT
ejpam-365	113	1	using	use	VERB
ejpam-365	113	2	stirling	stirling	NOUN
ejpam-365	113	3	formula	formula	NOUN
ejpam-365	113	4	for	for	ADP
ejpam-365	113	5	the	the	DET
ejpam-365	113	6	approximate	approximate	ADJ
ejpam-365	113	7	value	value	NOUN
ejpam-365	113	8	of	of	ADP
ejpam-365	113	9	n	n	CCONJ
ejpam-365	113	10	!	!	PUNCT
ejpam-365	114	1	≈	≈	PROPN
ejpam-365	114	2	e−nnn+1/2	e−nnn+1/2	ADP
ejpam-365	114	3	p	p	ADP
ejpam-365	114	4	2π	2π	NOUN
ejpam-365	114	5	,	,	PUNCT
ejpam-365	114	6	we	we	PRON
ejpam-365	114	7	get	get	VERB
ejpam-365	114	8	n∗	n∗	PROPN
ejpam-365	115	1	≈	≈	PROPN
ejpam-365	115	2	nn	nn	PROPN
ejpam-365	115	3	n	n	PROPN
ejpam-365	115	4	!	!	PUNCT
ejpam-365	116	1	for	for	ADP
ejpam-365	116	2	all	all	DET
ejpam-365	116	3	large	large	ADJ
ejpam-365	116	4	values	value	NOUN
ejpam-365	116	5	of	of	ADP
ejpam-365	116	6	n.	n.	NOUN
ejpam-365	116	7	hence	hence	ADV
ejpam-365	116	8	for	for	ADP
ejpam-365	116	9	all	all	DET
ejpam-365	116	10	large	large	ADJ
ejpam-365	116	11	values	value	NOUN
ejpam-365	116	12	of	of	ADP
ejpam-365	116	13	n	n	CCONJ
ejpam-365	116	14	,	,	PUNCT
ejpam-365	116	15	we	we	PRON
ejpam-365	116	16	have	have	VERB
ejpam-365	116	17	e1	e1	NOUN
ejpam-365	116	18	n	n	PRON
ejpam-365	116	19	≤	≤	NOUN
ejpam-365	116	20	e2	e2	PROPN
ejpam-365	116	21	n	n	CCONJ
ejpam-365	116	22	≤	≤	NUM
ejpam-365	116	23	nn	nn	X
ejpam-365	116	24	n	n	NOUN
ejpam-365	116	25	!	!	PUNCT
ejpam-365	117	1	[	[	X
ejpam-365	117	2	1	1	NUM
ejpam-365	117	3	+	+	NUM
ejpam-365	117	4	o(1)]e1	o(1)]e1	NOUN
ejpam-365	117	5	n	n	NOUN
ejpam-365	117	6	and	and	CCONJ
ejpam-365	117	7	e3	e3	VERB
ejpam-365	117	8	n	n	PRON
ejpam-365	117	9	≤	≤	NUM
ejpam-365	117	10	2	2	NUM
ejpam-365	117	11	nn	nn	NOUN
ejpam-365	117	12	n	n	NOUN
ejpam-365	117	13	!	!	PUNCT
ejpam-365	118	1	[	[	X
ejpam-365	118	2	1	1	NUM
ejpam-365	118	3	+	+	NUM
ejpam-365	118	4	o(1)]e1	o(1)]e1	ADJ
ejpam-365	118	5	n	n	NOUN
ejpam-365	118	6	.	.	PUNCT
ejpam-365	119	1	thus	thus	ADV
ejpam-365	119	2	η3	η3	PROPN
ejpam-365	119	3	≤	≤	NUM
ejpam-365	119	4	η2	η2	VERB
ejpam-365	119	5	=	=	SYM
ejpam-365	119	6	η1	η1	NOUN
ejpam-365	119	7	and	and	CCONJ
ejpam-365	119	8	it	it	PRON
ejpam-365	119	9	suffices	suffice	VERB
ejpam-365	119	10	to	to	PART
ejpam-365	119	11	prove	prove	VERB
ejpam-365	119	12	that	that	SCONJ
ejpam-365	119	13	η1	η1	NOUN
ejpam-365	119	14	≤	≤	PROPN
ejpam-365	119	15	σ	σ	NOUN
ejpam-365	119	16	≤	≤	PROPN
ejpam-365	119	17	η3	η3	NOUN
ejpam-365	119	18	.	.	PUNCT
ejpam-365	120	1	first	first	ADV
ejpam-365	120	2	we	we	PRON
ejpam-365	120	3	prove	prove	VERB
ejpam-365	120	4	that	that	SCONJ
ejpam-365	120	5	η1	η1	NOUN
ejpam-365	120	6	≤	≤	PROPN
ejpam-365	120	7	σ	σ	PROPN
ejpam-365	120	8	.	.	PUNCT
ejpam-365	121	1	using	use	VERB
ejpam-365	121	2	the	the	DET
ejpam-365	121	3	definition	definition	NOUN
ejpam-365	121	4	of	of	ADP
ejpam-365	121	5	the	the	DET
ejpam-365	121	6	generalized	generalized	ADJ
ejpam-365	121	7	type	type	NOUN
ejpam-365	121	8	,	,	PUNCT
ejpam-365	121	9	for	for	ADP
ejpam-365	121	10	ǫ	ǫ	PRON
ejpam-365	121	11	>	>	SYM
ejpam-365	121	12	0	0	PUNCT
ejpam-365	121	13	and	and	CCONJ
ejpam-365	121	14	r	r	X
ejpam-365	121	15	>	>	X
ejpam-365	121	16	r0(ǫ	r0(ǫ	NOUN
ejpam-365	121	17	)	)	PUNCT
ejpam-365	121	18	,	,	PUNCT
ejpam-365	121	19	we	we	PRON
ejpam-365	121	20	have	have	VERB
ejpam-365	121	21	s(r	s(r	ADJ
ejpam-365	121	22	,	,	PUNCT
ejpam-365	121	23	g)≤	g)≤	NOUN
ejpam-365	121	24	exp[α−1{σβ({γ(r)}ρ	exp[α−1{σβ({γ(r)}ρ	NOUN
ejpam-365	121	25	)	)	PUNCT
ejpam-365	121	26	}	}	PUNCT
ejpam-365	121	27	]	]	PUNCT
ejpam-365	121	28	,	,	PUNCT
ejpam-365	121	29	where	where	SCONJ
ejpam-365	121	30	σ	σ	NOUN
ejpam-365	121	31	=	=	PUNCT
ejpam-365	121	32	σ+	σ+	PUNCT
ejpam-365	121	33	ǫ	ǫ	PRON
ejpam-365	121	34	provided	provide	VERB
ejpam-365	121	35	r	r	NOUN
ejpam-365	121	36	is	be	AUX
ejpam-365	121	37	sufficiently	sufficiently	ADV
ejpam-365	121	38	large	large	ADJ
ejpam-365	121	39	.	.	PUNCT
ejpam-365	122	1	without	without	ADP
ejpam-365	122	2	loss	loss	NOUN
ejpam-365	122	3	of	of	ADP
ejpam-365	122	4	generality	generality	NOUN
ejpam-365	122	5	,	,	PUNCT
ejpam-365	122	6	we	we	PRON
ejpam-365	122	7	may	may	AUX
ejpam-365	122	8	suppose	suppose	VERB
ejpam-365	122	9	that	that	SCONJ
ejpam-365	122	10	k	k	PROPN
ejpam-365	123	1	⊂	⊂	PROPN
ejpam-365	123	2	b	b	PROPN
ejpam-365	123	3	=	=	PRON
ejpam-365	123	4	{	{	PUNCT
ejpam-365	123	5	z	z	NOUN
ejpam-365	123	6	∈	∈	PROPN
ejpam-365	123	7	c	c	NOUN
ejpam-365	123	8	n	n	NOUN
ejpam-365	123	9	:	:	PUNCT
ejpam-365	123	10	|z1|2	|z1|2	PROPN
ejpam-365	123	11	+	+	NUM
ejpam-365	123	12	|z2|2	|z2|2	PUNCT
ejpam-365	123	13	+	+	NUM
ejpam-365	123	14	...	...	PUNCT
ejpam-365	123	15	+	+	CCONJ
ejpam-365	123	16	|zn	|zn	X
ejpam-365	123	17	|2	|2	X
ejpam-365	123	18	≤	≤	NUM
ejpam-365	123	19	1	1	NUM
ejpam-365	123	20	}	}	PUNCT
ejpam-365	123	21	.	.	PUNCT
ejpam-365	124	1	then	then	ADV
ejpam-365	124	2	e1	e1	VERB
ejpam-365	124	3	n	n	PRON
ejpam-365	124	4	≤	≤	NUM
ejpam-365	124	5	e1	e1	PROPN
ejpam-365	124	6	n	n	CCONJ
ejpam-365	124	7	(	(	PUNCT
ejpam-365	124	8	g	g	PROPN
ejpam-365	124	9	,	,	PUNCT
ejpam-365	124	10	b	b	NOUN
ejpam-365	124	11	)	)	PUNCT
ejpam-365	124	12	.	.	PUNCT
ejpam-365	125	1	g.	g.	PROPN
ejpam-365	125	2	srivastava	srivastava	PROPN
ejpam-365	125	3	and	and	CCONJ
ejpam-365	125	4	s.	s.	PROPN
ejpam-365	125	5	kumar	kumar	PROPN
ejpam-365	125	6	/	/	SYM
ejpam-365	125	7	eur	eur	PROPN
ejpam-365	125	8	.	.	PUNCT
ejpam-365	126	1	j.	j.	PROPN
ejpam-365	126	2	pure	pure	PROPN
ejpam-365	126	3	appl	appl	PROPN
ejpam-365	126	4	.	.	PROPN
ejpam-365	126	5	math	math	PROPN
ejpam-365	126	6	,	,	PUNCT
ejpam-365	126	7	2	2	NUM
ejpam-365	126	8	(	(	PUNCT
ejpam-365	126	9	2009	2009	NUM
ejpam-365	126	10	)	)	PUNCT
ejpam-365	126	11	,	,	PUNCT
ejpam-365	126	12	(	(	PUNCT
ejpam-365	126	13	520	520	NUM
ejpam-365	126	14	-	-	SYM
ejpam-365	126	15	531	531	NUM
ejpam-365	126	16	)	)	PUNCT
ejpam-365	126	17	528	528	NUM
ejpam-365	126	18	now	now	ADV
ejpam-365	126	19	following	follow	VERB
ejpam-365	126	20	janik	janik	X
ejpam-365	126	21	(	(	PUNCT
ejpam-365	126	22	[	[	X
ejpam-365	126	23	3	3	X
ejpam-365	126	24	]	]	PUNCT
ejpam-365	126	25	p.324	p.324	ADJ
ejpam-365	126	26	)	)	PUNCT
ejpam-365	126	27	,	,	PUNCT
ejpam-365	126	28	we	we	PRON
ejpam-365	126	29	get	get	VERB
ejpam-365	126	30	e1	e1	NOUN
ejpam-365	126	31	n	n	CCONJ
ejpam-365	126	32	(	(	PUNCT
ejpam-365	126	33	g	g	PROPN
ejpam-365	126	34	,	,	PUNCT
ejpam-365	126	35	b	b	NOUN
ejpam-365	126	36	)	)	PUNCT
ejpam-365	126	37	≤	≤	NOUN
ejpam-365	126	38	r−ns(r	r−ns(r	ADJ
ejpam-365	126	39	,	,	PUNCT
ejpam-365	126	40	g	g	NOUN
ejpam-365	126	41	)	)	PUNCT
ejpam-365	126	42	,	,	PUNCT
ejpam-365	126	43	r	r	NOUN
ejpam-365	126	44	≥	≥	NOUN
ejpam-365	126	45	2	2	NUM
ejpam-365	126	46	,	,	PUNCT
ejpam-365	126	47	n	n	PRON
ejpam-365	126	48	≥	≥	NOUN
ejpam-365	126	49	0	0	NUM
ejpam-365	126	50	or	or	CCONJ
ejpam-365	126	51	e1	e1	VERB
ejpam-365	126	52	n	n	CCONJ
ejpam-365	126	53	≤	≤	ADJ
ejpam-365	126	54	r−n	r−n	ADJ
ejpam-365	126	55	exp[α−1{σβ({γ(r)}ρ	exp[α−1{σβ({γ(r)}ρ	NOUN
ejpam-365	126	56	)	)	PUNCT
ejpam-365	126	57	}	}	PUNCT
ejpam-365	126	58	]	]	PUNCT
ejpam-365	126	59	.	.	PUNCT
ejpam-365	127	1	putting	put	VERB
ejpam-365	127	2	r	r	NOUN
ejpam-365	127	3	=	=	SYM
ejpam-365	127	4	r(n	r(n	PROPN
ejpam-365	127	5	)	)	PUNCT
ejpam-365	127	6	=	=	SYM
ejpam-365	127	7	f(n	f(n	PROPN
ejpam-365	127	8	/	/	SYM
ejpam-365	127	9	ρ	ρ	PROPN
ejpam-365	127	10	,	,	PUNCT
ejpam-365	127	11	1	1	NUM
ejpam-365	127	12	/	/	SYM
ejpam-365	127	13	σ	σ	PROPN
ejpam-365	127	14	,	,	PUNCT
ejpam-365	127	15	ρ	ρ	NOUN
ejpam-365	127	16	)	)	PUNCT
ejpam-365	127	17	=	=	SYM
ejpam-365	127	18	γ−1	γ−1	PROPN
ejpam-365	127	19	¨	¨	ADJ
ejpam-365	127	20	�	�	PROPN
ejpam-365	127	21	β−1	β−1	SYM
ejpam-365	127	22	�	�	PROPN
ejpam-365	127	23	1	1	NUM
ejpam-365	127	24	σ	σ	PROPN
ejpam-365	127	25	α(n	α(n	PROPN
ejpam-365	127	26	/	/	SYM
ejpam-365	127	27	ρ	ρ	PROPN
ejpam-365	127	28	)	)	PUNCT
ejpam-365	127	29	�	�	PROPN
ejpam-365	127	30	�	�	PROPN
ejpam-365	127	31	1	1	NUM
ejpam-365	127	32	/	/	SYM
ejpam-365	127	33	ρ	ρ	NOUN
ejpam-365	127	34	«	«	PUNCT
ejpam-365	127	35	,	,	PUNCT
ejpam-365	127	36	we	we	PRON
ejpam-365	127	37	get	get	VERB
ejpam-365	127	38	e1	e1	NOUN
ejpam-365	127	39	n	n	PRON
ejpam-365	127	40	≤	≤	NUM
ejpam-365	127	41	en	en	ADP
ejpam-365	127	42	/	/	SYM
ejpam-365	127	43	ρ	ρ	PROPN
ejpam-365	127	44	�	�	PROPN
ejpam-365	127	45	γ−1	γ−1	PROPN
ejpam-365	127	46	¨	¨	ADJ
ejpam-365	127	47	�	�	PROPN
ejpam-365	127	48	β−1	β−1	SYM
ejpam-365	127	49	�	�	PROPN
ejpam-365	127	50	1	1	NUM
ejpam-365	127	51	σ	σ	PROPN
ejpam-365	127	52	α(n	α(n	PROPN
ejpam-365	127	53	/	/	SYM
ejpam-365	127	54	ρ	ρ	PROPN
ejpam-365	127	55	)	)	PUNCT
ejpam-365	127	56	�	�	PROPN
ejpam-365	127	57	�	�	PROPN
ejpam-365	127	58	1	1	NUM
ejpam-365	127	59	/	/	SYM
ejpam-365	127	60	ρ	ρ	PRON
ejpam-365	127	61	«	«	PUNCT
ejpam-365	127	62	�	�	X
ejpam-365	127	63	−n	−n	NOUN
ejpam-365	127	64	or	or	CCONJ
ejpam-365	127	65	[	[	X
ejpam-365	127	66	e1	e1	PROPN
ejpam-365	127	67	n	n	X
ejpam-365	127	68	]	]	X
ejpam-365	127	69	−1	−1	NOUN
ejpam-365	127	70	/	/	SYM
ejpam-365	127	71	n	n	CCONJ
ejpam-365	127	72	≥	≥	NOUN
ejpam-365	127	73	e−1	e−1	PROPN
ejpam-365	127	74	/	/	SYM
ejpam-365	127	75	ργ−1	ργ−1	PROPN
ejpam-365	127	76	¨	¨	NOUN
ejpam-365	127	77	�	�	PROPN
ejpam-365	127	78	β−1	β−1	SYM
ejpam-365	127	79	�	�	PROPN
ejpam-365	127	80	1	1	NUM
ejpam-365	127	81	σ	σ	PROPN
ejpam-365	127	82	α(n	α(n	PROPN
ejpam-365	127	83	/	/	SYM
ejpam-365	127	84	ρ	ρ	PROPN
ejpam-365	127	85	)	)	PUNCT
ejpam-365	127	86	�	�	PROPN
ejpam-365	127	87	�	�	PROPN
ejpam-365	127	88	1	1	NUM
ejpam-365	127	89	/	/	SYM
ejpam-365	127	90	ρ	ρ	PROPN
ejpam-365	127	91	«	«	PUNCT
ejpam-365	127	92	or	or	CCONJ
ejpam-365	127	93	α(n	α(n	NOUN
ejpam-365	127	94	/	/	SYM
ejpam-365	127	95	ρ	ρ	NOUN
ejpam-365	127	96	)	)	PUNCT
ejpam-365	127	97	β{[γ(e1	β{[γ(e1	NOUN
ejpam-365	127	98	/	/	SYM
ejpam-365	127	99	ρ[e1	ρ[e1	NOUN
ejpam-365	127	100	n	n	CCONJ
ejpam-365	127	101	]	]	X
ejpam-365	127	102	−1	−1	NOUN
ejpam-365	127	103	/	/	SYM
ejpam-365	127	104	n)]ρ	n)]ρ	NOUN
ejpam-365	127	105	}	}	PUNCT
ejpam-365	127	106	≤	≤	PROPN
ejpam-365	127	107	σ	σ	PROPN
ejpam-365	127	108	.	.	PUNCT
ejpam-365	128	1	taking	take	VERB
ejpam-365	128	2	limits	limit	NOUN
ejpam-365	128	3	as	as	ADP
ejpam-365	128	4	n→∞	n→∞	NUM
ejpam-365	128	5	,	,	PUNCT
ejpam-365	128	6	we	we	PRON
ejpam-365	128	7	get	get	VERB
ejpam-365	128	8	lim	lim	PROPN
ejpam-365	128	9	n→∞	n→∞	NUM
ejpam-365	128	10	sup	sup	NOUN
ejpam-365	128	11	α(n	α(n	NOUN
ejpam-365	128	12	/	/	SYM
ejpam-365	128	13	ρ	ρ	NOUN
ejpam-365	128	14	)	)	PUNCT
ejpam-365	128	15	β{[γ(e1	β{[γ(e1	NOUN
ejpam-365	128	16	/	/	SYM
ejpam-365	128	17	ρ[e1	ρ[e1	NOUN
ejpam-365	128	18	n	n	CCONJ
ejpam-365	128	19	]	]	X
ejpam-365	128	20	−1	−1	NOUN
ejpam-365	128	21	/	/	SYM
ejpam-365	128	22	n)]ρ	n)]ρ	NOUN
ejpam-365	128	23	}	}	PUNCT
ejpam-365	128	24	≤	≤	NUM
ejpam-365	128	25	σ	σ	PROPN
ejpam-365	128	26	.	.	PUNCT
ejpam-365	129	1	since	since	SCONJ
ejpam-365	129	2	ǫ	ǫ	PRON
ejpam-365	129	3	>	>	SYM
ejpam-365	129	4	0	0	PUNCT
ejpam-365	129	5	is	be	AUX
ejpam-365	129	6	arbitrarily	arbitrarily	ADV
ejpam-365	129	7	small	small	ADJ
ejpam-365	129	8	,	,	PUNCT
ejpam-365	129	9	therefore	therefore	ADV
ejpam-365	129	10	finally	finally	ADV
ejpam-365	129	11	we	we	PRON
ejpam-365	129	12	get	get	VERB
ejpam-365	129	13	η1	η1	NOUN
ejpam-365	129	14	≤	≤	NUM
ejpam-365	129	15	σ	σ	PROPN
ejpam-365	129	16	.	.	PUNCT
ejpam-365	130	1	now	now	ADV
ejpam-365	130	2	we	we	PRON
ejpam-365	130	3	will	will	AUX
ejpam-365	130	4	prove	prove	VERB
ejpam-365	130	5	that	that	SCONJ
ejpam-365	130	6	σ	σ	NOUN
ejpam-365	130	7	≤	≤	PROPN
ejpam-365	130	8	η3	η3	NOUN
ejpam-365	130	9	.	.	PUNCT
ejpam-365	131	1	suppose	suppose	VERB
ejpam-365	131	2	that	that	SCONJ
ejpam-365	131	3	η3	η3	PROPN
ejpam-365	131	4	<	<	X
ejpam-365	131	5	σ	σ	PROPN
ejpam-365	131	6	.	.	PUNCT
ejpam-365	132	1	then	then	ADV
ejpam-365	132	2	for	for	ADP
ejpam-365	132	3	every	every	DET
ejpam-365	132	4	λ	λ	NOUN
ejpam-365	132	5	,	,	PUNCT
ejpam-365	132	6	η3	η3	NOUN
ejpam-365	132	7	<	<	X
ejpam-365	132	8	λ	λ	X
ejpam-365	132	9	<	<	X
ejpam-365	132	10	σ	σ	PROPN
ejpam-365	132	11	,	,	PUNCT
ejpam-365	132	12	α(n	α(n	PROPN
ejpam-365	132	13	/	/	SYM
ejpam-365	132	14	ρ	ρ	NOUN
ejpam-365	132	15	)	)	PUNCT
ejpam-365	132	16	β{[γ(e1	β{[γ(e1	NOUN
ejpam-365	132	17	/	/	SYM
ejpam-365	132	18	ρ[e3	ρ[e3	NOUN
ejpam-365	132	19	n	n	X
ejpam-365	132	20	]	]	X
ejpam-365	132	21	−1	−1	NOUN
ejpam-365	132	22	/	/	SYM
ejpam-365	132	23	n)]ρ	n)]ρ	NOUN
ejpam-365	132	24	}	}	PUNCT
ejpam-365	132	25	≤	≤	NUM
ejpam-365	132	26	λ	λ	NOUN
ejpam-365	132	27	provided	provide	VERB
ejpam-365	132	28	n	n	CCONJ
ejpam-365	132	29	is	be	AUX
ejpam-365	132	30	sufficiently	sufficiently	ADV
ejpam-365	132	31	large	large	ADJ
ejpam-365	132	32	.	.	PUNCT
ejpam-365	133	1	thus	thus	ADV
ejpam-365	133	2	e3	e3	VERB
ejpam-365	133	3	n	n	PRON
ejpam-365	133	4	≤	≤	X
ejpam-365	133	5	en	en	ADP
ejpam-365	133	6	/	/	SYM
ejpam-365	133	7	ρ	ρ	PROPN
ejpam-365	133	8	�	�	PROPN
ejpam-365	133	9	γ−1	γ−1	PROPN
ejpam-365	133	10	¨	¨	ADJ
ejpam-365	133	11	�	�	PROPN
ejpam-365	133	12	β−1	β−1	SYM
ejpam-365	133	13	�	�	PROPN
ejpam-365	133	14	1	1	NUM
ejpam-365	133	15	λ	λ	PROPN
ejpam-365	133	16	α(n	α(n	NOUN
ejpam-365	133	17	/	/	SYM
ejpam-365	133	18	ρ	ρ	PROPN
ejpam-365	133	19	)	)	PUNCT
ejpam-365	133	20	�	�	PROPN
ejpam-365	133	21	�	�	PROPN
ejpam-365	133	22	1	1	NUM
ejpam-365	133	23	/	/	SYM
ejpam-365	133	24	ρ	ρ	PRON
ejpam-365	133	25	«	«	PUNCT
ejpam-365	133	26	�	�	X
ejpam-365	133	27	−n	−n	NUM
ejpam-365	133	28	.	.	PUNCT
ejpam-365	134	1	g.	g.	PROPN
ejpam-365	134	2	srivastava	srivastava	PROPN
ejpam-365	134	3	and	and	CCONJ
ejpam-365	134	4	s.	s.	PROPN
ejpam-365	134	5	kumar	kumar	PROPN
ejpam-365	134	6	/	/	SYM
ejpam-365	134	7	eur	eur	PROPN
ejpam-365	134	8	.	.	PUNCT
ejpam-365	135	1	j.	j.	PROPN
ejpam-365	135	2	pure	pure	PROPN
ejpam-365	135	3	appl	appl	PROPN
ejpam-365	135	4	.	.	PROPN
ejpam-365	135	5	math	math	PROPN
ejpam-365	135	6	,	,	PUNCT
ejpam-365	135	7	2	2	NUM
ejpam-365	135	8	(	(	PUNCT
ejpam-365	135	9	2009	2009	NUM
ejpam-365	135	10	)	)	PUNCT
ejpam-365	135	11	,	,	PUNCT
ejpam-365	135	12	(	(	PUNCT
ejpam-365	135	13	520	520	NUM
ejpam-365	135	14	-	-	SYM
ejpam-365	135	15	531	531	NUM
ejpam-365	135	16	)	)	PUNCT
ejpam-365	135	17	529	529	NUM
ejpam-365	135	18	also	also	ADV
ejpam-365	135	19	by	by	ADP
ejpam-365	135	20	previous	previous	ADJ
ejpam-365	135	21	lemma	lemma	PROPN
ejpam-365	135	22	,	,	PUNCT
ejpam-365	135	23	σ	σ	PROPN
ejpam-365	135	24	≤	≤	PROPN
ejpam-365	135	25	λ	λ	PROPN
ejpam-365	135	26	,	,	PUNCT
ejpam-365	135	27	where	where	SCONJ
ejpam-365	135	28	σ	σ	PROPN
ejpam-365	135	29	=	=	SYM
ejpam-365	135	30	σ(α	σ(α	PROPN
ejpam-365	135	31	,	,	PUNCT
ejpam-365	135	32	β	β	X
ejpam-365	135	33	,	,	PUNCT
ejpam-365	135	34	ρ	ρ	PROPN
ejpam-365	135	35	,	,	PUNCT
ejpam-365	135	36	g	g	NOUN
ejpam-365	135	37	)	)	PUNCT
ejpam-365	135	38	is	be	AUX
ejpam-365	135	39	the	the	DET
ejpam-365	135	40	generalized	generalized	ADJ
ejpam-365	135	41	type	type	NOUN
ejpam-365	135	42	of	of	ADP
ejpam-365	135	43	g(z	g(z	PROPN
ejpam-365	135	44	)	)	PUNCT
ejpam-365	135	45	as	as	SCONJ
ejpam-365	135	46	dfefined	dfefine	VERB
ejpam-365	135	47	on	on	ADP
ejpam-365	135	48	page	page	NOUN
ejpam-365	135	49	2	2	NUM
ejpam-365	135	50	.	.	PUNCT
ejpam-365	136	1	since	since	SCONJ
ejpam-365	136	2	λ	λ	PROPN
ejpam-365	136	3	has	have	AUX
ejpam-365	136	4	been	be	AUX
ejpam-365	136	5	chosen	choose	VERB
ejpam-365	136	6	less	less	ADJ
ejpam-365	136	7	than	than	ADP
ejpam-365	136	8	σ	σ	PROPN
ejpam-365	136	9	,	,	PUNCT
ejpam-365	136	10	we	we	PRON
ejpam-365	136	11	get	get	VERB
ejpam-365	136	12	a	a	DET
ejpam-365	136	13	contradiction	contradiction	NOUN
ejpam-365	136	14	.	.	PUNCT
ejpam-365	137	1	hence	hence	ADV
ejpam-365	137	2	σ	σ	NOUN
ejpam-365	137	3	≤	≤	PROPN
ejpam-365	137	4	η3	η3	NOUN
ejpam-365	137	5	.	.	PUNCT
ejpam-365	138	1	now	now	ADV
ejpam-365	138	2	let	let	VERB
ejpam-365	138	3	f	f	PRON
ejpam-365	138	4	be	be	AUX
ejpam-365	138	5	a	a	DET
ejpam-365	138	6	function	function	NOUN
ejpam-365	138	7	defined	define	VERB
ejpam-365	138	8	and	and	CCONJ
ejpam-365	138	9	bounded	bound	VERB
ejpam-365	138	10	on	on	ADP
ejpam-365	138	11	k	k	PROPN
ejpam-365	138	12	and	and	CCONJ
ejpam-365	138	13	such	such	ADJ
ejpam-365	138	14	that	that	PRON
ejpam-365	138	15	for	for	ADP
ejpam-365	138	16	s	s	NOUN
ejpam-365	138	17	=	=	SYM
ejpam-365	138	18	1	1	NUM
ejpam-365	138	19	,	,	PUNCT
ejpam-365	138	20	2	2	NUM
ejpam-365	138	21	,	,	PUNCT
ejpam-365	138	22	3	3	NUM
ejpam-365	138	23	,	,	PUNCT
ejpam-365	138	24	ηs	ηs	ADP
ejpam-365	138	25	=	=	SYM
ejpam-365	138	26	lim	lim	PROPN
ejpam-365	138	27	n→∞	n→∞	NUM
ejpam-365	138	28	sup	sup	NOUN
ejpam-365	138	29	α(n	α(n	NOUN
ejpam-365	138	30	/	/	SYM
ejpam-365	138	31	ρ	ρ	NOUN
ejpam-365	138	32	)	)	PUNCT
ejpam-365	138	33	β{[γ(e1	β{[γ(e1	NOUN
ejpam-365	138	34	/	/	SYM
ejpam-365	138	35	ρ[es	ρ[es	PROPN
ejpam-365	138	36	n	n	PROPN
ejpam-365	138	37	]	]	SYM
ejpam-365	138	38	−1	−1	NOUN
ejpam-365	138	39	/	/	SYM
ejpam-365	138	40	n)]ρ	n)]ρ	NOUN
ejpam-365	138	41	}	}	PUNCT
ejpam-365	138	42	.	.	PUNCT
ejpam-365	139	1	so	so	ADV
ejpam-365	139	2	for	for	ADP
ejpam-365	139	3	every	every	DET
ejpam-365	139	4	λ1	λ1	PROPN
ejpam-365	139	5	>	>	X
ejpam-365	139	6	ηs	ηs	PROPN
ejpam-365	139	7	and	and	CCONJ
ejpam-365	139	8	for	for	ADP
ejpam-365	139	9	sufficiently	sufficiently	ADV
ejpam-365	139	10	large	large	ADJ
ejpam-365	139	11	n	n	CCONJ
ejpam-365	139	12	,	,	PUNCT
ejpam-365	139	13	we	we	PRON
ejpam-365	139	14	have	have	VERB
ejpam-365	139	15	α(n	α(n	NOUN
ejpam-365	139	16	/	/	SYM
ejpam-365	139	17	ρ	ρ	NOUN
ejpam-365	139	18	)	)	PUNCT
ejpam-365	139	19	β{[γ(e1	β{[γ(e1	NOUN
ejpam-365	139	20	/	/	SYM
ejpam-365	139	21	ρ[es	ρ[es	PROPN
ejpam-365	139	22	n	n	PROPN
ejpam-365	139	23	]	]	SYM
ejpam-365	139	24	−1	−1	NOUN
ejpam-365	139	25	/	/	SYM
ejpam-365	139	26	n)]ρ	n)]ρ	NOUN
ejpam-365	139	27	}	}	PUNCT
ejpam-365	139	28	≤	≤	ADV
ejpam-365	139	29	λ1	λ1	ADJ
ejpam-365	139	30	or	or	CCONJ
ejpam-365	139	31	es	es	NOUN
ejpam-365	139	32	n	n	PRON
ejpam-365	139	33	≤	≤	X
ejpam-365	139	34	en	en	ADP
ejpam-365	139	35	/	/	SYM
ejpam-365	139	36	ρ	ρ	PROPN
ejpam-365	139	37	�	�	PROPN
ejpam-365	139	38	γ−1	γ−1	PROPN
ejpam-365	139	39	¨	¨	ADJ
ejpam-365	139	40	�	�	PROPN
ejpam-365	139	41	β−1	β−1	SYM
ejpam-365	139	42	�	�	PROPN
ejpam-365	139	43	1	1	NUM
ejpam-365	139	44	λ1	λ1	PROPN
ejpam-365	139	45	α(n	α(n	PROPN
ejpam-365	139	46	/	/	SYM
ejpam-365	139	47	ρ	ρ	PROPN
ejpam-365	139	48	)	)	PUNCT
ejpam-365	139	49	�	�	PROPN
ejpam-365	139	50	�	�	PROPN
ejpam-365	139	51	1	1	NUM
ejpam-365	139	52	/	/	SYM
ejpam-365	139	53	ρ	ρ	PRON
ejpam-365	139	54	«	«	PUNCT
ejpam-365	139	55	�	�	X
ejpam-365	139	56	−n	−n	NUM
ejpam-365	139	57	.	.	PUNCT
ejpam-365	140	1	proceeding	proceed	VERB
ejpam-365	140	2	to	to	ADP
ejpam-365	140	3	limits	limit	NOUN
ejpam-365	140	4	as	as	ADP
ejpam-365	140	5	n→∞	n→∞	NUM
ejpam-365	140	6	,	,	PUNCT
ejpam-365	140	7	we	we	PRON
ejpam-365	140	8	get	get	VERB
ejpam-365	140	9	lim	lim	PROPN
ejpam-365	140	10	n→∞[e	n→∞[e	PROPN
ejpam-365	140	11	s	s	PART
ejpam-365	140	12	n	n	X
ejpam-365	140	13	]	]	SYM
ejpam-365	140	14	1	1	NUM
ejpam-365	140	15	/	/	SYM
ejpam-365	140	16	n	n	CCONJ
ejpam-365	140	17	≤	≤	NOUN
ejpam-365	140	18	0	0	NUM
ejpam-365	140	19	.	.	PUNCT
ejpam-365	141	1	also	also	ADV
ejpam-365	141	2	it	it	PRON
ejpam-365	141	3	is	be	AUX
ejpam-365	141	4	obvious	obvious	ADJ
ejpam-365	141	5	that	that	SCONJ
ejpam-365	141	6	lim	lim	PROPN
ejpam-365	141	7	n→∞	n→∞	X
ejpam-365	142	1	[	[	X
ejpam-365	142	2	es	es	X
ejpam-365	142	3	n	n	X
ejpam-365	142	4	]	]	SYM
ejpam-365	142	5	1	1	NUM
ejpam-365	142	6	/	/	SYM
ejpam-365	142	7	n	n	CCONJ
ejpam-365	142	8	≥	≥	NOUN
ejpam-365	142	9	0	0	NUM
ejpam-365	142	10	.	.	PUNCT
ejpam-365	143	1	hence	hence	ADV
ejpam-365	143	2	finally	finally	ADV
ejpam-365	143	3	we	we	PRON
ejpam-365	143	4	get	get	VERB
ejpam-365	143	5	lim	lim	PROPN
ejpam-365	143	6	n→∞[e	n→∞[e	PROPN
ejpam-365	143	7	s	s	PART
ejpam-365	143	8	n	n	X
ejpam-365	143	9	]	]	SYM
ejpam-365	143	10	1	1	NUM
ejpam-365	143	11	/	/	SYM
ejpam-365	143	12	n	n	NOUN
ejpam-365	143	13	=	=	SYM
ejpam-365	143	14	0	0	NUM
ejpam-365	143	15	.	.	PUNCT
ejpam-365	144	1	so	so	ADV
ejpam-365	144	2	following	follow	VERB
ejpam-365	144	3	janik	janik	X
ejpam-365	144	4	(	(	PUNCT
ejpam-365	144	5	see	see	VERB
ejpam-365	144	6	[	[	X
ejpam-365	144	7	1	1	NUM
ejpam-365	144	8	]	]	PUNCT
ejpam-365	144	9	,	,	PUNCT
ejpam-365	144	10	prop	prop	NOUN
ejpam-365	144	11	.	.	NOUN
ejpam-365	144	12	3.1	3.1	NUM
ejpam-365	144	13	)	)	PUNCT
ejpam-365	144	14	,	,	PUNCT
ejpam-365	144	15	we	we	PRON
ejpam-365	144	16	claim	claim	VERB
ejpam-365	144	17	that	that	SCONJ
ejpam-365	144	18	the	the	DET
ejpam-365	144	19	function	function	NOUN
ejpam-365	144	20	f	f	PROPN
ejpam-365	144	21	can	can	AUX
ejpam-365	144	22	be	be	AUX
ejpam-365	144	23	continuously	continuously	ADV
ejpam-365	144	24	extended	extend	VERB
ejpam-365	144	25	to	to	ADP
ejpam-365	144	26	an	an	DET
ejpam-365	144	27	entire	entire	ADJ
ejpam-365	144	28	function	function	NOUN
ejpam-365	144	29	.	.	PUNCT
ejpam-365	145	1	let	let	VERB
ejpam-365	145	2	us	we	PRON
ejpam-365	145	3	put	put	VERB
ejpam-365	145	4	g	g	NOUN
ejpam-365	145	5	=	=	PUNCT
ejpam-365	145	6	l0	l0	PROPN
ejpam-365	145	7	+	+	CCONJ
ejpam-365	145	8	∞	∞	NUM
ejpam-365	145	9	∑	∑	PUNCT
ejpam-365	145	10	n=1	n=1	PROPN
ejpam-365	145	11	(	(	PUNCT
ejpam-365	145	12	ln	ln	ADJ
ejpam-365	145	13	−	−	PROPN
ejpam-365	145	14	ln−1	ln−1	PROPN
ejpam-365	145	15	)	)	PUNCT
ejpam-365	145	16	,	,	PUNCT
ejpam-365	145	17	references	reference	VERB
ejpam-365	145	18	530	530	NUM
ejpam-365	145	19	where	where	SCONJ
ejpam-365	145	20	{	{	PUNCT
ejpam-365	145	21	ln	ln	ADJ
ejpam-365	145	22	}	}	PUNCT
ejpam-365	145	23	is	be	AUX
ejpam-365	145	24	the	the	DET
ejpam-365	145	25	sequence	sequence	NOUN
ejpam-365	145	26	of	of	ADP
ejpam-365	145	27	lagrange	lagrange	NOUN
ejpam-365	145	28	interpolation	interpolation	NOUN
ejpam-365	145	29	polynomials	polynomial	NOUN
ejpam-365	145	30	of	of	ADP
ejpam-365	145	31	f	f	PROPN
ejpam-365	145	32	as	as	SCONJ
ejpam-365	145	33	defined	define	VERB
ejpam-365	145	34	earlier	early	ADV
ejpam-365	145	35	.	.	PUNCT
ejpam-365	146	1	now	now	ADV
ejpam-365	146	2	we	we	PRON
ejpam-365	146	3	claim	claim	VERB
ejpam-365	146	4	that	that	SCONJ
ejpam-365	146	5	g	g	PROPN
ejpam-365	146	6	is	be	AUX
ejpam-365	146	7	the	the	DET
ejpam-365	146	8	required	require	VERB
ejpam-365	146	9	continuation	continuation	NOUN
ejpam-365	146	10	of	of	ADP
ejpam-365	146	11	f	f	PROPN
ejpam-365	146	12	and	and	CCONJ
ejpam-365	146	13	σ(α	σ(α	PROPN
ejpam-365	146	14	,	,	PUNCT
ejpam-365	146	15	β	β	X
ejpam-365	146	16	,	,	PUNCT
ejpam-365	146	17	ρ	ρ	PROPN
ejpam-365	146	18	,	,	PUNCT
ejpam-365	146	19	g	g	NOUN
ejpam-365	146	20	)	)	PUNCT
ejpam-365	147	1	=	=	SYM
ejpam-365	147	2	ηs	ηs	PROPN
ejpam-365	147	3	.	.	PROPN
ejpam-365	148	1	for	for	ADP
ejpam-365	148	2	every	every	DET
ejpam-365	148	3	λ1	λ1	PROPN
ejpam-365	148	4	>	>	X
ejpam-365	148	5	η3	η3	PROPN
ejpam-365	148	6	and	and	CCONJ
ejpam-365	148	7	for	for	ADP
ejpam-365	148	8	sufficiently	sufficiently	ADV
ejpam-365	148	9	large	large	ADJ
ejpam-365	148	10	n	n	CCONJ
ejpam-365	148	11	,	,	PUNCT
ejpam-365	148	12	we	we	PRON
ejpam-365	148	13	have	have	VERB
ejpam-365	148	14	e3	e3	NOUN
ejpam-365	148	15	n	n	PRON
ejpam-365	148	16	≤	≤	X
ejpam-365	148	17	en	en	ADP
ejpam-365	148	18	/	/	SYM
ejpam-365	148	19	ρ	ρ	PROPN
ejpam-365	148	20	�	�	PROPN
ejpam-365	148	21	γ−1	γ−1	PROPN
ejpam-365	148	22	¨	¨	ADJ
ejpam-365	148	23	�	�	PROPN
ejpam-365	148	24	β−1	β−1	SYM
ejpam-365	148	25	�	�	PROPN
ejpam-365	148	26	1	1	NUM
ejpam-365	148	27	λ1	λ1	PROPN
ejpam-365	148	28	α(n	α(n	PROPN
ejpam-365	148	29	/	/	SYM
ejpam-365	148	30	ρ	ρ	PROPN
ejpam-365	148	31	)	)	PUNCT
ejpam-365	148	32	�	�	PROPN
ejpam-365	148	33	�	�	PROPN
ejpam-365	148	34	1	1	NUM
ejpam-365	148	35	/	/	SYM
ejpam-365	148	36	ρ	ρ	PRON
ejpam-365	148	37	«	«	PUNCT
ejpam-365	148	38	�	�	X
ejpam-365	148	39	−n	−n	NUM
ejpam-365	148	40	or	or	CCONJ
ejpam-365	148	41	||ln−	||ln−	NOUN
ejpam-365	148	42	ln−1||	ln−1||	VERB
ejpam-365	148	43	≤	≤	NUM
ejpam-365	148	44	en	en	PROPN
ejpam-365	148	45	/	/	SYM
ejpam-365	148	46	ρ	ρ	PROPN
ejpam-365	148	47	�	�	PROPN
ejpam-365	148	48	γ−1	γ−1	PROPN
ejpam-365	148	49	¨	¨	ADJ
ejpam-365	148	50	�	�	PROPN
ejpam-365	148	51	β−1	β−1	SYM
ejpam-365	148	52	�	�	PROPN
ejpam-365	148	53	1	1	NUM
ejpam-365	148	54	λ1	λ1	PROPN
ejpam-365	148	55	α(n	α(n	PROPN
ejpam-365	148	56	/	/	SYM
ejpam-365	148	57	ρ	ρ	PROPN
ejpam-365	148	58	)	)	PUNCT
ejpam-365	148	59	�	�	PROPN
ejpam-365	148	60	�	�	PROPN
ejpam-365	148	61	1	1	NUM
ejpam-365	148	62	/	/	SYM
ejpam-365	148	63	ρ	ρ	PRON
ejpam-365	148	64	«	«	PUNCT
ejpam-365	148	65	�	�	X
ejpam-365	148	66	−n	−n	NUM
ejpam-365	148	67	.	.	PUNCT
ejpam-365	149	1	so	so	ADV
ejpam-365	149	2	using	use	VERB
ejpam-365	149	3	the	the	DET
ejpam-365	149	4	lemma	lemma	PROPN
ejpam-365	149	5	1	1	NUM
ejpam-365	149	6	,	,	PUNCT
ejpam-365	149	7	we	we	PRON
ejpam-365	149	8	get	get	VERB
ejpam-365	149	9	σ(α	σ(α	PROPN
ejpam-365	149	10	,	,	PUNCT
ejpam-365	149	11	β	β	X
ejpam-365	149	12	,	,	PUNCT
ejpam-365	149	13	ρ	ρ	PROPN
ejpam-365	149	14	,	,	PUNCT
ejpam-365	149	15	g	g	NOUN
ejpam-365	149	16	)	)	PUNCT
ejpam-365	149	17	≤	≤	NOUN
ejpam-365	149	18	λ1	λ1	PROPN
ejpam-365	149	19	.	.	PUNCT
ejpam-365	150	1	since	since	SCONJ
ejpam-365	150	2	λ1	λ1	PROPN
ejpam-365	150	3	>	>	X
ejpam-365	150	4	η3	η3	PROPN
ejpam-365	150	5	is	be	AUX
ejpam-365	150	6	arbitrary	arbitrary	ADJ
ejpam-365	150	7	,	,	PUNCT
ejpam-365	150	8	so	so	ADV
ejpam-365	150	9	finally	finally	ADV
ejpam-365	150	10	we	we	PRON
ejpam-365	150	11	get	get	VERB
ejpam-365	150	12	σ(α	σ(α	PROPN
ejpam-365	150	13	,	,	PUNCT
ejpam-365	150	14	β	β	X
ejpam-365	150	15	,	,	PUNCT
ejpam-365	150	16	ρ	ρ	PROPN
ejpam-365	150	17	,	,	PUNCT
ejpam-365	150	18	g	g	NOUN
ejpam-365	150	19	)	)	PUNCT
ejpam-365	150	20	≤	≤	NOUN
ejpam-365	150	21	η3	η3	NOUN
ejpam-365	150	22	.	.	PUNCT
ejpam-365	151	1	using	use	VERB
ejpam-365	151	2	the	the	DET
ejpam-365	151	3	inequalities	inequality	NOUN
ejpam-365	151	4	6	6	NUM
ejpam-365	151	5	,	,	PUNCT
ejpam-365	151	6	7	7	NUM
ejpam-365	151	7	and	and	CCONJ
ejpam-365	151	8	the	the	DET
ejpam-365	151	9	proof	proof	NOUN
ejpam-365	151	10	of	of	ADP
ejpam-365	151	11	first	first	ADJ
ejpam-365	151	12	part	part	NOUN
ejpam-365	151	13	given	give	VERB
ejpam-365	151	14	above	above	ADV
ejpam-365	151	15	,	,	PUNCT
ejpam-365	151	16	we	we	PRON
ejpam-365	151	17	haveσ(α	haveσ(α	VERB
ejpam-365	151	18	,	,	PUNCT
ejpam-365	151	19	β	β	PROPN
ejpam-365	151	20	,	,	PUNCT
ejpam-365	151	21	ρ	ρ	PROPN
ejpam-365	151	22	,	,	PUNCT
ejpam-365	151	23	g	g	NOUN
ejpam-365	151	24	)	)	PUNCT
ejpam-365	151	25	=	=	SYM
ejpam-365	152	1	ηs	ηs	PROPN
ejpam-365	152	2	,	,	PUNCT
ejpam-365	152	3	as	as	SCONJ
ejpam-365	152	4	claimed	claim	VERB
ejpam-365	152	5	.	.	PUNCT
ejpam-365	153	1	this	this	PRON
ejpam-365	153	2	completes	complete	VERB
ejpam-365	153	3	the	the	DET
ejpam-365	153	4	proof	proof	NOUN
ejpam-365	153	5	of	of	ADP
ejpam-365	153	6	the	the	DET
ejpam-365	153	7	theorem	theorem	NOUN
ejpam-365	153	8	.	.	PUNCT
ejpam-365	154	1	acknowledgements	acknowledgement	NOUN
ejpam-365	154	2	the	the	DET
ejpam-365	154	3	authors	author	NOUN
ejpam-365	154	4	are	be	AUX
ejpam-365	154	5	very	very	ADV
ejpam-365	154	6	thankful	thankful	ADJ
ejpam-365	154	7	to	to	ADP
ejpam-365	154	8	the	the	DET
ejpam-365	154	9	referee	referee	NOUN
ejpam-365	154	10	for	for	ADP
ejpam-365	154	11	his	his	PRON
ejpam-365	154	12	valuable	valuable	ADJ
ejpam-365	154	13	comments	comment	NOUN
ejpam-365	154	14	and	and	CCONJ
ejpam-365	154	15	observations	observation	NOUN
ejpam-365	154	16	which	which	PRON
ejpam-365	154	17	helped	help	VERB
ejpam-365	154	18	in	in	ADP
ejpam-365	154	19	improving	improve	VERB
ejpam-365	154	20	the	the	DET
ejpam-365	154	21	paper	paper	NOUN
ejpam-365	154	22	.	.	PUNCT
ejpam-365	155	1	references	reference	NOUN
ejpam-365	155	2	[	[	X
ejpam-365	155	3	1	1	NUM
ejpam-365	155	4	]	]	PUNCT
ejpam-365	155	5	adam	adam	PROPN
ejpam-365	155	6	janik	janik	X
ejpam-365	155	7	,	,	PUNCT
ejpam-365	155	8	on	on	ADP
ejpam-365	155	9	approximation	approximation	NOUN
ejpam-365	155	10	and	and	CCONJ
ejpam-365	155	11	interpolation	interpolation	NOUN
ejpam-365	155	12	of	of	ADP
ejpam-365	155	13	entire	entire	ADJ
ejpam-365	155	14	functions	function	NOUN
ejpam-365	155	15	,	,	PUNCT
ejpam-365	155	16	zeszyty	zeszyty	VERB
ejpam-365	155	17	naukowe	naukowe	NOUN
ejpam-365	155	18	universtytetu	universtytetu	NOUN
ejpam-365	155	19	jagiellonskiego	jagiellonskiego	NOUN
ejpam-365	155	20	,	,	PUNCT
ejpam-365	155	21	22	22	NUM
ejpam-365	155	22	(	(	PUNCT
ejpam-365	155	23	1981	1981	NUM
ejpam-365	155	24	)	)	PUNCT
ejpam-365	155	25	,	,	PUNCT
ejpam-365	155	26	173	173	NUM
ejpam-365	155	27	-	-	SYM
ejpam-365	155	28	188	188	NUM
ejpam-365	155	29	.	.	PUNCT
ejpam-365	156	1	[	[	X
ejpam-365	156	2	2	2	X
ejpam-365	156	3	]	]	PUNCT
ejpam-365	156	4	adam	adam	PROPN
ejpam-365	156	5	janik	janik	X
ejpam-365	156	6	,	,	PUNCT
ejpam-365	156	7	a	a	DET
ejpam-365	156	8	characterization	characterization	NOUN
ejpam-365	156	9	of	of	ADP
ejpam-365	156	10	the	the	DET
ejpam-365	156	11	growth	growth	NOUN
ejpam-365	156	12	of	of	ADP
ejpam-365	156	13	analytic	analytic	ADJ
ejpam-365	156	14	functions	function	NOUN
ejpam-365	156	15	by	by	ADP
ejpam-365	156	16	means	mean	NOUN
ejpam-365	156	17	of	of	ADP
ejpam-365	156	18	polynomial	polynomial	ADJ
ejpam-365	156	19	approximation	approximation	NOUN
ejpam-365	156	20	,	,	PUNCT
ejpam-365	156	21	univ	univ	PROPN
ejpam-365	156	22	.	.	PUNCT
ejpam-365	156	23	iagel	iagel	PROPN
ejpam-365	156	24	.	.	PUNCT
ejpam-365	157	1	acta	acta	PROPN
ejpam-365	157	2	math	math	PROPN
ejpam-365	157	3	.	.	PUNCT
ejpam-365	158	1	,	,	PUNCT
ejpam-365	158	2	24	24	NUM
ejpam-365	158	3	(	(	PUNCT
ejpam-365	158	4	1984	1984	NUM
ejpam-365	158	5	)	)	PUNCT
ejpam-365	158	6	,	,	PUNCT
ejpam-365	158	7	295	295	NUM
ejpam-365	158	8	-	-	SYM
ejpam-365	158	9	319	319	NUM
ejpam-365	158	10	.	.	PUNCT
ejpam-365	159	1	[	[	X
ejpam-365	159	2	3	3	X
ejpam-365	159	3	]	]	X
ejpam-365	159	4	adam	adam	PROPN
ejpam-365	159	5	janik	janik	X
ejpam-365	159	6	,	,	PUNCT
ejpam-365	159	7	on	on	ADP
ejpam-365	159	8	approximation	approximation	NOUN
ejpam-365	159	9	of	of	ADP
ejpam-365	159	10	entire	entire	ADJ
ejpam-365	159	11	functions	function	NOUN
ejpam-365	159	12	and	and	CCONJ
ejpam-365	159	13	generalized	generalized	ADJ
ejpam-365	159	14	order	order	NOUN
ejpam-365	159	15	,	,	PUNCT
ejpam-365	159	16	univ	univ	PROPN
ejpam-365	159	17	.	.	PUNCT
ejpam-365	159	18	iagel	iagel	PROPN
ejpam-365	159	19	.	.	PUNCT
ejpam-365	160	1	acta	acta	PROPN
ejpam-365	160	2	math	math	PROPN
ejpam-365	160	3	.	.	PUNCT
ejpam-365	161	1	,	,	PUNCT
ejpam-365	161	2	24	24	NUM
ejpam-365	161	3	(	(	PUNCT
ejpam-365	161	4	1984	1984	NUM
ejpam-365	161	5	)	)	PUNCT
ejpam-365	161	6	,	,	PUNCT
ejpam-365	161	7	321	321	NUM
ejpam-365	161	8	-	-	SYM
ejpam-365	161	9	326	326	NUM
ejpam-365	161	10	.	.	PUNCT
ejpam-365	162	1	references	reference	NOUN
ejpam-365	162	2	531	531	NUM
ejpam-365	162	3	[	[	X
ejpam-365	162	4	4	4	NUM
ejpam-365	162	5	]	]	PUNCT
ejpam-365	162	6	m.	m.	NOUN
ejpam-365	162	7	n.	n.	PROPN
ejpam-365	162	8	seremeta	seremeta	PROPN
ejpam-365	162	9	,	,	PUNCT
ejpam-365	162	10	on	on	ADP
ejpam-365	162	11	the	the	DET
ejpam-365	162	12	connection	connection	NOUN
ejpam-365	162	13	between	between	ADP
ejpam-365	162	14	the	the	DET
ejpam-365	162	15	growth	growth	NOUN
ejpam-365	162	16	of	of	ADP
ejpam-365	162	17	the	the	DET
ejpam-365	162	18	maximum	maximum	ADJ
ejpam-365	162	19	modulus	modulus	NOUN
ejpam-365	162	20	of	of	ADP
ejpam-365	162	21	an	an	DET
ejpam-365	162	22	entire	entire	ADJ
ejpam-365	162	23	function	function	NOUN
ejpam-365	162	24	and	and	CCONJ
ejpam-365	162	25	the	the	DET
ejpam-365	162	26	moduli	modulus	NOUN
ejpam-365	162	27	of	of	ADP
ejpam-365	162	28	the	the	DET
ejpam-365	162	29	coefficients	coefficient	NOUN
ejpam-365	162	30	of	of	ADP
ejpam-365	162	31	its	its	PRON
ejpam-365	162	32	power	power	NOUN
ejpam-365	162	33	series	series	NOUN
ejpam-365	162	34	expansion	expansion	NOUN
ejpam-365	162	35	,	,	PUNCT
ejpam-365	162	36	amer	amer	PROPN
ejpam-365	162	37	.	.	PROPN
ejpam-365	162	38	math	math	PROPN
ejpam-365	162	39	.	.	PUNCT
ejpam-365	163	1	soc	soc	PROPN
ejpam-365	163	2	.	.	PUNCT
ejpam-365	164	1	transl	transl	PROPN
ejpam-365	164	2	.	.	PUNCT
ejpam-365	165	1	,	,	PUNCT
ejpam-365	165	2	88	88	NUM
ejpam-365	165	3	(	(	PUNCT
ejpam-365	165	4	2	2	NUM
ejpam-365	165	5	)	)	PUNCT
ejpam-365	165	6	(	(	PUNCT
ejpam-365	165	7	1970	1970	NUM
ejpam-365	165	8	)	)	PUNCT
ejpam-365	165	9	,	,	PUNCT
ejpam-365	165	10	291	291	NUM
ejpam-365	165	11	-	-	SYM
ejpam-365	165	12	301	301	NUM
ejpam-365	165	13	.	.	PUNCT
ejpam-365	166	1	[	[	X
ejpam-365	166	2	5	5	X
ejpam-365	166	3	]	]	PUNCT
ejpam-365	166	4	s.	s.	PROPN
ejpam-365	166	5	m.	m.	PROPN
ejpam-365	166	6	shah	shah	PROPN
ejpam-365	166	7	,	,	PUNCT
ejpam-365	166	8	polynomial	polynomial	ADJ
ejpam-365	166	9	approximation	approximation	NOUN
ejpam-365	166	10	of	of	ADP
ejpam-365	166	11	an	an	DET
ejpam-365	166	12	entire	entire	ADJ
ejpam-365	166	13	function	function	NOUN
ejpam-365	166	14	and	and	CCONJ
ejpam-365	166	15	generalized	generalized	ADJ
ejpam-365	166	16	order	order	NOUN
ejpam-365	166	17	,	,	PUNCT
ejpam-365	166	18	j.	j.	PROPN
ejpam-365	166	19	approx	approx	PROPN
ejpam-365	166	20	.	.	PUNCT
ejpam-365	167	1	theory	theory	NOUN
ejpam-365	167	2	,	,	PUNCT
ejpam-365	167	3	19	19	NUM
ejpam-365	167	4	(	(	PUNCT
ejpam-365	167	5	1977	1977	NUM
ejpam-365	167	6	)	)	PUNCT
ejpam-365	167	7	,	,	PUNCT
ejpam-365	167	8	315	315	NUM
ejpam-365	167	9	-	-	SYM
ejpam-365	167	10	324	324	NUM
ejpam-365	167	11	.	.	PUNCT
ejpam-365	168	1	[	[	X
ejpam-365	168	2	6	6	NUM
ejpam-365	168	3	]	]	PUNCT
ejpam-365	168	4	t.	t.	PROPN
ejpam-365	168	5	winiarski	winiarski	PROPN
ejpam-365	168	6	,	,	PUNCT
ejpam-365	168	7	application	application	NOUN
ejpam-365	168	8	of	of	ADP
ejpam-365	168	9	approximation	approximation	NOUN
ejpam-365	168	10	and	and	CCONJ
ejpam-365	168	11	interpolation	interpolation	NOUN
ejpam-365	168	12	methods	method	NOUN
ejpam-365	168	13	to	to	ADP
ejpam-365	168	14	the	the	DET
ejpam-365	168	15	examination	examination	NOUN
ejpam-365	168	16	of	of	ADP
ejpam-365	168	17	entire	entire	ADJ
ejpam-365	168	18	functions	function	NOUN
ejpam-365	168	19	of	of	ADP
ejpam-365	168	20	n	n	PRON
ejpam-365	168	21	complex	complex	ADJ
ejpam-365	168	22	variables	variable	NOUN
ejpam-365	168	23	,	,	PUNCT
ejpam-365	168	24	ann	ann	PROPN
ejpam-365	168	25	.	.	PUNCT
ejpam-365	168	26	pol	pol	PROPN
ejpam-365	168	27	.	.	PUNCT
ejpam-365	168	28	math	math	PROPN
ejpam-365	168	29	,	,	PUNCT
ejpam-365	168	30	28	28	NUM
ejpam-365	168	31	(	(	PUNCT
ejpam-365	168	32	1973	1973	NUM
ejpam-365	168	33	)	)	PUNCT
ejpam-365	168	34	,	,	PUNCT
ejpam-365	168	35	97	97	NUM
ejpam-365	168	36	-	-	SYM
ejpam-365	168	37	121	121	NUM
ejpam-365	168	38	.	.	PUNCT