id	sid	tid	token	lemma	pos
ejpam-3373	1	1	european	european	PROPN
ejpam-3373	1	2	journal	journal	PROPN
ejpam-3373	1	3	of	of	ADP
ejpam-3373	1	4	pure	pure	ADJ
ejpam-3373	1	5	and	and	CCONJ
ejpam-3373	1	6	applied	apply	VERB
ejpam-3373	1	7	mathematics	mathematic	NOUN
ejpam-3373	1	8	vol	vol	NOUN
ejpam-3373	1	9	.	.	PROPN
ejpam-3373	2	1	12	12	NUM
ejpam-3373	2	2	,	,	PUNCT
ejpam-3373	2	3	no	no	INTJ
ejpam-3373	2	4	.	.	NOUN
ejpam-3373	2	5	2	2	NUM
ejpam-3373	2	6	,	,	PUNCT
ejpam-3373	2	7	2019	2019	NUM
ejpam-3373	2	8	,	,	PUNCT
ejpam-3373	2	9	486	486	NUM
ejpam-3373	2	10	-	-	SYM
ejpam-3373	2	11	498	498	NUM
ejpam-3373	2	12	issn	issn	PROPN
ejpam-3373	2	13	1307	1307	NUM
ejpam-3373	2	14	-	-	SYM
ejpam-3373	2	15	5543	5543	NUM
ejpam-3373	2	16	–	–	PUNCT
ejpam-3373	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3373	2	18	published	publish	VERB
ejpam-3373	2	19	by	by	ADP
ejpam-3373	2	20	new	new	PROPN
ejpam-3373	2	21	york	york	PROPN
ejpam-3373	2	22	business	business	PROPN
ejpam-3373	2	23	global	global	ADJ
ejpam-3373	2	24	(	(	PUNCT
ejpam-3373	2	25	p	p	NOUN
ejpam-3373	2	26	,	,	PUNCT
ejpam-3373	3	1	q)-growth	q)-growth	NOUN
ejpam-3373	3	2	of	of	ADP
ejpam-3373	3	3	entire	entire	ADJ
ejpam-3373	3	4	harmonic	harmonic	ADJ
ejpam-3373	3	5	functions	function	NOUN
ejpam-3373	3	6	in	in	ADP
ejpam-3373	3	7	rn	rn	PROPN
ejpam-3373	3	8	in	in	ADP
ejpam-3373	3	9	terms	term	NOUN
ejpam-3373	3	10	of	of	ADP
ejpam-3373	3	11	approximation	approximation	NOUN
ejpam-3373	3	12	errors	error	NOUN
ejpam-3373	3	13	devendra	devendra	PROPN
ejpam-3373	3	14	kumar1,2	kumar1,2	PROPN
ejpam-3373	3	15	,	,	PUNCT
ejpam-3373	3	16	rifaqat	rifaqat	NOUN
ejpam-3373	3	17	ali3,∗	ali3,∗	PROPN
ejpam-3373	3	18	1	1	NUM
ejpam-3373	3	19	department	department	NOUN
ejpam-3373	3	20	of	of	ADP
ejpam-3373	3	21	mathematics	mathematic	NOUN
ejpam-3373	3	22	,	,	PUNCT
ejpam-3373	3	23	faculty	faculty	NOUN
ejpam-3373	3	24	of	of	ADP
ejpam-3373	3	25	sciences	sciences	PROPN
ejpam-3373	3	26	al	al	PROPN
ejpam-3373	3	27	-	-	PUNCT
ejpam-3373	3	28	baha	baha	PROPN
ejpam-3373	3	29	university	university	PROPN
ejpam-3373	3	30	,	,	PUNCT
ejpam-3373	3	31	p.o.box-1988	p.o.box-1988	PROPN
ejpam-3373	3	32	,	,	PUNCT
ejpam-3373	3	33	alaqiq	alaqiq	PROPN
ejpam-3373	3	34	,	,	PUNCT
ejpam-3373	4	1	al	al	PROPN
ejpam-3373	4	2	-	-	PUNCT
ejpam-3373	4	3	baha-65431	baha-65431	NOUN
ejpam-3373	4	4	,	,	PUNCT
ejpam-3373	4	5	saudi	saudi	PROPN
ejpam-3373	4	6	arabia	arabia	PROPN
ejpam-3373	4	7	,	,	PUNCT
ejpam-3373	4	8	k.s.a	k.s.a	NOUN
ejpam-3373	4	9	.	.	NOUN
ejpam-3373	4	10	2	2	NUM
ejpam-3373	4	11	research	research	NOUN
ejpam-3373	4	12	and	and	CCONJ
ejpam-3373	4	13	post	post	VERB
ejpam-3373	4	14	graduate	graduate	ADJ
ejpam-3373	4	15	studies	study	NOUN
ejpam-3373	4	16	,	,	PUNCT
ejpam-3373	4	17	department	department	NOUN
ejpam-3373	4	18	of	of	ADP
ejpam-3373	4	19	mathematics	mathematic	NOUN
ejpam-3373	4	20	,	,	PUNCT
ejpam-3373	4	21	m.	m.	NOUN
ejpam-3373	4	22	m.	m.	PROPN
ejpam-3373	4	23	h.	h.	PROPN
ejpam-3373	4	24	college	college	PROPN
ejpam-3373	4	25	,	,	PUNCT
ejpam-3373	4	26	model	model	NOUN
ejpam-3373	4	27	town	town	NOUN
ejpam-3373	4	28	,	,	PUNCT
ejpam-3373	4	29	ghaziabad-201001	ghaziabad-201001	NOUN
ejpam-3373	4	30	,	,	PUNCT
ejpam-3373	4	31	u.p	u.p	PROPN
ejpam-3373	4	32	.	.	PROPN
ejpam-3373	4	33	,	,	PUNCT
ejpam-3373	4	34	india	india	PROPN
ejpam-3373	4	35	3	3	PROPN
ejpam-3373	4	36	department	department	NOUN
ejpam-3373	4	37	of	of	ADP
ejpam-3373	4	38	mathematics	mathematics	PROPN
ejpam-3373	4	39	,	,	PUNCT
ejpam-3373	4	40	college	college	NOUN
ejpam-3373	4	41	of	of	ADP
ejpam-3373	4	42	science	science	NOUN
ejpam-3373	4	43	,	,	PUNCT
ejpam-3373	4	44	king	king	PROPN
ejpam-3373	4	45	khalid	khalid	PROPN
ejpam-3373	4	46	university	university	PROPN
ejpam-3373	4	47	,	,	PUNCT
ejpam-3373	4	48	p.o.box:9004	p.o.box:9004	PROPN
ejpam-3373	4	49	,	,	PUNCT
ejpam-3373	4	50	postal	postal	ADJ
ejpam-3373	4	51	code:61413	code:61413	NOUN
ejpam-3373	4	52	.	.	PUNCT
ejpam-3373	4	53	abha	abha	PROPN
ejpam-3373	4	54	,	,	PUNCT
ejpam-3373	4	55	saudi	saudi	PROPN
ejpam-3373	4	56	arabia	arabia	PROPN
ejpam-3373	4	57	,	,	PUNCT
ejpam-3373	4	58	k.s.a	k.s.a	PROPN
ejpam-3373	4	59	.	.	PUNCT
ejpam-3373	5	1	abstract	abstract	PROPN
ejpam-3373	5	2	.	.	PUNCT
ejpam-3373	6	1	the	the	DET
ejpam-3373	6	2	relationship	relationship	NOUN
ejpam-3373	6	3	between	between	ADP
ejpam-3373	6	4	the	the	DET
ejpam-3373	6	5	generalized	generalized	ADJ
ejpam-3373	6	6	growth	growth	NOUN
ejpam-3373	6	7	parameters	parameter	NOUN
ejpam-3373	6	8	of	of	ADP
ejpam-3373	6	9	an	an	DET
ejpam-3373	6	10	entire	entire	ADJ
ejpam-3373	6	11	harmonic	harmonic	ADJ
ejpam-3373	6	12	function	function	NOUN
ejpam-3373	6	13	in	in	ADP
ejpam-3373	6	14	space	space	PROPN
ejpam-3373	6	15	rn	rn	PROPN
ejpam-3373	6	16	,	,	PUNCT
ejpam-3373	6	17	n	n	PRON
ejpam-3373	6	18	≥	≥	NOUN
ejpam-3373	6	19	3	3	NUM
ejpam-3373	6	20	,	,	PUNCT
ejpam-3373	6	21	with	with	ADP
ejpam-3373	6	22	the	the	DET
ejpam-3373	6	23	rate	rate	NOUN
ejpam-3373	6	24	of	of	ADP
ejpam-3373	6	25	its	its	PRON
ejpam-3373	6	26	best	good	ADJ
ejpam-3373	6	27	harmonic	harmonic	ADJ
ejpam-3373	6	28	polynomial	polynomial	ADJ
ejpam-3373	6	29	approximation	approximation	NOUN
ejpam-3373	6	30	error	error	NOUN
ejpam-3373	6	31	and	and	CCONJ
ejpam-3373	6	32	ratios	ratio	NOUN
ejpam-3373	6	33	of	of	ADP
ejpam-3373	6	34	these	these	DET
ejpam-3373	6	35	errors	error	NOUN
ejpam-3373	6	36	of	of	ADP
ejpam-3373	6	37	functions	function	NOUN
ejpam-3373	6	38	harmonic	harmonic	VERB
ejpam-3373	6	39	in	in	ADP
ejpam-3373	6	40	the	the	DET
ejpam-3373	6	41	ball	ball	NOUN
ejpam-3373	6	42	of	of	ADP
ejpam-3373	6	43	radius	radius	NOUN
ejpam-3373	6	44	r	r	NOUN
ejpam-3373	6	45	has	have	AUX
ejpam-3373	6	46	been	be	AUX
ejpam-3373	6	47	studied	study	VERB
ejpam-3373	6	48	.	.	PUNCT
ejpam-3373	7	1	2010	2010	NUM
ejpam-3373	7	2	mathematics	mathematic	NOUN
ejpam-3373	7	3	subject	subject	NOUN
ejpam-3373	7	4	classifications	classification	NOUN
ejpam-3373	7	5	:	:	PUNCT
ejpam-3373	7	6	30e10	30e10	NUM
ejpam-3373	7	7	,	,	PUNCT
ejpam-3373	7	8	41a15	41a15	ADJ
ejpam-3373	7	9	key	key	ADJ
ejpam-3373	7	10	words	word	NOUN
ejpam-3373	7	11	and	and	CCONJ
ejpam-3373	7	12	phrases	phrase	NOUN
ejpam-3373	7	13	:	:	PUNCT
ejpam-3373	7	14	entire	entire	ADJ
ejpam-3373	7	15	harmonic	harmonic	ADJ
ejpam-3373	7	16	function	function	NOUN
ejpam-3373	7	17	,	,	PUNCT
ejpam-3373	7	18	approximation	approximation	NOUN
ejpam-3373	7	19	errors	error	NOUN
ejpam-3373	7	20	,	,	PUNCT
ejpam-3373	7	21	n	n	CCONJ
ejpam-3373	7	22	-	-	PUNCT
ejpam-3373	7	23	dimensional	dimensional	ADJ
ejpam-3373	7	24	spaces	space	NOUN
ejpam-3373	7	25	,	,	PUNCT
ejpam-3373	7	26	(	(	PUNCT
ejpam-3373	7	27	p	p	NOUN
ejpam-3373	7	28	,	,	PUNCT
ejpam-3373	7	29	q)-order	q)-order	PUNCT
ejpam-3373	7	30	and	and	CCONJ
ejpam-3373	7	31	(	(	PUNCT
ejpam-3373	7	32	p	p	X
ejpam-3373	7	33	,	,	PUNCT
ejpam-3373	7	34	q)-type	q)-type	PUNCT
ejpam-3373	7	35	,	,	PUNCT
ejpam-3373	7	36	harmonic	harmonic	ADJ
ejpam-3373	7	37	polynomials	polynomial	NOUN
ejpam-3373	7	38	and	and	CCONJ
ejpam-3373	7	39	spherical	spherical	ADJ
ejpam-3373	7	40	harmonics	harmonic	NOUN
ejpam-3373	7	41	1	1	NUM
ejpam-3373	7	42	.	.	PUNCT
ejpam-3373	7	43	introduction	introduction	NOUN
ejpam-3373	7	44	the	the	DET
ejpam-3373	7	45	approximation	approximation	NOUN
ejpam-3373	7	46	of	of	ADP
ejpam-3373	7	47	entire	entire	ADJ
ejpam-3373	7	48	functions	function	NOUN
ejpam-3373	7	49	on	on	ADP
ejpam-3373	7	50	compact	compact	ADJ
ejpam-3373	7	51	sets	set	NOUN
ejpam-3373	7	52	was	be	AUX
ejpam-3373	7	53	studied	study	VERB
ejpam-3373	7	54	by	by	ADP
ejpam-3373	7	55	srivastava	srivastava	PROPN
ejpam-3373	7	56	and	and	CCONJ
ejpam-3373	7	57	kumar	kumar	PROPN
ejpam-3373	8	1	[	[	X
ejpam-3373	8	2	14,15	14,15	NUM
ejpam-3373	8	3	]	]	PUNCT
ejpam-3373	8	4	and	and	CCONJ
ejpam-3373	8	5	obtained	obtain	VERB
ejpam-3373	8	6	generalized	generalized	ADJ
ejpam-3373	8	7	growth	growth	NOUN
ejpam-3373	8	8	parameters	parameter	NOUN
ejpam-3373	8	9	in	in	ADP
ejpam-3373	8	10	terms	term	NOUN
ejpam-3373	8	11	of	of	ADP
ejpam-3373	8	12	approximation	approximation	NOUN
ejpam-3373	8	13	and	and	CCONJ
ejpam-3373	8	14	interpolation	interpolation	NOUN
ejpam-3373	8	15	error	error	NOUN
ejpam-3373	8	16	.	.	PUNCT
ejpam-3373	9	1	similar	similar	ADJ
ejpam-3373	9	2	studies	study	NOUN
ejpam-3373	9	3	have	have	AUX
ejpam-3373	9	4	been	be	AUX
ejpam-3373	9	5	done	do	VERB
ejpam-3373	9	6	for	for	ADP
ejpam-3373	9	7	harmonic	harmonic	ADJ
ejpam-3373	9	8	functions	function	NOUN
ejpam-3373	9	9	.	.	PUNCT
ejpam-3373	10	1	the	the	DET
ejpam-3373	10	2	harmonic	harmonic	ADJ
ejpam-3373	10	3	functions	function	NOUN
ejpam-3373	10	4	play	play	VERB
ejpam-3373	10	5	an	an	DET
ejpam-3373	10	6	important	important	ADJ
ejpam-3373	10	7	role	role	NOUN
ejpam-3373	10	8	not	not	PART
ejpam-3373	10	9	only	only	ADV
ejpam-3373	10	10	in	in	ADP
ejpam-3373	10	11	theoretical	theoretical	ADJ
ejpam-3373	10	12	mathematics	mathematic	NOUN
ejpam-3373	10	13	but	but	CCONJ
ejpam-3373	10	14	also	also	ADV
ejpam-3373	10	15	in	in	ADP
ejpam-3373	10	16	physics	physics	NOUN
ejpam-3373	10	17	and	and	CCONJ
ejpam-3373	10	18	mechanics	mechanic	NOUN
ejpam-3373	10	19	to	to	PART
ejpam-3373	10	20	describe	describe	VERB
ejpam-3373	10	21	different	different	ADJ
ejpam-3373	10	22	stationary	stationary	ADJ
ejpam-3373	10	23	processes	process	NOUN
ejpam-3373	10	24	.	.	PUNCT
ejpam-3373	11	1	therefore	therefore	ADV
ejpam-3373	11	2	,	,	PUNCT
ejpam-3373	11	3	it	it	PRON
ejpam-3373	11	4	is	be	AUX
ejpam-3373	11	5	significant	significant	ADJ
ejpam-3373	11	6	to	to	PART
ejpam-3373	11	7	mention	mention	VERB
ejpam-3373	11	8	here	here	ADV
ejpam-3373	11	9	that	that	SCONJ
ejpam-3373	11	10	the	the	DET
ejpam-3373	11	11	study	study	NOUN
ejpam-3373	11	12	of	of	ADP
ejpam-3373	11	13	generalized	generalized	ADJ
ejpam-3373	11	14	growth	growth	NOUN
ejpam-3373	11	15	parameters	parameter	NOUN
ejpam-3373	11	16	of	of	ADP
ejpam-3373	11	17	a	a	DET
ejpam-3373	11	18	harmonic	harmonic	ADJ
ejpam-3373	11	19	function	function	NOUN
ejpam-3373	11	20	in	in	ADP
ejpam-3373	11	21	an	an	DET
ejpam-3373	11	22	n	n	ADV
ejpam-3373	11	23	-	-	PUNCT
ejpam-3373	11	24	dimensional	dimensional	ADJ
ejpam-3373	11	25	spaces	space	NOUN
ejpam-3373	11	26	has	have	VERB
ejpam-3373	11	27	relevance	relevance	NOUN
ejpam-3373	11	28	.	.	PUNCT
ejpam-3373	12	1	harmonic	harmonic	ADJ
ejpam-3373	12	2	functions	function	NOUN
ejpam-3373	12	3	can	can	AUX
ejpam-3373	12	4	be	be	AUX
ejpam-3373	12	5	expanded	expand	VERB
ejpam-3373	12	6	into	into	ADP
ejpam-3373	12	7	series	series	NOUN
ejpam-3373	12	8	in	in	ADP
ejpam-3373	12	9	spherical	spherical	ADJ
ejpam-3373	12	10	harmonics	harmonic	NOUN
ejpam-3373	12	11	in	in	ADP
ejpam-3373	12	12	space	space	NOUN
ejpam-3373	12	13	rn	rn	PROPN
ejpam-3373	12	14	,	,	PUNCT
ejpam-3373	12	15	n	n	PRON
ejpam-3373	12	16	≥	≥	NOUN
ejpam-3373	12	17	3	3	NUM
ejpam-3373	12	18	and	and	CCONJ
ejpam-3373	12	19	in	in	ADP
ejpam-3373	12	20	the	the	DET
ejpam-3373	12	21	adjoined	adjoin	VERB
ejpam-3373	12	22	legendre	legendre	NOUN
ejpam-3373	12	23	polynomials	polynomial	NOUN
ejpam-3373	12	24	in	in	ADP
ejpam-3373	12	25	space	space	NOUN
ejpam-3373	12	26	r3	r3	PROPN
ejpam-3373	12	27	.	.	PUNCT
ejpam-3373	13	1	the	the	DET
ejpam-3373	13	2	growth	growth	NOUN
ejpam-3373	13	3	characteristics	characteristic	NOUN
ejpam-3373	13	4	of	of	ADP
ejpam-3373	13	5	harmonic	harmonic	ADJ
ejpam-3373	13	6	functions	function	NOUN
ejpam-3373	13	7	in	in	ADP
ejpam-3373	13	8	terms	term	NOUN
ejpam-3373	13	9	of	of	ADP
ejpam-3373	13	10	the	the	DET
ejpam-3373	13	11	coefficients	coefficient	NOUN
ejpam-3373	13	12	of	of	ADP
ejpam-3373	13	13	their	their	PRON
ejpam-3373	13	14	expansion	expansion	NOUN
ejpam-3373	13	15	into	into	ADP
ejpam-3373	13	16	series	series	NOUN
ejpam-3373	13	17	as	as	ADV
ejpam-3373	13	18	well	well	ADV
ejpam-3373	13	19	as	as	ADP
ejpam-3373	13	20	not	not	PART
ejpam-3373	13	21	related	relate	VERB
ejpam-3373	13	22	the	the	DET
ejpam-3373	13	23	expansion	expansion	NOUN
ejpam-3373	13	24	coefficients	coefficient	NOUN
ejpam-3373	13	25	,	,	PUNCT
ejpam-3373	13	26	in	in	ADP
ejpam-3373	13	27	particular	particular	ADJ
ejpam-3373	13	28	,	,	PUNCT
ejpam-3373	13	29	in	in	ADP
ejpam-3373	13	30	terms	term	NOUN
ejpam-3373	13	31	of	of	ADP
ejpam-3373	13	32	the	the	DET
ejpam-3373	13	33	norm	norm	NOUN
ejpam-3373	13	34	of	of	ADP
ejpam-3373	13	35	their	their	PRON
ejpam-3373	13	36	gradient	gradient	NOUN
ejpam-3373	13	37	at	at	ADP
ejpam-3373	13	38	the	the	DET
ejpam-3373	13	39	origin	origin	NOUN
ejpam-3373	13	40	were	be	AUX
ejpam-3373	13	41	obtained	obtain	VERB
ejpam-3373	13	42	.	.	PUNCT
ejpam-3373	14	1	also	also	ADV
ejpam-3373	14	2	,	,	PUNCT
ejpam-3373	14	3	the	the	DET
ejpam-3373	14	4	growth	growth	NOUN
ejpam-3373	14	5	of	of	ADP
ejpam-3373	14	6	harmonic	harmonic	ADJ
ejpam-3373	14	7	function	function	NOUN
ejpam-3373	14	8	in	in	ADP
ejpam-3373	14	9	terms	term	NOUN
ejpam-3373	14	10	of	of	ADP
ejpam-3373	14	11	approximation	approximation	NOUN
ejpam-3373	14	12	errors	error	NOUN
ejpam-3373	14	13	by	by	ADP
ejpam-3373	14	14	harmonic	harmonic	ADJ
ejpam-3373	14	15	polynomials	polynomial	NOUN
ejpam-3373	14	16	in	in	ADP
ejpam-3373	14	17	rn	rn	PROPN
ejpam-3373	14	18	,	,	PUNCT
ejpam-3373	14	19	n	n	PRON
ejpam-3373	14	20	≥	≥	NOUN
ejpam-3373	14	21	3	3	NUM
ejpam-3373	14	22	was	be	AUX
ejpam-3373	14	23	considered	consider	VERB
ejpam-3373	14	24	by	by	ADP
ejpam-3373	14	25	various	various	ADJ
ejpam-3373	14	26	authors	author	NOUN
ejpam-3373	14	27	(	(	PUNCT
ejpam-3373	14	28	see,[3,6	see,[3,6	NOUN
ejpam-3373	14	29	-	-	PUNCT
ejpam-3373	14	30	13	13	NUM
ejpam-3373	14	31	]	]	PUNCT
ejpam-3373	14	32	)	)	PUNCT
ejpam-3373	14	33	.	.	PUNCT
ejpam-3373	15	1	the	the	DET
ejpam-3373	15	2	aim	aim	NOUN
ejpam-3373	15	3	of	of	ADP
ejpam-3373	15	4	the	the	DET
ejpam-3373	15	5	present	present	ADJ
ejpam-3373	15	6	work	work	NOUN
ejpam-3373	15	7	is	be	AUX
ejpam-3373	15	8	to	to	PART
ejpam-3373	15	9	investigate	investigate	VERB
ejpam-3373	15	10	∗corresponding	∗corresponde	VERB
ejpam-3373	15	11	author	author	NOUN
ejpam-3373	15	12	.	.	PUNCT
ejpam-3373	16	1	doi	doi	NOUN
ejpam-3373	16	2	:	:	PUNCT
ejpam-3373	16	3	https://doi.org/10.29020/nybg.ejpam.v12i2.3373	https://doi.org/10.29020/nybg.ejpam.v12i2.3373	PROPN
ejpam-3373	16	4	email	email	NOUN
ejpam-3373	16	5	addresses	address	VERB
ejpam-3373	16	6	:	:	PUNCT
ejpam-3373	16	7	d	d	X
ejpam-3373	16	8	kumar001@rediffmail.com	kumar001@rediffmail.com	X
ejpam-3373	16	9	(	(	PUNCT
ejpam-3373	16	10	d.kumar	d.kumar	NOUN
ejpam-3373	16	11	)	)	PUNCT
ejpam-3373	16	12	,	,	PUNCT
ejpam-3373	16	13	(	(	PUNCT
ejpam-3373	16	14	rifaqat.ali1@gmail.com	rifaqat.ali1@gmail.com	X
ejpam-3373	16	15	;	;	PUNCT
ejpam-3373	16	16	rrafat@kku.edu.sa	rrafat@kku.edu.sa	PROPN
ejpam-3373	16	17	(	(	PUNCT
ejpam-3373	16	18	r.	r.	PROPN
ejpam-3373	16	19	ali	ali	PROPN
ejpam-3373	16	20	)	)	PUNCT
ejpam-3373	16	21	)	)	PUNCT
ejpam-3373	16	22	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3373	17	1	486	486	NUM
ejpam-3373	17	2	c	c	X
ejpam-3373	17	3	©	©	PROPN
ejpam-3373	17	4	2019	2019	NUM
ejpam-3373	17	5	ejpam	ejpam	NOUN
ejpam-3373	17	6	all	all	DET
ejpam-3373	17	7	rights	right	NOUN
ejpam-3373	17	8	reserved	reserve	VERB
ejpam-3373	17	9	.	.	PUNCT
ejpam-3373	18	1	d.	d.	PROPN
ejpam-3373	18	2	kumar	kumar	PROPN
ejpam-3373	18	3	,	,	PUNCT
ejpam-3373	18	4	r.	r.	PROPN
ejpam-3373	18	5	ali	ali	PROPN
ejpam-3373	18	6	/	/	SYM
ejpam-3373	18	7	eur	eur	PROPN
ejpam-3373	18	8	.	.	PUNCT
ejpam-3373	19	1	j.	j.	PROPN
ejpam-3373	19	2	pure	pure	PROPN
ejpam-3373	19	3	appl	appl	PROPN
ejpam-3373	19	4	.	.	PROPN
ejpam-3373	19	5	math	math	PROPN
ejpam-3373	19	6	,	,	PUNCT
ejpam-3373	19	7	12	12	NUM
ejpam-3373	19	8	(	(	PUNCT
ejpam-3373	19	9	2	2	NUM
ejpam-3373	19	10	)	)	PUNCT
ejpam-3373	19	11	(	(	PUNCT
ejpam-3373	19	12	2019	2019	NUM
ejpam-3373	19	13	)	)	PUNCT
ejpam-3373	19	14	,	,	PUNCT
ejpam-3373	19	15	486	486	NUM
ejpam-3373	19	16	-	-	SYM
ejpam-3373	19	17	498	498	NUM
ejpam-3373	19	18	487	487	NUM
ejpam-3373	19	19	conditions	condition	NOUN
ejpam-3373	19	20	under	under	ADP
ejpam-3373	19	21	which	which	PRON
ejpam-3373	19	22	a	a	DET
ejpam-3373	19	23	harmonic	harmonic	ADJ
ejpam-3373	19	24	function	function	NOUN
ejpam-3373	19	25	in	in	ADP
ejpam-3373	19	26	the	the	DET
ejpam-3373	19	27	ball	ball	NOUN
ejpam-3373	19	28	of	of	ADP
ejpam-3373	19	29	n	n	CCONJ
ejpam-3373	19	30	-	-	PUNCT
ejpam-3373	19	31	dimensional	dimensional	ADJ
ejpam-3373	19	32	space	space	NOUN
ejpam-3373	19	33	continues	continue	VERB
ejpam-3373	19	34	to	to	ADP
ejpam-3373	19	35	the	the	DET
ejpam-3373	19	36	entire	entire	ADJ
ejpam-3373	19	37	harmonic	harmonic	ADJ
ejpam-3373	19	38	function	function	NOUN
ejpam-3373	19	39	,	,	PUNCT
ejpam-3373	19	40	and	and	CCONJ
ejpam-3373	19	41	to	to	PART
ejpam-3373	19	42	derive	derive	VERB
ejpam-3373	19	43	formulae	formulae	NOUN
ejpam-3373	19	44	for	for	ADP
ejpam-3373	19	45	the	the	DET
ejpam-3373	19	46	generalized	generalize	VERB
ejpam-3373	19	47	growth	growth	NOUN
ejpam-3373	19	48	parameters	parameter	NOUN
ejpam-3373	19	49	(	(	PUNCT
ejpam-3373	19	50	p	p	X
ejpam-3373	19	51	,	,	PUNCT
ejpam-3373	19	52	q)-order	q)-order	ADJ
ejpam-3373	19	53	,	,	PUNCT
ejpam-3373	19	54	lower(p	lower(p	VERB
ejpam-3373	19	55	,	,	PUNCT
ejpam-3373	19	56	q)-order	q)-order	NOUN
ejpam-3373	19	57	,	,	PUNCT
ejpam-3373	19	58	(	(	PUNCT
ejpam-3373	19	59	p	p	NOUN
ejpam-3373	19	60	,	,	PUNCT
ejpam-3373	19	61	q)-type	q)-type	PUNCT
ejpam-3373	19	62	and	and	CCONJ
ejpam-3373	19	63	lower(p	lower(p	VERB
ejpam-3373	19	64	,	,	PUNCT
ejpam-3373	19	65	q)-type	q)-type	PUNCT
ejpam-3373	19	66	of	of	ADP
ejpam-3373	19	67	harmonic	harmonic	ADJ
ejpam-3373	19	68	function	function	NOUN
ejpam-3373	19	69	in	in	ADP
ejpam-3373	19	70	space	space	NOUN
ejpam-3373	19	71	in	in	ADP
ejpam-3373	19	72	terms	term	NOUN
ejpam-3373	19	73	of	of	ADP
ejpam-3373	19	74	harmonic	harmonic	ADJ
ejpam-3373	19	75	polynomial	polynomial	ADJ
ejpam-3373	19	76	approximation	approximation	NOUN
ejpam-3373	19	77	errors	error	NOUN
ejpam-3373	19	78	.	.	PUNCT
ejpam-3373	20	1	here	here	ADV
ejpam-3373	20	2	p	p	PROPN
ejpam-3373	20	3	and	and	CCONJ
ejpam-3373	20	4	q	q	NOUN
ejpam-3373	20	5	are	be	AUX
ejpam-3373	20	6	integers	integer	NOUN
ejpam-3373	20	7	such	such	ADJ
ejpam-3373	20	8	that	that	SCONJ
ejpam-3373	20	9	p	p	PROPN
ejpam-3373	20	10	≥	≥	X
ejpam-3373	20	11	q	q	X
ejpam-3373	20	12	≥	≥	NUM
ejpam-3373	20	13	1	1	NUM
ejpam-3373	20	14	.	.	PUNCT
ejpam-3373	21	1	let	let	VERB
ejpam-3373	21	2	u	u	PRON
ejpam-3373	21	3	be	be	AUX
ejpam-3373	21	4	an	an	DET
ejpam-3373	21	5	entire	entire	ADJ
ejpam-3373	21	6	harmonic	harmonic	ADJ
ejpam-3373	21	7	function	function	NOUN
ejpam-3373	21	8	in	in	ADP
ejpam-3373	21	9	rn	rn	PROPN
ejpam-3373	21	10	and	and	CCONJ
ejpam-3373	21	11	has	have	VERB
ejpam-3373	21	12	a	a	DET
ejpam-3373	21	13	fourier	fourier	ADJ
ejpam-3373	21	14	-	-	PUNCT
ejpam-3373	21	15	laplace	laplace	NOUN
ejpam-3373	21	16	series	series	NOUN
ejpam-3373	21	17	expansion	expansion	NOUN
ejpam-3373	22	1	[	[	X
ejpam-3373	22	2	16	16	NUM
ejpam-3373	22	3	]	]	PUNCT
ejpam-3373	22	4	u(rx	u(rx	NUM
ejpam-3373	22	5	)	)	PUNCT
ejpam-3373	22	6	=	=	PUNCT
ejpam-3373	23	1	∞∑	∞∑	NUM
ejpam-3373	23	2	k=0	k=0	PROPN
ejpam-3373	23	3	y	y	PROPN
ejpam-3373	23	4	(	(	PUNCT
ejpam-3373	23	5	k)(x;u)rk	k)(x;u)rk	PROPN
ejpam-3373	23	6	,	,	PUNCT
ejpam-3373	23	7	(	(	PUNCT
ejpam-3373	23	8	1.1	1.1	NUM
ejpam-3373	23	9	)	)	PUNCT
ejpam-3373	23	10	where	where	SCONJ
ejpam-3373	23	11	x	x	SYM
ejpam-3373	23	12	∈	∈	PROPN
ejpam-3373	23	13	sn	sn	NOUN
ejpam-3373	23	14	=	=	PRON
ejpam-3373	23	15	{	{	PUNCT
ejpam-3373	23	16	x	x	PUNCT
ejpam-3373	23	17	∈	∈	PROPN
ejpam-3373	23	18	rn	rn	NOUN
ejpam-3373	23	19	:	:	PUNCT
ejpam-3373	23	20	|x|	|x|	PROPN
ejpam-3373	23	21	=	=	SYM
ejpam-3373	23	22	1	1	X
ejpam-3373	23	23	}	}	PUNCT
ejpam-3373	23	24	a	a	DET
ejpam-3373	23	25	unit	unit	NOUN
ejpam-3373	23	26	sphere	sphere	ADV
ejpam-3373	23	27	in	in	ADP
ejpam-3373	23	28	rn	rn	PROPN
ejpam-3373	23	29	centered	center	VERB
ejpam-3373	23	30	at	at	ADP
ejpam-3373	23	31	the	the	DET
ejpam-3373	23	32	origin	origin	NOUN
ejpam-3373	23	33	y	y	PROPN
ejpam-3373	23	34	(	(	PUNCT
ejpam-3373	23	35	k)(x;u	k)(x;u	PROPN
ejpam-3373	23	36	)	)	PUNCT
ejpam-3373	23	37	=	=	NOUN
ejpam-3373	23	38	a	a	PRON
ejpam-3373	23	39	(	(	PUNCT
ejpam-3373	23	40	k	k	NOUN
ejpam-3373	23	41	)	)	PUNCT
ejpam-3373	23	42	1	1	NUM
ejpam-3373	23	43	y	y	PROPN
ejpam-3373	23	44	(	(	PUNCT
ejpam-3373	23	45	k	k	NOUN
ejpam-3373	23	46	)	)	PUNCT
ejpam-3373	23	47	1	1	NUM
ejpam-3373	23	48	(	(	PUNCT
ejpam-3373	23	49	x	x	NOUN
ejpam-3373	23	50	)	)	PUNCT
ejpam-3373	23	51	+	+	CCONJ
ejpam-3373	23	52	a	a	DET
ejpam-3373	23	53	(	(	PUNCT
ejpam-3373	23	54	k	k	NOUN
ejpam-3373	23	55	)	)	PUNCT
ejpam-3373	23	56	2	2	NUM
ejpam-3373	23	57	y	y	PROPN
ejpam-3373	23	58	(	(	PUNCT
ejpam-3373	23	59	k	k	NOUN
ejpam-3373	23	60	)	)	PUNCT
ejpam-3373	23	61	2	2	NUM
ejpam-3373	23	62	(	(	PUNCT
ejpam-3373	23	63	x	x	NOUN
ejpam-3373	23	64	)	)	PUNCT
ejpam-3373	23	65	+	+	CCONJ
ejpam-3373	23	66	·	·	PUNCT
ejpam-3373	23	67	·	·	PUNCT
ejpam-3373	23	68	·	·	PUNCT
ejpam-3373	23	69	+	+	NUM
ejpam-3373	23	70	a(k)γk	a(k)γk	PROPN
ejpam-3373	23	71	y	y	PROPN
ejpam-3373	23	72	(	(	PUNCT
ejpam-3373	23	73	k	k	NOUN
ejpam-3373	23	74	)	)	PUNCT
ejpam-3373	23	75	γk	γk	NOUN
ejpam-3373	23	76	(	(	PUNCT
ejpam-3373	23	77	x	x	NOUN
ejpam-3373	23	78	)	)	PUNCT
ejpam-3373	23	79	,	,	PUNCT
ejpam-3373	23	80	a	a	DET
ejpam-3373	23	81	(	(	PUNCT
ejpam-3373	23	82	k	k	NOUN
ejpam-3373	23	83	)	)	PUNCT
ejpam-3373	23	84	j	j	NOUN
ejpam-3373	23	85	=	=	SYM
ejpam-3373	23	86	(	(	PUNCT
ejpam-3373	23	87	u	u	PROPN
ejpam-3373	23	88	,	,	PUNCT
ejpam-3373	23	89	y	y	PROPN
ejpam-3373	23	90	(	(	PUNCT
ejpam-3373	23	91	k	k	PROPN
ejpam-3373	23	92	)	)	PUNCT
ejpam-3373	23	93	j	j	NOUN
ejpam-3373	23	94	)	)	PUNCT
ejpam-3373	23	95	=	=	SYM
ejpam-3373	23	96	γ(n/2	γ(n/2	PROPN
ejpam-3373	23	97	)	)	PUNCT
ejpam-3373	23	98	2(π	2(π	NUM
ejpam-3373	23	99	)	)	PUNCT
ejpam-3373	23	100	n	n	PRON
ejpam-3373	23	101	2	2	NUM
ejpam-3373	23	102	∫	∫	NOUN
ejpam-3373	23	103	sn	sn	PROPN
ejpam-3373	23	104	u(x)y	u(x)y	PROPN
ejpam-3373	23	105	(	(	PUNCT
ejpam-3373	23	106	k	k	NOUN
ejpam-3373	23	107	)	)	PUNCT
ejpam-3373	23	108	j	j	NOUN
ejpam-3373	23	109	(	(	PUNCT
ejpam-3373	23	110	x)ds	x)ds	PROPN
ejpam-3373	23	111	,	,	PUNCT
ejpam-3373	23	112	j	j	NOUN
ejpam-3373	23	113	=	=	SYM
ejpam-3373	23	114	1	1	NUM
ejpam-3373	23	115	,	,	PUNCT
ejpam-3373	23	116	γk	γk	NOUN
ejpam-3373	23	117	,	,	PUNCT
ejpam-3373	23	118	γk	γk	X
ejpam-3373	23	119	=	=	SYM
ejpam-3373	23	120	(	(	PUNCT
ejpam-3373	23	121	2k	2k	NUM
ejpam-3373	23	122	+	+	CCONJ
ejpam-3373	23	123	n−	n−	NOUN
ejpam-3373	23	124	2)(k	2)(k	NUM
ejpam-3373	23	125	+	+	CCONJ
ejpam-3373	23	126	n−	n−	NOUN
ejpam-3373	23	127	3	3	NUM
ejpam-3373	23	128	)	)	PUNCT
ejpam-3373	23	129	!	!	PUNCT
ejpam-3373	24	1	k!(n−	k!(n−	PROPN
ejpam-3373	24	2	2	2	NUM
ejpam-3373	24	3	)	)	PUNCT
ejpam-3373	24	4	!	!	PUNCT
ejpam-3373	24	5	.	.	PUNCT
ejpam-3373	25	1	here	here	ADV
ejpam-3373	25	2	ds	ds	NOUN
ejpam-3373	25	3	is	be	AUX
ejpam-3373	25	4	the	the	DET
ejpam-3373	25	5	element	element	NOUN
ejpam-3373	25	6	of	of	ADP
ejpam-3373	25	7	the	the	DET
ejpam-3373	25	8	surface	surface	NOUN
ejpam-3373	25	9	area	area	NOUN
ejpam-3373	25	10	on	on	ADP
ejpam-3373	25	11	the	the	DET
ejpam-3373	25	12	sphere	sphere	NOUN
ejpam-3373	25	13	sn	sn	PROPN
ejpam-3373	25	14	,	,	PUNCT
ejpam-3373	25	15	(	(	PUNCT
ejpam-3373	25	16	u	u	NOUN
ejpam-3373	25	17	,	,	PUNCT
ejpam-3373	25	18	y	y	PROPN
ejpam-3373	25	19	(	(	PUNCT
ejpam-3373	25	20	k	k	PROPN
ejpam-3373	25	21	)	)	PUNCT
ejpam-3373	25	22	j	j	PROPN
ejpam-3373	25	23	)	)	PUNCT
ejpam-3373	25	24	is	be	AUX
ejpam-3373	25	25	the	the	DET
ejpam-3373	25	26	scalor	scalor	NOUN
ejpam-3373	25	27	product	product	NOUN
ejpam-3373	25	28	in	in	ADP
ejpam-3373	25	29	l2(sn	l2(sn	PROPN
ejpam-3373	25	30	)	)	PUNCT
ejpam-3373	25	31	and	and	CCONJ
ejpam-3373	25	32	y	y	PROPN
ejpam-3373	25	33	(	(	PUNCT
ejpam-3373	25	34	k	k	NOUN
ejpam-3373	25	35	)	)	PUNCT
ejpam-3373	25	36	is	be	AUX
ejpam-3373	25	37	a	a	DET
ejpam-3373	25	38	spherical	spherical	ADJ
ejpam-3373	25	39	harmonic	harmonic	NOUN
ejpam-3373	25	40	of	of	ADP
ejpam-3373	25	41	degree	degree	NOUN
ejpam-3373	25	42	k	k	PROPN
ejpam-3373	25	43	,	,	PUNCT
ejpam-3373	25	44	k	k	PROPN
ejpam-3373	25	45	∈	∈	PROPN
ejpam-3373	25	46	z+	z+	NUM
ejpam-3373	25	47	=	=	SYM
ejpam-3373	25	48	{	{	PUNCT
ejpam-3373	25	49	0	0	NUM
ejpam-3373	25	50	,	,	PUNCT
ejpam-3373	25	51	1	1	NUM
ejpam-3373	25	52	,	,	PUNCT
ejpam-3373	25	53	2	2	NUM
ejpam-3373	25	54	,	,	PUNCT
ejpam-3373	25	55	.	.	PUNCT
ejpam-3373	25	56	.	.	PUNCT
ejpam-3373	26	1	.	.	PUNCT
ejpam-3373	27	1	,	,	PUNCT
ejpam-3373	27	2	}	}	PUNCT
ejpam-3373	27	3	on	on	ADP
ejpam-3373	27	4	the	the	DET
ejpam-3373	27	5	unit	unit	NOUN
ejpam-3373	27	6	sphere	sphere	NOUN
ejpam-3373	27	7	sn(n	sn(n	X
ejpam-3373	27	8	≥	≥	NOUN
ejpam-3373	27	9	2	2	NUM
ejpam-3373	27	10	)	)	PUNCT
ejpam-3373	27	11	[	[	X
ejpam-3373	27	12	16	16	NUM
ejpam-3373	27	13	]	]	PUNCT
ejpam-3373	27	14	.	.	PUNCT
ejpam-3373	28	1	let	let	VERB
ejpam-3373	28	2	bn	bn	INTJ
ejpam-3373	28	3	r	r	VERB
ejpam-3373	28	4	=	=	PUNCT
ejpam-3373	28	5	{	{	PUNCT
ejpam-3373	28	6	y	y	PROPN
ejpam-3373	28	7	∈	∈	PROPN
ejpam-3373	28	8	rn	rn	PROPN
ejpam-3373	28	9	:	:	PUNCT
ejpam-3373	28	10	|y|	|y|	VERB
ejpam-3373	28	11	≤	≤	ADJ
ejpam-3373	28	12	r	r	AUX
ejpam-3373	28	13	}	}	PUNCT
ejpam-3373	28	14	be	be	AUX
ejpam-3373	28	15	the	the	DET
ejpam-3373	28	16	ball	ball	NOUN
ejpam-3373	28	17	of	of	ADP
ejpam-3373	28	18	radius	radius	NOUN
ejpam-3373	28	19	r	r	NOUN
ejpam-3373	28	20	in	in	ADP
ejpam-3373	28	21	space	space	NOUN
ejpam-3373	28	22	rn	rn	PROPN
ejpam-3373	28	23	,	,	PUNCT
ejpam-3373	28	24	n	n	PRON
ejpam-3373	28	25	≥	≥	NOUN
ejpam-3373	28	26	3	3	NUM
ejpam-3373	28	27	centered	center	VERB
ejpam-3373	28	28	at	at	ADP
ejpam-3373	28	29	the	the	DET
ejpam-3373	28	30	origin	origin	NOUN
ejpam-3373	28	31	,	,	PUNCT
ejpam-3373	28	32	and	and	CCONJ
ejpam-3373	28	33	bn	bn	X
ejpam-3373	28	34	r	r	NOUN
ejpam-3373	28	35	be	be	VERB
ejpam-3373	28	36	the	the	DET
ejpam-3373	28	37	closure	closure	NOUN
ejpam-3373	28	38	of	of	ADP
ejpam-3373	28	39	bn	bn	PROPN
ejpam-3373	28	40	r.	r.	PROPN
ejpam-3373	28	41	we	we	PRON
ejpam-3373	28	42	denote	denote	VERB
ejpam-3373	28	43	hr	hr	NOUN
ejpam-3373	28	44	,	,	PUNCT
ejpam-3373	28	45	the	the	DET
ejpam-3373	28	46	class	class	NOUN
ejpam-3373	28	47	of	of	ADP
ejpam-3373	28	48	harmonic	harmonic	ADJ
ejpam-3373	28	49	functions	function	NOUN
ejpam-3373	28	50	in	in	ADP
ejpam-3373	28	51	bn	bn	NOUN
ejpam-3373	28	52	r	r	NOUN
ejpam-3373	28	53	and	and	CCONJ
ejpam-3373	28	54	continuous	continuous	ADJ
ejpam-3373	28	55	on	on	ADP
ejpam-3373	28	56	bn	bn	NOUN
ejpam-3373	28	57	r	r	NOUN
ejpam-3373	28	58	,	,	PUNCT
ejpam-3373	28	59	0	0	NUM
ejpam-3373	28	60	<	<	X
ejpam-3373	28	61	r	r	NOUN
ejpam-3373	28	62	<	<	X
ejpam-3373	28	63	∞.	∞.	PROPN
ejpam-3373	28	64	let	let	VERB
ejpam-3373	28	65	πk	πk	PART
ejpam-3373	28	66	be	be	AUX
ejpam-3373	28	67	the	the	DET
ejpam-3373	28	68	set	set	NOUN
ejpam-3373	28	69	of	of	ADP
ejpam-3373	28	70	harmonic	harmonic	ADJ
ejpam-3373	28	71	polynomials	polynomial	NOUN
ejpam-3373	28	72	of	of	ADP
ejpam-3373	28	73	degree≤	degree≤	NOUN
ejpam-3373	28	74	k.	k.	PUNCT
ejpam-3373	29	1	the	the	DET
ejpam-3373	29	2	approximation	approximation	NOUN
ejpam-3373	29	3	error	error	NOUN
ejpam-3373	29	4	of	of	ADP
ejpam-3373	29	5	function	function	NOUN
ejpam-3373	29	6	u	u	PROPN
ejpam-3373	29	7	∈	∈	PROPN
ejpam-3373	29	8	hr	hr	NOUN
ejpam-3373	29	9	by	by	ADP
ejpam-3373	29	10	harmonic	harmonic	ADJ
ejpam-3373	29	11	polynomials	polynomial	NOUN
ejpam-3373	29	12	p	p	NOUN
ejpam-3373	29	13	∈	∈	PROPN
ejpam-3373	29	14	πk	πk	PART
ejpam-3373	29	15	be	be	AUX
ejpam-3373	29	16	defined	define	VERB
ejpam-3373	29	17	as	as	ADP
ejpam-3373	29	18	e	e	NOUN
ejpam-3373	29	19	(	(	PUNCT
ejpam-3373	29	20	k	k	NOUN
ejpam-3373	29	21	)	)	PUNCT
ejpam-3373	29	22	r	r	NOUN
ejpam-3373	29	23	(	(	PUNCT
ejpam-3373	29	24	u	u	NOUN
ejpam-3373	29	25	)	)	PUNCT
ejpam-3373	29	26	=	=	SYM
ejpam-3373	29	27	inf	inf	NOUN
ejpam-3373	29	28	p∈πk	p∈πk	PROPN
ejpam-3373	29	29	{	{	PUNCT
ejpam-3373	29	30	max	max	PROPN
ejpam-3373	29	31	y∈bnr	y∈bnr	PROPN
ejpam-3373	29	32	|u(y)−	|u(y)−	PROPN
ejpam-3373	29	33	p	p	X
ejpam-3373	29	34	(	(	PUNCT
ejpam-3373	29	35	y)|	y)|	PROPN
ejpam-3373	29	36	}	}	PUNCT
ejpam-3373	29	37	.	.	PUNCT
ejpam-3373	30	1	(	(	PUNCT
ejpam-3373	30	2	1.2	1.2	NUM
ejpam-3373	30	3	)	)	PUNCT
ejpam-3373	30	4	for	for	SCONJ
ejpam-3373	30	5	u	u	PROPN
ejpam-3373	30	6	∈	∈	PROPN
ejpam-3373	30	7	hr	hr	NOUN
ejpam-3373	30	8	continue	continue	VERB
ejpam-3373	30	9	to	to	ADP
ejpam-3373	30	10	the	the	DET
ejpam-3373	30	11	entire	entire	ADJ
ejpam-3373	30	12	harmonic	harmonic	ADJ
ejpam-3373	30	13	function	function	NOUN
ejpam-3373	30	14	of	of	ADP
ejpam-3373	30	15	n	n	CCONJ
ejpam-3373	30	16	-	-	PUNCT
ejpam-3373	30	17	dimensional	dimensional	ADJ
ejpam-3373	30	18	space	space	NOUN
ejpam-3373	30	19	rn	rn	PROPN
ejpam-3373	30	20	,	,	PUNCT
ejpam-3373	30	21	n	n	PRON
ejpam-3373	30	22	≥	≥	NOUN
ejpam-3373	30	23	3	3	NUM
ejpam-3373	30	24	,	,	PUNCT
ejpam-3373	30	25	it	it	PRON
ejpam-3373	30	26	is	be	AUX
ejpam-3373	30	27	known	know	VERB
ejpam-3373	30	28	[	[	PUNCT
ejpam-3373	30	29	17	17	NUM
ejpam-3373	30	30	,	,	PUNCT
ejpam-3373	30	31	p.45	p.45	X
ejpam-3373	30	32	]	]	PUNCT
ejpam-3373	30	33	that	that	SCONJ
ejpam-3373	30	34	lim	lim	PROPN
ejpam-3373	30	35	k→∞	k→∞	X
ejpam-3373	30	36	(	(	PUNCT
ejpam-3373	30	37	e	e	X
ejpam-3373	30	38	(	(	PUNCT
ejpam-3373	30	39	k	k	NOUN
ejpam-3373	30	40	)	)	PUNCT
ejpam-3373	30	41	r	r	NOUN
ejpam-3373	30	42	(	(	PUNCT
ejpam-3373	30	43	u	u	NOUN
ejpam-3373	30	44	)	)	PUNCT
ejpam-3373	30	45	)	)	PUNCT
ejpam-3373	31	1	1	1	NUM
ejpam-3373	31	2	k	k	X
ejpam-3373	31	3	=	=	SYM
ejpam-3373	31	4	0	0	PROPN
ejpam-3373	31	5	.	.	PUNCT
ejpam-3373	31	6	(	(	PUNCT
ejpam-3373	31	7	1.3	1.3	NUM
ejpam-3373	31	8	)	)	PUNCT
ejpam-3373	31	9	the	the	DET
ejpam-3373	31	10	concept	concept	NOUN
ejpam-3373	31	11	of	of	ADP
ejpam-3373	31	12	order	order	NOUN
ejpam-3373	31	13	ρ(f	ρ(f	NOUN
ejpam-3373	31	14	)	)	PUNCT
ejpam-3373	31	15	and	and	CCONJ
ejpam-3373	31	16	lower	low	ADJ
ejpam-3373	31	17	order	order	NOUN
ejpam-3373	31	18	λ(f	λ(f	NOUN
ejpam-3373	31	19	)	)	PUNCT
ejpam-3373	31	20	of	of	ADP
ejpam-3373	31	21	an	an	DET
ejpam-3373	31	22	entire	entire	ADJ
ejpam-3373	31	23	function	function	NOUN
ejpam-3373	31	24	f	f	NOUN
ejpam-3373	31	25	(	(	PUNCT
ejpam-3373	31	26	z	z	NOUN
ejpam-3373	31	27	)	)	PUNCT
ejpam-3373	31	28	=	=	NOUN
ejpam-3373	31	29	∑∞	∑∞	NOUN
ejpam-3373	32	1	n=0	n=0	PUNCT
ejpam-3373	32	2	anz	anz	NOUN
ejpam-3373	32	3	n	n	CCONJ
ejpam-3373	32	4	was	be	AUX
ejpam-3373	32	5	introduced	introduce	VERB
ejpam-3373	32	6	by	by	ADP
ejpam-3373	32	7	r.p	r.p	PROPN
ejpam-3373	32	8	.	.	PROPN
ejpam-3373	32	9	boas	boas	PROPN
ejpam-3373	33	1	[	[	X
ejpam-3373	33	2	1	1	NUM
ejpam-3373	33	3	]	]	PUNCT
ejpam-3373	33	4	as	as	ADP
ejpam-3373	33	5	ρ(f	ρ(f	NOUN
ejpam-3373	33	6	)	)	PUNCT
ejpam-3373	34	1	=	=	PROPN
ejpam-3373	34	2	lim	lim	PROPN
ejpam-3373	34	3	r→∞	r→∞	NUM
ejpam-3373	34	4	sup	sup	PROPN
ejpam-3373	34	5	log	log	NOUN
ejpam-3373	34	6	logm(r	logm(r	NOUN
ejpam-3373	34	7	,	,	PUNCT
ejpam-3373	34	8	f	f	PROPN
ejpam-3373	34	9	)	)	PUNCT
ejpam-3373	34	10	log	log	NOUN
ejpam-3373	34	11	r	r	NOUN
ejpam-3373	34	12	,	,	PUNCT
ejpam-3373	34	13	λ(f	λ(f	PROPN
ejpam-3373	34	14	)	)	PUNCT
ejpam-3373	35	1	=	=	SYM
ejpam-3373	35	2	lim	lim	PROPN
ejpam-3373	35	3	r→∞	r→∞	PROPN
ejpam-3373	35	4	inf	inf	PROPN
ejpam-3373	35	5	log	log	NOUN
ejpam-3373	35	6	logm(r	logm(r	PROPN
ejpam-3373	35	7	,	,	PUNCT
ejpam-3373	35	8	f	f	PROPN
ejpam-3373	35	9	)	)	PUNCT
ejpam-3373	35	10	log	log	PROPN
ejpam-3373	35	11	r	r	NOUN
ejpam-3373	35	12	.	.	PUNCT
ejpam-3373	36	1	the	the	DET
ejpam-3373	36	2	concept	concept	NOUN
ejpam-3373	36	3	of	of	ADP
ejpam-3373	36	4	type	type	NOUN
ejpam-3373	36	5	t	t	PROPN
ejpam-3373	36	6	(	(	PUNCT
ejpam-3373	36	7	f	f	PROPN
ejpam-3373	36	8	)	)	PUNCT
ejpam-3373	36	9	and	and	CCONJ
ejpam-3373	36	10	lower	low	ADJ
ejpam-3373	36	11	type	type	NOUN
ejpam-3373	36	12	t(f	t(f	NOUN
ejpam-3373	36	13	)	)	PUNCT
ejpam-3373	36	14	has	have	AUX
ejpam-3373	36	15	been	be	AUX
ejpam-3373	36	16	introduced	introduce	VERB
ejpam-3373	36	17	when	when	SCONJ
ejpam-3373	36	18	the	the	DET
ejpam-3373	36	19	entire	entire	ADJ
ejpam-3373	36	20	functions	function	NOUN
ejpam-3373	36	21	have	have	VERB
ejpam-3373	36	22	same	same	ADJ
ejpam-3373	36	23	nonzero	nonzero	ADJ
ejpam-3373	36	24	finite	finite	ADJ
ejpam-3373	36	25	order	order	NOUN
ejpam-3373	36	26	.	.	PUNCT
ejpam-3373	37	1	an	an	DET
ejpam-3373	37	2	entire	entire	ADJ
ejpam-3373	37	3	function	function	NOUN
ejpam-3373	37	4	of	of	ADP
ejpam-3373	37	5	order	order	NOUN
ejpam-3373	37	6	ρ	ρ	NOUN
ejpam-3373	37	7	,	,	PUNCT
ejpam-3373	37	8	0	0	PUNCT
ejpam-3373	37	9	<	<	X
ejpam-3373	37	10	ρ	ρ	PROPN
ejpam-3373	37	11	<	<	X
ejpam-3373	37	12	∞	∞	PROPN
ejpam-3373	37	13	,	,	PUNCT
ejpam-3373	37	14	is	be	AUX
ejpam-3373	37	15	said	say	VERB
ejpam-3373	37	16	to	to	PART
ejpam-3373	37	17	be	be	AUX
ejpam-3373	37	18	of	of	ADP
ejpam-3373	37	19	type	type	NOUN
ejpam-3373	37	20	t	t	PROPN
ejpam-3373	37	21	(	(	PUNCT
ejpam-3373	37	22	f	f	PROPN
ejpam-3373	37	23	)	)	PUNCT
ejpam-3373	37	24	and	and	CCONJ
ejpam-3373	37	25	lower	low	ADJ
ejpam-3373	37	26	type	type	NOUN
ejpam-3373	37	27	t(f	t(f	NOUN
ejpam-3373	37	28	)	)	PUNCT
ejpam-3373	37	29	if	if	SCONJ
ejpam-3373	37	30	t	t	PROPN
ejpam-3373	37	31	(	(	PUNCT
ejpam-3373	37	32	f	f	PROPN
ejpam-3373	37	33	)	)	PUNCT
ejpam-3373	38	1	=	=	SYM
ejpam-3373	38	2	lim	lim	PROPN
ejpam-3373	38	3	r→∞	r→∞	PRON
ejpam-3373	38	4	sup	sup	NOUN
ejpam-3373	38	5	logm(r	logm(r	NOUN
ejpam-3373	38	6	,	,	PUNCT
ejpam-3373	38	7	f	f	PROPN
ejpam-3373	38	8	)	)	PUNCT
ejpam-3373	38	9	rρ(f	rρ(f	NUM
ejpam-3373	38	10	)	)	PUNCT
ejpam-3373	38	11	,	,	PUNCT
ejpam-3373	38	12	t(f	t(f	X
ejpam-3373	38	13	)	)	PUNCT
ejpam-3373	39	1	=	=	SYM
ejpam-3373	39	2	lim	lim	PROPN
ejpam-3373	39	3	r→∞	r→∞	PROPN
ejpam-3373	39	4	inf	inf	PROPN
ejpam-3373	39	5	logm(r	logm(r	PROPN
ejpam-3373	39	6	,	,	PUNCT
ejpam-3373	39	7	f	f	PROPN
ejpam-3373	39	8	)	)	PUNCT
ejpam-3373	39	9	rρ(f	rρ(f	NUM
ejpam-3373	39	10	)	)	PUNCT
ejpam-3373	39	11	,	,	PUNCT
ejpam-3373	39	12	d.	d.	PROPN
ejpam-3373	39	13	kumar	kumar	PROPN
ejpam-3373	39	14	,	,	PUNCT
ejpam-3373	39	15	r.	r.	PROPN
ejpam-3373	39	16	ali	ali	PROPN
ejpam-3373	39	17	/	/	SYM
ejpam-3373	39	18	eur	eur	PROPN
ejpam-3373	39	19	.	.	PUNCT
ejpam-3373	40	1	j.	j.	PROPN
ejpam-3373	40	2	pure	pure	PROPN
ejpam-3373	40	3	appl	appl	PROPN
ejpam-3373	40	4	.	.	PROPN
ejpam-3373	40	5	math	math	PROPN
ejpam-3373	40	6	,	,	PUNCT
ejpam-3373	40	7	12	12	NUM
ejpam-3373	40	8	(	(	PUNCT
ejpam-3373	40	9	2	2	NUM
ejpam-3373	40	10	)	)	PUNCT
ejpam-3373	40	11	(	(	PUNCT
ejpam-3373	40	12	2019	2019	NUM
ejpam-3373	40	13	)	)	PUNCT
ejpam-3373	40	14	,	,	PUNCT
ejpam-3373	40	15	486	486	NUM
ejpam-3373	40	16	-	-	SYM
ejpam-3373	40	17	498	498	NUM
ejpam-3373	40	18	488	488	NUM
ejpam-3373	40	19	where	where	SCONJ
ejpam-3373	40	20	0	0	NUM
ejpam-3373	40	21	<	<	X
ejpam-3373	40	22	ρ(f	ρ(f	PROPN
ejpam-3373	40	23	)	)	PUNCT
ejpam-3373	41	1	<	<	X
ejpam-3373	41	2	∞,m(r	∞,m(r	NOUN
ejpam-3373	41	3	,	,	PUNCT
ejpam-3373	41	4	f	f	PROPN
ejpam-3373	41	5	)	)	PUNCT
ejpam-3373	41	6	=	=	SYM
ejpam-3373	41	7	max0≤θ≤2π	max0≤θ≤2π	PROPN
ejpam-3373	41	8	|f	|f	X
ejpam-3373	41	9	(	(	PUNCT
ejpam-3373	41	10	r	r	NOUN
ejpam-3373	41	11	,	,	PUNCT
ejpam-3373	41	12	θ)|	θ)|	PROPN
ejpam-3373	41	13	.	.	PUNCT
ejpam-3373	42	1	for	for	ADP
ejpam-3373	42	2	the	the	DET
ejpam-3373	42	3	class	class	NOUN
ejpam-3373	42	4	of	of	ADP
ejpam-3373	42	5	order	order	NOUN
ejpam-3373	42	6	ρ(f	ρ(f	NOUN
ejpam-3373	42	7	)	)	PUNCT
ejpam-3373	42	8	=	=	SYM
ejpam-3373	42	9	0	0	NUM
ejpam-3373	42	10	and	and	CCONJ
ejpam-3373	42	11	ρ(f	ρ(f	PROPN
ejpam-3373	42	12	)	)	PUNCT
ejpam-3373	42	13	=	=	SYM
ejpam-3373	42	14	∞	∞	PROPN
ejpam-3373	42	15	,	,	PUNCT
ejpam-3373	42	16	the	the	DET
ejpam-3373	42	17	type	type	NOUN
ejpam-3373	42	18	can	can	AUX
ejpam-3373	42	19	not	not	PART
ejpam-3373	42	20	be	be	AUX
ejpam-3373	42	21	defined	define	VERB
ejpam-3373	42	22	.	.	PUNCT
ejpam-3373	43	1	to	to	PART
ejpam-3373	43	2	refine	refine	VERB
ejpam-3373	43	3	the	the	DET
ejpam-3373	43	4	above	above	ADJ
ejpam-3373	43	5	concept	concept	NOUN
ejpam-3373	43	6	of	of	ADP
ejpam-3373	43	7	order	order	NOUN
ejpam-3373	43	8	and	and	CCONJ
ejpam-3373	43	9	type	type	NOUN
ejpam-3373	43	10	,	,	PUNCT
ejpam-3373	43	11	juneja	juneja	ADJ
ejpam-3373	43	12	et	et	PROPN
ejpam-3373	43	13	.	.	PUNCT
ejpam-3373	44	1	al	al	PROPN
ejpam-3373	44	2	.	.	PROPN
ejpam-3373	44	3	,	,	PUNCT
ejpam-3373	45	1	[	[	X
ejpam-3373	45	2	4,5	4,5	NUM
ejpam-3373	45	3	]	]	PUNCT
ejpam-3373	45	4	introduced	introduce	VERB
ejpam-3373	45	5	the	the	DET
ejpam-3373	45	6	concept	concept	NOUN
ejpam-3373	45	7	of	of	ADP
ejpam-3373	45	8	(	(	PUNCT
ejpam-3373	45	9	p	p	X
ejpam-3373	45	10	,	,	PUNCT
ejpam-3373	45	11	q)orders	q)order	NOUN
ejpam-3373	45	12	and	and	CCONJ
ejpam-3373	45	13	(	(	PUNCT
ejpam-3373	45	14	p	p	X
ejpam-3373	45	15	,	,	PUNCT
ejpam-3373	45	16	q)-types	q)-type	NOUN
ejpam-3373	45	17	.	.	PUNCT
ejpam-3373	46	1	therefore	therefore	ADV
ejpam-3373	46	2	,	,	PUNCT
ejpam-3373	46	3	we	we	PRON
ejpam-3373	46	4	define	define	VERB
ejpam-3373	46	5	the	the	DET
ejpam-3373	46	6	(	(	PUNCT
ejpam-3373	46	7	p	p	NOUN
ejpam-3373	46	8	,	,	PUNCT
ejpam-3373	46	9	q)-order	q)-order	PUNCT
ejpam-3373	46	10	and	and	CCONJ
ejpam-3373	46	11	lower(p	lower(p	VERB
ejpam-3373	46	12	,	,	PUNCT
ejpam-3373	46	13	q)-order	q)-order	PUNCT
ejpam-3373	46	14	as	as	ADP
ejpam-3373	46	15	ρ(p	ρ(p	PROPN
ejpam-3373	46	16	,	,	PUNCT
ejpam-3373	46	17	q	q	X
ejpam-3373	46	18	,	,	PUNCT
ejpam-3373	46	19	f	f	PROPN
ejpam-3373	46	20	)	)	PUNCT
ejpam-3373	47	1	=	=	SYM
ejpam-3373	47	2	lim	lim	PROPN
ejpam-3373	47	3	sup	sup	PROPN
ejpam-3373	47	4	r→∞	r→∞	PROPN
ejpam-3373	47	5	log[p]m(r	log[p]m(r	NOUN
ejpam-3373	47	6	,	,	PUNCT
ejpam-3373	47	7	f	f	PROPN
ejpam-3373	47	8	)	)	PUNCT
ejpam-3373	47	9	log[q	log[q	NOUN
ejpam-3373	47	10	]	]	X
ejpam-3373	48	1	r	r	NOUN
ejpam-3373	48	2	,	,	PUNCT
ejpam-3373	48	3	λ(p	λ(p	PROPN
ejpam-3373	48	4	,	,	PUNCT
ejpam-3373	48	5	q	q	X
ejpam-3373	48	6	,	,	PUNCT
ejpam-3373	48	7	f	f	PROPN
ejpam-3373	48	8	)	)	PUNCT
ejpam-3373	49	1	=	=	PROPN
ejpam-3373	49	2	lim	lim	PROPN
ejpam-3373	49	3	inf	inf	PROPN
ejpam-3373	49	4	r→∞	r→∞	PROPN
ejpam-3373	49	5	log[p]m(r	log[p]m(r	PROPN
ejpam-3373	49	6	,	,	PUNCT
ejpam-3373	49	7	f	f	PROPN
ejpam-3373	49	8	)	)	PUNCT
ejpam-3373	49	9	log[q	log[q	NOUN
ejpam-3373	49	10	]	]	X
ejpam-3373	50	1	r	r	NOUN
ejpam-3373	50	2	,	,	PUNCT
ejpam-3373	50	3	(	(	PUNCT
ejpam-3373	50	4	1.4	1.4	NUM
ejpam-3373	50	5	)	)	PUNCT
ejpam-3373	50	6	b	b	NOUN
ejpam-3373	50	7	≤	≤	ADJ
ejpam-3373	50	8	ρ(p	ρ(p	NUM
ejpam-3373	50	9	,	,	PUNCT
ejpam-3373	50	10	q	q	X
ejpam-3373	50	11	,	,	PUNCT
ejpam-3373	50	12	f	f	PROPN
ejpam-3373	50	13	)	)	PUNCT
ejpam-3373	50	14	≤	≤	NOUN
ejpam-3373	50	15	∞	∞	PROPN
ejpam-3373	50	16	,	,	PUNCT
ejpam-3373	50	17	b	b	X
ejpam-3373	50	18	=	=	SYM
ejpam-3373	50	19	0	0	PUNCT
ejpam-3373	50	20	if	if	SCONJ
ejpam-3373	50	21	p	p	X
ejpam-3373	50	22	>	>	X
ejpam-3373	50	23	q	q	PROPN
ejpam-3373	50	24	and	and	CCONJ
ejpam-3373	50	25	b	b	X
ejpam-3373	50	26	=	=	SYM
ejpam-3373	50	27	1	1	NUM
ejpam-3373	50	28	if	if	SCONJ
ejpam-3373	50	29	p	p	PRON
ejpam-3373	50	30	=	=	X
ejpam-3373	50	31	q.	q.	NOUN
ejpam-3373	51	1	the	the	DET
ejpam-3373	51	2	(	(	PUNCT
ejpam-3373	51	3	p	p	NOUN
ejpam-3373	51	4	,	,	PUNCT
ejpam-3373	51	5	q)-type	q)-type	PUNCT
ejpam-3373	51	6	and	and	CCONJ
ejpam-3373	51	7	lower(p	lower(p	VERB
ejpam-3373	51	8	,	,	PUNCT
ejpam-3373	51	9	q)-type	q)-type	PUNCT
ejpam-3373	51	10	are	be	AUX
ejpam-3373	51	11	defined	define	VERB
ejpam-3373	51	12	as	as	ADP
ejpam-3373	51	13	t	t	PROPN
ejpam-3373	51	14	(	(	PUNCT
ejpam-3373	51	15	p	p	X
ejpam-3373	51	16	,	,	PUNCT
ejpam-3373	51	17	q	q	NOUN
ejpam-3373	51	18	,	,	PUNCT
ejpam-3373	51	19	f	f	PROPN
ejpam-3373	51	20	)	)	PUNCT
ejpam-3373	52	1	=	=	SYM
ejpam-3373	52	2	lim	lim	PROPN
ejpam-3373	52	3	sup	sup	PROPN
ejpam-3373	52	4	r→∞	r→∞	X
ejpam-3373	52	5	log[p−1]m(r	log[p−1]m(r	PROPN
ejpam-3373	52	6	,	,	PUNCT
ejpam-3373	52	7	f	f	NOUN
ejpam-3373	52	8	)	)	PUNCT
ejpam-3373	52	9	log[q−1	log[q−1	X
ejpam-3373	52	10	]	]	PUNCT
ejpam-3373	52	11	rρ(p	rρ(p	NOUN
ejpam-3373	52	12	,	,	PUNCT
ejpam-3373	52	13	q	q	NOUN
ejpam-3373	52	14	,	,	PUNCT
ejpam-3373	52	15	f	f	PROPN
ejpam-3373	52	16	)	)	PUNCT
ejpam-3373	52	17	,	,	PUNCT
ejpam-3373	52	18	t(f	t(f	X
ejpam-3373	52	19	)	)	PUNCT
ejpam-3373	52	20	=	=	PROPN
ejpam-3373	52	21	lim	lim	PROPN
ejpam-3373	52	22	inf	inf	PROPN
ejpam-3373	52	23	r→∞	r→∞	PROPN
ejpam-3373	52	24	log[p−1]m(r	log[p−1]m(r	PROPN
ejpam-3373	52	25	,	,	PUNCT
ejpam-3373	52	26	f	f	NOUN
ejpam-3373	52	27	)	)	PUNCT
ejpam-3373	52	28	log[q−1	log[q−1	X
ejpam-3373	52	29	]	]	PUNCT
ejpam-3373	52	30	rρ(p	rρ(p	NOUN
ejpam-3373	52	31	,	,	PUNCT
ejpam-3373	52	32	q	q	NOUN
ejpam-3373	52	33	,	,	PUNCT
ejpam-3373	52	34	f	f	PROPN
ejpam-3373	52	35	)	)	PUNCT
ejpam-3373	52	36	,	,	PUNCT
ejpam-3373	52	37	(	(	PUNCT
ejpam-3373	52	38	1.5	1.5	NUM
ejpam-3373	52	39	)	)	PUNCT
ejpam-3373	52	40	where	where	SCONJ
ejpam-3373	52	41	log[0](x	log[0](x	NOUN
ejpam-3373	52	42	)	)	PUNCT
ejpam-3373	52	43	=	=	SYM
ejpam-3373	52	44	x	x	X
ejpam-3373	52	45	and	and	CCONJ
ejpam-3373	52	46	log[m](x	log[m](x	PROPN
ejpam-3373	52	47	)	)	PUNCT
ejpam-3373	52	48	=	=	SYM
ejpam-3373	52	49	log[m−1	log[m−1	X
ejpam-3373	52	50	]	]	PUNCT
ejpam-3373	53	1	log(x	log(x	X
ejpam-3373	53	2	)	)	PUNCT
ejpam-3373	53	3	for	for	ADP
ejpam-3373	53	4	m	m	PROPN
ejpam-3373	53	5	≥	≥	NOUN
ejpam-3373	53	6	1	1	NUM
ejpam-3373	53	7	.	.	PUNCT
ejpam-3373	53	8	notations	notation	NOUN
ejpam-3373	53	9	:	:	PUNCT
ejpam-3373	53	10	p	p	X
ejpam-3373	53	11	(	(	PUNCT
ejpam-3373	53	12	α	α	NOUN
ejpam-3373	53	13	)	)	PUNCT
ejpam-3373	53	14	=	=	SYM
ejpam-3373	54	1	p	p	X
ejpam-3373	54	2	(	(	PUNCT
ejpam-3373	54	3	α	α	NOUN
ejpam-3373	54	4	,	,	PUNCT
ejpam-3373	54	5	p	p	X
ejpam-3373	54	6	,	,	PUNCT
ejpam-3373	54	7	q	q	NOUN
ejpam-3373	54	8	)	)	PUNCT
ejpam-3373	54	9	=	=	SYM
ejpam-3373	54	10	{	{	PUNCT
ejpam-3373	54	11	α	α	NOUN
ejpam-3373	54	12	if	if	SCONJ
ejpam-3373	54	13	p	p	PROPN
ejpam-3373	54	14	>	>	X
ejpam-3373	54	15	q	q	X
ejpam-3373	54	16	,	,	PUNCT
ejpam-3373	54	17	{	{	PUNCT
ejpam-3373	54	18	1	1	NUM
ejpam-3373	54	19	+	+	NUM
ejpam-3373	54	20	α	α	NOUN
ejpam-3373	54	21	if	if	SCONJ
ejpam-3373	54	22	p	p	NOUN
ejpam-3373	54	23	=	=	X
ejpam-3373	54	24	q	q	NOUN
ejpam-3373	54	25	=	=	SYM
ejpam-3373	54	26	2	2	NUM
ejpam-3373	54	27	,	,	PUNCT
ejpam-3373	54	28	{	{	PUNCT
ejpam-3373	54	29	max(1	max(1	NOUN
ejpam-3373	54	30	,	,	PUNCT
ejpam-3373	54	31	α	α	NOUN
ejpam-3373	54	32	)	)	PUNCT
ejpam-3373	54	33	if	if	SCONJ
ejpam-3373	54	34	3	3	NUM
ejpam-3373	54	35	≤	≤	NOUN
ejpam-3373	54	36	p	p	NOUN
ejpam-3373	54	37	=	=	X
ejpam-3373	54	38	q	q	X
ejpam-3373	54	39	<	<	X
ejpam-3373	54	40	∞	∞	PROPN
ejpam-3373	54	41	,	,	PUNCT
ejpam-3373	54	42	{	{	PUNCT
ejpam-3373	54	43	∞	∞	NOUN
ejpam-3373	54	44	if	if	SCONJ
ejpam-3373	54	45	p	p	NOUN
ejpam-3373	54	46	=	=	X
ejpam-3373	54	47	q	q	X
ejpam-3373	54	48	=	=	NOUN
ejpam-3373	54	49	∞	∞	PROPN
ejpam-3373	54	50	,	,	PUNCT
ejpam-3373	54	51	}	}	PUNCT
ejpam-3373	54	52	and	and	CCONJ
ejpam-3373	54	53	m(α	m(α	PROPN
ejpam-3373	54	54	)	)	PUNCT
ejpam-3373	54	55	=	=	SYM
ejpam-3373	54	56	m(α	m(α	PROPN
ejpam-3373	54	57	,	,	PUNCT
ejpam-3373	54	58	p	p	X
ejpam-3373	54	59	,	,	PUNCT
ejpam-3373	54	60	q	q	NOUN
ejpam-3373	54	61	)	)	PUNCT
ejpam-3373	54	62	=	=	SYM
ejpam-3373	54	63	{	{	PUNCT
ejpam-3373	54	64	1	1	NUM
ejpam-3373	54	65	eα	eα	NOUN
ejpam-3373	54	66	if	if	SCONJ
ejpam-3373	54	67	(	(	PUNCT
ejpam-3373	54	68	p	p	X
ejpam-3373	54	69	,	,	PUNCT
ejpam-3373	54	70	q	q	NOUN
ejpam-3373	54	71	)	)	PUNCT
ejpam-3373	54	72	=	=	SYM
ejpam-3373	54	73	(	(	PUNCT
ejpam-3373	54	74	2	2	NUM
ejpam-3373	54	75	,	,	PUNCT
ejpam-3373	54	76	1	1	NUM
ejpam-3373	54	77	)	)	PUNCT
ejpam-3373	54	78	,	,	PUNCT
ejpam-3373	54	79	{	{	PUNCT
ejpam-3373	54	80	(	(	PUNCT
ejpam-3373	54	81	α−	α−	ADP
ejpam-3373	54	82	1)(α−1	1)(α−1	NUM
ejpam-3373	54	83	)	)	PUNCT
ejpam-3373	54	84	αα	αα	VERB
ejpam-3373	54	85	if	if	SCONJ
ejpam-3373	54	86	(	(	PUNCT
ejpam-3373	54	87	p	p	X
ejpam-3373	54	88	,	,	PUNCT
ejpam-3373	54	89	q	q	NOUN
ejpam-3373	54	90	)	)	PUNCT
ejpam-3373	54	91	=	=	SYM
ejpam-3373	54	92	(	(	PUNCT
ejpam-3373	54	93	2	2	NUM
ejpam-3373	54	94	,	,	PUNCT
ejpam-3373	54	95	2	2	NUM
ejpam-3373	54	96	)	)	PUNCT
ejpam-3373	54	97	,	,	PUNCT
ejpam-3373	54	98	{	{	PUNCT
ejpam-3373	54	99	1	1	NUM
ejpam-3373	54	100	if	if	SCONJ
ejpam-3373	54	101	p	p	PRON
ejpam-3373	54	102	≥	≥	NOUN
ejpam-3373	54	103	3	3	NUM
ejpam-3373	54	104	,	,	PUNCT
ejpam-3373	54	105	}	}	PUNCT
ejpam-3373	54	106	from	from	ADP
ejpam-3373	54	107	[	[	X
ejpam-3373	54	108	4	4	X
ejpam-3373	54	109	]	]	PUNCT
ejpam-3373	54	110	we	we	PRON
ejpam-3373	54	111	define	define	VERB
ejpam-3373	54	112	the	the	DET
ejpam-3373	54	113	relations	relation	NOUN
ejpam-3373	54	114	between(p	between(p	NOUN
ejpam-3373	54	115	,	,	PUNCT
ejpam-3373	54	116	q)-order	q)-order	NOUN
ejpam-3373	54	117	,	,	PUNCT
ejpam-3373	54	118	lower(p	lower(p	VERB
ejpam-3373	54	119	,	,	PUNCT
ejpam-3373	54	120	q)-order	q)-order	NOUN
ejpam-3373	54	121	,	,	PUNCT
ejpam-3373	54	122	the	the	DET
ejpam-3373	54	123	coefficients	coefficient	NOUN
ejpam-3373	54	124	of	of	ADP
ejpam-3373	54	125	f	f	PROPN
ejpam-3373	54	126	(	(	PUNCT
ejpam-3373	54	127	z	z	NOUN
ejpam-3373	54	128	)	)	PUNCT
ejpam-3373	54	129	and	and	CCONJ
ejpam-3373	54	130	ratios	ratio	NOUN
ejpam-3373	54	131	of	of	ADP
ejpam-3373	54	132	these	these	DET
ejpam-3373	54	133	successive	successive	ADJ
ejpam-3373	54	134	coefficients	coefficient	NOUN
ejpam-3373	54	135	as	as	ADP
ejpam-3373	54	136	following	follow	VERB
ejpam-3373	54	137	:	:	PUNCT
ejpam-3373	54	138	theorem	theorem	ADJ
ejpam-3373	54	139	a.	a.	NOUN
ejpam-3373	54	140	let	let	VERB
ejpam-3373	54	141	f	f	PROPN
ejpam-3373	54	142	(	(	PUNCT
ejpam-3373	54	143	z	z	NOUN
ejpam-3373	54	144	)	)	PUNCT
ejpam-3373	54	145	=	=	NOUN
ejpam-3373	54	146	∑∞	∑∞	NOUN
ejpam-3373	55	1	n=0	n=0	PUNCT
ejpam-3373	55	2	anz	anz	NOUN
ejpam-3373	55	3	n	n	PRON
ejpam-3373	55	4	be	be	AUX
ejpam-3373	55	5	an	an	DET
ejpam-3373	55	6	entire	entire	ADJ
ejpam-3373	55	7	function	function	NOUN
ejpam-3373	55	8	of	of	ADP
ejpam-3373	55	9	(	(	PUNCT
ejpam-3373	55	10	p	p	X
ejpam-3373	55	11	,	,	PUNCT
ejpam-3373	55	12	q)-order	q)-order	ADJ
ejpam-3373	55	13	ρ(p	ρ(p	PROPN
ejpam-3373	55	14	,	,	PUNCT
ejpam-3373	55	15	q	q	X
ejpam-3373	55	16	,	,	PUNCT
ejpam-3373	55	17	f	f	PROPN
ejpam-3373	55	18	)	)	PUNCT
ejpam-3373	55	19	,	,	PUNCT
ejpam-3373	55	20	then	then	ADV
ejpam-3373	55	21	ρ(p	ρ(p	NUM
ejpam-3373	55	22	,	,	PUNCT
ejpam-3373	55	23	q	q	X
ejpam-3373	55	24	,	,	PUNCT
ejpam-3373	55	25	f	f	PROPN
ejpam-3373	55	26	)	)	PUNCT
ejpam-3373	56	1	=	=	SYM
ejpam-3373	56	2	p	p	X
ejpam-3373	56	3	(	(	PUNCT
ejpam-3373	56	4	l(p	l(p	PROPN
ejpam-3373	56	5	,	,	PUNCT
ejpam-3373	56	6	q	q	NOUN
ejpam-3373	56	7	,	,	PUNCT
ejpam-3373	56	8	f	f	PROPN
ejpam-3373	56	9	)	)	PUNCT
ejpam-3373	56	10	)	)	PUNCT
ejpam-3373	57	1	where	where	SCONJ
ejpam-3373	57	2	l(p	l(p	NOUN
ejpam-3373	57	3	,	,	PUNCT
ejpam-3373	57	4	q	q	NOUN
ejpam-3373	57	5	,	,	PUNCT
ejpam-3373	57	6	f	f	PROPN
ejpam-3373	57	7	)	)	PUNCT
ejpam-3373	57	8	=	=	SYM
ejpam-3373	57	9	lim	lim	PROPN
ejpam-3373	57	10	sup	sup	VERB
ejpam-3373	57	11	n→∞	n→∞	NUM
ejpam-3373	57	12	log[p−1	log[p−1	NOUN
ejpam-3373	57	13	]	]	PUNCT
ejpam-3373	58	1	n	n	DET
ejpam-3373	58	2	log[q	log[q	NOUN
ejpam-3373	58	3	]	]	PUNCT
ejpam-3373	59	1	|an|−	|an|−	PRON
ejpam-3373	59	2	1	1	NUM
ejpam-3373	59	3	n	n	NOUN
ejpam-3373	59	4	.	.	PUNCT
ejpam-3373	60	1	theorem	theorem	PROPN
ejpam-3373	60	2	b.	b.	PROPN
ejpam-3373	61	1	let	let	VERB
ejpam-3373	61	2	f	f	PROPN
ejpam-3373	61	3	(	(	PUNCT
ejpam-3373	61	4	z	z	NOUN
ejpam-3373	61	5	)	)	PUNCT
ejpam-3373	61	6	=	=	NOUN
ejpam-3373	62	1	∑∞	∑∞	NOUN
ejpam-3373	62	2	n=0	n=0	PUNCT
ejpam-3373	62	3	anz	anz	NOUN
ejpam-3373	63	1	n	n	PRON
ejpam-3373	63	2	be	be	AUX
ejpam-3373	63	3	an	an	DET
ejpam-3373	63	4	entire	entire	ADJ
ejpam-3373	63	5	function	function	NOUN
ejpam-3373	63	6	of	of	ADP
ejpam-3373	63	7	(	(	PUNCT
ejpam-3373	63	8	p	p	X
ejpam-3373	63	9	,	,	PUNCT
ejpam-3373	63	10	q)-order	q)-order	ADJ
ejpam-3373	63	11	ρ(p	ρ(p	PROPN
ejpam-3373	63	12	,	,	PUNCT
ejpam-3373	63	13	q	q	X
ejpam-3373	63	14	,	,	PUNCT
ejpam-3373	63	15	f	f	PROPN
ejpam-3373	63	16	)	)	PUNCT
ejpam-3373	63	17	,	,	PUNCT
ejpam-3373	63	18	then	then	ADV
ejpam-3373	63	19	ρ(p	ρ(p	NUM
ejpam-3373	63	20	,	,	PUNCT
ejpam-3373	63	21	q	q	X
ejpam-3373	63	22	,	,	PUNCT
ejpam-3373	63	23	f	f	PROPN
ejpam-3373	63	24	)	)	PUNCT
ejpam-3373	64	1	=	=	SYM
ejpam-3373	65	1	p	p	X
ejpam-3373	65	2	(	(	PUNCT
ejpam-3373	65	3	l∗(p	l∗(p	PROPN
ejpam-3373	65	4	,	,	PUNCT
ejpam-3373	65	5	q	q	X
ejpam-3373	65	6	,	,	PUNCT
ejpam-3373	65	7	f	f	PROPN
ejpam-3373	65	8	)	)	PUNCT
ejpam-3373	65	9	)	)	PUNCT
ejpam-3373	66	1	d.	d.	PROPN
ejpam-3373	66	2	kumar	kumar	PROPN
ejpam-3373	66	3	,	,	PUNCT
ejpam-3373	66	4	r.	r.	PROPN
ejpam-3373	66	5	ali	ali	PROPN
ejpam-3373	66	6	/	/	SYM
ejpam-3373	66	7	eur	eur	PROPN
ejpam-3373	66	8	.	.	PUNCT
ejpam-3373	67	1	j.	j.	PROPN
ejpam-3373	67	2	pure	pure	PROPN
ejpam-3373	67	3	appl	appl	PROPN
ejpam-3373	67	4	.	.	PROPN
ejpam-3373	67	5	math	math	PROPN
ejpam-3373	67	6	,	,	PUNCT
ejpam-3373	67	7	12	12	NUM
ejpam-3373	67	8	(	(	PUNCT
ejpam-3373	67	9	2	2	NUM
ejpam-3373	67	10	)	)	PUNCT
ejpam-3373	67	11	(	(	PUNCT
ejpam-3373	67	12	2019	2019	NUM
ejpam-3373	67	13	)	)	PUNCT
ejpam-3373	67	14	,	,	PUNCT
ejpam-3373	67	15	486	486	NUM
ejpam-3373	67	16	-	-	SYM
ejpam-3373	67	17	498	498	NUM
ejpam-3373	67	18	489	489	NUM
ejpam-3373	67	19	where	where	SCONJ
ejpam-3373	67	20	l∗(p	l∗(p	PROPN
ejpam-3373	67	21	,	,	PUNCT
ejpam-3373	67	22	q	q	X
ejpam-3373	67	23	,	,	PUNCT
ejpam-3373	67	24	f	f	PROPN
ejpam-3373	67	25	)	)	PUNCT
ejpam-3373	68	1	=	=	SYM
ejpam-3373	68	2	lim	lim	PROPN
ejpam-3373	68	3	sup	sup	VERB
ejpam-3373	68	4	n→∞	n→∞	NUM
ejpam-3373	68	5	log[p−1	log[p−1	NOUN
ejpam-3373	68	6	]	]	PUNCT
ejpam-3373	68	7	n	n	DET
ejpam-3373	68	8	log[q	log[q	NOUN
ejpam-3373	68	9	]	]	PUNCT
ejpam-3373	68	10	|	|	ADV
ejpam-3373	68	11	anan+1	anan+1	VERB
ejpam-3373	68	12	|	|	ADV
ejpam-3373	68	13	.	.	PUNCT
ejpam-3373	69	1	theorem	theorem	PROPN
ejpam-3373	69	2	c.	c.	PROPN
ejpam-3373	69	3	let	let	VERB
ejpam-3373	69	4	f	f	PROPN
ejpam-3373	69	5	(	(	PUNCT
ejpam-3373	69	6	z	z	NOUN
ejpam-3373	69	7	)	)	PUNCT
ejpam-3373	70	1	=	=	NOUN
ejpam-3373	70	2	∑∞	∑∞	NOUN
ejpam-3373	70	3	n=0	n=0	PUNCT
ejpam-3373	70	4	anz	anz	NOUN
ejpam-3373	71	1	n	n	PRON
ejpam-3373	71	2	be	be	AUX
ejpam-3373	71	3	an	an	DET
ejpam-3373	71	4	entire	entire	ADJ
ejpam-3373	71	5	function	function	NOUN
ejpam-3373	71	6	of	of	ADP
ejpam-3373	71	7	(	(	PUNCT
ejpam-3373	71	8	p	p	X
ejpam-3373	71	9	,	,	PUNCT
ejpam-3373	71	10	q)-order	q)-order	ADJ
ejpam-3373	71	11	ρ(p	ρ(p	PROPN
ejpam-3373	71	12	,	,	PUNCT
ejpam-3373	71	13	q	q	X
ejpam-3373	71	14	,	,	PUNCT
ejpam-3373	71	15	f	f	PROPN
ejpam-3373	71	16	)	)	PUNCT
ejpam-3373	71	17	and	and	CCONJ
ejpam-3373	71	18	(	(	PUNCT
ejpam-3373	71	19	|	|	ADV
ejpam-3373	71	20	anan+1	anan+1	VERB
ejpam-3373	71	21	|	|	ADV
ejpam-3373	71	22	)	)	PUNCT
ejpam-3373	71	23	a	a	DET
ejpam-3373	71	24	nondecreasing	nondecrease	VERB
ejpam-3373	71	25	function	function	NOUN
ejpam-3373	71	26	of	of	ADP
ejpam-3373	71	27	n	n	PROPN
ejpam-3373	71	28	for	for	ADP
ejpam-3373	71	29	n	n	PROPN
ejpam-3373	71	30	>	>	X
ejpam-3373	71	31	n0	n0	X
ejpam-3373	71	32	then	then	ADV
ejpam-3373	71	33	λ(p	λ(p	PROPN
ejpam-3373	71	34	,	,	PUNCT
ejpam-3373	71	35	q	q	X
ejpam-3373	71	36	,	,	PUNCT
ejpam-3373	71	37	f	f	PROPN
ejpam-3373	71	38	)	)	PUNCT
ejpam-3373	72	1	=	=	SYM
ejpam-3373	72	2	p	p	X
ejpam-3373	72	3	(	(	PUNCT
ejpam-3373	72	4	l(p	l(p	PROPN
ejpam-3373	72	5	,	,	PUNCT
ejpam-3373	72	6	q	q	NOUN
ejpam-3373	72	7	,	,	PUNCT
ejpam-3373	72	8	f	f	PROPN
ejpam-3373	72	9	)	)	PUNCT
ejpam-3373	72	10	)	)	PUNCT
ejpam-3373	73	1	where	where	SCONJ
ejpam-3373	73	2	l(p	l(p	NOUN
ejpam-3373	73	3	,	,	PUNCT
ejpam-3373	73	4	q	q	NOUN
ejpam-3373	73	5	,	,	PUNCT
ejpam-3373	73	6	f	f	PROPN
ejpam-3373	73	7	)	)	PUNCT
ejpam-3373	73	8	=	=	PROPN
ejpam-3373	73	9	lim	lim	PROPN
ejpam-3373	73	10	inf	inf	PROPN
ejpam-3373	73	11	n→∞	n→∞	NUM
ejpam-3373	73	12	log[p−1	log[p−1	NOUN
ejpam-3373	73	13	]	]	PUNCT
ejpam-3373	73	14	n	n	DET
ejpam-3373	73	15	log[q	log[q	NOUN
ejpam-3373	73	16	]	]	PUNCT
ejpam-3373	74	1	|an|−	|an|−	PRON
ejpam-3373	74	2	1	1	NUM
ejpam-3373	74	3	n	n	NOUN
ejpam-3373	74	4	.	.	PUNCT
ejpam-3373	75	1	theorem	theorem	PROPN
ejpam-3373	75	2	d.	d.	PROPN
ejpam-3373	75	3	let	let	VERB
ejpam-3373	75	4	f	f	PROPN
ejpam-3373	75	5	(	(	PUNCT
ejpam-3373	75	6	z	z	NOUN
ejpam-3373	75	7	)	)	PUNCT
ejpam-3373	75	8	=	=	NOUN
ejpam-3373	76	1	∑∞	∑∞	NOUN
ejpam-3373	76	2	n=0	n=0	PUNCT
ejpam-3373	76	3	anz	anz	NOUN
ejpam-3373	77	1	n	n	PRON
ejpam-3373	77	2	be	be	AUX
ejpam-3373	77	3	an	an	DET
ejpam-3373	77	4	entire	entire	ADJ
ejpam-3373	77	5	function	function	NOUN
ejpam-3373	77	6	of	of	ADP
ejpam-3373	77	7	(	(	PUNCT
ejpam-3373	77	8	p	p	X
ejpam-3373	77	9	,	,	PUNCT
ejpam-3373	77	10	q)-order	q)-order	ADJ
ejpam-3373	77	11	ρ(p	ρ(p	PROPN
ejpam-3373	77	12	,	,	PUNCT
ejpam-3373	77	13	q	q	X
ejpam-3373	77	14	,	,	PUNCT
ejpam-3373	77	15	f	f	PROPN
ejpam-3373	77	16	)	)	PUNCT
ejpam-3373	77	17	and	and	CCONJ
ejpam-3373	77	18	(	(	PUNCT
ejpam-3373	77	19	|	|	ADV
ejpam-3373	77	20	anan+1	anan+1	VERB
ejpam-3373	77	21	|	|	ADV
ejpam-3373	77	22	)	)	PUNCT
ejpam-3373	77	23	a	a	DET
ejpam-3373	77	24	nondecreasing	nondecrease	VERB
ejpam-3373	77	25	function	function	NOUN
ejpam-3373	77	26	of	of	ADP
ejpam-3373	77	27	n	n	PROPN
ejpam-3373	77	28	for	for	ADP
ejpam-3373	77	29	n	n	PROPN
ejpam-3373	77	30	>	>	X
ejpam-3373	77	31	n0	n0	X
ejpam-3373	77	32	then	then	ADV
ejpam-3373	77	33	λ(p	λ(p	PROPN
ejpam-3373	77	34	,	,	PUNCT
ejpam-3373	77	35	q	q	X
ejpam-3373	77	36	,	,	PUNCT
ejpam-3373	77	37	f	f	PROPN
ejpam-3373	77	38	)	)	PUNCT
ejpam-3373	78	1	=	=	SYM
ejpam-3373	79	1	p	p	X
ejpam-3373	79	2	(	(	PUNCT
ejpam-3373	79	3	l∗(p	l∗(p	PROPN
ejpam-3373	79	4	,	,	PUNCT
ejpam-3373	79	5	q	q	X
ejpam-3373	79	6	,	,	PUNCT
ejpam-3373	79	7	f	f	PROPN
ejpam-3373	79	8	)	)	PUNCT
ejpam-3373	79	9	)	)	PUNCT
ejpam-3373	79	10	where	where	SCONJ
ejpam-3373	79	11	l∗(p	l∗(p	PROPN
ejpam-3373	79	12	,	,	PUNCT
ejpam-3373	79	13	q	q	X
ejpam-3373	79	14	,	,	PUNCT
ejpam-3373	79	15	f	f	PROPN
ejpam-3373	79	16	)	)	PUNCT
ejpam-3373	80	1	=	=	PROPN
ejpam-3373	80	2	lim	lim	PROPN
ejpam-3373	80	3	inf	inf	PROPN
ejpam-3373	80	4	n→∞	n→∞	NUM
ejpam-3373	80	5	log[p−1	log[p−1	NOUN
ejpam-3373	80	6	]	]	PUNCT
ejpam-3373	80	7	n	n	DET
ejpam-3373	80	8	log[q	log[q	NOUN
ejpam-3373	80	9	]	]	PUNCT
ejpam-3373	80	10	|	|	ADV
ejpam-3373	80	11	anan+1	anan+1	VERB
ejpam-3373	80	12	|	|	ADV
ejpam-3373	80	13	.	.	PUNCT
ejpam-3373	81	1	from	from	ADP
ejpam-3373	81	2	[	[	X
ejpam-3373	81	3	5	5	X
ejpam-3373	81	4	]	]	PUNCT
ejpam-3373	81	5	we	we	PRON
ejpam-3373	81	6	define	define	VERB
ejpam-3373	81	7	the	the	DET
ejpam-3373	81	8	relation	relation	NOUN
ejpam-3373	81	9	between	between	ADP
ejpam-3373	81	10	(	(	PUNCT
ejpam-3373	81	11	p	p	NOUN
ejpam-3373	81	12	,	,	PUNCT
ejpam-3373	81	13	q)-type	q)-type	PUNCT
ejpam-3373	81	14	,	,	PUNCT
ejpam-3373	81	15	lower(p	lower(p	NOUN
ejpam-3373	81	16	,	,	PUNCT
ejpam-3373	81	17	q)-type	q)-type	PUNCT
ejpam-3373	81	18	and	and	CCONJ
ejpam-3373	81	19	the	the	DET
ejpam-3373	81	20	coefficients	coefficient	NOUN
ejpam-3373	81	21	of	of	ADP
ejpam-3373	81	22	f	f	PROPN
ejpam-3373	81	23	(	(	PUNCT
ejpam-3373	81	24	z	z	NOUN
ejpam-3373	81	25	)	)	PUNCT
ejpam-3373	81	26	as	as	ADP
ejpam-3373	81	27	:	:	PUNCT
ejpam-3373	81	28	theorem	theorem	ADJ
ejpam-3373	81	29	e.	e.	PROPN
ejpam-3373	81	30	let	let	VERB
ejpam-3373	81	31	f	f	PROPN
ejpam-3373	81	32	(	(	PUNCT
ejpam-3373	81	33	z	z	NOUN
ejpam-3373	81	34	)	)	PUNCT
ejpam-3373	81	35	=	=	NOUN
ejpam-3373	82	1	∑∞	∑∞	NOUN
ejpam-3373	82	2	n=0	n=0	PUNCT
ejpam-3373	82	3	anz	anz	NOUN
ejpam-3373	83	1	n	n	PRON
ejpam-3373	83	2	be	be	AUX
ejpam-3373	83	3	an	an	DET
ejpam-3373	83	4	entire	entire	ADJ
ejpam-3373	83	5	function	function	NOUN
ejpam-3373	83	6	of	of	ADP
ejpam-3373	83	7	(	(	PUNCT
ejpam-3373	83	8	p	p	X
ejpam-3373	83	9	,	,	PUNCT
ejpam-3373	83	10	q)-order	q)-order	ADJ
ejpam-3373	83	11	ρ(p	ρ(p	PROPN
ejpam-3373	83	12	,	,	PUNCT
ejpam-3373	83	13	q	q	X
ejpam-3373	83	14	,	,	PUNCT
ejpam-3373	83	15	f	f	PROPN
ejpam-3373	83	16	)	)	PUNCT
ejpam-3373	83	17	and	and	CCONJ
ejpam-3373	83	18	(	(	PUNCT
ejpam-3373	83	19	p	p	X
ejpam-3373	83	20	,	,	PUNCT
ejpam-3373	83	21	q)-type	q)-type	PUNCT
ejpam-3373	83	22	t	t	NOUN
ejpam-3373	83	23	(	(	PUNCT
ejpam-3373	83	24	p	p	X
ejpam-3373	83	25	,	,	PUNCT
ejpam-3373	83	26	q	q	PROPN
ejpam-3373	83	27	,	,	PUNCT
ejpam-3373	83	28	f	f	PROPN
ejpam-3373	83	29	)	)	PUNCT
ejpam-3373	84	1	if	if	SCONJ
ejpam-3373	84	2	and	and	CCONJ
ejpam-3373	84	3	only	only	ADV
ejpam-3373	84	4	if	if	SCONJ
ejpam-3373	84	5	t	t	NOUN
ejpam-3373	84	6	=	=	PUNCT
ejpam-3373	84	7	mv	mv	PROPN
ejpam-3373	84	8	,	,	PUNCT
ejpam-3373	84	9	where	where	SCONJ
ejpam-3373	84	10	v	v	X
ejpam-3373	84	11	(	(	PUNCT
ejpam-3373	84	12	p	p	X
ejpam-3373	84	13	,	,	PUNCT
ejpam-3373	84	14	q	q	NOUN
ejpam-3373	84	15	,	,	PUNCT
ejpam-3373	84	16	f	f	PROPN
ejpam-3373	84	17	)	)	PUNCT
ejpam-3373	85	1	=	=	SYM
ejpam-3373	85	2	lim	lim	PROPN
ejpam-3373	85	3	sup	sup	PROPN
ejpam-3373	85	4	n→∞	n→∞	NUM
ejpam-3373	85	5	log[p−2	log[p−2	NOUN
ejpam-3373	85	6	]	]	PUNCT
ejpam-3373	86	1	n	n	CCONJ
ejpam-3373	86	2	(	(	PUNCT
ejpam-3373	86	3	log[q−1	log[q−1	X
ejpam-3373	86	4	]	]	PUNCT
ejpam-3373	87	1	|an|−	|an|−	PRON
ejpam-3373	87	2	1	1	NUM
ejpam-3373	87	3	n	n	NUM
ejpam-3373	87	4	)	)	PUNCT
ejpam-3373	87	5	ρ−a	ρ−a	PROPN
ejpam-3373	87	6	.	.	PUNCT
ejpam-3373	88	1	with	with	ADP
ejpam-3373	88	2	a	a	DET
ejpam-3373	88	3	=	=	SYM
ejpam-3373	88	4	1	1	NUM
ejpam-3373	88	5	if	if	SCONJ
ejpam-3373	88	6	(	(	PUNCT
ejpam-3373	88	7	p	p	X
ejpam-3373	88	8	,	,	PUNCT
ejpam-3373	88	9	q	q	NOUN
ejpam-3373	88	10	)	)	PUNCT
ejpam-3373	88	11	=	=	SYM
ejpam-3373	88	12	(	(	PUNCT
ejpam-3373	88	13	2	2	NUM
ejpam-3373	88	14	,	,	PUNCT
ejpam-3373	88	15	2	2	NUM
ejpam-3373	88	16	)	)	PUNCT
ejpam-3373	88	17	and	and	CCONJ
ejpam-3373	88	18	a	a	DET
ejpam-3373	88	19	=	=	SYM
ejpam-3373	88	20	0	0	PUNCT
ejpam-3373	89	1	if	if	SCONJ
ejpam-3373	89	2	(	(	PUNCT
ejpam-3373	89	3	p	p	X
ejpam-3373	89	4	,	,	PUNCT
ejpam-3373	89	5	q	q	NOUN
ejpam-3373	89	6	)	)	PUNCT
ejpam-3373	89	7	6=	6=	ADP
ejpam-3373	89	8	(	(	PUNCT
ejpam-3373	89	9	2	2	NUM
ejpam-3373	89	10	,	,	PUNCT
ejpam-3373	89	11	2	2	NUM
ejpam-3373	89	12	)	)	PUNCT
ejpam-3373	89	13	.	.	PUNCT
ejpam-3373	89	14	theorem	theorem	PROPN
ejpam-3373	89	15	f.	f.	PROPN
ejpam-3373	89	16	let	let	VERB
ejpam-3373	89	17	f	f	PROPN
ejpam-3373	89	18	(	(	PUNCT
ejpam-3373	89	19	z	z	NOUN
ejpam-3373	89	20	)	)	PUNCT
ejpam-3373	89	21	=	=	NOUN
ejpam-3373	90	1	∑∞	∑∞	NOUN
ejpam-3373	90	2	n=0	n=0	PUNCT
ejpam-3373	90	3	anz	anz	NOUN
ejpam-3373	91	1	n	n	PRON
ejpam-3373	91	2	be	be	AUX
ejpam-3373	91	3	an	an	DET
ejpam-3373	91	4	entire	entire	ADJ
ejpam-3373	91	5	function	function	NOUN
ejpam-3373	91	6	of	of	ADP
ejpam-3373	91	7	(	(	PUNCT
ejpam-3373	91	8	p	p	X
ejpam-3373	91	9	,	,	PUNCT
ejpam-3373	91	10	q)-order	q)-order	ADJ
ejpam-3373	91	11	ρ(p	ρ(p	PROPN
ejpam-3373	91	12	,	,	PUNCT
ejpam-3373	91	13	q	q	X
ejpam-3373	91	14	,	,	PUNCT
ejpam-3373	91	15	f	f	PROPN
ejpam-3373	91	16	)	)	PUNCT
ejpam-3373	91	17	,	,	PUNCT
ejpam-3373	91	18	lower(p	lower(p	VERB
ejpam-3373	91	19	,	,	PUNCT
ejpam-3373	91	20	q)-type	q)-type	PUNCT
ejpam-3373	91	21	t(p	t(p	PROPN
ejpam-3373	91	22	,	,	PUNCT
ejpam-3373	91	23	q	q	NOUN
ejpam-3373	91	24	,	,	PUNCT
ejpam-3373	91	25	f	f	PROPN
ejpam-3373	91	26	)	)	PUNCT
ejpam-3373	91	27	and	and	CCONJ
ejpam-3373	91	28	(	(	PUNCT
ejpam-3373	91	29	|	|	ADV
ejpam-3373	91	30	anan+1	anan+1	VERB
ejpam-3373	91	31	|	|	ADV
ejpam-3373	91	32	)	)	PUNCT
ejpam-3373	91	33	a	a	DET
ejpam-3373	91	34	nondecreasing	nondecrease	VERB
ejpam-3373	91	35	function	function	NOUN
ejpam-3373	91	36	of	of	ADP
ejpam-3373	91	37	n	n	PROPN
ejpam-3373	91	38	for	for	ADP
ejpam-3373	91	39	n	n	PROPN
ejpam-3373	91	40	>	>	X
ejpam-3373	91	41	n0	n0	X
ejpam-3373	91	42	then	then	ADV
ejpam-3373	91	43	t	t	PROPN
ejpam-3373	91	44	=	=	PUNCT
ejpam-3373	91	45	mv	mv	PROPN
ejpam-3373	91	46	,	,	PUNCT
ejpam-3373	91	47	where	where	SCONJ
ejpam-3373	91	48	v(p	v(p	NOUN
ejpam-3373	91	49	,	,	PUNCT
ejpam-3373	91	50	q	q	NOUN
ejpam-3373	91	51	,	,	PUNCT
ejpam-3373	91	52	f	f	PROPN
ejpam-3373	91	53	)	)	PUNCT
ejpam-3373	92	1	=	=	PROPN
ejpam-3373	92	2	lim	lim	PROPN
ejpam-3373	92	3	inf	inf	PROPN
ejpam-3373	92	4	n→∞	n→∞	NUM
ejpam-3373	92	5	log[p−2	log[p−2	NOUN
ejpam-3373	92	6	]	]	PUNCT
ejpam-3373	93	1	n	n	CCONJ
ejpam-3373	93	2	(	(	PUNCT
ejpam-3373	93	3	log[q−1	log[q−1	X
ejpam-3373	93	4	]	]	PUNCT
ejpam-3373	94	1	|an|−	|an|−	PRON
ejpam-3373	94	2	1	1	NUM
ejpam-3373	94	3	n	n	NUM
ejpam-3373	94	4	)	)	PUNCT
ejpam-3373	94	5	ρ−a	ρ−a	PROPN
ejpam-3373	94	6	.	.	PUNCT
ejpam-3373	95	1	2	2	X
ejpam-3373	95	2	.	.	X
ejpam-3373	95	3	auxiliary	auxiliary	ADJ
ejpam-3373	95	4	results	result	NOUN
ejpam-3373	95	5	in	in	ADP
ejpam-3373	95	6	this	this	DET
ejpam-3373	95	7	section	section	NOUN
ejpam-3373	95	8	we	we	PRON
ejpam-3373	95	9	will	will	AUX
ejpam-3373	95	10	prove	prove	VERB
ejpam-3373	95	11	some	some	DET
ejpam-3373	95	12	auxiliary	auxiliary	ADJ
ejpam-3373	95	13	results	result	NOUN
ejpam-3373	95	14	which	which	PRON
ejpam-3373	95	15	will	will	AUX
ejpam-3373	95	16	be	be	AUX
ejpam-3373	95	17	used	use	VERB
ejpam-3373	95	18	in	in	ADP
ejpam-3373	95	19	the	the	DET
ejpam-3373	95	20	sequel	sequel	NOUN
ejpam-3373	95	21	.	.	PUNCT
ejpam-3373	96	1	consider	consider	VERB
ejpam-3373	96	2	the	the	DET
ejpam-3373	96	3	two	two	NUM
ejpam-3373	96	4	functions	function	NOUN
ejpam-3373	96	5	f	f	NOUN
ejpam-3373	96	6	and	and	CCONJ
ejpam-3373	96	7	g	g	PROPN
ejpam-3373	96	8	of	of	ADP
ejpam-3373	96	9	complex	complex	ADJ
ejpam-3373	96	10	variable	variable	ADJ
ejpam-3373	96	11	z	z	NOUN
ejpam-3373	96	12	:	:	PUNCT
ejpam-3373	96	13	f(z	f(z	NUM
ejpam-3373	96	14	)	)	PUNCT
ejpam-3373	96	15	=	=	PUNCT
ejpam-3373	97	1	∞∑	∞∑	NUM
ejpam-3373	97	2	k=0	k=0	ADJ
ejpam-3373	97	3	√	√	NUM
ejpam-3373	97	4	(	(	PUNCT
ejpam-3373	97	5	2ν)!√	2ν)!√	PROPN
ejpam-3373	97	6	2(2ν	2(2ν	NUM
ejpam-3373	97	7	+	+	SYM
ejpam-3373	97	8	1)!(k	1)!(k	NUM
ejpam-3373	97	9	+	+	NUM
ejpam-3373	97	10	2ν)2ν	2ν)2ν	NUM
ejpam-3373	97	11	e	e	X
ejpam-3373	97	12	(	(	PUNCT
ejpam-3373	97	13	k	k	NOUN
ejpam-3373	97	14	)	)	PUNCT
ejpam-3373	97	15	r	r	NOUN
ejpam-3373	97	16	(	(	PUNCT
ejpam-3373	97	17	u	u	NOUN
ejpam-3373	97	18	)	)	PUNCT
ejpam-3373	97	19	(	(	PUNCT
ejpam-3373	97	20	z	z	NOUN
ejpam-3373	97	21	r	r	NOUN
ejpam-3373	97	22	)	)	PUNCT
ejpam-3373	97	23	k	k	NOUN
ejpam-3373	97	24	(	(	PUNCT
ejpam-3373	97	25	2.1	2.1	NUM
ejpam-3373	97	26	)	)	PUNCT
ejpam-3373	97	27	d.	d.	PROPN
ejpam-3373	97	28	kumar	kumar	PROPN
ejpam-3373	97	29	,	,	PUNCT
ejpam-3373	97	30	r.	r.	PROPN
ejpam-3373	97	31	ali	ali	PROPN
ejpam-3373	97	32	/	/	SYM
ejpam-3373	97	33	eur	eur	PROPN
ejpam-3373	97	34	.	.	PUNCT
ejpam-3373	98	1	j.	j.	PROPN
ejpam-3373	98	2	pure	pure	PROPN
ejpam-3373	98	3	appl	appl	PROPN
ejpam-3373	98	4	.	.	PROPN
ejpam-3373	98	5	math	math	PROPN
ejpam-3373	98	6	,	,	PUNCT
ejpam-3373	98	7	12	12	NUM
ejpam-3373	98	8	(	(	PUNCT
ejpam-3373	98	9	2	2	NUM
ejpam-3373	98	10	)	)	PUNCT
ejpam-3373	98	11	(	(	PUNCT
ejpam-3373	98	12	2019	2019	NUM
ejpam-3373	98	13	)	)	PUNCT
ejpam-3373	98	14	,	,	PUNCT
ejpam-3373	98	15	486	486	NUM
ejpam-3373	98	16	-	-	SYM
ejpam-3373	98	17	498	498	NUM
ejpam-3373	98	18	490	490	NUM
ejpam-3373	98	19	and	and	CCONJ
ejpam-3373	98	20	g(z	g(z	ADJ
ejpam-3373	98	21	)	)	PUNCT
ejpam-3373	99	1	=	=	PUNCT
ejpam-3373	100	1	∞∑	∞∑	NUM
ejpam-3373	100	2	k=1	k=1	ADP
ejpam-3373	100	3	4	4	NUM
ejpam-3373	100	4	(	(	PUNCT
ejpam-3373	100	5	2ν	2ν	NOUN
ejpam-3373	100	6	)	)	PUNCT
ejpam-3373	100	7	!	!	PUNCT
ejpam-3373	101	1	(	(	PUNCT
ejpam-3373	101	2	k	k	X
ejpam-3373	101	3	+	+	NUM
ejpam-3373	101	4	2ν)2νe	2ν)2νe	NUM
ejpam-3373	101	5	(	(	PUNCT
ejpam-3373	101	6	k	k	NOUN
ejpam-3373	101	7	)	)	PUNCT
ejpam-3373	101	8	r	r	NOUN
ejpam-3373	101	9	(	(	PUNCT
ejpam-3373	101	10	u	u	NOUN
ejpam-3373	101	11	)	)	PUNCT
ejpam-3373	101	12	(	(	PUNCT
ejpam-3373	101	13	z	z	NOUN
ejpam-3373	101	14	r	r	NOUN
ejpam-3373	101	15	)	)	PUNCT
ejpam-3373	101	16	k.	k.	PROPN
ejpam-3373	101	17	(	(	PUNCT
ejpam-3373	101	18	2.2	2.2	NUM
ejpam-3373	101	19	)	)	PUNCT
ejpam-3373	101	20	in	in	ADP
ejpam-3373	101	21	view	view	NOUN
ejpam-3373	101	22	of	of	ADP
ejpam-3373	101	23	[	[	X
ejpam-3373	101	24	17	17	NUM
ejpam-3373	101	25	,	,	PUNCT
ejpam-3373	101	26	pp	pp	ADJ
ejpam-3373	101	27	.	.	PUNCT
ejpam-3373	102	1	47	47	NUM
ejpam-3373	102	2	]	]	PUNCT
ejpam-3373	102	3	we	we	PRON
ejpam-3373	102	4	see	see	VERB
ejpam-3373	102	5	that	that	SCONJ
ejpam-3373	102	6	if	if	SCONJ
ejpam-3373	102	7	u	u	NOUN
ejpam-3373	102	8	is	be	AUX
ejpam-3373	102	9	an	an	DET
ejpam-3373	102	10	entire	entire	ADJ
ejpam-3373	102	11	function	function	NOUN
ejpam-3373	102	12	then	then	ADV
ejpam-3373	102	13	f	f	PROPN
ejpam-3373	102	14	and	and	CCONJ
ejpam-3373	102	15	g	g	PROPN
ejpam-3373	102	16	are	be	AUX
ejpam-3373	102	17	also	also	ADV
ejpam-3373	102	18	entire	entire	ADJ
ejpam-3373	102	19	functions	function	NOUN
ejpam-3373	102	20	of	of	ADP
ejpam-3373	102	21	the	the	DET
ejpam-3373	102	22	complex	complex	ADJ
ejpam-3373	102	23	variable	variable	ADJ
ejpam-3373	102	24	z.	z.	NOUN
ejpam-3373	102	25	using	use	VERB
ejpam-3373	102	26	lemma	lemma	PROPN
ejpam-3373	102	27	3	3	NUM
ejpam-3373	102	28	with	with	ADP
ejpam-3373	102	29	inequality	inequality	NOUN
ejpam-3373	102	30	(	(	PUNCT
ejpam-3373	102	31	8)	8)	NUM
ejpam-3373	102	32	of	of	ADP
ejpam-3373	102	33	[	[	X
ejpam-3373	102	34	17	17	NUM
ejpam-3373	102	35	]	]	PUNCT
ejpam-3373	102	36	,	,	PUNCT
ejpam-3373	102	37	we	we	PRON
ejpam-3373	102	38	get	get	VERB
ejpam-3373	102	39	m(r	m(r	PROPN
ejpam-3373	102	40	,	,	PUNCT
ejpam-3373	102	41	f	f	X
ejpam-3373	102	42	)	)	PUNCT
ejpam-3373	102	43	≤m(r	≤m(r	NOUN
ejpam-3373	102	44	,	,	PUNCT
ejpam-3373	102	45	u	u	NOUN
ejpam-3373	102	46	)	)	PUNCT
ejpam-3373	102	47	≤	≤	NOUN
ejpam-3373	102	48	|y	|y	NOUN
ejpam-3373	102	49	(	(	PUNCT
ejpam-3373	102	50	0)(ξ	0)(ξ	NOUN
ejpam-3373	102	51	,	,	PUNCT
ejpam-3373	102	52	u)|+m(r	u)|+m(r	NOUN
ejpam-3373	102	53	,	,	PUNCT
ejpam-3373	102	54	g	g	NOUN
ejpam-3373	102	55	)	)	PUNCT
ejpam-3373	102	56	(	(	PUNCT
ejpam-3373	102	57	2.3	2.3	NUM
ejpam-3373	102	58	)	)	PUNCT
ejpam-3373	102	59	where	where	SCONJ
ejpam-3373	102	60	m(r	m(r	PROPN
ejpam-3373	102	61	,	,	PUNCT
ejpam-3373	102	62	f	f	X
ejpam-3373	102	63	)	)	PUNCT
ejpam-3373	102	64	is	be	AUX
ejpam-3373	102	65	the	the	DET
ejpam-3373	102	66	maximum	maximum	ADJ
ejpam-3373	102	67	term	term	NOUN
ejpam-3373	102	68	of	of	ADP
ejpam-3373	102	69	power	power	NOUN
ejpam-3373	102	70	series	series	NOUN
ejpam-3373	102	71	of	of	ADP
ejpam-3373	102	72	function	function	NOUN
ejpam-3373	102	73	f(z	f(z	PROPN
ejpam-3373	102	74	)	)	PUNCT
ejpam-3373	102	75	on	on	ADP
ejpam-3373	102	76	the	the	DET
ejpam-3373	102	77	circle{z	circle{z	PROPN
ejpam-3373	102	78	:	:	PUNCT
ejpam-3373	102	79	|z|	|z|	NOUN
ejpam-3373	102	80	=	=	SYM
ejpam-3373	102	81	r	r	NOUN
ejpam-3373	102	82	}	}	PUNCT
ejpam-3373	102	83	,	,	PUNCT
ejpam-3373	102	84	and	and	CCONJ
ejpam-3373	102	85	m(r	m(r	PROPN
ejpam-3373	102	86	,	,	PUNCT
ejpam-3373	102	87	g	g	NOUN
ejpam-3373	102	88	)	)	PUNCT
ejpam-3373	102	89	=	=	SYM
ejpam-3373	102	90	max|z|=r	max|z|=r	NOUN
ejpam-3373	103	1	|g(z)|	|g(z)|	PROPN
ejpam-3373	103	2	.	.	PUNCT
ejpam-3373	103	3	lemma	lemma	PROPN
ejpam-3373	103	4	2.1	2.1	NUM
ejpam-3373	103	5	.	.	PUNCT
ejpam-3373	104	1	let	let	VERB
ejpam-3373	104	2	f	f	PROPN
ejpam-3373	104	3	and	and	CCONJ
ejpam-3373	104	4	g	g	PROPN
ejpam-3373	104	5	be	be	AUX
ejpam-3373	104	6	defined	define	VERB
ejpam-3373	104	7	by	by	ADP
ejpam-3373	104	8	(	(	PUNCT
ejpam-3373	104	9	2.1	2.1	NUM
ejpam-3373	104	10	)	)	PUNCT
ejpam-3373	104	11	and	and	CCONJ
ejpam-3373	104	12	(	(	PUNCT
ejpam-3373	104	13	2.2	2.2	NUM
ejpam-3373	104	14	)	)	PUNCT
ejpam-3373	104	15	.	.	PUNCT
ejpam-3373	105	1	then	then	ADV
ejpam-3373	105	2	the	the	DET
ejpam-3373	105	3	(	(	PUNCT
ejpam-3373	105	4	p	p	NOUN
ejpam-3373	105	5	,	,	PUNCT
ejpam-3373	105	6	q)-orders	q)-order	NOUN
ejpam-3373	105	7	and	and	CCONJ
ejpam-3373	105	8	(	(	PUNCT
ejpam-3373	105	9	p	p	NOUN
ejpam-3373	105	10	,	,	PUNCT
ejpam-3373	105	11	q)-types	q)-type	NOUN
ejpam-3373	105	12	of	of	ADP
ejpam-3373	105	13	f	f	PROPN
ejpam-3373	105	14	and	and	CCONJ
ejpam-3373	105	15	g	g	PROPN
ejpam-3373	105	16	respectively	respectively	ADV
ejpam-3373	105	17	are	be	AUX
ejpam-3373	105	18	equal	equal	ADJ
ejpam-3373	105	19	.	.	PUNCT
ejpam-3373	106	1	proof	proof	NOUN
ejpam-3373	106	2	.	.	PUNCT
ejpam-3373	107	1	first	first	ADV
ejpam-3373	107	2	we	we	PRON
ejpam-3373	107	3	consider	consider	VERB
ejpam-3373	107	4	the	the	DET
ejpam-3373	107	5	case	case	NOUN
ejpam-3373	107	6	(	(	PUNCT
ejpam-3373	107	7	p	p	X
ejpam-3373	107	8	,	,	PUNCT
ejpam-3373	107	9	q	q	NOUN
ejpam-3373	107	10	)	)	PUNCT
ejpam-3373	107	11	=	=	SYM
ejpam-3373	107	12	(	(	PUNCT
ejpam-3373	107	13	2	2	NUM
ejpam-3373	107	14	,	,	PUNCT
ejpam-3373	107	15	1	1	NUM
ejpam-3373	107	16	)	)	PUNCT
ejpam-3373	107	17	,	,	PUNCT
ejpam-3373	107	18	1	1	NUM
ejpam-3373	107	19	ρ(2	ρ(2	PROPN
ejpam-3373	107	20	,	,	PUNCT
ejpam-3373	107	21	1	1	NUM
ejpam-3373	107	22	,	,	PUNCT
ejpam-3373	107	23	f	f	X
ejpam-3373	107	24	)	)	PUNCT
ejpam-3373	107	25	=	=	SYM
ejpam-3373	107	26	lim	lim	PROPN
ejpam-3373	107	27	inf	inf	PROPN
ejpam-3373	107	28	k→∞	k→∞	NOUN
ejpam-3373	107	29	−	−	PROPN
ejpam-3373	107	30	1	1	NUM
ejpam-3373	107	31	k	k	PROPN
ejpam-3373	107	32	log	log	PROPN
ejpam-3373	107	33	(	(	PUNCT
ejpam-3373	107	34	√	√	PROPN
ejpam-3373	107	35	(	(	PUNCT
ejpam-3373	107	36	2ν)!√	2ν)!√	PROPN
ejpam-3373	107	37	2(2ν+1)!(k+2ν)2ν	2(2ν+1)!(k+2ν)2ν	NUM
ejpam-3373	107	38	r−ke	r−ke	NOUN
ejpam-3373	107	39	(	(	PUNCT
ejpam-3373	107	40	k	k	NOUN
ejpam-3373	107	41	)	)	PUNCT
ejpam-3373	107	42	r	r	NOUN
ejpam-3373	107	43	(	(	PUNCT
ejpam-3373	107	44	u	u	NOUN
ejpam-3373	107	45	)	)	PUNCT
ejpam-3373	107	46	)	)	PUNCT
ejpam-3373	107	47	log	log	VERB
ejpam-3373	107	48	k	k	NOUN
ejpam-3373	107	49	,	,	PUNCT
ejpam-3373	107	50	=	=	PROPN
ejpam-3373	107	51	lim	lim	PROPN
ejpam-3373	107	52	inf	inf	PROPN
ejpam-3373	107	53	k→∞	k→∞	NOUN
ejpam-3373	107	54	logrk(e	logrk(e	PROPN
ejpam-3373	107	55	(	(	PUNCT
ejpam-3373	107	56	k	k	NOUN
ejpam-3373	107	57	)	)	PUNCT
ejpam-3373	107	58	r	r	NOUN
ejpam-3373	107	59	(	(	PUNCT
ejpam-3373	107	60	u))−1	u))−1	ADP
ejpam-3373	107	61	+	+	CCONJ
ejpam-3373	107	62	log	log	NOUN
ejpam-3373	107	63	√	√	NUM
ejpam-3373	107	64	2(2ν	2(2ν	NUM
ejpam-3373	108	1	+	+	SYM
ejpam-3373	108	2	1)!(k	1)!(k	NUM
ejpam-3373	108	3	+	+	NUM
ejpam-3373	108	4	2ν)2ν	2ν)2ν	NUM
ejpam-3373	108	5	−	−	NOUN
ejpam-3373	108	6	log	log	NOUN
ejpam-3373	108	7	√	√	INTJ
ejpam-3373	108	8	(	(	PUNCT
ejpam-3373	108	9	2ν	2ν	NUM
ejpam-3373	108	10	)	)	PUNCT
ejpam-3373	108	11	!	!	PUNCT
ejpam-3373	109	1	k	k	PROPN
ejpam-3373	109	2	log	log	VERB
ejpam-3373	109	3	k	k	PROPN
ejpam-3373	109	4	,	,	PUNCT
ejpam-3373	109	5	=	=	PROPN
ejpam-3373	109	6	lim	lim	PROPN
ejpam-3373	109	7	inf	inf	PROPN
ejpam-3373	109	8	k→∞	k→∞	NOUN
ejpam-3373	109	9	logrk(e	logrk(e	PROPN
ejpam-3373	109	10	(	(	PUNCT
ejpam-3373	109	11	k	k	NOUN
ejpam-3373	109	12	)	)	PUNCT
ejpam-3373	109	13	r	r	NOUN
ejpam-3373	109	14	(	(	PUNCT
ejpam-3373	109	15	u))−1	u))−1	ADP
ejpam-3373	109	16	k	k	PROPN
ejpam-3373	109	17	log	log	NOUN
ejpam-3373	109	18	k	k	PROPN
ejpam-3373	110	1	+	+	NOUN
ejpam-3373	110	2	1	1	NUM
ejpam-3373	110	3	,	,	PUNCT
ejpam-3373	110	4	then	then	ADV
ejpam-3373	110	5	1	1	NUM
ejpam-3373	110	6	ρ(2,1,f	ρ(2,1,f	NOUN
ejpam-3373	110	7	)	)	PUNCT
ejpam-3373	110	8	≥	≥	NOUN
ejpam-3373	110	9	1	1	NUM
ejpam-3373	110	10	and	and	CCONJ
ejpam-3373	110	11	ρ(2	ρ(2	PROPN
ejpam-3373	110	12	,	,	PUNCT
ejpam-3373	110	13	1	1	NUM
ejpam-3373	110	14	,	,	PUNCT
ejpam-3373	110	15	f	f	X
ejpam-3373	110	16	)	)	PUNCT
ejpam-3373	110	17	≤	≤	NUM
ejpam-3373	110	18	1	1	NUM
ejpam-3373	110	19	.	.	PUNCT
ejpam-3373	111	1	this	this	PRON
ejpam-3373	111	2	implies	imply	VERB
ejpam-3373	111	3	necessarily	necessarily	ADV
ejpam-3373	111	4	we	we	PRON
ejpam-3373	111	5	have	have	VERB
ejpam-3373	111	6	ρ(2	ρ(2	PROPN
ejpam-3373	111	7	,	,	PUNCT
ejpam-3373	111	8	1	1	NUM
ejpam-3373	111	9	,	,	PUNCT
ejpam-3373	111	10	f	f	X
ejpam-3373	111	11	)	)	PUNCT
ejpam-3373	111	12	=	=	SYM
ejpam-3373	111	13	0	0	PUNCT
ejpam-3373	111	14	to	to	PART
ejpam-3373	111	15	define	define	VERB
ejpam-3373	111	16	ρ(p	ρ(p	PROPN
ejpam-3373	111	17	,	,	PUNCT
ejpam-3373	111	18	q	q	X
ejpam-3373	111	19	,	,	PUNCT
ejpam-3373	111	20	f	f	NOUN
ejpam-3373	111	21	)	)	PUNCT
ejpam-3373	111	22	.	.	PUNCT
ejpam-3373	112	1	now	now	ADV
ejpam-3373	112	2	ρ(2	ρ(2	PROPN
ejpam-3373	112	3	,	,	PUNCT
ejpam-3373	112	4	1	1	NUM
ejpam-3373	112	5	,	,	PUNCT
ejpam-3373	112	6	f	f	X
ejpam-3373	112	7	)	)	PUNCT
ejpam-3373	112	8	=	=	SYM
ejpam-3373	112	9	0⇒	0⇒	PROPN
ejpam-3373	112	10	lim	lim	PROPN
ejpam-3373	112	11	inf	inf	PROPN
ejpam-3373	112	12	k→∞	k→∞	NOUN
ejpam-3373	112	13	1	1	NUM
ejpam-3373	112	14	ρ(2	ρ(2	PROPN
ejpam-3373	112	15	,	,	PUNCT
ejpam-3373	112	16	1	1	NUM
ejpam-3373	112	17	,	,	PUNCT
ejpam-3373	112	18	f	f	X
ejpam-3373	112	19	)	)	PUNCT
ejpam-3373	113	1	=	=	PUNCT
ejpam-3373	114	1	+	+	NUM
ejpam-3373	114	2	∞	∞	PROPN
ejpam-3373	114	3	⇒	⇒	PROPN
ejpam-3373	114	4	lim	lim	PROPN
ejpam-3373	114	5	inf	inf	PROPN
ejpam-3373	114	6	k→∞	k→∞	NOUN
ejpam-3373	114	7	logrk(e	logrk(e	PROPN
ejpam-3373	114	8	(	(	PUNCT
ejpam-3373	114	9	k	k	NOUN
ejpam-3373	114	10	)	)	PUNCT
ejpam-3373	114	11	r	r	NOUN
ejpam-3373	114	12	(	(	PUNCT
ejpam-3373	114	13	u))−1	u))−1	ADP
ejpam-3373	114	14	k	k	PROPN
ejpam-3373	114	15	log	log	NOUN
ejpam-3373	114	16	k	k	PROPN
ejpam-3373	114	17	=	=	PUNCT
ejpam-3373	115	1	+	+	NOUN
ejpam-3373	115	2	∞	∞	PROPN
ejpam-3373	115	3	⇒	⇒	PROPN
ejpam-3373	115	4	lim	lim	PROPN
ejpam-3373	115	5	inf	inf	PROPN
ejpam-3373	115	6	k→∞	k→∞	PROPN
ejpam-3373	116	1	k	k	PROPN
ejpam-3373	116	2	log	log	PROPN
ejpam-3373	116	3	k	k	PROPN
ejpam-3373	116	4	logrk(e	logrk(e	PROPN
ejpam-3373	116	5	(	(	PUNCT
ejpam-3373	116	6	k	k	NOUN
ejpam-3373	116	7	)	)	PUNCT
ejpam-3373	116	8	r	r	NOUN
ejpam-3373	116	9	(	(	PUNCT
ejpam-3373	116	10	u))−1	u))−1	NOUN
ejpam-3373	116	11	=	=	PUNCT
ejpam-3373	116	12	0	0	NUM
ejpam-3373	116	13	⇒	⇒	PROPN
ejpam-3373	116	14	lim	lim	PROPN
ejpam-3373	116	15	inf	inf	PROPN
ejpam-3373	116	16	k→∞	k→∞	PROPN
ejpam-3373	116	17	log	log	NOUN
ejpam-3373	116	18	k	k	X
ejpam-3373	116	19	!	!	PUNCT
ejpam-3373	117	1	logrk(e	logrk(e	PROPN
ejpam-3373	117	2	(	(	PUNCT
ejpam-3373	117	3	k	k	NOUN
ejpam-3373	117	4	)	)	PUNCT
ejpam-3373	117	5	r	r	NOUN
ejpam-3373	117	6	(	(	PUNCT
ejpam-3373	117	7	u))−1	u))−1	NOUN
ejpam-3373	117	8	=	=	PUNCT
ejpam-3373	117	9	0	0	NUM
ejpam-3373	118	1	⇒	⇒	NOUN
ejpam-3373	119	1	(	(	PUNCT
ejpam-3373	120	1	e	e	X
ejpam-3373	120	2	(	(	PUNCT
ejpam-3373	120	3	k	k	NOUN
ejpam-3373	120	4	)	)	PUNCT
ejpam-3373	120	5	r	r	NOUN
ejpam-3373	120	6	(	(	PUNCT
ejpam-3373	120	7	u)r−1	u)r−1	PROPN
ejpam-3373	120	8	)	)	PUNCT
ejpam-3373	120	9	1	1	NUM
ejpam-3373	120	10	k	k	PROPN
ejpam-3373	120	11	→	→	SYM
ejpam-3373	120	12	0	0	X
ejpam-3373	120	13	.	.	PUNCT
ejpam-3373	120	14	d.	d.	PROPN
ejpam-3373	120	15	kumar	kumar	PROPN
ejpam-3373	120	16	,	,	PUNCT
ejpam-3373	120	17	r.	r.	PROPN
ejpam-3373	120	18	ali	ali	PROPN
ejpam-3373	120	19	/	/	SYM
ejpam-3373	120	20	eur	eur	PROPN
ejpam-3373	120	21	.	.	PUNCT
ejpam-3373	121	1	j.	j.	PROPN
ejpam-3373	121	2	pure	pure	PROPN
ejpam-3373	121	3	appl	appl	PROPN
ejpam-3373	121	4	.	.	PROPN
ejpam-3373	121	5	math	math	PROPN
ejpam-3373	121	6	,	,	PUNCT
ejpam-3373	121	7	12	12	NUM
ejpam-3373	121	8	(	(	PUNCT
ejpam-3373	121	9	2	2	NUM
ejpam-3373	121	10	)	)	PUNCT
ejpam-3373	121	11	(	(	PUNCT
ejpam-3373	121	12	2019	2019	NUM
ejpam-3373	121	13	)	)	PUNCT
ejpam-3373	121	14	,	,	PUNCT
ejpam-3373	121	15	486	486	NUM
ejpam-3373	121	16	-	-	SYM
ejpam-3373	121	17	498	498	NUM
ejpam-3373	121	18	491	491	NUM
ejpam-3373	121	19	for	for	ADP
ejpam-3373	121	20	p	p	PROPN
ejpam-3373	121	21	≥	≥	NOUN
ejpam-3373	121	22	q	q	X
ejpam-3373	121	23	>	>	X
ejpam-3373	121	24	1	1	NUM
ejpam-3373	122	1	,	,	PUNCT
ejpam-3373	122	2	we	we	PRON
ejpam-3373	122	3	have	have	VERB
ejpam-3373	122	4	1	1	NUM
ejpam-3373	122	5	l(p	l(p	NOUN
ejpam-3373	122	6	,	,	PUNCT
ejpam-3373	122	7	q	q	NOUN
ejpam-3373	122	8	,	,	PUNCT
ejpam-3373	122	9	f	f	X
ejpam-3373	122	10	)	)	PUNCT
ejpam-3373	122	11	=	=	SYM
ejpam-3373	122	12	lim	lim	PROPN
ejpam-3373	122	13	inf	inf	PROPN
ejpam-3373	122	14	k→∞	k→∞	PROPN
ejpam-3373	122	15	log[q−1](−	log[q−1](−	PROPN
ejpam-3373	122	16	1	1	NUM
ejpam-3373	122	17	k	k	NOUN
ejpam-3373	122	18	log	log	PROPN
ejpam-3373	122	19	(	(	PUNCT
ejpam-3373	122	20	√	√	PROPN
ejpam-3373	122	21	(	(	PUNCT
ejpam-3373	122	22	2ν)!√	2ν)!√	PROPN
ejpam-3373	122	23	2(2ν+1)!(k+2ν)2ν	2(2ν+1)!(k+2ν)2ν	NUM
ejpam-3373	122	24	r−ke	r−ke	NOUN
ejpam-3373	122	25	(	(	PUNCT
ejpam-3373	122	26	k	k	NOUN
ejpam-3373	122	27	)	)	PUNCT
ejpam-3373	122	28	r	r	NOUN
ejpam-3373	122	29	(	(	PUNCT
ejpam-3373	122	30	u	u	NOUN
ejpam-3373	122	31	)	)	PUNCT
ejpam-3373	122	32	)	)	PUNCT
ejpam-3373	122	33	)	)	PUNCT
ejpam-3373	122	34	log[p−1	log[p−1	NOUN
ejpam-3373	122	35	]	]	PUNCT
ejpam-3373	123	1	k	k	X
ejpam-3373	123	2	=	=	SYM
ejpam-3373	123	3	lim	lim	PROPN
ejpam-3373	123	4	inf	inf	PROPN
ejpam-3373	123	5	k→∞	k→∞	PROPN
ejpam-3373	123	6	log[q−1	log[q−1	X
ejpam-3373	123	7	]	]	X
ejpam-3373	123	8	(	(	PUNCT
ejpam-3373	123	9	log[r−k(e	log[r−k(e	X
ejpam-3373	123	10	(	(	PUNCT
ejpam-3373	123	11	k	k	NOUN
ejpam-3373	123	12	)	)	PUNCT
ejpam-3373	123	13	r	r	NOUN
ejpam-3373	123	14	(	(	PUNCT
ejpam-3373	123	15	u))]−1	u))]−1	PROPN
ejpam-3373	123	16	k	k	NOUN
ejpam-3373	123	17	+	+	CCONJ
ejpam-3373	123	18	log	log	VERB
ejpam-3373	123	19	√	√	NUM
ejpam-3373	123	20	2(2ν+1)!(k+2ν)2ν	2(2ν+1)!(k+2ν)2ν	NUM
ejpam-3373	123	21	k	k	NOUN
ejpam-3373	123	22	)	)	PUNCT
ejpam-3373	123	23	−	−	PROPN
ejpam-3373	124	1	log	log	NOUN
ejpam-3373	124	2	√	√	NUM
ejpam-3373	124	3	(	(	PUNCT
ejpam-3373	124	4	2ν	2ν	NUM
ejpam-3373	124	5	)	)	PUNCT
ejpam-3373	124	6	!	!	PUNCT
ejpam-3373	125	1	k	k	PROPN
ejpam-3373	125	2	log[p−1	log[p−1	PROPN
ejpam-3373	125	3	]	]	X
ejpam-3373	126	1	k	k	X
ejpam-3373	126	2	=	=	SYM
ejpam-3373	126	3	lim	lim	PROPN
ejpam-3373	126	4	inf	inf	PROPN
ejpam-3373	126	5	k→∞	k→∞	NOUN
ejpam-3373	126	6	1	1	NUM
ejpam-3373	126	7	log[p−1	log[p−1	NOUN
ejpam-3373	126	8	]	]	PUNCT
ejpam-3373	127	1	k	k	X
ejpam-3373	127	2	log[q−1	log[q−1	X
ejpam-3373	127	3	]	]	X
ejpam-3373	127	4	(	(	PUNCT
ejpam-3373	127	5	logr−k(e	logr−k(e	PROPN
ejpam-3373	127	6	(	(	PUNCT
ejpam-3373	127	7	k	k	NOUN
ejpam-3373	127	8	)	)	PUNCT
ejpam-3373	127	9	r	r	NOUN
ejpam-3373	127	10	(	(	PUNCT
ejpam-3373	127	11	u))−1	u))−1	ADP
ejpam-3373	127	12	k	k	PROPN
ejpam-3373	127	13	)	)	PUNCT
ejpam-3373	127	14	×	×	NOUN
ejpam-3373	127	15	(	(	PUNCT
ejpam-3373	127	16	1	1	NUM
ejpam-3373	127	17	+	+	CCONJ
ejpam-3373	127	18	log	log	VERB
ejpam-3373	127	19	√	√	NUM
ejpam-3373	127	20	2(2ν	2(2ν	NUM
ejpam-3373	128	1	+	+	SYM
ejpam-3373	128	2	1)!(k	1)!(k	NUM
ejpam-3373	128	3	+	+	NUM
ejpam-3373	128	4	2ν)2ν	2ν)2ν	NUM
ejpam-3373	128	5	log[r−k(e	log[r−k(e	VERB
ejpam-3373	128	6	(	(	PUNCT
ejpam-3373	128	7	k	k	X
ejpam-3373	128	8	)	)	PUNCT
ejpam-3373	128	9	r	r	NOUN
ejpam-3373	128	10	(	(	PUNCT
ejpam-3373	128	11	u))]−1	u))]−1	PROPN
ejpam-3373	128	12	−	−	NOUN
ejpam-3373	128	13	log	log	NOUN
ejpam-3373	128	14	√	√	INTJ
ejpam-3373	128	15	(	(	PUNCT
ejpam-3373	128	16	2ν	2ν	NUM
ejpam-3373	128	17	)	)	PUNCT
ejpam-3373	128	18	!	!	PUNCT
ejpam-3373	129	1	log[r−k(e	log[r−k(e	PROPN
ejpam-3373	130	1	(	(	PUNCT
ejpam-3373	130	2	k	k	X
ejpam-3373	130	3	)	)	PUNCT
ejpam-3373	130	4	r	r	NOUN
ejpam-3373	130	5	(	(	PUNCT
ejpam-3373	130	6	u))]−1	u))]−1	PROPN
ejpam-3373	130	7	)	)	PUNCT
ejpam-3373	131	1	=	=	SYM
ejpam-3373	131	2	lim	lim	PROPN
ejpam-3373	131	3	inf	inf	PROPN
ejpam-3373	131	4	k→∞	k→∞	PROPN
ejpam-3373	131	5	log[q−1](−	log[q−1](−	PROPN
ejpam-3373	131	6	1	1	NUM
ejpam-3373	131	7	k	k	PROPN
ejpam-3373	131	8	log(r−ke	log(r−ke	PROPN
ejpam-3373	131	9	(	(	PUNCT
ejpam-3373	131	10	k	k	NOUN
ejpam-3373	131	11	)	)	PUNCT
ejpam-3373	131	12	r	r	NOUN
ejpam-3373	131	13	(	(	PUNCT
ejpam-3373	131	14	u	u	NOUN
ejpam-3373	131	15	)	)	PUNCT
ejpam-3373	131	16	)	)	PUNCT
ejpam-3373	131	17	)	)	PUNCT
ejpam-3373	131	18	log[p−1	log[p−1	NOUN
ejpam-3373	131	19	]	]	PUNCT
ejpam-3373	132	1	k	k	X
ejpam-3373	133	1	+	+	PUNCT
ejpam-3373	133	2	log(1	log(1	NOUN
ejpam-3373	133	3	+	+	CCONJ
ejpam-3373	133	4	o(1	o(1	NOUN
ejpam-3373	133	5	)	)	PUNCT
ejpam-3373	133	6	)	)	PUNCT
ejpam-3373	133	7	log[p−1	log[p−1	NOUN
ejpam-3373	133	8	]	]	PUNCT
ejpam-3373	134	1	k	k	X
ejpam-3373	134	2	=	=	SYM
ejpam-3373	134	3	lim	lim	PROPN
ejpam-3373	134	4	inf	inf	PROPN
ejpam-3373	134	5	k→∞	k→∞	NOUN
ejpam-3373	134	6	log[q−1](−	log[q−1](−	PROPN
ejpam-3373	134	7	1	1	NUM
ejpam-3373	134	8	k	k	PROPN
ejpam-3373	134	9	log(r−ke	log(r−ke	PROPN
ejpam-3373	134	10	(	(	PUNCT
ejpam-3373	134	11	k	k	NOUN
ejpam-3373	134	12	)	)	PUNCT
ejpam-3373	134	13	r	r	NOUN
ejpam-3373	134	14	(	(	PUNCT
ejpam-3373	134	15	u	u	NOUN
ejpam-3373	134	16	)	)	PUNCT
ejpam-3373	134	17	)	)	PUNCT
ejpam-3373	134	18	)	)	PUNCT
ejpam-3373	134	19	log[p−1	log[p−1	NOUN
ejpam-3373	134	20	]	]	PUNCT
ejpam-3373	135	1	k	k	X
ejpam-3373	135	2	,	,	PUNCT
ejpam-3373	135	3	and	and	CCONJ
ejpam-3373	135	4	1	1	NUM
ejpam-3373	135	5	l(p	l(p	NOUN
ejpam-3373	135	6	,	,	PUNCT
ejpam-3373	135	7	q	q	NOUN
ejpam-3373	135	8	,	,	PUNCT
ejpam-3373	135	9	g	g	NOUN
ejpam-3373	135	10	)	)	PUNCT
ejpam-3373	135	11	=	=	SYM
ejpam-3373	135	12	lim	lim	PROPN
ejpam-3373	135	13	inf	inf	PROPN
ejpam-3373	135	14	k→∞	k→∞	PROPN
ejpam-3373	135	15	log[q−1](−	log[q−1](−	PROPN
ejpam-3373	135	16	1	1	NUM
ejpam-3373	135	17	k	k	NOUN
ejpam-3373	135	18	log	log	NOUN
ejpam-3373	135	19	(	(	PUNCT
ejpam-3373	135	20	4	4	NUM
ejpam-3373	135	21	(	(	PUNCT
ejpam-3373	135	22	2ν)!(k	2ν)!(k	PROPN
ejpam-3373	135	23	+	+	CCONJ
ejpam-3373	135	24	2ν)2νe	2ν)2νe	NUM
ejpam-3373	135	25	(	(	PUNCT
ejpam-3373	135	26	k−1	k−1	PROPN
ejpam-3373	135	27	)	)	PUNCT
ejpam-3373	135	28	r	r	NOUN
ejpam-3373	135	29	(	(	PUNCT
ejpam-3373	135	30	u)r−k	u)r−k	NOUN
ejpam-3373	135	31	)	)	PUNCT
ejpam-3373	135	32	)	)	PUNCT
ejpam-3373	135	33	log[p−1	log[p−1	NOUN
ejpam-3373	135	34	]	]	PUNCT
ejpam-3373	135	35	k	k	X
ejpam-3373	136	1	=	=	SYM
ejpam-3373	136	2	lim	lim	PROPN
ejpam-3373	136	3	inf	inf	PROPN
ejpam-3373	136	4	k→∞	k→∞	PROPN
ejpam-3373	136	5	log[q−1	log[q−1	X
ejpam-3373	136	6	]	]	X
ejpam-3373	136	7	(	(	PUNCT
ejpam-3373	136	8	log[r−k(e	log[r−k(e	X
ejpam-3373	136	9	(	(	PUNCT
ejpam-3373	136	10	k	k	NOUN
ejpam-3373	136	11	)	)	PUNCT
ejpam-3373	136	12	r	r	NOUN
ejpam-3373	136	13	(	(	PUNCT
ejpam-3373	136	14	u))]−1	u))]−1	PROPN
ejpam-3373	136	15	k	k	NOUN
ejpam-3373	136	16	+	+	X
ejpam-3373	136	17	log(2ν	log(2ν	NOUN
ejpam-3373	136	18	)	)	PUNCT
ejpam-3373	136	19	!	!	PUNCT
ejpam-3373	137	1	k	k	PROPN
ejpam-3373	138	1	−	−	NOUN
ejpam-3373	138	2	1	1	NUM
ejpam-3373	139	1	k	k	NOUN
ejpam-3373	139	2	log	log	NOUN
ejpam-3373	139	3	4(k	4(k	NUM
ejpam-3373	139	4	+	+	NUM
ejpam-3373	139	5	2ν)2ν	2ν)2ν	X
ejpam-3373	139	6	)	)	PUNCT
ejpam-3373	139	7	log[p−1	log[p−1	NOUN
ejpam-3373	139	8	]	]	PUNCT
ejpam-3373	140	1	k	k	X
ejpam-3373	140	2	=	=	SYM
ejpam-3373	140	3	lim	lim	PROPN
ejpam-3373	140	4	inf	inf	PROPN
ejpam-3373	140	5	k→∞	k→∞	NOUN
ejpam-3373	140	6	log[q−1](−	log[q−1](−	PROPN
ejpam-3373	140	7	1	1	NUM
ejpam-3373	140	8	k	k	PROPN
ejpam-3373	140	9	log(r−ke	log(r−ke	PROPN
ejpam-3373	140	10	(	(	PUNCT
ejpam-3373	140	11	k	k	NOUN
ejpam-3373	140	12	)	)	PUNCT
ejpam-3373	140	13	r	r	NOUN
ejpam-3373	140	14	(	(	PUNCT
ejpam-3373	140	15	u	u	NOUN
ejpam-3373	140	16	)	)	PUNCT
ejpam-3373	140	17	)	)	PUNCT
ejpam-3373	140	18	)	)	PUNCT
ejpam-3373	140	19	log[p−1	log[p−1	NOUN
ejpam-3373	140	20	]	]	PUNCT
ejpam-3373	141	1	k	k	X
ejpam-3373	142	1	+	+	PUNCT
ejpam-3373	142	2	log(1	log(1	NOUN
ejpam-3373	142	3	+	+	CCONJ
ejpam-3373	142	4	o(1	o(1	NOUN
ejpam-3373	142	5	)	)	PUNCT
ejpam-3373	142	6	)	)	PUNCT
ejpam-3373	142	7	log[p−1	log[p−1	NOUN
ejpam-3373	142	8	]	]	PUNCT
ejpam-3373	143	1	k	k	X
ejpam-3373	143	2	=	=	SYM
ejpam-3373	143	3	lim	lim	PROPN
ejpam-3373	143	4	inf	inf	PROPN
ejpam-3373	143	5	k→∞	k→∞	NOUN
ejpam-3373	143	6	log[q−1](−	log[q−1](−	PROPN
ejpam-3373	143	7	1	1	NUM
ejpam-3373	143	8	k	k	PROPN
ejpam-3373	143	9	log(r−ke	log(r−ke	PROPN
ejpam-3373	143	10	(	(	PUNCT
ejpam-3373	143	11	k	k	NOUN
ejpam-3373	143	12	)	)	PUNCT
ejpam-3373	143	13	r	r	NOUN
ejpam-3373	143	14	(	(	PUNCT
ejpam-3373	143	15	u	u	NOUN
ejpam-3373	143	16	)	)	PUNCT
ejpam-3373	143	17	)	)	PUNCT
ejpam-3373	143	18	)	)	PUNCT
ejpam-3373	143	19	log[p−1	log[p−1	NOUN
ejpam-3373	143	20	]	]	PUNCT
ejpam-3373	144	1	k	k	X
ejpam-3373	144	2	,	,	PUNCT
ejpam-3373	144	3	using	use	VERB
ejpam-3373	144	4	theorem	theorem	NOUN
ejpam-3373	144	5	a	a	PRON
ejpam-3373	144	6	,	,	PUNCT
ejpam-3373	144	7	we	we	PRON
ejpam-3373	144	8	see	see	VERB
ejpam-3373	144	9	that	that	SCONJ
ejpam-3373	144	10	the	the	DET
ejpam-3373	144	11	function	function	NOUN
ejpam-3373	144	12	f	f	PROPN
ejpam-3373	144	13	and	and	CCONJ
ejpam-3373	144	14	g	g	PROPN
ejpam-3373	144	15	have	have	VERB
ejpam-3373	144	16	same	same	ADJ
ejpam-3373	144	17	(	(	PUNCT
ejpam-3373	144	18	p	p	X
ejpam-3373	144	19	,	,	PUNCT
ejpam-3373	144	20	q)-order	q)-order	NOUN
ejpam-3373	144	21	,	,	PUNCT
ejpam-3373	144	22	it	it	PRON
ejpam-3373	144	23	leads	lead	VERB
ejpam-3373	144	24	to	to	ADP
ejpam-3373	144	25	the	the	DET
ejpam-3373	144	26	fact	fact	NOUN
ejpam-3373	144	27	that	that	SCONJ
ejpam-3373	144	28	ρ(p	ρ(p	PROPN
ejpam-3373	144	29	,	,	PUNCT
ejpam-3373	144	30	q	q	X
ejpam-3373	144	31	,	,	PUNCT
ejpam-3373	144	32	f	f	X
ejpam-3373	144	33	)	)	PUNCT
ejpam-3373	144	34	=	=	SYM
ejpam-3373	144	35	ρ(p	ρ(p	NOUN
ejpam-3373	144	36	,	,	PUNCT
ejpam-3373	144	37	q	q	NOUN
ejpam-3373	144	38	,	,	PUNCT
ejpam-3373	144	39	g	g	NOUN
ejpam-3373	144	40	)	)	PUNCT
ejpam-3373	144	41	=	=	SYM
ejpam-3373	145	1	ρ	ρ	PROPN
ejpam-3373	145	2	.	.	PUNCT
ejpam-3373	146	1	now	now	ADV
ejpam-3373	146	2	we	we	PRON
ejpam-3373	146	3	consider	consider	VERB
ejpam-3373	146	4	the	the	DET
ejpam-3373	146	5	(	(	PUNCT
ejpam-3373	146	6	p	p	NOUN
ejpam-3373	146	7	,	,	PUNCT
ejpam-3373	146	8	q)-type	q)-type	PUNCT
ejpam-3373	146	9	for	for	ADP
ejpam-3373	146	10	q	q	NOUN
ejpam-3373	146	11	=	=	SYM
ejpam-3373	146	12	2	2	NUM
ejpam-3373	146	13	as	as	ADP
ejpam-3373	146	14	d.	d.	PROPN
ejpam-3373	146	15	kumar	kumar	PROPN
ejpam-3373	146	16	,	,	PUNCT
ejpam-3373	146	17	r.	r.	PROPN
ejpam-3373	146	18	ali	ali	PROPN
ejpam-3373	146	19	/	/	SYM
ejpam-3373	146	20	eur	eur	PROPN
ejpam-3373	146	21	.	.	PUNCT
ejpam-3373	147	1	j.	j.	PROPN
ejpam-3373	147	2	pure	pure	PROPN
ejpam-3373	147	3	appl	appl	PROPN
ejpam-3373	147	4	.	.	PROPN
ejpam-3373	147	5	math	math	PROPN
ejpam-3373	147	6	,	,	PUNCT
ejpam-3373	147	7	12	12	NUM
ejpam-3373	147	8	(	(	PUNCT
ejpam-3373	147	9	2	2	NUM
ejpam-3373	147	10	)	)	PUNCT
ejpam-3373	147	11	(	(	PUNCT
ejpam-3373	147	12	2019	2019	NUM
ejpam-3373	147	13	)	)	PUNCT
ejpam-3373	147	14	,	,	PUNCT
ejpam-3373	147	15	486	486	NUM
ejpam-3373	147	16	-	-	SYM
ejpam-3373	147	17	498	498	NUM
ejpam-3373	147	18	492	492	NUM
ejpam-3373	147	19	1	1	NUM
ejpam-3373	147	20	v(p	v(p	PROPN
ejpam-3373	147	21	,	,	PUNCT
ejpam-3373	147	22	q	q	NOUN
ejpam-3373	147	23	,	,	PUNCT
ejpam-3373	147	24	f	f	X
ejpam-3373	147	25	)	)	PUNCT
ejpam-3373	147	26	=	=	SYM
ejpam-3373	147	27	lim	lim	PROPN
ejpam-3373	147	28	inf	inf	PROPN
ejpam-3373	147	29	k→∞	k→∞	NOUN
ejpam-3373	148	1	(	(	PUNCT
ejpam-3373	148	2	−	−	PROPN
ejpam-3373	148	3	1	1	NUM
ejpam-3373	148	4	k	k	PROPN
ejpam-3373	148	5	log	log	PROPN
ejpam-3373	148	6	(	(	PUNCT
ejpam-3373	148	7	√	√	PROPN
ejpam-3373	148	8	(	(	PUNCT
ejpam-3373	148	9	2ν)!√	2ν)!√	PROPN
ejpam-3373	148	10	2(2ν+1)!(k+2ν)2ν	2(2ν+1)!(k+2ν)2ν	NUM
ejpam-3373	148	11	r−ke	r−ke	NOUN
ejpam-3373	148	12	(	(	PUNCT
ejpam-3373	148	13	k	k	NOUN
ejpam-3373	148	14	)	)	PUNCT
ejpam-3373	148	15	r	r	NOUN
ejpam-3373	148	16	(	(	PUNCT
ejpam-3373	148	17	u)))ρ−1	u)))ρ−1	PROPN
ejpam-3373	148	18	log[p−2	log[p−2	NOUN
ejpam-3373	148	19	]	]	X
ejpam-3373	149	1	k	k	X
ejpam-3373	149	2	=	=	SYM
ejpam-3373	149	3	lim	lim	PROPN
ejpam-3373	149	4	inf	inf	PROPN
ejpam-3373	149	5	k→∞	k→∞	PROPN
ejpam-3373	149	6	(	(	PUNCT
ejpam-3373	149	7	log[r−k(e	log[r−k(e	PROPN
ejpam-3373	149	8	(	(	PUNCT
ejpam-3373	149	9	k	k	NOUN
ejpam-3373	149	10	)	)	PUNCT
ejpam-3373	149	11	r	r	NOUN
ejpam-3373	149	12	(	(	PUNCT
ejpam-3373	149	13	u))]−1	u))]−1	PROPN
ejpam-3373	149	14	k	k	NOUN
ejpam-3373	150	1	+	+	CCONJ
ejpam-3373	150	2	log	log	VERB
ejpam-3373	150	3	√	√	NUM
ejpam-3373	150	4	2(2ν+1)!(k+2ν)2ν	2(2ν+1)!(k+2ν)2ν	NUM
ejpam-3373	150	5	k	k	DET
ejpam-3373	150	6	−	−	NOUN
ejpam-3373	150	7	log	log	NOUN
ejpam-3373	150	8	√	√	INTJ
ejpam-3373	150	9	(	(	PUNCT
ejpam-3373	150	10	2ν	2ν	NUM
ejpam-3373	150	11	)	)	PUNCT
ejpam-3373	150	12	!	!	PUNCT
ejpam-3373	151	1	k	k	X
ejpam-3373	151	2	)	)	PUNCT
ejpam-3373	152	1	ρ−1	ρ−1	PROPN
ejpam-3373	152	2	log[p−2	log[p−2	NOUN
ejpam-3373	152	3	]	]	X
ejpam-3373	153	1	k	k	X
ejpam-3373	153	2	=	=	SYM
ejpam-3373	153	3	lim	lim	PROPN
ejpam-3373	153	4	inf	inf	PROPN
ejpam-3373	153	5	k→∞	k→∞	NOUN
ejpam-3373	153	6	1	1	NUM
ejpam-3373	153	7	log[p−2	log[p−2	NOUN
ejpam-3373	153	8	]	]	X
ejpam-3373	154	1	k	k	X
ejpam-3373	154	2	(	(	PUNCT
ejpam-3373	154	3	logr−k(e	logr−k(e	PROPN
ejpam-3373	154	4	(	(	PUNCT
ejpam-3373	154	5	k	k	NOUN
ejpam-3373	154	6	)	)	PUNCT
ejpam-3373	154	7	r	r	NOUN
ejpam-3373	154	8	(	(	PUNCT
ejpam-3373	154	9	u))−1	u))−1	ADP
ejpam-3373	154	10	k	k	PROPN
ejpam-3373	154	11	)	)	PUNCT
ejpam-3373	154	12	ρ−1×	ρ−1×	PROPN
ejpam-3373	154	13	(	(	PUNCT
ejpam-3373	154	14	1	1	NUM
ejpam-3373	154	15	+	+	CCONJ
ejpam-3373	154	16	log	log	VERB
ejpam-3373	154	17	√	√	NUM
ejpam-3373	154	18	2(2ν	2(2ν	NUM
ejpam-3373	155	1	+	+	SYM
ejpam-3373	155	2	1)!(k	1)!(k	NUM
ejpam-3373	155	3	+	+	NUM
ejpam-3373	155	4	2ν)2ν	2ν)2ν	NUM
ejpam-3373	155	5	log[r−k(e	log[r−k(e	VERB
ejpam-3373	155	6	(	(	PUNCT
ejpam-3373	155	7	k	k	X
ejpam-3373	155	8	)	)	PUNCT
ejpam-3373	155	9	r	r	NOUN
ejpam-3373	155	10	(	(	PUNCT
ejpam-3373	155	11	u))]−1	u))]−1	PROPN
ejpam-3373	155	12	−	−	NOUN
ejpam-3373	155	13	log	log	NOUN
ejpam-3373	155	14	√	√	INTJ
ejpam-3373	155	15	(	(	PUNCT
ejpam-3373	155	16	2ν	2ν	NUM
ejpam-3373	155	17	)	)	PUNCT
ejpam-3373	155	18	!	!	PUNCT
ejpam-3373	156	1	log[r−k(e	log[r−k(e	PROPN
ejpam-3373	157	1	(	(	PUNCT
ejpam-3373	157	2	k	k	X
ejpam-3373	157	3	)	)	PUNCT
ejpam-3373	157	4	r	r	NOUN
ejpam-3373	157	5	(	(	PUNCT
ejpam-3373	157	6	u))]−1	u))]−1	PROPN
ejpam-3373	157	7	)	)	PUNCT
ejpam-3373	157	8	ρ−1	ρ−1	PROPN
ejpam-3373	158	1	=	=	SYM
ejpam-3373	158	2	lim	lim	PROPN
ejpam-3373	158	3	inf	inf	PROPN
ejpam-3373	158	4	k→∞	k→∞	NOUN
ejpam-3373	158	5	(	(	PUNCT
ejpam-3373	158	6	−	−	PROPN
ejpam-3373	158	7	1	1	NUM
ejpam-3373	158	8	k	k	PROPN
ejpam-3373	158	9	log(r−ke	log(r−ke	PROPN
ejpam-3373	158	10	(	(	PUNCT
ejpam-3373	158	11	k	k	NOUN
ejpam-3373	158	12	)	)	PUNCT
ejpam-3373	158	13	r	r	NOUN
ejpam-3373	158	14	(	(	PUNCT
ejpam-3373	158	15	u)))ρ−1	u)))ρ−1	PROPN
ejpam-3373	158	16	log[p−2	log[p−2	NOUN
ejpam-3373	158	17	]	]	PUNCT
ejpam-3373	159	1	k	k	X
ejpam-3373	160	1	+	+	PUNCT
ejpam-3373	160	2	log(1	log(1	NOUN
ejpam-3373	160	3	+	+	CCONJ
ejpam-3373	160	4	o(1))ρ−1	o(1))ρ−1	ADV
ejpam-3373	160	5	log[p−2	log[p−2	NOUN
ejpam-3373	160	6	]	]	X
ejpam-3373	161	1	k	k	X
ejpam-3373	161	2	=	=	SYM
ejpam-3373	161	3	lim	lim	PROPN
ejpam-3373	161	4	inf	inf	PROPN
ejpam-3373	161	5	k→∞	k→∞	NOUN
ejpam-3373	162	1	(	(	PUNCT
ejpam-3373	162	2	−	−	PROPN
ejpam-3373	162	3	1	1	NUM
ejpam-3373	162	4	k	k	PROPN
ejpam-3373	162	5	log(r−ke	log(r−ke	PROPN
ejpam-3373	162	6	(	(	PUNCT
ejpam-3373	162	7	k	k	NOUN
ejpam-3373	162	8	)	)	PUNCT
ejpam-3373	162	9	r	r	NOUN
ejpam-3373	162	10	(	(	PUNCT
ejpam-3373	162	11	u)))ρ−1	u)))ρ−1	PROPN
ejpam-3373	162	12	log[p−2	log[p−2	NOUN
ejpam-3373	162	13	]	]	X
ejpam-3373	163	1	k	k	X
ejpam-3373	163	2	.	.	PUNCT
ejpam-3373	164	1	similarly	similarly	ADV
ejpam-3373	164	2	for	for	ADP
ejpam-3373	164	3	g	g	PROPN
ejpam-3373	164	4	we	we	PRON
ejpam-3373	164	5	have	have	VERB
ejpam-3373	164	6	1	1	NUM
ejpam-3373	164	7	v(p	v(p	NOUN
ejpam-3373	164	8	,	,	PUNCT
ejpam-3373	164	9	2	2	NUM
ejpam-3373	164	10	,	,	PUNCT
ejpam-3373	164	11	g	g	NOUN
ejpam-3373	164	12	)	)	PUNCT
ejpam-3373	164	13	=	=	SYM
ejpam-3373	164	14	lim	lim	PROPN
ejpam-3373	164	15	inf	inf	PROPN
ejpam-3373	164	16	k→∞	k→∞	NOUN
ejpam-3373	165	1	(	(	PUNCT
ejpam-3373	165	2	−	−	PROPN
ejpam-3373	165	3	1	1	NUM
ejpam-3373	165	4	k	k	PROPN
ejpam-3373	165	5	log(r−ke	log(r−ke	PROPN
ejpam-3373	165	6	(	(	PUNCT
ejpam-3373	165	7	k	k	NOUN
ejpam-3373	165	8	)	)	PUNCT
ejpam-3373	165	9	r	r	NOUN
ejpam-3373	165	10	(	(	PUNCT
ejpam-3373	165	11	u)))ρ	u)))ρ	PROPN
ejpam-3373	165	12	log[p−2	log[p−2	NOUN
ejpam-3373	165	13	]	]	X
ejpam-3373	166	1	k	k	X
ejpam-3373	166	2	.	.	PUNCT
ejpam-3373	167	1	now	now	ADV
ejpam-3373	167	2	for	for	ADP
ejpam-3373	167	3	the	the	DET
ejpam-3373	167	4	case	case	NOUN
ejpam-3373	167	5	q	q	X
ejpam-3373	167	6	≥	≥	NUM
ejpam-3373	167	7	3	3	NUM
ejpam-3373	167	8	,	,	PUNCT
ejpam-3373	167	9	we	we	PRON
ejpam-3373	167	10	have	have	VERB
ejpam-3373	167	11	1	1	NUM
ejpam-3373	167	12	v(p	v(p	NOUN
ejpam-3373	167	13	,	,	PUNCT
ejpam-3373	167	14	q	q	NOUN
ejpam-3373	167	15	,	,	PUNCT
ejpam-3373	167	16	f	f	X
ejpam-3373	167	17	)	)	PUNCT
ejpam-3373	168	1	=	=	SYM
ejpam-3373	168	2	lim	lim	PROPN
ejpam-3373	168	3	inf	inf	PROPN
ejpam-3373	168	4	k→∞	k→∞	NOUN
ejpam-3373	168	5	log[q−2](−	log[q−2](−	PROPN
ejpam-3373	168	6	1	1	NUM
ejpam-3373	168	7	k	k	NOUN
ejpam-3373	168	8	log	log	PROPN
ejpam-3373	168	9	(	(	PUNCT
ejpam-3373	168	10	√	√	PROPN
ejpam-3373	168	11	(	(	PUNCT
ejpam-3373	168	12	2ν)!√	2ν)!√	PROPN
ejpam-3373	168	13	2(2ν+1)!(k+2ν)2ν	2(2ν+1)!(k+2ν)2ν	NUM
ejpam-3373	168	14	r−ke	r−ke	NOUN
ejpam-3373	168	15	(	(	PUNCT
ejpam-3373	168	16	k	k	NOUN
ejpam-3373	168	17	)	)	PUNCT
ejpam-3373	168	18	r	r	NOUN
ejpam-3373	168	19	(	(	PUNCT
ejpam-3373	168	20	u)))ρ	u)))ρ	PROPN
ejpam-3373	168	21	log[p−2	log[p−2	NOUN
ejpam-3373	168	22	]	]	PUNCT
ejpam-3373	169	1	k	k	X
ejpam-3373	170	1	=	=	SYM
ejpam-3373	170	2	lim	lim	PROPN
ejpam-3373	170	3	inf	inf	PROPN
ejpam-3373	170	4	k→∞	k→∞	PROPN
ejpam-3373	170	5	log[q−2	log[q−2	PROPN
ejpam-3373	170	6	]	]	PUNCT
ejpam-3373	170	7	(	(	PUNCT
ejpam-3373	170	8	log[r−k(e	log[r−k(e	X
ejpam-3373	170	9	(	(	PUNCT
ejpam-3373	170	10	k	k	NOUN
ejpam-3373	170	11	)	)	PUNCT
ejpam-3373	170	12	r	r	NOUN
ejpam-3373	170	13	(	(	PUNCT
ejpam-3373	170	14	u))]−1	u))]−1	PROPN
ejpam-3373	170	15	k	k	NOUN
ejpam-3373	171	1	+	+	CCONJ
ejpam-3373	171	2	log	log	VERB
ejpam-3373	171	3	√	√	NUM
ejpam-3373	171	4	2(2ν+1)!(k+2ν)2ν	2(2ν+1)!(k+2ν)2ν	NUM
ejpam-3373	171	5	k	k	DET
ejpam-3373	171	6	−	−	NOUN
ejpam-3373	171	7	log	log	NOUN
ejpam-3373	171	8	√	√	INTJ
ejpam-3373	171	9	(	(	PUNCT
ejpam-3373	171	10	2ν	2ν	NUM
ejpam-3373	171	11	)	)	PUNCT
ejpam-3373	171	12	!	!	PUNCT
ejpam-3373	172	1	k	k	X
ejpam-3373	172	2	)	)	PUNCT
ejpam-3373	172	3	ρ	ρ	PROPN
ejpam-3373	172	4	log[p−2	log[p−2	NOUN
ejpam-3373	172	5	]	]	X
ejpam-3373	173	1	k	k	X
ejpam-3373	173	2	=	=	SYM
ejpam-3373	173	3	lim	lim	PROPN
ejpam-3373	173	4	inf	inf	PROPN
ejpam-3373	173	5	k→∞	k→∞	NOUN
ejpam-3373	173	6	1	1	NUM
ejpam-3373	173	7	log[p−2	log[p−2	NOUN
ejpam-3373	173	8	]	]	X
ejpam-3373	174	1	k	k	X
ejpam-3373	174	2	log[q−2	log[q−2	PROPN
ejpam-3373	174	3	]	]	PUNCT
ejpam-3373	174	4	(	(	PUNCT
ejpam-3373	174	5	logr−k(e	logr−k(e	PROPN
ejpam-3373	174	6	(	(	PUNCT
ejpam-3373	174	7	k	k	NOUN
ejpam-3373	174	8	)	)	PUNCT
ejpam-3373	174	9	r	r	NOUN
ejpam-3373	174	10	(	(	PUNCT
ejpam-3373	174	11	u))−1	u))−1	ADP
ejpam-3373	174	12	k	k	PROPN
ejpam-3373	174	13	)	)	PUNCT
ejpam-3373	174	14	ρ×	ρ×	SYM
ejpam-3373	174	15	(	(	PUNCT
ejpam-3373	174	16	1	1	NUM
ejpam-3373	174	17	+	+	CCONJ
ejpam-3373	174	18	log	log	VERB
ejpam-3373	174	19	√	√	NUM
ejpam-3373	174	20	2(2ν	2(2ν	NUM
ejpam-3373	174	21	+	+	SYM
ejpam-3373	174	22	1)!(k	1)!(k	NUM
ejpam-3373	174	23	+	+	NUM
ejpam-3373	174	24	2ν)2ν	2ν)2ν	NUM
ejpam-3373	174	25	log[r−k(e	log[r−k(e	VERB
ejpam-3373	174	26	(	(	PUNCT
ejpam-3373	174	27	k	k	X
ejpam-3373	174	28	)	)	PUNCT
ejpam-3373	174	29	r	r	NOUN
ejpam-3373	174	30	(	(	PUNCT
ejpam-3373	174	31	u))]−1	u))]−1	PROPN
ejpam-3373	174	32	−	−	NOUN
ejpam-3373	174	33	log	log	NOUN
ejpam-3373	174	34	√	√	INTJ
ejpam-3373	174	35	(	(	PUNCT
ejpam-3373	174	36	2ν	2ν	NUM
ejpam-3373	174	37	)	)	PUNCT
ejpam-3373	174	38	!	!	PUNCT
ejpam-3373	175	1	log[r−k(e	log[r−k(e	PROPN
ejpam-3373	176	1	(	(	PUNCT
ejpam-3373	176	2	k	k	X
ejpam-3373	176	3	)	)	PUNCT
ejpam-3373	176	4	r	r	NOUN
ejpam-3373	176	5	(	(	PUNCT
ejpam-3373	176	6	u))]−1	u))]−1	PROPN
ejpam-3373	176	7	)	)	PUNCT
ejpam-3373	176	8	ρ−1	ρ−1	PROPN
ejpam-3373	177	1	=	=	SYM
ejpam-3373	177	2	lim	lim	PROPN
ejpam-3373	177	3	inf	inf	PROPN
ejpam-3373	177	4	k→∞	k→∞	NOUN
ejpam-3373	177	5	log[q−2](−	log[q−2](−	PROPN
ejpam-3373	177	6	1	1	NUM
ejpam-3373	177	7	k	k	PROPN
ejpam-3373	177	8	log(r−ke	log(r−ke	PROPN
ejpam-3373	177	9	(	(	PUNCT
ejpam-3373	177	10	k	k	NOUN
ejpam-3373	177	11	)	)	PUNCT
ejpam-3373	177	12	r	r	NOUN
ejpam-3373	177	13	(	(	PUNCT
ejpam-3373	177	14	u)))ρ	u)))ρ	PROPN
ejpam-3373	177	15	log[p−2	log[p−2	NOUN
ejpam-3373	177	16	]	]	PUNCT
ejpam-3373	178	1	k	k	X
ejpam-3373	179	1	+	+	PUNCT
ejpam-3373	179	2	log(1	log(1	NOUN
ejpam-3373	180	1	+	+	CCONJ
ejpam-3373	180	2	o(1))ρ	o(1))ρ	PROPN
ejpam-3373	180	3	log[p−2	log[p−2	NOUN
ejpam-3373	180	4	]	]	PUNCT
ejpam-3373	181	1	k	k	X
ejpam-3373	181	2	=	=	SYM
ejpam-3373	181	3	lim	lim	PROPN
ejpam-3373	181	4	inf	inf	PROPN
ejpam-3373	181	5	k→∞	k→∞	NOUN
ejpam-3373	182	1	(	(	PUNCT
ejpam-3373	182	2	−	−	PROPN
ejpam-3373	182	3	1	1	NUM
ejpam-3373	182	4	k	k	PROPN
ejpam-3373	182	5	log(r−ke	log(r−ke	PROPN
ejpam-3373	182	6	(	(	PUNCT
ejpam-3373	182	7	k	k	NOUN
ejpam-3373	182	8	)	)	PUNCT
ejpam-3373	182	9	r	r	NOUN
ejpam-3373	182	10	(	(	PUNCT
ejpam-3373	182	11	u)))ρ	u)))ρ	PROPN
ejpam-3373	182	12	log[p−2	log[p−2	NOUN
ejpam-3373	182	13	]	]	X
ejpam-3373	183	1	k	k	X
ejpam-3373	183	2	.	.	PUNCT
ejpam-3373	184	1	in	in	ADP
ejpam-3373	184	2	the	the	DET
ejpam-3373	184	3	same	same	ADJ
ejpam-3373	184	4	manner	manner	NOUN
ejpam-3373	184	5	for	for	ADP
ejpam-3373	184	6	the	the	DET
ejpam-3373	184	7	function	function	NOUN
ejpam-3373	184	8	g	g	NOUN
ejpam-3373	184	9	,	,	PUNCT
ejpam-3373	184	10	we	we	PRON
ejpam-3373	184	11	obtain	obtain	VERB
ejpam-3373	184	12	1	1	NUM
ejpam-3373	184	13	v(p	v(p	NOUN
ejpam-3373	184	14	,	,	PUNCT
ejpam-3373	184	15	q	q	NOUN
ejpam-3373	184	16	,	,	PUNCT
ejpam-3373	184	17	g	g	NOUN
ejpam-3373	184	18	)	)	PUNCT
ejpam-3373	184	19	=	=	SYM
ejpam-3373	184	20	lim	lim	PROPN
ejpam-3373	184	21	inf	inf	PROPN
ejpam-3373	184	22	k→∞	k→∞	NOUN
ejpam-3373	184	23	(	(	PUNCT
ejpam-3373	184	24	−	−	PROPN
ejpam-3373	184	25	1	1	NUM
ejpam-3373	184	26	k	k	PROPN
ejpam-3373	184	27	log(r−ke	log(r−ke	PROPN
ejpam-3373	184	28	(	(	PUNCT
ejpam-3373	184	29	k	k	NOUN
ejpam-3373	184	30	)	)	PUNCT
ejpam-3373	184	31	r	r	NOUN
ejpam-3373	184	32	(	(	PUNCT
ejpam-3373	184	33	u)))ρ	u)))ρ	PROPN
ejpam-3373	184	34	log[p−2	log[p−2	NOUN
ejpam-3373	184	35	]	]	X
ejpam-3373	185	1	k	k	X
ejpam-3373	185	2	.	.	PUNCT
ejpam-3373	186	1	d.	d.	PROPN
ejpam-3373	186	2	kumar	kumar	PROPN
ejpam-3373	186	3	,	,	PUNCT
ejpam-3373	186	4	r.	r.	PROPN
ejpam-3373	186	5	ali	ali	PROPN
ejpam-3373	186	6	/	/	SYM
ejpam-3373	186	7	eur	eur	PROPN
ejpam-3373	186	8	.	.	PUNCT
ejpam-3373	187	1	j.	j.	PROPN
ejpam-3373	187	2	pure	pure	PROPN
ejpam-3373	187	3	appl	appl	PROPN
ejpam-3373	187	4	.	.	PROPN
ejpam-3373	187	5	math	math	PROPN
ejpam-3373	187	6	,	,	PUNCT
ejpam-3373	187	7	12	12	NUM
ejpam-3373	187	8	(	(	PUNCT
ejpam-3373	187	9	2	2	NUM
ejpam-3373	187	10	)	)	PUNCT
ejpam-3373	187	11	(	(	PUNCT
ejpam-3373	187	12	2019	2019	NUM
ejpam-3373	187	13	)	)	PUNCT
ejpam-3373	187	14	,	,	PUNCT
ejpam-3373	187	15	486	486	NUM
ejpam-3373	187	16	-	-	SYM
ejpam-3373	187	17	498	498	NUM
ejpam-3373	187	18	493	493	NUM
ejpam-3373	187	19	lemma	lemma	PROPN
ejpam-3373	187	20	2.2	2.2	NUM
ejpam-3373	187	21	.	.	PUNCT
ejpam-3373	188	1	let	let	VERB
ejpam-3373	188	2	u	u	PRON
ejpam-3373	188	3	be	be	AUX
ejpam-3373	188	4	an	an	DET
ejpam-3373	188	5	entire	entire	ADJ
ejpam-3373	188	6	harmonic	harmonic	ADJ
ejpam-3373	188	7	function	function	NOUN
ejpam-3373	188	8	of	of	ADP
ejpam-3373	188	9	an	an	DET
ejpam-3373	188	10	n	n	ADV
ejpam-3373	188	11	-	-	PUNCT
ejpam-3373	188	12	dimensional	dimensional	ADJ
ejpam-3373	188	13	space	space	NOUN
ejpam-3373	188	14	n	n	PRON
ejpam-3373	188	15	≥	≥	NOUN
ejpam-3373	188	16	3	3	NUM
ejpam-3373	188	17	with	with	ADP
ejpam-3373	188	18	(	(	PUNCT
ejpam-3373	188	19	p	p	NOUN
ejpam-3373	188	20	,	,	PUNCT
ejpam-3373	188	21	q)-order	q)-order	ADJ
ejpam-3373	188	22	ρ(p	ρ(p	NUM
ejpam-3373	188	23	,	,	PUNCT
ejpam-3373	188	24	q	q	NOUN
ejpam-3373	188	25	,	,	PUNCT
ejpam-3373	188	26	u	u	NOUN
ejpam-3373	188	27	)	)	PUNCT
ejpam-3373	188	28	,	,	PUNCT
ejpam-3373	188	29	lower	low	ADJ
ejpam-3373	188	30	(	(	PUNCT
ejpam-3373	188	31	p	p	NOUN
ejpam-3373	188	32	,	,	PUNCT
ejpam-3373	188	33	q)-order	q)-order	NOUN
ejpam-3373	188	34	λ(p	λ(p	PROPN
ejpam-3373	188	35	,	,	PUNCT
ejpam-3373	188	36	q	q	NOUN
ejpam-3373	188	37	,	,	PUNCT
ejpam-3373	188	38	u	u	NOUN
ejpam-3373	188	39	)	)	PUNCT
ejpam-3373	188	40	,	,	PUNCT
ejpam-3373	188	41	(	(	PUNCT
ejpam-3373	188	42	p	p	X
ejpam-3373	188	43	,	,	PUNCT
ejpam-3373	188	44	q)-type	q)-type	PUNCT
ejpam-3373	188	45	t	t	NOUN
ejpam-3373	188	46	(	(	PUNCT
ejpam-3373	188	47	p	p	X
ejpam-3373	188	48	,	,	PUNCT
ejpam-3373	188	49	q	q	NOUN
ejpam-3373	188	50	,	,	PUNCT
ejpam-3373	188	51	u	u	NOUN
ejpam-3373	188	52	)	)	PUNCT
ejpam-3373	188	53	and	and	CCONJ
ejpam-3373	188	54	lower	low	ADJ
ejpam-3373	188	55	(	(	PUNCT
ejpam-3373	188	56	p	p	NOUN
ejpam-3373	188	57	,	,	PUNCT
ejpam-3373	188	58	q)-type	q)-type	PUNCT
ejpam-3373	188	59	t(p	t(p	PROPN
ejpam-3373	188	60	,	,	PUNCT
ejpam-3373	188	61	q	q	NOUN
ejpam-3373	188	62	,	,	PUNCT
ejpam-3373	188	63	u	u	NOUN
ejpam-3373	188	64	)	)	PUNCT
ejpam-3373	188	65	.	.	PUNCT
ejpam-3373	189	1	if	if	SCONJ
ejpam-3373	189	2	f	f	PROPN
ejpam-3373	189	3	and	and	CCONJ
ejpam-3373	189	4	g	g	PROPN
ejpam-3373	189	5	are	be	AUX
ejpam-3373	189	6	entire	entire	ADJ
ejpam-3373	189	7	functions	function	NOUN
ejpam-3373	189	8	defined	define	VERB
ejpam-3373	189	9	as	as	ADP
ejpam-3373	189	10	in	in	ADP
ejpam-3373	189	11	(	(	PUNCT
ejpam-3373	189	12	2.1	2.1	NUM
ejpam-3373	189	13	)	)	PUNCT
ejpam-3373	189	14	and	and	CCONJ
ejpam-3373	189	15	(	(	PUNCT
ejpam-3373	189	16	2.2	2.2	NUM
ejpam-3373	189	17	)	)	PUNCT
ejpam-3373	189	18	,	,	PUNCT
ejpam-3373	189	19	then	then	ADV
ejpam-3373	189	20	ρ(p	ρ(p	NUM
ejpam-3373	189	21	,	,	PUNCT
ejpam-3373	189	22	q	q	X
ejpam-3373	189	23	,	,	PUNCT
ejpam-3373	189	24	f	f	X
ejpam-3373	189	25	)	)	PUNCT
ejpam-3373	189	26	=	=	SYM
ejpam-3373	189	27	ρ(p	ρ(p	NOUN
ejpam-3373	189	28	,	,	PUNCT
ejpam-3373	189	29	q	q	NOUN
ejpam-3373	189	30	,	,	PUNCT
ejpam-3373	189	31	u	u	NOUN
ejpam-3373	189	32	)	)	PUNCT
ejpam-3373	189	33	=	=	SYM
ejpam-3373	189	34	ρ(p	ρ(p	PROPN
ejpam-3373	189	35	,	,	PUNCT
ejpam-3373	189	36	q	q	X
ejpam-3373	189	37	,	,	PUNCT
ejpam-3373	189	38	g	g	NOUN
ejpam-3373	189	39	)	)	PUNCT
ejpam-3373	189	40	,	,	PUNCT
ejpam-3373	189	41	(	(	PUNCT
ejpam-3373	189	42	2.4	2.4	NUM
ejpam-3373	189	43	)	)	PUNCT
ejpam-3373	189	44	λ(p	λ(p	PROPN
ejpam-3373	189	45	,	,	PUNCT
ejpam-3373	189	46	q	q	X
ejpam-3373	189	47	,	,	PUNCT
ejpam-3373	189	48	f	f	NOUN
ejpam-3373	189	49	)	)	PUNCT
ejpam-3373	189	50	≤	≤	NOUN
ejpam-3373	189	51	λ(p	λ(p	PROPN
ejpam-3373	189	52	,	,	PUNCT
ejpam-3373	189	53	q	q	NOUN
ejpam-3373	189	54	,	,	PUNCT
ejpam-3373	189	55	u	u	NOUN
ejpam-3373	189	56	)	)	PUNCT
ejpam-3373	189	57	≤	≤	NOUN
ejpam-3373	190	1	λ(p	λ(p	PROPN
ejpam-3373	190	2	,	,	PUNCT
ejpam-3373	190	3	q	q	X
ejpam-3373	190	4	,	,	PUNCT
ejpam-3373	190	5	g	g	NOUN
ejpam-3373	190	6	)	)	PUNCT
ejpam-3373	190	7	,	,	PUNCT
ejpam-3373	190	8	(	(	PUNCT
ejpam-3373	190	9	2.5	2.5	NUM
ejpam-3373	190	10	)	)	PUNCT
ejpam-3373	190	11	t	t	NOUN
ejpam-3373	190	12	(	(	PUNCT
ejpam-3373	190	13	p	p	X
ejpam-3373	190	14	,	,	PUNCT
ejpam-3373	190	15	q	q	ADJ
ejpam-3373	190	16	,	,	PUNCT
ejpam-3373	190	17	f	f	X
ejpam-3373	190	18	)	)	PUNCT
ejpam-3373	191	1	=	=	SYM
ejpam-3373	191	2	t	t	PROPN
ejpam-3373	191	3	(	(	PUNCT
ejpam-3373	191	4	p	p	X
ejpam-3373	191	5	,	,	PUNCT
ejpam-3373	191	6	q	q	ADJ
ejpam-3373	191	7	,	,	PUNCT
ejpam-3373	191	8	u	u	NOUN
ejpam-3373	191	9	)	)	PUNCT
ejpam-3373	191	10	=	=	SYM
ejpam-3373	191	11	t	t	PROPN
ejpam-3373	191	12	(	(	PUNCT
ejpam-3373	191	13	p	p	X
ejpam-3373	191	14	,	,	PUNCT
ejpam-3373	191	15	q	q	ADJ
ejpam-3373	191	16	,	,	PUNCT
ejpam-3373	191	17	g	g	NOUN
ejpam-3373	191	18	)	)	PUNCT
ejpam-3373	191	19	,	,	PUNCT
ejpam-3373	191	20	(	(	PUNCT
ejpam-3373	191	21	2.6	2.6	NUM
ejpam-3373	191	22	)	)	PUNCT
ejpam-3373	191	23	t(p	t(p	PROPN
ejpam-3373	191	24	,	,	PUNCT
ejpam-3373	191	25	q	q	NOUN
ejpam-3373	191	26	,	,	PUNCT
ejpam-3373	191	27	f	f	NOUN
ejpam-3373	191	28	)	)	PUNCT
ejpam-3373	191	29	≤	≤	NOUN
ejpam-3373	191	30	t(p	t(p	PROPN
ejpam-3373	191	31	,	,	PUNCT
ejpam-3373	191	32	q	q	NOUN
ejpam-3373	191	33	,	,	PUNCT
ejpam-3373	191	34	u	u	NOUN
ejpam-3373	191	35	)	)	PUNCT
ejpam-3373	191	36	≤	≤	NOUN
ejpam-3373	191	37	t(p	t(p	PROPN
ejpam-3373	191	38	,	,	PUNCT
ejpam-3373	191	39	q	q	NOUN
ejpam-3373	191	40	,	,	PUNCT
ejpam-3373	191	41	g	g	NOUN
ejpam-3373	191	42	)	)	PUNCT
ejpam-3373	191	43	.	.	PUNCT
ejpam-3373	192	1	(	(	PUNCT
ejpam-3373	192	2	2.7	2.7	NUM
ejpam-3373	192	3	)	)	PUNCT
ejpam-3373	192	4	proof	proof	NOUN
ejpam-3373	192	5	.	.	PUNCT
ejpam-3373	193	1	from	from	ADP
ejpam-3373	193	2	(	(	PUNCT
ejpam-3373	193	3	2.3	2.3	NUM
ejpam-3373	193	4	)	)	PUNCT
ejpam-3373	193	5	with	with	ADP
ejpam-3373	193	6	(	(	PUNCT
ejpam-3373	193	7	1.4	1.4	NUM
ejpam-3373	193	8	)	)	PUNCT
ejpam-3373	193	9	and	and	CCONJ
ejpam-3373	193	10	(	(	PUNCT
ejpam-3373	193	11	1.5	1.5	NUM
ejpam-3373	193	12	)	)	PUNCT
ejpam-3373	193	13	we	we	PRON
ejpam-3373	193	14	have	have	VERB
ejpam-3373	193	15	ρ(p	ρ(p	PROPN
ejpam-3373	193	16	,	,	PUNCT
ejpam-3373	193	17	q	q	X
ejpam-3373	193	18	,	,	PUNCT
ejpam-3373	193	19	f	f	NOUN
ejpam-3373	193	20	)	)	PUNCT
ejpam-3373	193	21	≤	≤	NOUN
ejpam-3373	193	22	ρ(p	ρ(p	PROPN
ejpam-3373	193	23	,	,	PUNCT
ejpam-3373	193	24	q	q	NOUN
ejpam-3373	193	25	,	,	PUNCT
ejpam-3373	193	26	u	u	NOUN
ejpam-3373	193	27	)	)	PUNCT
ejpam-3373	193	28	≤	≤	NOUN
ejpam-3373	193	29	ρ(p	ρ(p	PROPN
ejpam-3373	193	30	,	,	PUNCT
ejpam-3373	193	31	q	q	X
ejpam-3373	193	32	,	,	PUNCT
ejpam-3373	193	33	g	g	NOUN
ejpam-3373	193	34	)	)	PUNCT
ejpam-3373	193	35	.	.	PUNCT
ejpam-3373	194	1	(	(	PUNCT
ejpam-3373	194	2	2.8	2.8	NUM
ejpam-3373	194	3	)	)	PUNCT
ejpam-3373	194	4	since	since	SCONJ
ejpam-3373	194	5	ρ(p	ρ(p	PROPN
ejpam-3373	194	6	,	,	PUNCT
ejpam-3373	194	7	q	q	X
ejpam-3373	194	8	,	,	PUNCT
ejpam-3373	194	9	f	f	X
ejpam-3373	194	10	)	)	PUNCT
ejpam-3373	194	11	=	=	SYM
ejpam-3373	194	12	ρ(p	ρ(p	NOUN
ejpam-3373	194	13	,	,	PUNCT
ejpam-3373	194	14	q	q	X
ejpam-3373	194	15	,	,	PUNCT
ejpam-3373	194	16	g	g	NOUN
ejpam-3373	194	17	)	)	PUNCT
ejpam-3373	194	18	,	,	PUNCT
ejpam-3373	194	19	now	now	ADV
ejpam-3373	194	20	(	(	PUNCT
ejpam-3373	194	21	2.4	2.4	NUM
ejpam-3373	194	22	)	)	PUNCT
ejpam-3373	194	23	easily	easily	ADV
ejpam-3373	194	24	obtain	obtain	VERB
ejpam-3373	194	25	by	by	ADP
ejpam-3373	194	26	using	use	VERB
ejpam-3373	194	27	(	(	PUNCT
ejpam-3373	194	28	2.8	2.8	NUM
ejpam-3373	194	29	)	)	PUNCT
ejpam-3373	194	30	.	.	PUNCT
ejpam-3373	195	1	from	from	ADP
ejpam-3373	195	2	(	(	PUNCT
ejpam-3373	195	3	2.3	2.3	NUM
ejpam-3373	195	4	)	)	PUNCT
ejpam-3373	195	5	we	we	PRON
ejpam-3373	195	6	can	can	AUX
ejpam-3373	195	7	get	get	VERB
ejpam-3373	195	8	(	(	PUNCT
ejpam-3373	195	9	2.5	2.5	NUM
ejpam-3373	195	10	)	)	PUNCT
ejpam-3373	195	11	immediately	immediately	ADV
ejpam-3373	195	12	.	.	PUNCT
ejpam-3373	196	1	we	we	PRON
ejpam-3373	196	2	denote	denote	VERB
ejpam-3373	196	3	the	the	DET
ejpam-3373	196	4	common	common	ADJ
ejpam-3373	196	5	value	value	NOUN
ejpam-3373	196	6	of	of	ADP
ejpam-3373	196	7	(	(	PUNCT
ejpam-3373	196	8	p	p	X
ejpam-3373	196	9	,	,	PUNCT
ejpam-3373	196	10	q)-order	q)-order	NOUN
ejpam-3373	196	11	of	of	ADP
ejpam-3373	196	12	f	f	PROPN
ejpam-3373	196	13	,	,	PUNCT
ejpam-3373	196	14	g	g	PROPN
ejpam-3373	196	15	and	and	CCONJ
ejpam-3373	196	16	u	u	PROPN
ejpam-3373	196	17	and	and	CCONJ
ejpam-3373	196	18	using	use	VERB
ejpam-3373	196	19	(	(	PUNCT
ejpam-3373	196	20	2.3	2.3	NUM
ejpam-3373	196	21	)	)	PUNCT
ejpam-3373	196	22	we	we	PRON
ejpam-3373	196	23	get	get	VERB
ejpam-3373	196	24	log[p−1]m(r	log[p−1]m(r	NOUN
ejpam-3373	196	25	,	,	PUNCT
ejpam-3373	196	26	f	f	X
ejpam-3373	196	27	)	)	PUNCT
ejpam-3373	196	28	(	(	PUNCT
ejpam-3373	196	29	log[q−1	log[q−1	X
ejpam-3373	196	30	]	]	PUNCT
ejpam-3373	196	31	r)ρ	r)ρ	PUNCT
ejpam-3373	196	32	≤	≤	NUM
ejpam-3373	196	33	log[p−1]m(r	log[p−1]m(r	NUM
ejpam-3373	196	34	,	,	PUNCT
ejpam-3373	196	35	u	u	NOUN
ejpam-3373	196	36	)	)	PUNCT
ejpam-3373	196	37	(	(	PUNCT
ejpam-3373	196	38	log[q−1	log[q−1	X
ejpam-3373	196	39	]	]	PUNCT
ejpam-3373	196	40	r)ρ	r)ρ	PUNCT
ejpam-3373	196	41	≤	≤	NUM
ejpam-3373	196	42	log[p−1]m(r	log[p−1]m(r	ADJ
ejpam-3373	196	43	,	,	PUNCT
ejpam-3373	196	44	g	g	NOUN
ejpam-3373	196	45	)	)	PUNCT
ejpam-3373	196	46	(	(	PUNCT
ejpam-3373	196	47	log[q−1	log[q−1	X
ejpam-3373	196	48	]	]	PUNCT
ejpam-3373	196	49	r)ρ	r)ρ	NUM
ejpam-3373	196	50	it	it	PRON
ejpam-3373	196	51	proves	prove	VERB
ejpam-3373	196	52	(	(	PUNCT
ejpam-3373	196	53	2.6	2.6	NUM
ejpam-3373	196	54	)	)	PUNCT
ejpam-3373	196	55	and	and	CCONJ
ejpam-3373	196	56	(	(	PUNCT
ejpam-3373	196	57	2.7	2.7	NUM
ejpam-3373	196	58	)	)	PUNCT
ejpam-3373	196	59	.	.	PUNCT
ejpam-3373	197	1	now	now	ADV
ejpam-3373	197	2	let	let	VERB
ejpam-3373	197	3	us	we	PRON
ejpam-3373	197	4	define	define	VERB
ejpam-3373	197	5	αk	αk	NOUN
ejpam-3373	197	6	=	=	NOUN
ejpam-3373	197	7	maxx∈sn	maxx∈sn	NOUN
ejpam-3373	198	1	|y	|y	NOUN
ejpam-3373	198	2	(	(	PUNCT
ejpam-3373	198	3	k)(x;u)|	k)(x;u)|	NOUN
ejpam-3373	198	4	,	,	PUNCT
ejpam-3373	198	5	βk	βk	ADP
ejpam-3373	198	6	=	=	PUNCT
ejpam-3373	198	7	√	√	INTJ
ejpam-3373	198	8	(	(	PUNCT
ejpam-3373	198	9	2ν)!√	2ν)!√	NUM
ejpam-3373	198	10	2(2ν+1)!(k+2ν)2ν	2(2ν+1)!(k+2ν)2ν	NUM
ejpam-3373	198	11	e	e	X
ejpam-3373	198	12	(	(	PUNCT
ejpam-3373	198	13	k	k	NOUN
ejpam-3373	198	14	)	)	PUNCT
ejpam-3373	198	15	r	r	NOUN
ejpam-3373	198	16	r−k	r−k	NUM
ejpam-3373	198	17	and	and	CCONJ
ejpam-3373	198	18	γk	γk	NOUN
ejpam-3373	198	19	=	=	SYM
ejpam-3373	198	20	4	4	NUM
ejpam-3373	198	21	(	(	PUNCT
ejpam-3373	198	22	2ν)!(k	2ν)!(k	PROPN
ejpam-3373	198	23	+	+	CCONJ
ejpam-3373	198	24	2ν)2νe	2ν)2νe	NUM
ejpam-3373	198	25	(	(	PUNCT
ejpam-3373	198	26	k−1	k−1	PROPN
ejpam-3373	198	27	)	)	PUNCT
ejpam-3373	198	28	r	r	NOUN
ejpam-3373	198	29	r−k	r−k	NOUN
ejpam-3373	198	30	.	.	PUNCT
ejpam-3373	199	1	3	3	X
ejpam-3373	199	2	.	.	X
ejpam-3373	199	3	main	main	ADJ
ejpam-3373	199	4	results	result	NOUN
ejpam-3373	199	5	theorem	theorem	VERB
ejpam-3373	199	6	3.1	3.1	NUM
ejpam-3373	199	7	.	.	PUNCT
ejpam-3373	200	1	let	let	VERB
ejpam-3373	200	2	u	u	PRON
ejpam-3373	200	3	be	be	AUX
ejpam-3373	200	4	an	an	DET
ejpam-3373	200	5	entire	entire	ADJ
ejpam-3373	200	6	harmonic	harmonic	ADJ
ejpam-3373	200	7	function	function	NOUN
ejpam-3373	200	8	in	in	ADP
ejpam-3373	200	9	rn	rn	PROPN
ejpam-3373	200	10	,	,	PUNCT
ejpam-3373	200	11	n	n	PRON
ejpam-3373	200	12	≥	≥	NOUN
ejpam-3373	200	13	3	3	NUM
ejpam-3373	200	14	with	with	ADP
ejpam-3373	200	15	(	(	PUNCT
ejpam-3373	200	16	p	p	NOUN
ejpam-3373	200	17	,	,	PUNCT
ejpam-3373	200	18	q)-order	q)-order	ADJ
ejpam-3373	200	19	ρ(p	ρ(p	NUM
ejpam-3373	200	20	,	,	PUNCT
ejpam-3373	200	21	q	q	NOUN
ejpam-3373	200	22	,	,	PUNCT
ejpam-3373	200	23	u	u	NOUN
ejpam-3373	200	24	)	)	PUNCT
ejpam-3373	200	25	and	and	CCONJ
ejpam-3373	200	26	(	(	PUNCT
ejpam-3373	200	27	p	p	X
ejpam-3373	200	28	,	,	PUNCT
ejpam-3373	200	29	q)-type	q)-type	PUNCT
ejpam-3373	200	30	t	t	NOUN
ejpam-3373	200	31	(	(	PUNCT
ejpam-3373	200	32	p	p	X
ejpam-3373	200	33	,	,	PUNCT
ejpam-3373	200	34	q	q	NOUN
ejpam-3373	200	35	,	,	PUNCT
ejpam-3373	200	36	u	u	NOUN
ejpam-3373	200	37	)	)	PUNCT
ejpam-3373	200	38	.	.	PUNCT
ejpam-3373	201	1	if	if	SCONJ
ejpam-3373	201	2	(	(	PUNCT
ejpam-3373	201	3	e	e	X
ejpam-3373	201	4	(	(	PUNCT
ejpam-3373	201	5	k	k	NOUN
ejpam-3373	201	6	)	)	PUNCT
ejpam-3373	201	7	r	r	NOUN
ejpam-3373	201	8	(	(	PUNCT
ejpam-3373	201	9	u	u	NOUN
ejpam-3373	201	10	)	)	PUNCT
ejpam-3373	201	11	e	e	NOUN
ejpam-3373	201	12	(	(	PUNCT
ejpam-3373	201	13	k−1	k−1	PROPN
ejpam-3373	201	14	)	)	PUNCT
ejpam-3373	201	15	r	r	NOUN
ejpam-3373	201	16	(	(	PUNCT
ejpam-3373	201	17	u	u	NOUN
ejpam-3373	201	18	)	)	PUNCT
ejpam-3373	201	19	)	)	PUNCT
ejpam-3373	201	20	is	be	AUX
ejpam-3373	201	21	a	a	DET
ejpam-3373	201	22	nondecreasing	nondecrease	VERB
ejpam-3373	201	23	function	function	NOUN
ejpam-3373	201	24	of	of	ADP
ejpam-3373	201	25	k	k	PROPN
ejpam-3373	201	26	for	for	ADP
ejpam-3373	201	27	k	k	PROPN
ejpam-3373	201	28	>	>	X
ejpam-3373	201	29	k0	k0	PROPN
ejpam-3373	201	30	,	,	PUNCT
ejpam-3373	201	31	then	then	ADV
ejpam-3373	201	32	ρ(p	ρ(p	NUM
ejpam-3373	201	33	,	,	PUNCT
ejpam-3373	201	34	q	q	NOUN
ejpam-3373	201	35	,	,	PUNCT
ejpam-3373	201	36	u	u	NOUN
ejpam-3373	201	37	)	)	PUNCT
ejpam-3373	201	38	=	=	SYM
ejpam-3373	201	39	p	p	X
ejpam-3373	201	40	(	(	PUNCT
ejpam-3373	201	41	l(p	l(p	PROPN
ejpam-3373	201	42	,	,	PUNCT
ejpam-3373	201	43	q	q	NOUN
ejpam-3373	201	44	,	,	PUNCT
ejpam-3373	201	45	u	u	NOUN
ejpam-3373	201	46	)	)	PUNCT
ejpam-3373	201	47	)	)	PUNCT
ejpam-3373	202	1	where	where	SCONJ
ejpam-3373	202	2	l(p	l(p	NOUN
ejpam-3373	202	3	,	,	PUNCT
ejpam-3373	202	4	q	q	NOUN
ejpam-3373	202	5	,	,	PUNCT
ejpam-3373	202	6	u	u	NOUN
ejpam-3373	202	7	)	)	PUNCT
ejpam-3373	202	8	=	=	SYM
ejpam-3373	203	1	lim	lim	PROPN
ejpam-3373	203	2	sup	sup	PROPN
ejpam-3373	203	3	k→∞	k→∞	X
ejpam-3373	203	4	log[p−1	log[p−1	X
ejpam-3373	203	5	]	]	X
ejpam-3373	204	1	k	k	PROPN
ejpam-3373	204	2	log[q](e	log[q](e	PROPN
ejpam-3373	204	3	(	(	PUNCT
ejpam-3373	204	4	k	k	NOUN
ejpam-3373	204	5	)	)	PUNCT
ejpam-3373	204	6	r	r	NOUN
ejpam-3373	204	7	(	(	PUNCT
ejpam-3373	204	8	u)r−k)−	u)r−k)−	PROPN
ejpam-3373	204	9	1	1	NUM
ejpam-3373	204	10	k	k	X
ejpam-3373	204	11	(	(	PUNCT
ejpam-3373	204	12	3.1	3.1	NUM
ejpam-3373	204	13	)	)	PUNCT
ejpam-3373	204	14	and	and	CCONJ
ejpam-3373	204	15	t	t	PROPN
ejpam-3373	204	16	(	(	PUNCT
ejpam-3373	204	17	p	p	X
ejpam-3373	204	18	,	,	PUNCT
ejpam-3373	204	19	q	q	ADJ
ejpam-3373	204	20	,	,	PUNCT
ejpam-3373	204	21	u	u	NOUN
ejpam-3373	204	22	)	)	PUNCT
ejpam-3373	204	23	=	=	SYM
ejpam-3373	204	24	mv∗(p	mv∗(p	PROPN
ejpam-3373	204	25	,	,	PUNCT
ejpam-3373	204	26	q	q	NOUN
ejpam-3373	204	27	,	,	PUNCT
ejpam-3373	204	28	u	u	NOUN
ejpam-3373	204	29	)	)	PUNCT
ejpam-3373	205	1	where	where	SCONJ
ejpam-3373	205	2	v∗(p	v∗(p	PROPN
ejpam-3373	205	3	,	,	PUNCT
ejpam-3373	205	4	q	q	NOUN
ejpam-3373	205	5	,	,	PUNCT
ejpam-3373	205	6	u	u	NOUN
ejpam-3373	205	7	)	)	PUNCT
ejpam-3373	205	8	=	=	SYM
ejpam-3373	205	9	lim	lim	PROPN
ejpam-3373	205	10	sup	sup	PROPN
ejpam-3373	205	11	k→∞	k→∞	ADV
ejpam-3373	205	12	log[p−2	log[p−2	NOUN
ejpam-3373	205	13	]	]	X
ejpam-3373	206	1	k	k	X
ejpam-3373	206	2	(	(	PUNCT
ejpam-3373	206	3	log[q−1](e	log[q−1](e	VERB
ejpam-3373	206	4	(	(	PUNCT
ejpam-3373	206	5	k	k	NOUN
ejpam-3373	206	6	)	)	PUNCT
ejpam-3373	206	7	r	r	NOUN
ejpam-3373	206	8	(	(	PUNCT
ejpam-3373	206	9	u)r−k)−	u)r−k)−	NOUN
ejpam-3373	206	10	1	1	NUM
ejpam-3373	206	11	k	k	NOUN
ejpam-3373	206	12	)	)	PUNCT
ejpam-3373	206	13	ρ−a	ρ−a	PROPN
ejpam-3373	206	14	,	,	PUNCT
ejpam-3373	206	15	ρ(p	ρ(p	PROPN
ejpam-3373	206	16	,	,	PUNCT
ejpam-3373	206	17	q	q	NOUN
ejpam-3373	206	18	,	,	PUNCT
ejpam-3373	206	19	u	u	NOUN
ejpam-3373	206	20	)	)	PUNCT
ejpam-3373	206	21	≡	≡	PROPN
ejpam-3373	206	22	ρ	ρ	PROPN
ejpam-3373	206	23	.	.	PUNCT
ejpam-3373	206	24	(	(	PUNCT
ejpam-3373	206	25	3.2	3.2	NUM
ejpam-3373	206	26	)	)	PUNCT
ejpam-3373	206	27	d.	d.	PROPN
ejpam-3373	206	28	kumar	kumar	PROPN
ejpam-3373	206	29	,	,	PUNCT
ejpam-3373	206	30	r.	r.	PROPN
ejpam-3373	206	31	ali	ali	PROPN
ejpam-3373	206	32	/	/	SYM
ejpam-3373	206	33	eur	eur	PROPN
ejpam-3373	206	34	.	.	PUNCT
ejpam-3373	207	1	j.	j.	PROPN
ejpam-3373	207	2	pure	pure	PROPN
ejpam-3373	207	3	appl	appl	PROPN
ejpam-3373	207	4	.	.	PROPN
ejpam-3373	207	5	math	math	PROPN
ejpam-3373	207	6	,	,	PUNCT
ejpam-3373	207	7	12	12	NUM
ejpam-3373	207	8	(	(	PUNCT
ejpam-3373	207	9	2	2	NUM
ejpam-3373	207	10	)	)	PUNCT
ejpam-3373	207	11	(	(	PUNCT
ejpam-3373	207	12	2019	2019	NUM
ejpam-3373	207	13	)	)	PUNCT
ejpam-3373	207	14	,	,	PUNCT
ejpam-3373	207	15	486	486	NUM
ejpam-3373	207	16	-	-	SYM
ejpam-3373	207	17	498	498	NUM
ejpam-3373	207	18	494	494	NUM
ejpam-3373	207	19	proof	proof	NOUN
ejpam-3373	207	20	.	.	PUNCT
ejpam-3373	208	1	corresponding	correspond	VERB
ejpam-3373	208	2	to	to	ADP
ejpam-3373	208	3	an	an	DET
ejpam-3373	208	4	entire	entire	ADJ
ejpam-3373	208	5	harmonic	harmonic	ADJ
ejpam-3373	208	6	function	function	NOUN
ejpam-3373	208	7	u(rx	u(rx	NOUN
ejpam-3373	208	8	)	)	PUNCT
ejpam-3373	208	9	=	=	SYM
ejpam-3373	208	10	∑∞	∑∞	NOUN
ejpam-3373	208	11	k=0	k=0	PROPN
ejpam-3373	208	12	y	y	PROPN
ejpam-3373	208	13	(	(	PUNCT
ejpam-3373	208	14	k)(x;u)rk	k)(x;u)rk	PROPN
ejpam-3373	208	15	we	we	PRON
ejpam-3373	208	16	define	define	VERB
ejpam-3373	208	17	the	the	DET
ejpam-3373	208	18	entire	entire	ADJ
ejpam-3373	208	19	function	function	NOUN
ejpam-3373	208	20	u(ζx	u(ζx	NOUN
ejpam-3373	208	21	)	)	PUNCT
ejpam-3373	208	22	=	=	SYM
ejpam-3373	208	23	∑∞	∑∞	NOUN
ejpam-3373	208	24	k=0	k=0	PROPN
ejpam-3373	208	25	max	max	PROPN
ejpam-3373	208	26	|y	|y	NOUN
ejpam-3373	208	27	(	(	PUNCT
ejpam-3373	208	28	k)(x;u)|ζk	k)(x;u)|ζk	PROPN
ejpam-3373	208	29	,	,	PUNCT
ejpam-3373	208	30	|x|	|x|	PROPN
ejpam-3373	208	31	=	=	SYM
ejpam-3373	208	32	1	1	NUM
ejpam-3373	208	33	[	[	X
ejpam-3373	208	34	2	2	NUM
ejpam-3373	208	35	]	]	PUNCT
ejpam-3373	208	36	,	,	PUNCT
ejpam-3373	208	37	now	now	ADV
ejpam-3373	208	38	applying	apply	VERB
ejpam-3373	208	39	theorem	theorem	NOUN
ejpam-3373	208	40	a	a	PRON
ejpam-3373	208	41	,	,	PUNCT
ejpam-3373	208	42	we	we	PRON
ejpam-3373	208	43	have	have	VERB
ejpam-3373	208	44	ρ(p	ρ(p	PROPN
ejpam-3373	208	45	,	,	PUNCT
ejpam-3373	208	46	q	q	NOUN
ejpam-3373	208	47	,	,	PUNCT
ejpam-3373	208	48	u	u	NOUN
ejpam-3373	208	49	)	)	PUNCT
ejpam-3373	208	50	=	=	SYM
ejpam-3373	209	1	p	p	X
ejpam-3373	209	2	(	(	PUNCT
ejpam-3373	209	3	l(p	l(p	PROPN
ejpam-3373	209	4	,	,	PUNCT
ejpam-3373	209	5	q	q	NOUN
ejpam-3373	209	6	,	,	PUNCT
ejpam-3373	209	7	u	u	NOUN
ejpam-3373	209	8	)	)	PUNCT
ejpam-3373	209	9	)	)	PUNCT
ejpam-3373	210	1	where	where	SCONJ
ejpam-3373	210	2	l(p	l(p	NOUN
ejpam-3373	210	3	,	,	PUNCT
ejpam-3373	210	4	q	q	NOUN
ejpam-3373	210	5	,	,	PUNCT
ejpam-3373	210	6	u	u	NOUN
ejpam-3373	210	7	)	)	PUNCT
ejpam-3373	210	8	=	=	SYM
ejpam-3373	210	9	lim	lim	PROPN
ejpam-3373	210	10	sup	sup	PROPN
ejpam-3373	210	11	k→∞	k→∞	X
ejpam-3373	210	12	log[p−1	log[p−1	X
ejpam-3373	210	13	]	]	X
ejpam-3373	210	14	k	k	PROPN
ejpam-3373	210	15	log[q](αk	log[q](αk	PROPN
ejpam-3373	210	16	)	)	PUNCT
ejpam-3373	210	17	−	−	PROPN
ejpam-3373	211	1	1	1	NUM
ejpam-3373	211	2	k	k	NOUN
ejpam-3373	211	3	.	.	PUNCT
ejpam-3373	212	1	we	we	PRON
ejpam-3373	212	2	know	know	VERB
ejpam-3373	212	3	that	that	PRON
ejpam-3373	212	4	(	(	PUNCT
ejpam-3373	212	5	αk	αk	ADP
ejpam-3373	212	6	αk+1	αk+1	NUM
ejpam-3373	212	7	)	)	PUNCT
ejpam-3373	212	8	is	be	AUX
ejpam-3373	212	9	a	a	DET
ejpam-3373	212	10	nondecreasing	nondecrease	VERB
ejpam-3373	212	11	function	function	NOUN
ejpam-3373	212	12	of	of	ADP
ejpam-3373	212	13	k	k	PROPN
ejpam-3373	212	14	,	,	PUNCT
ejpam-3373	212	15	k	k	PROPN
ejpam-3373	212	16	>	>	X
ejpam-3373	212	17	k0	k0	PROPN
ejpam-3373	212	18	if	if	SCONJ
ejpam-3373	212	19	(	(	PUNCT
ejpam-3373	212	20	e	e	X
ejpam-3373	212	21	(	(	PUNCT
ejpam-3373	212	22	k	k	NOUN
ejpam-3373	212	23	)	)	PUNCT
ejpam-3373	212	24	r	r	NOUN
ejpam-3373	212	25	(	(	PUNCT
ejpam-3373	212	26	u	u	NOUN
ejpam-3373	212	27	)	)	PUNCT
ejpam-3373	212	28	e	e	NOUN
ejpam-3373	212	29	(	(	PUNCT
ejpam-3373	212	30	k−1	k−1	PROPN
ejpam-3373	212	31	)	)	PUNCT
ejpam-3373	212	32	r	r	NOUN
ejpam-3373	212	33	(	(	PUNCT
ejpam-3373	212	34	u	u	NOUN
ejpam-3373	212	35	)	)	PUNCT
ejpam-3373	212	36	)	)	PUNCT
ejpam-3373	212	37	is	be	AUX
ejpam-3373	212	38	a	a	DET
ejpam-3373	212	39	nondecreasing	nondecrease	VERB
ejpam-3373	212	40	function	function	NOUN
ejpam-3373	212	41	of	of	ADP
ejpam-3373	212	42	k	k	PROPN
ejpam-3373	212	43	for	for	ADP
ejpam-3373	212	44	k	k	PROPN
ejpam-3373	212	45	>	>	X
ejpam-3373	212	46	k0	k0	PROPN
ejpam-3373	212	47	.	.	PUNCT
ejpam-3373	213	1	this	this	PRON
ejpam-3373	213	2	implies	imply	VERB
ejpam-3373	213	3	that	that	SCONJ
ejpam-3373	213	4	(	(	PUNCT
ejpam-3373	213	5	βk	βk	NOUN
ejpam-3373	213	6	βk+1	βk+1	NUM
ejpam-3373	213	7	)	)	PUNCT
ejpam-3373	213	8	and	and	CCONJ
ejpam-3373	213	9	(	(	PUNCT
ejpam-3373	213	10	γk	γk	PROPN
ejpam-3373	213	11	γk+1	γk+1	PROPN
ejpam-3373	213	12	)	)	PUNCT
ejpam-3373	213	13	are	be	AUX
ejpam-3373	213	14	also	also	ADV
ejpam-3373	213	15	nondecreasing	nondecrease	VERB
ejpam-3373	213	16	function	function	NOUN
ejpam-3373	213	17	of	of	ADP
ejpam-3373	213	18	k	k	PROPN
ejpam-3373	213	19	,	,	PUNCT
ejpam-3373	213	20	k	k	PROPN
ejpam-3373	213	21	>	>	X
ejpam-3373	213	22	k0	k0	PROPN
ejpam-3373	213	23	.	.	PUNCT
ejpam-3373	214	1	using	use	VERB
ejpam-3373	214	2	[	[	X
ejpam-3373	214	3	17	17	NUM
ejpam-3373	214	4	,	,	PUNCT
ejpam-3373	214	5	lemma	lemma	PROPN
ejpam-3373	214	6	1	1	NUM
ejpam-3373	214	7	]	]	PUNCT
ejpam-3373	214	8	we	we	PRON
ejpam-3373	214	9	obtain	obtain	VERB
ejpam-3373	214	10	αk	αk	NOUN
ejpam-3373	214	11	αk+1	αk+1	NUM
ejpam-3373	214	12	≤	≤	NOUN
ejpam-3373	214	13	(	(	PUNCT
ejpam-3373	214	14	k	k	PROPN
ejpam-3373	215	1	+	+	PROPN
ejpam-3373	215	2	2ν)2νe	2ν)2νe	NUM
ejpam-3373	215	3	(	(	PUNCT
ejpam-3373	215	4	k−1	k−1	PROPN
ejpam-3373	215	5	)	)	PUNCT
ejpam-3373	215	6	r	r	NOUN
ejpam-3373	215	7	(	(	PUNCT
ejpam-3373	215	8	u)r	u)r	X
ejpam-3373	215	9	(	(	PUNCT
ejpam-3373	215	10	k	k	X
ejpam-3373	215	11	+	+	PROPN
ejpam-3373	215	12	1	1	NUM
ejpam-3373	215	13	+	+	NUM
ejpam-3373	215	14	2ν)2νe	2ν)2νe	NUM
ejpam-3373	215	15	(	(	PUNCT
ejpam-3373	215	16	k	k	NOUN
ejpam-3373	215	17	)	)	PUNCT
ejpam-3373	215	18	r	r	NOUN
ejpam-3373	215	19	(	(	PUNCT
ejpam-3373	215	20	u	u	NOUN
ejpam-3373	215	21	)	)	PUNCT
ejpam-3373	215	22	.	.	PUNCT
ejpam-3373	216	1	let	let	VERB
ejpam-3373	216	2	p(x	p(x	VERB
ejpam-3373	216	3	)	)	PUNCT
ejpam-3373	216	4	=	=	PUNCT
ejpam-3373	217	1	(	(	PUNCT
ejpam-3373	217	2	x+2ν	x+2ν	PROPN
ejpam-3373	217	3	x+2ν+1)2ν	x+2ν+1)2ν	PROPN
ejpam-3373	217	4	,	,	PUNCT
ejpam-3373	217	5	log	log	PROPN
ejpam-3373	217	6	p(x	p(x	PROPN
ejpam-3373	217	7	)	)	PUNCT
ejpam-3373	217	8	=	=	SYM
ejpam-3373	217	9	2ν	2ν	NOUN
ejpam-3373	217	10	log(x+	log(x+	NUM
ejpam-3373	217	11	2ν)−	2ν)−	NUM
ejpam-3373	217	12	2ν	2ν	NOUN
ejpam-3373	217	13	log(x+	log(x+	ADV
ejpam-3373	217	14	1	1	NUM
ejpam-3373	217	15	+	+	NUM
ejpam-3373	217	16	2ν	2ν	NUM
ejpam-3373	217	17	)	)	PUNCT
ejpam-3373	217	18	,	,	PUNCT
ejpam-3373	217	19	p′(x	p′(x	NOUN
ejpam-3373	217	20	)	)	PUNCT
ejpam-3373	217	21	p(x	p(x	PROPN
ejpam-3373	217	22	)	)	PUNCT
ejpam-3373	217	23	=	=	SYM
ejpam-3373	217	24	2ν	2ν	NUM
ejpam-3373	217	25	x+	x+	NUM
ejpam-3373	217	26	2ν	2ν	NOUN
ejpam-3373	217	27	−	−	PROPN
ejpam-3373	217	28	2ν	2ν	NOUN
ejpam-3373	217	29	x+	x+	NUM
ejpam-3373	217	30	2ν	2ν	NOUN
ejpam-3373	217	31	+	+	SYM
ejpam-3373	217	32	1	1	NUM
ejpam-3373	217	33	,	,	PUNCT
ejpam-3373	217	34	taking	take	VERB
ejpam-3373	217	35	w(x	w(x	NOUN
ejpam-3373	217	36	)	)	PUNCT
ejpam-3373	217	37	=	=	SYM
ejpam-3373	218	1	2ν	2ν	NOUN
ejpam-3373	218	2	x+2ν	x+2ν	PROPN
ejpam-3373	218	3	,	,	PUNCT
ejpam-3373	218	4	w(x	w(x	PROPN
ejpam-3373	218	5	)	)	PUNCT
ejpam-3373	219	1	−	−	PROPN
ejpam-3373	219	2	w(x	w(x	NOUN
ejpam-3373	220	1	+	+	CCONJ
ejpam-3373	220	2	1	1	X
ejpam-3373	220	3	)	)	PUNCT
ejpam-3373	220	4	>	>	X
ejpam-3373	220	5	0	0	PUNCT
ejpam-3373	221	1	for	for	ADP
ejpam-3373	221	2	any	any	PRON
ejpam-3373	221	3	x	x	SYM
ejpam-3373	221	4	>	>	X
ejpam-3373	221	5	0	0	NUM
ejpam-3373	221	6	.	.	PUNCT
ejpam-3373	222	1	hence	hence	ADV
ejpam-3373	222	2	w(x	w(x	NOUN
ejpam-3373	222	3	)	)	PUNCT
ejpam-3373	222	4	is	be	AUX
ejpam-3373	222	5	a	a	DET
ejpam-3373	222	6	decreasing	decrease	VERB
ejpam-3373	222	7	function	function	NOUN
ejpam-3373	222	8	and	and	CCONJ
ejpam-3373	222	9	subsequently	subsequently	ADV
ejpam-3373	222	10	p′(x	p′(x	ADP
ejpam-3373	222	11	)	)	PUNCT
ejpam-3373	222	12	>	>	X
ejpam-3373	222	13	0	0	PUNCT
ejpam-3373	223	1	for	for	ADP
ejpam-3373	223	2	x	x	PUNCT
ejpam-3373	223	3	>	>	X
ejpam-3373	223	4	0	0	NUM
ejpam-3373	223	5	.	.	PUNCT
ejpam-3373	224	1	hence	hence	ADV
ejpam-3373	224	2	(	(	PUNCT
ejpam-3373	224	3	αk	αk	ADP
ejpam-3373	224	4	αk+1	αk+1	NUM
ejpam-3373	224	5	)	)	PUNCT
ejpam-3373	224	6	is	be	AUX
ejpam-3373	224	7	nondecreasing	nondecrease	VERB
ejpam-3373	224	8	if	if	SCONJ
ejpam-3373	224	9	(	(	PUNCT
ejpam-3373	224	10	e	e	X
ejpam-3373	224	11	(	(	PUNCT
ejpam-3373	224	12	k	k	NOUN
ejpam-3373	224	13	)	)	PUNCT
ejpam-3373	224	14	r	r	NOUN
ejpam-3373	224	15	(	(	PUNCT
ejpam-3373	224	16	u	u	NOUN
ejpam-3373	224	17	)	)	PUNCT
ejpam-3373	224	18	e	e	NOUN
ejpam-3373	224	19	(	(	PUNCT
ejpam-3373	224	20	k−1	k−1	PROPN
ejpam-3373	224	21	)	)	PUNCT
ejpam-3373	224	22	r	r	NOUN
ejpam-3373	224	23	(	(	PUNCT
ejpam-3373	224	24	u	u	NOUN
ejpam-3373	224	25	)	)	PUNCT
ejpam-3373	224	26	)	)	PUNCT
ejpam-3373	224	27	is	be	AUX
ejpam-3373	224	28	nondecreasing	nondecrease	VERB
ejpam-3373	224	29	function	function	NOUN
ejpam-3373	224	30	of	of	ADP
ejpam-3373	224	31	k	k	PROPN
ejpam-3373	224	32	for	for	ADP
ejpam-3373	224	33	k	k	PROPN
ejpam-3373	224	34	>	>	X
ejpam-3373	224	35	k0	k0	PROPN
ejpam-3373	224	36	.	.	PUNCT
ejpam-3373	225	1	the	the	DET
ejpam-3373	225	2	result	result	NOUN
ejpam-3373	225	3	(	(	PUNCT
ejpam-3373	225	4	3.1	3.1	NUM
ejpam-3373	225	5	)	)	PUNCT
ejpam-3373	225	6	is	be	AUX
ejpam-3373	225	7	obtain	obtain	VERB
ejpam-3373	225	8	by	by	ADP
ejpam-3373	225	9	using	use	VERB
ejpam-3373	225	10	the	the	DET
ejpam-3373	225	11	relation	relation	NOUN
ejpam-3373	225	12	(	(	PUNCT
ejpam-3373	225	13	2.4	2.4	NUM
ejpam-3373	225	14	)	)	PUNCT
ejpam-3373	225	15	and	and	CCONJ
ejpam-3373	225	16	the	the	DET
ejpam-3373	225	17	result	result	NOUN
ejpam-3373	225	18	(	(	PUNCT
ejpam-3373	225	19	3.2	3.2	NUM
ejpam-3373	225	20	)	)	PUNCT
ejpam-3373	225	21	is	be	AUX
ejpam-3373	225	22	found	find	VERB
ejpam-3373	225	23	from	from	ADP
ejpam-3373	225	24	(	(	PUNCT
ejpam-3373	225	25	2.6	2.6	NUM
ejpam-3373	225	26	)	)	PUNCT
ejpam-3373	225	27	.	.	PUNCT
ejpam-3373	226	1	theorem	theorem	ADJ
ejpam-3373	226	2	3.2	3.2	NUM
ejpam-3373	226	3	.	.	PUNCT
ejpam-3373	227	1	let	let	VERB
ejpam-3373	227	2	u	u	PRON
ejpam-3373	227	3	be	be	AUX
ejpam-3373	227	4	an	an	DET
ejpam-3373	227	5	entire	entire	ADJ
ejpam-3373	227	6	harmonic	harmonic	ADJ
ejpam-3373	227	7	function	function	NOUN
ejpam-3373	227	8	in	in	ADP
ejpam-3373	227	9	rn	rn	PROPN
ejpam-3373	227	10	,	,	PUNCT
ejpam-3373	227	11	n	n	PRON
ejpam-3373	227	12	≥	≥	NOUN
ejpam-3373	227	13	3	3	NUM
ejpam-3373	227	14	with	with	ADP
ejpam-3373	227	15	(	(	PUNCT
ejpam-3373	227	16	p	p	NOUN
ejpam-3373	227	17	,	,	PUNCT
ejpam-3373	227	18	q)-order	q)-order	ADJ
ejpam-3373	227	19	ρ(p	ρ(p	NUM
ejpam-3373	227	20	,	,	PUNCT
ejpam-3373	227	21	q	q	NOUN
ejpam-3373	227	22	,	,	PUNCT
ejpam-3373	227	23	u	u	NOUN
ejpam-3373	227	24	)	)	PUNCT
ejpam-3373	227	25	and	and	CCONJ
ejpam-3373	227	26	(	(	PUNCT
ejpam-3373	227	27	e	e	X
ejpam-3373	227	28	(	(	PUNCT
ejpam-3373	227	29	k	k	NOUN
ejpam-3373	227	30	)	)	PUNCT
ejpam-3373	227	31	r	r	NOUN
ejpam-3373	227	32	(	(	PUNCT
ejpam-3373	227	33	u	u	NOUN
ejpam-3373	227	34	)	)	PUNCT
ejpam-3373	227	35	e	e	NOUN
ejpam-3373	227	36	(	(	PUNCT
ejpam-3373	227	37	k−1	k−1	PROPN
ejpam-3373	227	38	)	)	PUNCT
ejpam-3373	227	39	r	r	NOUN
ejpam-3373	227	40	(	(	PUNCT
ejpam-3373	227	41	u	u	NOUN
ejpam-3373	227	42	)	)	PUNCT
ejpam-3373	227	43	)	)	PUNCT
ejpam-3373	227	44	is	be	AUX
ejpam-3373	227	45	a	a	DET
ejpam-3373	227	46	nondecreasing	nondecrease	VERB
ejpam-3373	227	47	function	function	NOUN
ejpam-3373	227	48	of	of	ADP
ejpam-3373	227	49	k	k	PROPN
ejpam-3373	227	50	for	for	ADP
ejpam-3373	227	51	k	k	PROPN
ejpam-3373	227	52	>	>	X
ejpam-3373	227	53	k0	k0	PROPN
ejpam-3373	227	54	,	,	PUNCT
ejpam-3373	227	55	then	then	ADV
ejpam-3373	227	56	ρ(p	ρ(p	NUM
ejpam-3373	227	57	,	,	PUNCT
ejpam-3373	227	58	q	q	NOUN
ejpam-3373	227	59	,	,	PUNCT
ejpam-3373	227	60	u	u	NOUN
ejpam-3373	227	61	)	)	PUNCT
ejpam-3373	228	1	=	=	SYM
ejpam-3373	228	2	p	p	X
ejpam-3373	228	3	(	(	PUNCT
ejpam-3373	228	4	l(p	l(p	PROPN
ejpam-3373	228	5	,	,	PUNCT
ejpam-3373	228	6	q	q	NOUN
ejpam-3373	228	7	,	,	PUNCT
ejpam-3373	228	8	u	u	NOUN
ejpam-3373	228	9	)	)	PUNCT
ejpam-3373	228	10	)	)	PUNCT
ejpam-3373	228	11	(	(	PUNCT
ejpam-3373	228	12	3.3	3.3	NUM
ejpam-3373	228	13	)	)	PUNCT
ejpam-3373	229	1	where	where	SCONJ
ejpam-3373	229	2	l(p	l(p	NOUN
ejpam-3373	229	3	,	,	PUNCT
ejpam-3373	229	4	q	q	NOUN
ejpam-3373	229	5	,	,	PUNCT
ejpam-3373	229	6	u	u	NOUN
ejpam-3373	229	7	)	)	PUNCT
ejpam-3373	229	8	=	=	SYM
ejpam-3373	229	9	lim	lim	PROPN
ejpam-3373	229	10	sup	sup	PROPN
ejpam-3373	229	11	k→∞	k→∞	X
ejpam-3373	229	12	log[p−1	log[p−1	X
ejpam-3373	229	13	]	]	X
ejpam-3373	230	1	k	k	X
ejpam-3373	230	2	log[q	log[q	PROPN
ejpam-3373	230	3	]	]	X
ejpam-3373	230	4	(	(	PUNCT
ejpam-3373	230	5	e	e	X
ejpam-3373	230	6	(	(	PUNCT
ejpam-3373	230	7	k−1	k−1	PROPN
ejpam-3373	230	8	)	)	PUNCT
ejpam-3373	230	9	r	r	NOUN
ejpam-3373	230	10	(	(	PUNCT
ejpam-3373	230	11	u)r	u)r	X
ejpam-3373	230	12	e	e	X
ejpam-3373	230	13	(	(	PUNCT
ejpam-3373	230	14	k	k	NOUN
ejpam-3373	230	15	)	)	PUNCT
ejpam-3373	230	16	r	r	NOUN
ejpam-3373	230	17	(	(	PUNCT
ejpam-3373	230	18	u	u	NOUN
ejpam-3373	230	19	)	)	PUNCT
ejpam-3373	230	20	)	)	PUNCT
ejpam-3373	230	21	proof	proof	NOUN
ejpam-3373	230	22	.	.	PUNCT
ejpam-3373	231	1	for	for	ADP
ejpam-3373	231	2	an	an	DET
ejpam-3373	231	3	entire	entire	ADJ
ejpam-3373	231	4	function	function	NOUN
ejpam-3373	231	5	u(zx	u(zx	NUM
ejpam-3373	231	6	)	)	PUNCT
ejpam-3373	231	7	=	=	NOUN
ejpam-3373	231	8	∑∞	∑∞	NOUN
ejpam-3373	231	9	k=0	k=0	PROPN
ejpam-3373	231	10	max	max	PROPN
ejpam-3373	231	11	|y	|y	NOUN
ejpam-3373	231	12	(	(	PUNCT
ejpam-3373	231	13	k)(x;u)|zk	k)(x;u)|zk	X
ejpam-3373	231	14	,	,	PUNCT
ejpam-3373	231	15	using	use	VERB
ejpam-3373	231	16	theorem	theorem	PROPN
ejpam-3373	231	17	b	b	X
ejpam-3373	231	18	we	we	PRON
ejpam-3373	231	19	have	have	AUX
ejpam-3373	231	20	ρ(p	ρ(p	PROPN
ejpam-3373	231	21	,	,	PUNCT
ejpam-3373	231	22	q	q	NOUN
ejpam-3373	231	23	,	,	PUNCT
ejpam-3373	231	24	u	u	NOUN
ejpam-3373	231	25	)	)	PUNCT
ejpam-3373	231	26	=	=	SYM
ejpam-3373	231	27	p	p	X
ejpam-3373	231	28	(	(	PUNCT
ejpam-3373	231	29	l(p	l(p	PROPN
ejpam-3373	231	30	,	,	PUNCT
ejpam-3373	231	31	q	q	NOUN
ejpam-3373	231	32	,	,	PUNCT
ejpam-3373	231	33	u	u	NOUN
ejpam-3373	231	34	)	)	PUNCT
ejpam-3373	231	35	)	)	PUNCT
ejpam-3373	231	36	d.	d.	PROPN
ejpam-3373	231	37	kumar	kumar	PROPN
ejpam-3373	231	38	,	,	PUNCT
ejpam-3373	231	39	r.	r.	PROPN
ejpam-3373	231	40	ali	ali	PROPN
ejpam-3373	231	41	/	/	SYM
ejpam-3373	231	42	eur	eur	PROPN
ejpam-3373	231	43	.	.	PUNCT
ejpam-3373	232	1	j.	j.	PROPN
ejpam-3373	232	2	pure	pure	PROPN
ejpam-3373	232	3	appl	appl	PROPN
ejpam-3373	232	4	.	.	PROPN
ejpam-3373	232	5	math	math	PROPN
ejpam-3373	232	6	,	,	PUNCT
ejpam-3373	232	7	12	12	NUM
ejpam-3373	232	8	(	(	PUNCT
ejpam-3373	232	9	2	2	NUM
ejpam-3373	232	10	)	)	PUNCT
ejpam-3373	232	11	(	(	PUNCT
ejpam-3373	232	12	2019	2019	NUM
ejpam-3373	232	13	)	)	PUNCT
ejpam-3373	232	14	,	,	PUNCT
ejpam-3373	232	15	486	486	NUM
ejpam-3373	232	16	-	-	SYM
ejpam-3373	232	17	498	498	NUM
ejpam-3373	232	18	495	495	NUM
ejpam-3373	232	19	where	where	SCONJ
ejpam-3373	232	20	l(p	l(p	NOUN
ejpam-3373	232	21	,	,	PUNCT
ejpam-3373	232	22	q	q	NOUN
ejpam-3373	232	23	,	,	PUNCT
ejpam-3373	232	24	u	u	NOUN
ejpam-3373	232	25	)	)	PUNCT
ejpam-3373	233	1	=	=	SYM
ejpam-3373	233	2	lim	lim	PROPN
ejpam-3373	233	3	sup	sup	PROPN
ejpam-3373	233	4	k→∞	k→∞	X
ejpam-3373	233	5	log[p−1	log[p−1	X
ejpam-3373	233	6	]	]	X
ejpam-3373	234	1	k	k	X
ejpam-3373	234	2	log[q	log[q	PROPN
ejpam-3373	234	3	]	]	X
ejpam-3373	234	4	(	(	PUNCT
ejpam-3373	234	5	αk	αk	ADP
ejpam-3373	234	6	αk+1	αk+1	NUM
ejpam-3373	234	7	)	)	PUNCT
ejpam-3373	234	8	if	if	SCONJ
ejpam-3373	234	9	(	(	PUNCT
ejpam-3373	234	10	αk	αk	SCONJ
ejpam-3373	234	11	αk+1	αk+1	NUM
ejpam-3373	234	12	)	)	PUNCT
ejpam-3373	234	13	is	be	AUX
ejpam-3373	234	14	a	a	DET
ejpam-3373	234	15	nondecreasing	nondecrease	VERB
ejpam-3373	234	16	function	function	NOUN
ejpam-3373	234	17	of	of	ADP
ejpam-3373	234	18	k	k	PROPN
ejpam-3373	234	19	for	for	ADP
ejpam-3373	234	20	k	k	PROPN
ejpam-3373	234	21	>	>	X
ejpam-3373	234	22	k0	k0	PROPN
ejpam-3373	234	23	.	.	PUNCT
ejpam-3373	234	24	applying	apply	VERB
ejpam-3373	234	25	above	above	ADP
ejpam-3373	234	26	relation	relation	NOUN
ejpam-3373	234	27	for	for	ADP
ejpam-3373	234	28	the	the	DET
ejpam-3373	234	29	entire	entire	ADJ
ejpam-3373	234	30	function	function	NOUN
ejpam-3373	234	31	f	f	NOUN
ejpam-3373	234	32	,	,	PUNCT
ejpam-3373	234	33	we	we	PRON
ejpam-3373	234	34	obtain	obtain	VERB
ejpam-3373	234	35	ρ(p	ρ(p	PROPN
ejpam-3373	234	36	,	,	PUNCT
ejpam-3373	234	37	q	q	X
ejpam-3373	234	38	,	,	PUNCT
ejpam-3373	234	39	f	f	X
ejpam-3373	234	40	)	)	PUNCT
ejpam-3373	234	41	=	=	SYM
ejpam-3373	235	1	p	p	X
ejpam-3373	235	2	(	(	PUNCT
ejpam-3373	235	3	l(p	l(p	PROPN
ejpam-3373	235	4	,	,	PUNCT
ejpam-3373	235	5	q	q	NOUN
ejpam-3373	235	6	,	,	PUNCT
ejpam-3373	235	7	f	f	NOUN
ejpam-3373	235	8	)	)	PUNCT
ejpam-3373	235	9	)	)	PUNCT
ejpam-3373	235	10	,	,	PUNCT
ejpam-3373	235	11	(	(	PUNCT
ejpam-3373	235	12	3.4	3.4	NUM
ejpam-3373	235	13	)	)	PUNCT
ejpam-3373	235	14	l(p	l(p	PROPN
ejpam-3373	235	15	,	,	PUNCT
ejpam-3373	235	16	q	q	NOUN
ejpam-3373	235	17	,	,	PUNCT
ejpam-3373	235	18	f	f	X
ejpam-3373	235	19	)	)	PUNCT
ejpam-3373	236	1	=	=	SYM
ejpam-3373	236	2	lim	lim	PROPN
ejpam-3373	236	3	sup	sup	PROPN
ejpam-3373	236	4	k→∞	k→∞	X
ejpam-3373	236	5	log[p−1	log[p−1	X
ejpam-3373	236	6	]	]	X
ejpam-3373	237	1	k	k	X
ejpam-3373	237	2	log[q	log[q	PROPN
ejpam-3373	237	3	]	]	X
ejpam-3373	237	4	(	(	PUNCT
ejpam-3373	237	5	βk	βk	NOUN
ejpam-3373	237	6	βk+1	βk+1	PUNCT
ejpam-3373	237	7	)	)	PUNCT
ejpam-3373	238	1	=	=	SYM
ejpam-3373	238	2	lim	lim	PROPN
ejpam-3373	238	3	sup	sup	PROPN
ejpam-3373	238	4	k→∞	k→∞	X
ejpam-3373	238	5	log[p−1	log[p−1	X
ejpam-3373	238	6	]	]	X
ejpam-3373	239	1	k	k	X
ejpam-3373	239	2	log[q	log[q	PROPN
ejpam-3373	239	3	]	]	X
ejpam-3373	239	4	(	(	PUNCT
ejpam-3373	239	5	e	e	X
ejpam-3373	239	6	(	(	PUNCT
ejpam-3373	239	7	k−1	k−1	PROPN
ejpam-3373	239	8	)	)	PUNCT
ejpam-3373	239	9	r	r	NOUN
ejpam-3373	239	10	(	(	PUNCT
ejpam-3373	239	11	u)r	u)r	X
ejpam-3373	239	12	e	e	X
ejpam-3373	239	13	(	(	PUNCT
ejpam-3373	239	14	k	k	NOUN
ejpam-3373	239	15	)	)	PUNCT
ejpam-3373	239	16	r	r	NOUN
ejpam-3373	239	17	(	(	PUNCT
ejpam-3373	239	18	u	u	NOUN
ejpam-3373	239	19	)	)	PUNCT
ejpam-3373	239	20	(	(	PUNCT
ejpam-3373	239	21	k+1	k+1	X
ejpam-3373	239	22	+	+	NOUN
ejpam-3373	239	23	2ν	2ν	NOUN
ejpam-3373	239	24	k+2ν	k+2ν	PROPN
ejpam-3373	239	25	)	)	PUNCT
ejpam-3373	239	26	2ν	2ν	NUM
ejpam-3373	239	27	)	)	PUNCT
ejpam-3373	240	1	=	=	SYM
ejpam-3373	240	2	lim	lim	PROPN
ejpam-3373	240	3	sup	sup	PROPN
ejpam-3373	240	4	k→∞	k→∞	X
ejpam-3373	240	5	log[p−1	log[p−1	PROPN
ejpam-3373	240	6	]	]	PUNCT
ejpam-3373	240	7	k(log[q−1](log	k(log[q−1](log	PROPN
ejpam-3373	240	8	(	(	PUNCT
ejpam-3373	240	9	e	e	X
ejpam-3373	240	10	(	(	PUNCT
ejpam-3373	240	11	k	k	NOUN
ejpam-3373	240	12	)	)	PUNCT
ejpam-3373	240	13	r	r	NOUN
ejpam-3373	240	14	(	(	PUNCT
ejpam-3373	240	15	u)r	u)r	X
ejpam-3373	240	16	e	e	X
ejpam-3373	240	17	(	(	PUNCT
ejpam-3373	240	18	k+1	k+1	NOUN
ejpam-3373	240	19	)	)	PUNCT
ejpam-3373	240	20	r	r	NOUN
ejpam-3373	240	21	(	(	PUNCT
ejpam-3373	240	22	u	u	NOUN
ejpam-3373	240	23	)	)	PUNCT
ejpam-3373	240	24	)	)	PUNCT
ejpam-3373	241	1	+	+	CCONJ
ejpam-3373	241	2	2ν	2ν	NUM
ejpam-3373	241	3	log	log	NOUN
ejpam-3373	241	4	(	(	PUNCT
ejpam-3373	241	5	k	k	NOUN
ejpam-3373	241	6	+	+	PROPN
ejpam-3373	241	7	1	1	NUM
ejpam-3373	241	8	+	+	NUM
ejpam-3373	241	9	2ν	2ν	NOUN
ejpam-3373	241	10	k	k	NOUN
ejpam-3373	241	11	+	+	NUM
ejpam-3373	241	12	2ν	2ν	NUM
ejpam-3373	241	13	)	)	PUNCT
ejpam-3373	241	14	−1	−1	NOUN
ejpam-3373	241	15	)	)	PUNCT
ejpam-3373	241	16	)	)	PUNCT
ejpam-3373	242	1	=	=	SYM
ejpam-3373	242	2	lim	lim	PROPN
ejpam-3373	242	3	sup	sup	VERB
ejpam-3373	242	4	k→∞	k→∞	X
ejpam-3373	242	5	log[p−1	log[p−1	X
ejpam-3373	242	6	]	]	X
ejpam-3373	243	1	k	k	X
ejpam-3373	243	2	log[q	log[q	PROPN
ejpam-3373	243	3	]	]	X
ejpam-3373	243	4	(	(	PUNCT
ejpam-3373	243	5	e	e	X
ejpam-3373	243	6	(	(	PUNCT
ejpam-3373	243	7	k	k	NOUN
ejpam-3373	243	8	)	)	PUNCT
ejpam-3373	243	9	r	r	NOUN
ejpam-3373	243	10	(	(	PUNCT
ejpam-3373	243	11	u)r	u)r	X
ejpam-3373	243	12	e	e	X
ejpam-3373	243	13	(	(	PUNCT
ejpam-3373	243	14	k+1	k+1	NOUN
ejpam-3373	243	15	)	)	PUNCT
ejpam-3373	243	16	r	r	NOUN
ejpam-3373	243	17	(	(	PUNCT
ejpam-3373	243	18	u	u	NOUN
ejpam-3373	243	19	)	)	PUNCT
ejpam-3373	243	20	)	)	PUNCT
ejpam-3373	243	21	.	.	PUNCT
ejpam-3373	244	1	similarly	similarly	ADV
ejpam-3373	244	2	for	for	ADP
ejpam-3373	244	3	the	the	DET
ejpam-3373	244	4	entire	entire	ADJ
ejpam-3373	244	5	function	function	NOUN
ejpam-3373	244	6	g	g	NOUN
ejpam-3373	244	7	,	,	PUNCT
ejpam-3373	244	8	we	we	PRON
ejpam-3373	244	9	have	have	VERB
ejpam-3373	244	10	l(p	l(p	PROPN
ejpam-3373	244	11	,	,	PUNCT
ejpam-3373	244	12	q	q	NOUN
ejpam-3373	244	13	,	,	PUNCT
ejpam-3373	244	14	g	g	NOUN
ejpam-3373	244	15	)	)	PUNCT
ejpam-3373	245	1	=	=	SYM
ejpam-3373	245	2	lim	lim	PROPN
ejpam-3373	245	3	sup	sup	PROPN
ejpam-3373	245	4	k→∞	k→∞	X
ejpam-3373	245	5	log[p−1	log[p−1	X
ejpam-3373	245	6	]	]	X
ejpam-3373	246	1	k	k	X
ejpam-3373	246	2	log[q	log[q	PROPN
ejpam-3373	246	3	]	]	X
ejpam-3373	246	4	(	(	PUNCT
ejpam-3373	246	5	e	e	X
ejpam-3373	246	6	(	(	PUNCT
ejpam-3373	246	7	k	k	NOUN
ejpam-3373	246	8	)	)	PUNCT
ejpam-3373	246	9	r	r	NOUN
ejpam-3373	246	10	(	(	PUNCT
ejpam-3373	246	11	u)r	u)r	X
ejpam-3373	246	12	e	e	X
ejpam-3373	246	13	(	(	PUNCT
ejpam-3373	246	14	k+	k+	X
ejpam-3373	246	15	!	!	PUNCT
ejpam-3373	246	16	)	)	PUNCT
ejpam-3373	247	1	r	r	NOUN
ejpam-3373	247	2	(	(	PUNCT
ejpam-3373	247	3	u	u	NOUN
ejpam-3373	247	4	)	)	PUNCT
ejpam-3373	247	5	)	)	PUNCT
ejpam-3373	247	6	.	.	PUNCT
ejpam-3373	248	1	ρ(p	ρ(p	PROPN
ejpam-3373	248	2	,	,	PUNCT
ejpam-3373	248	3	q	q	X
ejpam-3373	248	4	,	,	PUNCT
ejpam-3373	248	5	g	g	NOUN
ejpam-3373	248	6	)	)	PUNCT
ejpam-3373	248	7	=	=	SYM
ejpam-3373	249	1	p	p	X
ejpam-3373	249	2	(	(	PUNCT
ejpam-3373	249	3	l(p	l(p	PROPN
ejpam-3373	249	4	,	,	PUNCT
ejpam-3373	249	5	q	q	NOUN
ejpam-3373	249	6	,	,	PUNCT
ejpam-3373	249	7	g	g	NOUN
ejpam-3373	249	8	)	)	PUNCT
ejpam-3373	249	9	)	)	PUNCT
ejpam-3373	250	1	now	now	ADV
ejpam-3373	250	2	(	(	PUNCT
ejpam-3373	250	3	3.3)follows	3.3)follows	NUM
ejpam-3373	250	4	from	from	ADP
ejpam-3373	250	5	(	(	PUNCT
ejpam-3373	250	6	2.4	2.4	NUM
ejpam-3373	250	7	)	)	PUNCT
ejpam-3373	250	8	.	.	PUNCT
ejpam-3373	251	1	theorem	theorem	VERB
ejpam-3373	251	2	3.3	3.3	NUM
ejpam-3373	251	3	.	.	PUNCT
ejpam-3373	252	1	let	let	VERB
ejpam-3373	252	2	u	u	PRON
ejpam-3373	252	3	be	be	AUX
ejpam-3373	252	4	an	an	DET
ejpam-3373	252	5	entire	entire	ADJ
ejpam-3373	252	6	harmonic	harmonic	ADJ
ejpam-3373	252	7	function	function	NOUN
ejpam-3373	252	8	in	in	ADP
ejpam-3373	252	9	rn	rn	PROPN
ejpam-3373	252	10	,	,	PUNCT
ejpam-3373	252	11	n	n	PRON
ejpam-3373	252	12	≥	≥	NOUN
ejpam-3373	252	13	3	3	NUM
ejpam-3373	252	14	with	with	ADP
ejpam-3373	252	15	(	(	PUNCT
ejpam-3373	252	16	p	p	NOUN
ejpam-3373	252	17	,	,	PUNCT
ejpam-3373	252	18	q)-order	q)-order	ADJ
ejpam-3373	252	19	ρ(p	ρ(p	NUM
ejpam-3373	252	20	,	,	PUNCT
ejpam-3373	252	21	q	q	NOUN
ejpam-3373	252	22	,	,	PUNCT
ejpam-3373	252	23	u	u	NOUN
ejpam-3373	252	24	)	)	PUNCT
ejpam-3373	252	25	,	,	PUNCT
ejpam-3373	252	26	lower	low	ADJ
ejpam-3373	252	27	(	(	PUNCT
ejpam-3373	252	28	p	p	NOUN
ejpam-3373	252	29	,	,	PUNCT
ejpam-3373	252	30	q)-order	q)-order	NOUN
ejpam-3373	252	31	λ(p	λ(p	PROPN
ejpam-3373	252	32	,	,	PUNCT
ejpam-3373	252	33	q	q	NOUN
ejpam-3373	252	34	,	,	PUNCT
ejpam-3373	252	35	u	u	NOUN
ejpam-3373	252	36	)	)	PUNCT
ejpam-3373	252	37	,	,	PUNCT
ejpam-3373	252	38	lower	low	ADJ
ejpam-3373	252	39	(	(	PUNCT
ejpam-3373	252	40	p	p	NOUN
ejpam-3373	252	41	,	,	PUNCT
ejpam-3373	252	42	q)-type	q)-type	PUNCT
ejpam-3373	252	43	t(p	t(p	PROPN
ejpam-3373	252	44	,	,	PUNCT
ejpam-3373	252	45	q	q	NOUN
ejpam-3373	252	46	,	,	PUNCT
ejpam-3373	252	47	u	u	NOUN
ejpam-3373	252	48	)	)	PUNCT
ejpam-3373	252	49	and	and	CCONJ
ejpam-3373	252	50	let	let	VERB
ejpam-3373	252	51	(	(	PUNCT
ejpam-3373	252	52	e	e	X
ejpam-3373	252	53	(	(	PUNCT
ejpam-3373	252	54	k	k	NOUN
ejpam-3373	252	55	)	)	PUNCT
ejpam-3373	252	56	r	r	NOUN
ejpam-3373	252	57	(	(	PUNCT
ejpam-3373	252	58	u	u	NOUN
ejpam-3373	252	59	)	)	PUNCT
ejpam-3373	252	60	e	e	NOUN
ejpam-3373	252	61	(	(	PUNCT
ejpam-3373	252	62	k+1	k+1	NOUN
ejpam-3373	252	63	)	)	PUNCT
ejpam-3373	252	64	r	r	NOUN
ejpam-3373	252	65	(	(	PUNCT
ejpam-3373	252	66	u	u	NOUN
ejpam-3373	252	67	)	)	PUNCT
ejpam-3373	252	68	)	)	PUNCT
ejpam-3373	252	69	is	be	AUX
ejpam-3373	252	70	a	a	DET
ejpam-3373	252	71	nondecreasing	nondecrease	VERB
ejpam-3373	252	72	function	function	NOUN
ejpam-3373	252	73	of	of	ADP
ejpam-3373	252	74	k	k	PROPN
ejpam-3373	252	75	for	for	ADP
ejpam-3373	252	76	k	k	PROPN
ejpam-3373	252	77	>	>	X
ejpam-3373	252	78	k0	k0	PROPN
ejpam-3373	252	79	,	,	PUNCT
ejpam-3373	252	80	then	then	ADV
ejpam-3373	252	81	λ(p	λ(p	PROPN
ejpam-3373	252	82	,	,	PUNCT
ejpam-3373	252	83	q	q	NOUN
ejpam-3373	252	84	,	,	PUNCT
ejpam-3373	252	85	u	u	NOUN
ejpam-3373	252	86	)	)	PUNCT
ejpam-3373	253	1	=	=	SYM
ejpam-3373	253	2	p	p	X
ejpam-3373	253	3	(	(	PUNCT
ejpam-3373	253	4	l∗(p	l∗(p	PROPN
ejpam-3373	253	5	,	,	PUNCT
ejpam-3373	253	6	q	q	NOUN
ejpam-3373	253	7	,	,	PUNCT
ejpam-3373	253	8	u	u	NOUN
ejpam-3373	253	9	)	)	PUNCT
ejpam-3373	253	10	)	)	PUNCT
ejpam-3373	253	11	(	(	PUNCT
ejpam-3373	253	12	3.5	3.5	NUM
ejpam-3373	253	13	)	)	PUNCT
ejpam-3373	253	14	where	where	SCONJ
ejpam-3373	253	15	l∗(p	l∗(p	PROPN
ejpam-3373	253	16	,	,	PUNCT
ejpam-3373	253	17	q	q	NOUN
ejpam-3373	253	18	,	,	PUNCT
ejpam-3373	253	19	u	u	NOUN
ejpam-3373	253	20	)	)	PUNCT
ejpam-3373	253	21	=	=	SYM
ejpam-3373	253	22	lim	lim	PROPN
ejpam-3373	253	23	inf	inf	PROPN
ejpam-3373	253	24	k→∞	k→∞	PROPN
ejpam-3373	253	25	log[p−1	log[p−1	PROPN
ejpam-3373	253	26	]	]	X
ejpam-3373	254	1	k	k	PROPN
ejpam-3373	254	2	log[q](r−ke	log[q](r−ke	PROPN
ejpam-3373	254	3	(	(	PUNCT
ejpam-3373	254	4	k	k	NOUN
ejpam-3373	254	5	)	)	PUNCT
ejpam-3373	254	6	r	r	NOUN
ejpam-3373	254	7	(	(	PUNCT
ejpam-3373	254	8	u))−	u))−	PROPN
ejpam-3373	254	9	1	1	NUM
ejpam-3373	254	10	k	k	NOUN
ejpam-3373	254	11	and	and	CCONJ
ejpam-3373	254	12	t(p	t(p	PROPN
ejpam-3373	254	13	,	,	PUNCT
ejpam-3373	254	14	q	q	NOUN
ejpam-3373	254	15	,	,	PUNCT
ejpam-3373	254	16	u	u	NOUN
ejpam-3373	254	17	)	)	PUNCT
ejpam-3373	254	18	=	=	SYM
ejpam-3373	254	19	mv(p	mv(p	X
ejpam-3373	254	20	,	,	PUNCT
ejpam-3373	254	21	q	q	NOUN
ejpam-3373	254	22	,	,	PUNCT
ejpam-3373	254	23	u	u	NOUN
ejpam-3373	254	24	)	)	PUNCT
ejpam-3373	254	25	(	(	PUNCT
ejpam-3373	254	26	3.6	3.6	NUM
ejpam-3373	254	27	)	)	PUNCT
ejpam-3373	254	28	where	where	SCONJ
ejpam-3373	254	29	v(p	v(p	NOUN
ejpam-3373	254	30	,	,	PUNCT
ejpam-3373	254	31	q	q	NOUN
ejpam-3373	254	32	,	,	PUNCT
ejpam-3373	254	33	u	u	NOUN
ejpam-3373	254	34	)	)	PUNCT
ejpam-3373	254	35	=	=	SYM
ejpam-3373	254	36	lim	lim	PROPN
ejpam-3373	254	37	inf	inf	PROPN
ejpam-3373	254	38	k→∞	k→∞	PROPN
ejpam-3373	254	39	log[p−2	log[p−2	NOUN
ejpam-3373	254	40	]	]	X
ejpam-3373	255	1	k	k	X
ejpam-3373	255	2	(	(	PUNCT
ejpam-3373	255	3	log[q−1](r−ke	log[q−1](r−ke	PROPN
ejpam-3373	255	4	(	(	PUNCT
ejpam-3373	255	5	k	k	NOUN
ejpam-3373	255	6	)	)	PUNCT
ejpam-3373	255	7	r	r	NOUN
ejpam-3373	255	8	(	(	PUNCT
ejpam-3373	255	9	u))−	u))−	PROPN
ejpam-3373	255	10	1	1	NUM
ejpam-3373	255	11	k	k	NOUN
ejpam-3373	255	12	)	)	PUNCT
ejpam-3373	255	13	ρ−a	ρ−a	PROPN
ejpam-3373	255	14	d.	d.	PROPN
ejpam-3373	255	15	kumar	kumar	PROPN
ejpam-3373	255	16	,	,	PUNCT
ejpam-3373	255	17	r.	r.	PROPN
ejpam-3373	255	18	ali	ali	PROPN
ejpam-3373	255	19	/	/	SYM
ejpam-3373	255	20	eur	eur	PROPN
ejpam-3373	255	21	.	.	PUNCT
ejpam-3373	256	1	j.	j.	PROPN
ejpam-3373	256	2	pure	pure	PROPN
ejpam-3373	256	3	appl	appl	PROPN
ejpam-3373	256	4	.	.	PROPN
ejpam-3373	256	5	math	math	PROPN
ejpam-3373	256	6	,	,	PUNCT
ejpam-3373	256	7	12	12	NUM
ejpam-3373	256	8	(	(	PUNCT
ejpam-3373	256	9	2	2	NUM
ejpam-3373	256	10	)	)	PUNCT
ejpam-3373	256	11	(	(	PUNCT
ejpam-3373	256	12	2019	2019	NUM
ejpam-3373	256	13	)	)	PUNCT
ejpam-3373	256	14	,	,	PUNCT
ejpam-3373	256	15	486	486	NUM
ejpam-3373	256	16	-	-	SYM
ejpam-3373	256	17	498	498	NUM
ejpam-3373	256	18	496	496	NUM
ejpam-3373	256	19	proof	proof	NOUN
ejpam-3373	256	20	.	.	PUNCT
ejpam-3373	257	1	applying	apply	VERB
ejpam-3373	257	2	theorem	theorem	NOUN
ejpam-3373	257	3	d	d	NOUN
ejpam-3373	257	4	to	to	ADP
ejpam-3373	257	5	the	the	DET
ejpam-3373	257	6	function	function	NOUN
ejpam-3373	257	7	f	f	PROPN
ejpam-3373	257	8	and	and	CCONJ
ejpam-3373	257	9	g	g	NOUN
ejpam-3373	257	10	we	we	PRON
ejpam-3373	257	11	can	can	AUX
ejpam-3373	257	12	easily	easily	ADV
ejpam-3373	257	13	obtain	obtain	VERB
ejpam-3373	257	14	λ(p	λ(p	PROPN
ejpam-3373	257	15	,	,	PUNCT
ejpam-3373	257	16	q	q	X
ejpam-3373	257	17	,	,	PUNCT
ejpam-3373	257	18	f	f	X
ejpam-3373	257	19	)	)	PUNCT
ejpam-3373	258	1	=	=	SYM
ejpam-3373	258	2	p	p	X
ejpam-3373	258	3	(	(	PUNCT
ejpam-3373	258	4	l∗(p	l∗(p	PROPN
ejpam-3373	258	5	,	,	PUNCT
ejpam-3373	258	6	q	q	X
ejpam-3373	258	7	,	,	PUNCT
ejpam-3373	258	8	f	f	NOUN
ejpam-3373	258	9	)	)	PUNCT
ejpam-3373	258	10	)	)	PUNCT
ejpam-3373	258	11	and	and	CCONJ
ejpam-3373	258	12	λ(p	λ(p	PROPN
ejpam-3373	258	13	,	,	PUNCT
ejpam-3373	258	14	q	q	X
ejpam-3373	258	15	,	,	PUNCT
ejpam-3373	258	16	g	g	NOUN
ejpam-3373	258	17	)	)	PUNCT
ejpam-3373	258	18	=	=	SYM
ejpam-3373	259	1	p	p	X
ejpam-3373	259	2	(	(	PUNCT
ejpam-3373	259	3	l∗(p	l∗(p	PROPN
ejpam-3373	259	4	,	,	PUNCT
ejpam-3373	259	5	q	q	X
ejpam-3373	259	6	,	,	PUNCT
ejpam-3373	259	7	g	g	NOUN
ejpam-3373	259	8	)	)	PUNCT
ejpam-3373	259	9	)	)	PUNCT
ejpam-3373	259	10	where	where	SCONJ
ejpam-3373	259	11	l∗(p	l∗(p	PROPN
ejpam-3373	259	12	,	,	PUNCT
ejpam-3373	259	13	q	q	X
ejpam-3373	259	14	,	,	PUNCT
ejpam-3373	259	15	f	f	X
ejpam-3373	259	16	)	)	PUNCT
ejpam-3373	260	1	=	=	SYM
ejpam-3373	260	2	lim	lim	PROPN
ejpam-3373	260	3	inf	inf	PROPN
ejpam-3373	260	4	k→∞	k→∞	PROPN
ejpam-3373	260	5	log[p−1	log[p−1	PROPN
ejpam-3373	260	6	]	]	X
ejpam-3373	261	1	k	k	PROPN
ejpam-3373	261	2	log[q](r−ke	log[q](r−ke	PROPN
ejpam-3373	261	3	(	(	PUNCT
ejpam-3373	261	4	k	k	NOUN
ejpam-3373	261	5	)	)	PUNCT
ejpam-3373	261	6	r	r	NOUN
ejpam-3373	261	7	(	(	PUNCT
ejpam-3373	261	8	u))−	u))−	PROPN
ejpam-3373	261	9	1	1	NUM
ejpam-3373	261	10	k	k	PROPN
ejpam-3373	261	11	,	,	PUNCT
ejpam-3373	261	12	l∗(p	l∗(p	PROPN
ejpam-3373	261	13	,	,	PUNCT
ejpam-3373	261	14	q	q	X
ejpam-3373	261	15	,	,	PUNCT
ejpam-3373	261	16	g	g	NOUN
ejpam-3373	261	17	)	)	PUNCT
ejpam-3373	261	18	=	=	SYM
ejpam-3373	261	19	lim	lim	PROPN
ejpam-3373	261	20	inf	inf	PROPN
ejpam-3373	261	21	k→∞	k→∞	PROPN
ejpam-3373	261	22	log[p−1	log[p−1	PROPN
ejpam-3373	261	23	]	]	X
ejpam-3373	262	1	k	k	PROPN
ejpam-3373	262	2	log[q](r−ke	log[q](r−ke	PROPN
ejpam-3373	262	3	(	(	PUNCT
ejpam-3373	262	4	k	k	NOUN
ejpam-3373	262	5	)	)	PUNCT
ejpam-3373	262	6	r	r	NOUN
ejpam-3373	262	7	(	(	PUNCT
ejpam-3373	262	8	u))−	u))−	PROPN
ejpam-3373	262	9	1	1	NUM
ejpam-3373	262	10	k	k	NOUN
ejpam-3373	262	11	now	now	ADV
ejpam-3373	262	12	the	the	DET
ejpam-3373	262	13	result	result	NOUN
ejpam-3373	262	14	(	(	PUNCT
ejpam-3373	262	15	3.6	3.6	NUM
ejpam-3373	262	16	)	)	PUNCT
ejpam-3373	262	17	follows	follow	VERB
ejpam-3373	262	18	from	from	ADP
ejpam-3373	262	19	(	(	PUNCT
ejpam-3373	262	20	2.5	2.5	NUM
ejpam-3373	262	21	)	)	PUNCT
ejpam-3373	262	22	.	.	PUNCT
ejpam-3373	263	1	similarly	similarly	ADV
ejpam-3373	263	2	applying	apply	VERB
ejpam-3373	263	3	theorem	theorem	ADJ
ejpam-3373	263	4	f	f	PROPN
ejpam-3373	263	5	to	to	ADP
ejpam-3373	263	6	the	the	DET
ejpam-3373	263	7	entire	entire	ADJ
ejpam-3373	263	8	function	function	NOUN
ejpam-3373	263	9	f	f	PROPN
ejpam-3373	263	10	and	and	CCONJ
ejpam-3373	263	11	g	g	NOUN
ejpam-3373	263	12	,	,	PUNCT
ejpam-3373	263	13	we	we	PRON
ejpam-3373	263	14	get	get	VERB
ejpam-3373	263	15	t(p	t(p	NOUN
ejpam-3373	263	16	,	,	PUNCT
ejpam-3373	263	17	q	q	NOUN
ejpam-3373	263	18	,	,	PUNCT
ejpam-3373	263	19	f	f	X
ejpam-3373	263	20	)	)	PUNCT
ejpam-3373	263	21	=	=	SYM
ejpam-3373	263	22	mv(p	mv(p	X
ejpam-3373	263	23	,	,	PUNCT
ejpam-3373	263	24	q	q	X
ejpam-3373	263	25	,	,	PUNCT
ejpam-3373	263	26	f	f	NOUN
ejpam-3373	263	27	)	)	PUNCT
ejpam-3373	263	28	,	,	PUNCT
ejpam-3373	263	29	t(p	t(p	PROPN
ejpam-3373	263	30	,	,	PUNCT
ejpam-3373	263	31	q	q	NOUN
ejpam-3373	263	32	,	,	PUNCT
ejpam-3373	263	33	g	g	NOUN
ejpam-3373	263	34	)	)	PUNCT
ejpam-3373	263	35	=	=	SYM
ejpam-3373	264	1	mv(p	mv(p	X
ejpam-3373	264	2	,	,	PUNCT
ejpam-3373	264	3	q	q	NOUN
ejpam-3373	264	4	,	,	PUNCT
ejpam-3373	264	5	g	g	NOUN
ejpam-3373	264	6	)	)	PUNCT
ejpam-3373	264	7	where	where	SCONJ
ejpam-3373	264	8	v(p	v(p	NOUN
ejpam-3373	264	9	,	,	PUNCT
ejpam-3373	264	10	q	q	NOUN
ejpam-3373	264	11	,	,	PUNCT
ejpam-3373	264	12	f	f	X
ejpam-3373	264	13	)	)	PUNCT
ejpam-3373	264	14	=	=	SYM
ejpam-3373	264	15	lim	lim	PROPN
ejpam-3373	264	16	inf	inf	PROPN
ejpam-3373	264	17	k→∞	k→∞	PROPN
ejpam-3373	264	18	log[p−2	log[p−2	NOUN
ejpam-3373	264	19	]	]	X
ejpam-3373	265	1	k	k	X
ejpam-3373	265	2	(	(	PUNCT
ejpam-3373	265	3	log[q−1](r−ke	log[q−1](r−ke	PROPN
ejpam-3373	265	4	(	(	PUNCT
ejpam-3373	265	5	k	k	NOUN
ejpam-3373	265	6	)	)	PUNCT
ejpam-3373	265	7	r	r	NOUN
ejpam-3373	265	8	(	(	PUNCT
ejpam-3373	265	9	u))−	u))−	PROPN
ejpam-3373	265	10	1	1	NUM
ejpam-3373	265	11	k	k	NOUN
ejpam-3373	265	12	)	)	PUNCT
ejpam-3373	265	13	ρ−a	ρ−a	PROPN
ejpam-3373	265	14	v(p	v(p	PROPN
ejpam-3373	265	15	,	,	PUNCT
ejpam-3373	265	16	q	q	NOUN
ejpam-3373	265	17	,	,	PUNCT
ejpam-3373	265	18	g	g	NOUN
ejpam-3373	265	19	)	)	PUNCT
ejpam-3373	265	20	=	=	SYM
ejpam-3373	265	21	lim	lim	PROPN
ejpam-3373	265	22	inf	inf	PROPN
ejpam-3373	265	23	k→∞	k→∞	PROPN
ejpam-3373	265	24	log[p−2	log[p−2	NOUN
ejpam-3373	265	25	]	]	X
ejpam-3373	266	1	k	k	X
ejpam-3373	266	2	(	(	PUNCT
ejpam-3373	266	3	log[q−1](r−ke	log[q−1](r−ke	PROPN
ejpam-3373	266	4	(	(	PUNCT
ejpam-3373	266	5	k	k	NOUN
ejpam-3373	266	6	)	)	PUNCT
ejpam-3373	266	7	r	r	NOUN
ejpam-3373	266	8	(	(	PUNCT
ejpam-3373	266	9	u))−	u))−	PROPN
ejpam-3373	266	10	1	1	NUM
ejpam-3373	266	11	k	k	NOUN
ejpam-3373	266	12	)	)	PUNCT
ejpam-3373	266	13	ρ−a	ρ−a	PROPN
ejpam-3373	266	14	the	the	DET
ejpam-3373	266	15	result	result	NOUN
ejpam-3373	266	16	(	(	PUNCT
ejpam-3373	266	17	3.7	3.7	NUM
ejpam-3373	266	18	)	)	PUNCT
ejpam-3373	266	19	follows	follow	VERB
ejpam-3373	266	20	from	from	ADP
ejpam-3373	266	21	(	(	PUNCT
ejpam-3373	266	22	2.7	2.7	NUM
ejpam-3373	266	23	)	)	PUNCT
ejpam-3373	266	24	and	and	CCONJ
ejpam-3373	266	25	above	above	ADP
ejpam-3373	266	26	relations	relation	NOUN
ejpam-3373	266	27	.	.	PUNCT
ejpam-3373	267	1	acknowledgements	acknowledgement	NOUN
ejpam-3373	267	2	the	the	DET
ejpam-3373	267	3	authors	author	NOUN
ejpam-3373	267	4	are	be	AUX
ejpam-3373	267	5	gratful	gratful	ADJ
ejpam-3373	267	6	to	to	ADP
ejpam-3373	267	7	akram	akram	PROPN
ejpam-3373	267	8	ali	ali	PROPN
ejpam-3373	267	9	for	for	ADP
ejpam-3373	267	10	his	his	PRON
ejpam-3373	267	11	useful	useful	ADJ
ejpam-3373	267	12	comments	comment	NOUN
ejpam-3373	267	13	,	,	PUNCT
ejpam-3373	267	14	discussions	discussion	NOUN
ejpam-3373	267	15	and	and	CCONJ
ejpam-3373	267	16	constant	constant	ADJ
ejpam-3373	267	17	encouragement	encouragement	NOUN
ejpam-3373	267	18	,	,	PUNCT
ejpam-3373	267	19	and	and	CCONJ
ejpam-3373	267	20	the	the	DET
ejpam-3373	267	21	referees	referee	NOUN
ejpam-3373	267	22	for	for	ADP
ejpam-3373	267	23	their	their	PRON
ejpam-3373	267	24	valuable	valuable	ADJ
ejpam-3373	267	25	suggestions	suggestion	NOUN
ejpam-3373	267	26	which	which	PRON
ejpam-3373	267	27	improved	improve	VERB
ejpam-3373	267	28	the	the	DET
ejpam-3373	267	29	paper	paper	NOUN
ejpam-3373	267	30	.	.	PUNCT
ejpam-3373	268	1	they	they	PRON
ejpam-3373	268	2	also	also	ADV
ejpam-3373	268	3	would	would	AUX
ejpam-3373	268	4	like	like	VERB
ejpam-3373	268	5	to	to	PART
ejpam-3373	268	6	express	express	VERB
ejpam-3373	268	7	their	their	PRON
ejpam-3373	268	8	gratitude	gratitude	NOUN
ejpam-3373	268	9	to	to	ADP
ejpam-3373	268	10	king	king	PROPN
ejpam-3373	268	11	khalid	khalid	PROPN
ejpam-3373	268	12	university	university	PROPN
ejpam-3373	268	13	for	for	ADP
ejpam-3373	268	14	providing	provide	VERB
ejpam-3373	268	15	administrative	administrative	ADJ
ejpam-3373	268	16	and	and	CCONJ
ejpam-3373	268	17	technical	technical	ADJ
ejpam-3373	268	18	support	support	NOUN
ejpam-3373	268	19	.	.	PUNCT
ejpam-3373	269	1	references	reference	NOUN
ejpam-3373	269	2	497	497	NUM
ejpam-3373	269	3	references	reference	NOUN
ejpam-3373	269	4	[	[	X
ejpam-3373	269	5	1	1	NUM
ejpam-3373	269	6	]	]	X
ejpam-3373	269	7	r.p	r.p	PROPN
ejpam-3373	269	8	.	.	NOUN
ejpam-3373	269	9	boas	boas	PROPN
ejpam-3373	269	10	,	,	PUNCT
ejpam-3373	269	11	entire	entire	ADJ
ejpam-3373	269	12	functions	function	NOUN
ejpam-3373	269	13	,	,	PUNCT
ejpam-3373	269	14	academic	academic	ADJ
ejpam-3373	269	15	press	press	NOUN
ejpam-3373	269	16	,	,	PUNCT
ejpam-3373	269	17	new	new	PROPN
ejpam-3373	269	18	york	york	PROPN
ejpam-3373	269	19	,	,	PUNCT
ejpam-3373	269	20	n	n	PROPN
ejpam-3373	269	21	y	y	PROPN
ejpam-3373	269	22	,	,	PUNCT
ejpam-3373	269	23	usa	usa	PROPN
ejpam-3373	269	24	,	,	PUNCT
ejpam-3373	269	25	1954	1954	NUM
ejpam-3373	269	26	.	.	PUNCT
ejpam-3373	270	1	[	[	X
ejpam-3373	270	2	2	2	NUM
ejpam-3373	270	3	]	]	X
ejpam-3373	270	4	a.j	a.j	PROPN
ejpam-3373	270	5	.	.	PROPN
ejpam-3373	270	6	fryant	fryant	PROPN
ejpam-3373	270	7	,	,	PUNCT
ejpam-3373	270	8	growth	growth	NOUN
ejpam-3373	270	9	of	of	ADP
ejpam-3373	270	10	entire	entire	ADJ
ejpam-3373	270	11	harmonic	harmonic	ADJ
ejpam-3373	270	12	functions	function	NOUN
ejpam-3373	270	13	in	in	ADP
ejpam-3373	270	14	r3	r3	PROPN
ejpam-3373	270	15	,	,	PUNCT
ejpam-3373	270	16	j.	j.	PROPN
ejpam-3373	270	17	math	math	PROPN
ejpam-3373	270	18	.	.	PUNCT
ejpam-3373	271	1	anal	anal	PROPN
ejpam-3373	271	2	.	.	PUNCT
ejpam-3373	271	3	appl	appl	PROPN
ejpam-3373	271	4	.	.	PUNCT
ejpam-3373	272	1	66(1978	66(1978	PROPN
ejpam-3373	272	2	)	)	PUNCT
ejpam-3373	272	3	,	,	PUNCT
ejpam-3373	272	4	599	599	NUM
ejpam-3373	272	5	-	-	SYM
ejpam-3373	272	6	605	605	NUM
ejpam-3373	272	7	.	.	PUNCT
ejpam-3373	273	1	[	[	X
ejpam-3373	273	2	3	3	X
ejpam-3373	273	3	]	]	X
ejpam-3373	273	4	t.b	t.b	PROPN
ejpam-3373	273	5	.	.	PROPN
ejpam-3373	273	6	fugard	fugard	PROPN
ejpam-3373	273	7	,	,	PUNCT
ejpam-3373	273	8	growth	growth	NOUN
ejpam-3373	273	9	of	of	ADP
ejpam-3373	273	10	entire	entire	ADJ
ejpam-3373	273	11	harmonic	harmonic	ADJ
ejpam-3373	273	12	functions	function	NOUN
ejpam-3373	273	13	in	in	ADP
ejpam-3373	273	14	rn	rn	PROPN
ejpam-3373	273	15	,	,	PUNCT
ejpam-3373	273	16	n	n	PRON
ejpam-3373	273	17	≥	≥	NOUN
ejpam-3373	273	18	2	2	NUM
ejpam-3373	273	19	,	,	PUNCT
ejpam-3373	273	20	j.	j.	PROPN
ejpam-3373	273	21	math	math	PROPN
ejpam-3373	273	22	.	.	PUNCT
ejpam-3373	274	1	anal	anal	PROPN
ejpam-3373	274	2	.	.	PUNCT
ejpam-3373	275	1	appl	appl	PROPN
ejpam-3373	275	2	.	.	PROPN
ejpam-3373	276	1	74	74	NUM
ejpam-3373	276	2	,	,	PUNCT
ejpam-3373	276	3	issue	issue	NOUN
ejpam-3373	276	4	1	1	NUM
ejpam-3373	276	5	(	(	PUNCT
ejpam-3373	276	6	1980	1980	NUM
ejpam-3373	276	7	)	)	PUNCT
ejpam-3373	276	8	,	,	PUNCT
ejpam-3373	276	9	289	289	NUM
ejpam-3373	276	10	-	-	SYM
ejpam-3373	276	11	291	291	NUM
ejpam-3373	276	12	.	.	PUNCT
ejpam-3373	277	1	[	[	X
ejpam-3373	277	2	4	4	NUM
ejpam-3373	277	3	]	]	X
ejpam-3373	277	4	o.p	o.p	PROPN
ejpam-3373	277	5	.	.	PROPN
ejpam-3373	277	6	juneja	juneja	PROPN
ejpam-3373	277	7	,	,	PUNCT
ejpam-3373	277	8	g.p	g.p	PROPN
ejpam-3373	277	9	.	.	PROPN
ejpam-3373	277	10	kapoor	kapoor	PROPN
ejpam-3373	277	11	and	and	CCONJ
ejpam-3373	277	12	s.k	s.k	PROPN
ejpam-3373	277	13	.	.	PROPN
ejpam-3373	277	14	bajpai	bajpai	PROPN
ejpam-3373	277	15	,	,	PUNCT
ejpam-3373	277	16	on	on	ADP
ejpam-3373	277	17	the	the	DET
ejpam-3373	277	18	(	(	PUNCT
ejpam-3373	277	19	p	p	NOUN
ejpam-3373	277	20	,	,	PUNCT
ejpam-3373	277	21	q)-order	q)-order	NOUN
ejpam-3373	277	22	and	and	CCONJ
ejpam-3373	277	23	lower	low	ADJ
ejpam-3373	277	24	(	(	PUNCT
ejpam-3373	277	25	p	p	NOUN
ejpam-3373	277	26	,	,	PUNCT
ejpam-3373	277	27	q)-order	q)-order	NOUN
ejpam-3373	277	28	of	of	ADP
ejpam-3373	277	29	an	an	DET
ejpam-3373	277	30	entire	entire	ADJ
ejpam-3373	277	31	function	function	NOUN
ejpam-3373	277	32	,	,	PUNCT
ejpam-3373	277	33	j.	j.	PROPN
ejpam-3373	277	34	reine	reine	PROPN
ejpam-3373	277	35	angew	angew	PROPN
ejpam-3373	277	36	math	math	PROPN
ejpam-3373	277	37	.	.	PUNCT
ejpam-3373	278	1	282(1976	282(1976	NOUN
ejpam-3373	278	2	)	)	PUNCT
ejpam-3373	278	3	,	,	PUNCT
ejpam-3373	278	4	53	53	NUM
ejpam-3373	278	5	-	-	SYM
ejpam-3373	278	6	67	67	NUM
ejpam-3373	278	7	.	.	PUNCT
ejpam-3373	279	1	[	[	X
ejpam-3373	279	2	5	5	NUM
ejpam-3373	279	3	]	]	X
ejpam-3373	279	4	o.p	o.p	PROPN
ejpam-3373	279	5	.	.	PROPN
ejpam-3373	279	6	juneja	juneja	PROPN
ejpam-3373	279	7	,	,	PUNCT
ejpam-3373	279	8	g.p	g.p	PROPN
ejpam-3373	279	9	.	.	PROPN
ejpam-3373	279	10	kapoor	kapoor	PROPN
ejpam-3373	279	11	and	and	CCONJ
ejpam-3373	279	12	s.k	s.k	PROPN
ejpam-3373	279	13	.	.	PROPN
ejpam-3373	279	14	bajpai	bajpai	PROPN
ejpam-3373	279	15	,	,	PUNCT
ejpam-3373	279	16	on	on	ADP
ejpam-3373	279	17	the	the	DET
ejpam-3373	279	18	(	(	PUNCT
ejpam-3373	279	19	p	p	NOUN
ejpam-3373	279	20	,	,	PUNCT
ejpam-3373	279	21	q)-type	q)-type	PUNCT
ejpam-3373	279	22	and	and	CCONJ
ejpam-3373	279	23	lower	low	ADJ
ejpam-3373	279	24	(	(	PUNCT
ejpam-3373	279	25	p	p	NOUN
ejpam-3373	279	26	,	,	PUNCT
ejpam-3373	279	27	q)-type	q)-type	ADV
ejpam-3373	279	28	of	of	ADP
ejpam-3373	279	29	an	an	DET
ejpam-3373	279	30	entire	entire	ADJ
ejpam-3373	279	31	function	function	NOUN
ejpam-3373	279	32	,	,	PUNCT
ejpam-3373	279	33	j.	j.	PROPN
ejpam-3373	279	34	reine	reine	PROPN
ejpam-3373	279	35	angew	angew	PROPN
ejpam-3373	279	36	math	math	PROPN
ejpam-3373	279	37	.	.	PUNCT
ejpam-3373	280	1	290(1977	290(1977	NUM
ejpam-3373	280	2	)	)	PUNCT
ejpam-3373	280	3	,	,	PUNCT
ejpam-3373	280	4	180	180	NUM
ejpam-3373	280	5	-	-	SYM
ejpam-3373	280	6	190	190	NUM
ejpam-3373	280	7	.	.	PUNCT
ejpam-3373	281	1	[	[	X
ejpam-3373	281	2	6	6	NUM
ejpam-3373	281	3	]	]	X
ejpam-3373	281	4	g.p	g.p	PROPN
ejpam-3373	281	5	.	.	PROPN
ejpam-3373	281	6	kapoor	kapoor	PROPN
ejpam-3373	281	7	,	,	PUNCT
ejpam-3373	281	8	and	and	CCONJ
ejpam-3373	281	9	a.	a.	NOUN
ejpam-3373	281	10	nautiyal	nautiyal	PROPN
ejpam-3373	281	11	,	,	PUNCT
ejpam-3373	281	12	approximation	approximation	NOUN
ejpam-3373	281	13	of	of	ADP
ejpam-3373	281	14	entire	entire	ADJ
ejpam-3373	281	15	harmonic	harmonic	ADJ
ejpam-3373	281	16	functions	function	NOUN
ejpam-3373	281	17	in	in	ADP
ejpam-3373	281	18	r3	r3	PROPN
ejpam-3373	281	19	,	,	PUNCT
ejpam-3373	281	20	indian	indian	PROPN
ejpam-3373	281	21	j.	j.	PROPN
ejpam-3373	281	22	pure	pure	PROPN
ejpam-3373	281	23	and	and	CCONJ
ejpam-3373	281	24	appl	appl	PROPN
ejpam-3373	281	25	.	.	PROPN
ejpam-3373	281	26	math	math	NOUN
ejpam-3373	281	27	.	.	PUNCT
ejpam-3373	282	1	13	13	NUM
ejpam-3373	282	2	,	,	PUNCT
ejpam-3373	282	3	issue	issue	NOUN
ejpam-3373	282	4	9	9	NUM
ejpam-3373	282	5	(	(	PUNCT
ejpam-3373	282	6	1982	1982	NUM
ejpam-3373	282	7	)	)	PUNCT
ejpam-3373	282	8	,	,	PUNCT
ejpam-3373	282	9	1024	1024	NUM
ejpam-3373	282	10	-	-	SYM
ejpam-3373	282	11	1030	1030	NUM
ejpam-3373	282	12	.	.	PUNCT
ejpam-3373	283	1	[	[	X
ejpam-3373	283	2	7	7	X
ejpam-3373	283	3	]	]	X
ejpam-3373	283	4	d.	d.	PROPN
ejpam-3373	283	5	kumar	kumar	PROPN
ejpam-3373	283	6	,	,	PUNCT
ejpam-3373	283	7	the	the	DET
ejpam-3373	283	8	growth	growth	NOUN
ejpam-3373	283	9	of	of	ADP
ejpam-3373	283	10	harmonic	harmonic	ADJ
ejpam-3373	283	11	functions	function	NOUN
ejpam-3373	283	12	in	in	ADP
ejpam-3373	283	13	hyperspheres	hypersphere	NOUN
ejpam-3373	283	14	,	,	PUNCT
ejpam-3373	283	15	demonstr	demonstr	NOUN
ejpam-3373	283	16	.	.	PUNCT
ejpam-3373	283	17	math	math	NOUN
ejpam-3373	283	18	.	.	PUNCT
ejpam-3373	284	1	32	32	NUM
ejpam-3373	284	2	,	,	PUNCT
ejpam-3373	284	3	no.4	no.4	PROPN
ejpam-3373	284	4	(	(	PUNCT
ejpam-3373	284	5	1999	1999	NUM
ejpam-3373	284	6	)	)	PUNCT
ejpam-3373	284	7	,	,	PUNCT
ejpam-3373	284	8	717	717	NUM
ejpam-3373	284	9	-	-	SYM
ejpam-3373	284	10	724	724	NUM
ejpam-3373	284	11	.	.	PUNCT
ejpam-3373	285	1	[	[	X
ejpam-3373	285	2	8	8	NUM
ejpam-3373	285	3	]	]	X
ejpam-3373	285	4	d.	d.	PROPN
ejpam-3373	285	5	kumar	kumar	PROPN
ejpam-3373	285	6	,	,	PUNCT
ejpam-3373	285	7	g.s	g.s	PROPN
ejpam-3373	285	8	.	.	PROPN
ejpam-3373	285	9	srivastava	srivastava	PROPN
ejpam-3373	285	10	,	,	PUNCT
ejpam-3373	285	11	and	and	CCONJ
ejpam-3373	285	12	h.s	h.s	PROPN
ejpam-3373	285	13	.	.	PROPN
ejpam-3373	285	14	kasana	kasana	PROPN
ejpam-3373	285	15	,	,	PUNCT
ejpam-3373	285	16	approximation	approximation	NOUN
ejpam-3373	285	17	of	of	ADP
ejpam-3373	285	18	entire	entire	ADJ
ejpam-3373	285	19	harmonic	harmonic	ADJ
ejpam-3373	285	20	functions	function	NOUN
ejpam-3373	285	21	in	in	ADP
ejpam-3373	285	22	r3	r3	PROPN
ejpam-3373	285	23	having	have	VERB
ejpam-3373	285	24	index	index	NOUN
ejpam-3373	285	25	-	-	PUNCT
ejpam-3373	285	26	pair	pair	NOUN
ejpam-3373	285	27	(	(	PUNCT
ejpam-3373	285	28	p	p	X
ejpam-3373	285	29	,	,	PUNCT
ejpam-3373	285	30	q	q	NOUN
ejpam-3373	285	31	)	)	PUNCT
ejpam-3373	285	32	,	,	PUNCT
ejpam-3373	285	33	anal	anal	NOUN
ejpam-3373	285	34	.	.	PUNCT
ejpam-3373	286	1	numer	numer	PROPN
ejpam-3373	286	2	.	.	PUNCT
ejpam-3373	287	1	theor	theor	PROPN
ejpam-3373	287	2	.	.	PUNCT
ejpam-3373	288	1	approx	approx	PROPN
ejpam-3373	288	2	.	.	PUNCT
ejpam-3373	289	1	20	20	NUM
ejpam-3373	289	2	,	,	PUNCT
ejpam-3373	289	3	no	no	INTJ
ejpam-3373	289	4	.	.	NOUN
ejpam-3373	289	5	1	1	NUM
ejpam-3373	289	6	-	-	SYM
ejpam-3373	289	7	2	2	NUM
ejpam-3373	289	8	(	(	PUNCT
ejpam-3373	289	9	1991	1991	NUM
ejpam-3373	289	10	)	)	PUNCT
ejpam-3373	289	11	,	,	PUNCT
ejpam-3373	289	12	47	47	NUM
ejpam-3373	289	13	-	-	SYM
ejpam-3373	289	14	57	57	NUM
ejpam-3373	289	15	.	.	PUNCT
ejpam-3373	290	1	[	[	X
ejpam-3373	290	2	9	9	NUM
ejpam-3373	290	3	]	]	X
ejpam-3373	290	4	d.	d.	PROPN
ejpam-3373	290	5	kumar	kumar	PROPN
ejpam-3373	290	6	,	,	PUNCT
ejpam-3373	290	7	and	and	CCONJ
ejpam-3373	290	8	h.s	h.s	PROPN
ejpam-3373	290	9	kasana	kasana	ADJ
ejpam-3373	290	10	,	,	PUNCT
ejpam-3373	290	11	approximation	approximation	NOUN
ejpam-3373	290	12	of	of	ADP
ejpam-3373	290	13	entire	entire	ADJ
ejpam-3373	290	14	harmonic	harmonic	ADJ
ejpam-3373	290	15	functions	function	NOUN
ejpam-3373	290	16	in	in	ADP
ejpam-3373	290	17	r3	r3	PROPN
ejpam-3373	290	18	in	in	ADP
ejpam-3373	290	19	lβ	lβ	PROPN
ejpam-3373	290	20	-	-	PUNCT
ejpam-3373	290	21	norm	norm	NOUN
ejpam-3373	290	22	,	,	PUNCT
ejpam-3373	290	23	fasciculi	fasciculi	ADJ
ejpam-3373	290	24	math	math	NOUN
ejpam-3373	290	25	.	.	PUNCT
ejpam-3373	291	1	34	34	NUM
ejpam-3373	291	2	(	(	PUNCT
ejpam-3373	291	3	2004	2004	NUM
ejpam-3373	291	4	)	)	PUNCT
ejpam-3373	291	5	,	,	PUNCT
ejpam-3373	291	6	55	55	NUM
ejpam-3373	291	7	-	-	SYM
ejpam-3373	291	8	64	64	NUM
ejpam-3373	291	9	.	.	PUNCT
ejpam-3373	292	1	[	[	X
ejpam-3373	292	2	10	10	NUM
ejpam-3373	292	3	]	]	X
ejpam-3373	292	4	d.	d.	PROPN
ejpam-3373	292	5	kumar	kumar	PROPN
ejpam-3373	292	6	,	,	PUNCT
ejpam-3373	292	7	growth	growth	NOUN
ejpam-3373	292	8	and	and	CCONJ
ejpam-3373	292	9	approximation	approximation	NOUN
ejpam-3373	292	10	of	of	ADP
ejpam-3373	292	11	entire	entire	ADJ
ejpam-3373	292	12	harmonic	harmonic	ADJ
ejpam-3373	292	13	functions	function	NOUN
ejpam-3373	292	14	in	in	ADP
ejpam-3373	292	15	rn	rn	PROPN
ejpam-3373	292	16	,	,	PUNCT
ejpam-3373	292	17	n	n	PROPN
ejpam-3373	292	18	>	>	X
ejpam-3373	292	19	3	3	NUM
ejpam-3373	292	20	,	,	PUNCT
ejpam-3373	292	21	georgion	georgion	NOUN
ejpam-3373	292	22	math	math	NOUN
ejpam-3373	292	23	.	.	PUNCT
ejpam-3373	293	1	j.	j.	PROPN
ejpam-3373	293	2	15	15	PROPN
ejpam-3373	293	3	,	,	PUNCT
ejpam-3373	293	4	no.1	no.1	X
ejpam-3373	293	5	(	(	PUNCT
ejpam-3373	293	6	2008	2008	NUM
ejpam-3373	293	7	)	)	PUNCT
ejpam-3373	293	8	,	,	PUNCT
ejpam-3373	293	9	1	1	NUM
ejpam-3373	293	10	-	-	SYM
ejpam-3373	293	11	12	12	NUM
ejpam-3373	293	12	.	.	PUNCT
ejpam-3373	294	1	[	[	X
ejpam-3373	294	2	11	11	NUM
ejpam-3373	294	3	]	]	X
ejpam-3373	294	4	d.	d.	PROPN
ejpam-3373	294	5	kumar	kumar	PROPN
ejpam-3373	294	6	,	,	PUNCT
ejpam-3373	294	7	and	and	CCONJ
ejpam-3373	294	8	h.s	h.s	PROPN
ejpam-3373	294	9	.	.	PROPN
ejpam-3373	294	10	kasana	kasana	PROPN
ejpam-3373	294	11	,	,	PUNCT
ejpam-3373	294	12	on	on	ADP
ejpam-3373	294	13	maximum	maximum	ADJ
ejpam-3373	294	14	term	term	NOUN
ejpam-3373	294	15	,	,	PUNCT
ejpam-3373	294	16	maximum	maximum	ADJ
ejpam-3373	294	17	modulus	modulus	NOUN
ejpam-3373	294	18	and	and	CCONJ
ejpam-3373	294	19	approximation	approximation	NOUN
ejpam-3373	294	20	error	error	NOUN
ejpam-3373	294	21	of	of	ADP
ejpam-3373	294	22	an	an	DET
ejpam-3373	294	23	entire	entire	ADJ
ejpam-3373	294	24	harmonic	harmonic	ADJ
ejpam-3373	294	25	function	function	NOUN
ejpam-3373	294	26	in	in	ADP
ejpam-3373	294	27	r3	r3	PROPN
ejpam-3373	294	28	,	,	PUNCT
ejpam-3373	294	29	rev	rev	PROPN
ejpam-3373	294	30	.	.	PROPN
ejpam-3373	294	31	mat	mat	PROPN
ejpam-3373	294	32	.	.	PROPN
ejpam-3373	294	33	univ	univ	PROPN
ejpam-3373	294	34	.	.	PUNCT
ejpam-3373	295	1	parma	parma	PROPN
ejpam-3373	295	2	6(1	6(1	NUM
ejpam-3373	295	3	)	)	PUNCT
ejpam-3373	295	4	(	(	PUNCT
ejpam-3373	295	5	1998	1998	NUM
ejpam-3373	295	6	)	)	PUNCT
ejpam-3373	295	7	,	,	PUNCT
ejpam-3373	295	8	215	215	NUM
ejpam-3373	295	9	-	-	SYM
ejpam-3373	295	10	223	223	NUM
ejpam-3373	295	11	.	.	PUNCT
ejpam-3373	296	1	[	[	X
ejpam-3373	296	2	12	12	NUM
ejpam-3373	296	3	]	]	PUNCT
ejpam-3373	296	4	h.h.khan	h.h.khan	NOUN
ejpam-3373	296	5	and	and	CCONJ
ejpam-3373	296	6	r.	r.	PROPN
ejpam-3373	296	7	ali	ali	PROPN
ejpam-3373	296	8	,	,	PUNCT
ejpam-3373	296	9	growth	growth	NOUN
ejpam-3373	296	10	and	and	CCONJ
ejpam-3373	296	11	approximation	approximation	NOUN
ejpam-3373	296	12	of	of	ADP
ejpam-3373	296	13	entire	entire	ADJ
ejpam-3373	296	14	series	series	NOUN
ejpam-3373	296	15	having	have	VERB
ejpam-3373	296	16	index	index	NOUN
ejpam-3373	296	17	-	-	PUNCT
ejpam-3373	296	18	pair	pair	NOUN
ejpam-3373	296	19	(	(	PUNCT
ejpam-3373	296	20	p	p	X
ejpam-3373	296	21	,	,	PUNCT
ejpam-3373	296	22	q	q	NOUN
ejpam-3373	296	23	)	)	PUNCT
ejpam-3373	296	24	,	,	PUNCT
ejpam-3373	296	25	fasciculi	fasciculi	PROPN
ejpam-3373	296	26	math	math	NOUN
ejpam-3373	296	27	.	.	PUNCT
ejpam-3373	297	1	49	49	NUM
ejpam-3373	297	2	(	(	PUNCT
ejpam-3373	297	3	2012	2012	NUM
ejpam-3373	297	4	)	)	PUNCT
ejpam-3373	297	5	,	,	PUNCT
ejpam-3373	297	6	61	61	NUM
ejpam-3373	297	7	-	-	SYM
ejpam-3373	297	8	73	73	NUM
ejpam-3373	297	9	.	.	PUNCT
ejpam-3373	298	1	[	[	X
ejpam-3373	298	2	13	13	NUM
ejpam-3373	298	3	]	]	X
ejpam-3373	298	4	g.s.srivastava	g.s.srivastava	NOUN
ejpam-3373	298	5	,	,	PUNCT
ejpam-3373	298	6	generalized	generalized	ADJ
ejpam-3373	298	7	growth	growth	NOUN
ejpam-3373	298	8	of	of	ADP
ejpam-3373	298	9	entire	entire	ADJ
ejpam-3373	298	10	harmonic	harmonic	ADJ
ejpam-3373	298	11	functions	function	NOUN
ejpam-3373	298	12	,	,	PUNCT
ejpam-3373	298	13	fasciculi	fasciculi	PROPN
ejpam-3373	298	14	math	math	NOUN
ejpam-3373	298	15	.	.	PUNCT
ejpam-3373	299	1	40	40	NUM
ejpam-3373	299	2	(	(	PUNCT
ejpam-3373	299	3	2008	2008	NUM
ejpam-3373	299	4	)	)	PUNCT
ejpam-3373	299	5	,	,	PUNCT
ejpam-3373	299	6	79	79	NUM
ejpam-3373	299	7	-	-	SYM
ejpam-3373	299	8	89	89	NUM
ejpam-3373	299	9	.	.	PUNCT
ejpam-3373	300	1	[	[	X
ejpam-3373	300	2	14	14	NUM
ejpam-3373	300	3	]	]	X
ejpam-3373	300	4	g.s	g.s	PROPN
ejpam-3373	300	5	srivastava	srivastava	PROPN
ejpam-3373	300	6	,	,	PUNCT
ejpam-3373	300	7	and	and	CCONJ
ejpam-3373	300	8	s.	s.	PROPN
ejpam-3373	300	9	kumar	kumar	PROPN
ejpam-3373	300	10	,	,	PUNCT
ejpam-3373	300	11	uniform	uniform	ADJ
ejpam-3373	300	12	approximation	approximation	NOUN
ejpam-3373	300	13	of	of	ADP
ejpam-3373	300	14	entire	entire	ADJ
ejpam-3373	300	15	functions	function	NOUN
ejpam-3373	300	16	on	on	ADP
ejpam-3373	300	17	compact	compact	ADJ
ejpam-3373	300	18	sets	set	NOUN
ejpam-3373	300	19	and	and	CCONJ
ejpam-3373	300	20	their	their	PRON
ejpam-3373	300	21	generalized	generalized	ADJ
ejpam-3373	300	22	growth	growth	NOUN
ejpam-3373	300	23	,	,	PUNCT
ejpam-3373	300	24	new	new	PROPN
ejpam-3373	300	25	zealand	zealand	PROPN
ejpam-3373	300	26	j.	j.	PROPN
ejpam-3373	300	27	math	math	PROPN
ejpam-3373	300	28	.	.	PUNCT
ejpam-3373	301	1	39	39	NUM
ejpam-3373	301	2	(	(	PUNCT
ejpam-3373	301	3	2009	2009	NUM
ejpam-3373	301	4	)	)	PUNCT
ejpam-3373	301	5	,	,	PUNCT
ejpam-3373	301	6	33	33	NUM
ejpam-3373	301	7	-	-	SYM
ejpam-3373	301	8	43	43	NUM
ejpam-3373	301	9	.	.	PUNCT
ejpam-3373	302	1	[	[	X
ejpam-3373	302	2	15	15	NUM
ejpam-3373	302	3	]	]	X
ejpam-3373	302	4	g.s	g.s	PROPN
ejpam-3373	302	5	srivastava	srivastava	PROPN
ejpam-3373	302	6	and	and	CCONJ
ejpam-3373	302	7	s.	s.	PROPN
ejpam-3373	302	8	kumar	kumar	PROPN
ejpam-3373	302	9	,	,	PUNCT
ejpam-3373	302	10	approximation	approximation	NOUN
ejpam-3373	302	11	of	of	ADP
ejpam-3373	302	12	entire	entire	ADJ
ejpam-3373	302	13	functions	function	NOUN
ejpam-3373	302	14	of	of	ADP
ejpam-3373	302	15	slow	slow	ADJ
ejpam-3373	302	16	growth	growth	NOUN
ejpam-3373	302	17	on	on	ADP
ejpam-3373	302	18	compact	compact	ADJ
ejpam-3373	302	19	sets	set	NOUN
ejpam-3373	302	20	,	,	PUNCT
ejpam-3373	302	21	archivum	archivum	PROPN
ejpam-3373	302	22	math	math	NOUN
ejpam-3373	302	23	.	.	PUNCT
ejpam-3373	303	1	(	(	PUNCT
ejpam-3373	303	2	brno	brno	NOUN
ejpam-3373	303	3	)	)	PUNCT
ejpam-3373	303	4	45	45	NUM
ejpam-3373	303	5	(	(	PUNCT
ejpam-3373	303	6	2009),137	2009),137	NUM
ejpam-3373	303	7	-	-	SYM
ejpam-3373	303	8	146	146	NUM
ejpam-3373	303	9	.	.	PUNCT
ejpam-3373	304	1	references	reference	NOUN
ejpam-3373	304	2	498	498	NUM
ejpam-3373	305	1	[	[	X
ejpam-3373	305	2	16	16	NUM
ejpam-3373	305	3	]	]	PUNCT
ejpam-3373	305	4	a.	a.	NOUN
ejpam-3373	305	5	tyman	tyman	NOUN
ejpam-3373	305	6	,	,	PUNCT
ejpam-3373	305	7	and	and	CCONJ
ejpam-3373	305	8	v.n	v.n	PROPN
ejpam-3373	305	9	.	.	PROPN
ejpam-3373	305	10	trofymov	trofymov	PROPN
ejpam-3373	305	11	,	,	PUNCT
ejpam-3373	305	12	vvedenye	vvedenye	PROPN
ejpam-3373	305	13	v	v	ADP
ejpam-3373	305	14	teoryiu	teoryiu	NOUN
ejpam-3373	305	15	harmony	harmony	NOUN
ejpam-3373	305	16	ches	che	NOUN
ejpam-3373	305	17	kykh	kykh	PROPN
ejpam-3373	305	18	funktsii	funktsii	PROPN
ejpam-3373	305	19	,	,	PUNCT
ejpam-3373	305	20	moscow	moscow	PROPN
ejpam-3373	305	21	,	,	PUNCT
ejpam-3373	305	22	nauka	nauka	PROPN
ejpam-3373	305	23	,	,	PUNCT
ejpam-3373	305	24	(	(	PUNCT
ejpam-3373	305	25	1968	1968	NUM
ejpam-3373	305	26	)	)	PUNCT
ejpam-3373	305	27	,	,	PUNCT
ejpam-3373	305	28	208	208	NUM
ejpam-3373	305	29	.	.	PUNCT
ejpam-3373	306	1	[	[	X
ejpam-3373	306	2	17	17	NUM
ejpam-3373	306	3	]	]	X
ejpam-3373	306	4	o.	o.	PROPN
ejpam-3373	306	5	veselovska	veselovska	PROPN
ejpam-3373	306	6	,	,	PUNCT
ejpam-3373	306	7	k.	k.	PROPN
ejpam-3373	306	8	drohomyretska	drohomyretska	PROPN
ejpam-3373	306	9	and	and	CCONJ
ejpam-3373	306	10	l.	l.	PROPN
ejpam-3373	306	11	kolyasa	kolyasa	PROPN
ejpam-3373	306	12	,	,	PUNCT
ejpam-3373	306	13	criterian	criterian	ADJ
ejpam-3373	306	14	of	of	ADP
ejpam-3373	306	15	the	the	DET
ejpam-3373	306	16	continuation	continuation	NOUN
ejpam-3373	306	17	of	of	ADP
ejpam-3373	306	18	harmonic	harmonic	ADJ
ejpam-3373	306	19	functions	function	NOUN
ejpam-3373	306	20	in	in	ADP
ejpam-3373	306	21	the	the	DET
ejpam-3373	306	22	ball	ball	NOUN
ejpam-3373	306	23	of	of	ADP
ejpam-3373	306	24	n	n	CCONJ
ejpam-3373	306	25	-	-	PUNCT
ejpam-3373	306	26	dimensional	dimensional	ADJ
ejpam-3373	306	27	space	space	NOUN
ejpam-3373	306	28	and	and	CCONJ
ejpam-3373	306	29	representation	representation	NOUN
ejpam-3373	306	30	of	of	ADP
ejpam-3373	306	31	the	the	DET
ejpam-3373	306	32	generalized	generalize	VERB
ejpam-3373	306	33	orders	order	NOUN
ejpam-3373	306	34	of	of	ADP
ejpam-3373	306	35	the	the	DET
ejpam-3373	306	36	entire	entire	ADJ
ejpam-3373	306	37	harmonic	harmonic	ADJ
ejpam-3373	306	38	functions	function	NOUN
ejpam-3373	306	39	in	in	ADP
ejpam-3373	306	40	rn	rn	PROPN
ejpam-3373	306	41	in	in	ADP
ejpam-3373	306	42	terms	term	NOUN
ejpam-3373	306	43	of	of	ADP
ejpam-3373	306	44	approximation	approximation	NOUN
ejpam-3373	306	45	error	error	NOUN
ejpam-3373	306	46	,	,	PUNCT
ejpam-3373	306	47	mathematics	mathematic	NOUN
ejpam-3373	306	48	and	and	CCONJ
ejpam-3373	306	49	cybernetics	cybernetic	NOUN
ejpam-3373	306	50	-	-	PUNCT
ejpam-3373	306	51	applied	apply	VERB
ejpam-3373	306	52	aspects	aspect	NOUN
ejpam-3373	306	53	,	,	PUNCT
ejpam-3373	306	54	estern	estern	ADJ
ejpam-3373	306	55	european	european	PROPN
ejpam-3373	306	56	j.	j.	PROPN
ejpam-3373	306	57	enterprise	enterprise	PROPN
ejpam-3373	306	58	technologies	technology	NOUN
ejpam-3373	306	59	(	(	PUNCT
ejpam-3373	306	60	2017),43	2017),43	NUM
ejpam-3373	306	61	-	-	SYM
ejpam-3373	306	62	49	49	NUM
ejpam-3373	306	63	.	.	PUNCT