id	sid	tid	token	lemma	pos
ejpam-3636	1	1	european	european	PROPN
ejpam-3636	1	2	journal	journal	PROPN
ejpam-3636	1	3	of	of	ADP
ejpam-3636	1	4	pure	pure	ADJ
ejpam-3636	1	5	and	and	CCONJ
ejpam-3636	1	6	applied	apply	VERB
ejpam-3636	1	7	mathematics	mathematic	NOUN
ejpam-3636	1	8	vol	vol	NOUN
ejpam-3636	1	9	.	.	PROPN
ejpam-3636	2	1	13	13	NUM
ejpam-3636	2	2	,	,	PUNCT
ejpam-3636	2	3	no	no	INTJ
ejpam-3636	2	4	.	.	NOUN
ejpam-3636	2	5	2	2	NUM
ejpam-3636	2	6	,	,	PUNCT
ejpam-3636	2	7	2020	2020	NUM
ejpam-3636	2	8	,	,	PUNCT
ejpam-3636	2	9	258	258	NUM
ejpam-3636	2	10	-	-	SYM
ejpam-3636	2	11	268	268	NUM
ejpam-3636	2	12	issn	issn	PROPN
ejpam-3636	2	13	1307	1307	NUM
ejpam-3636	2	14	-	-	SYM
ejpam-3636	2	15	5543	5543	NUM
ejpam-3636	2	16	–	–	PUNCT
ejpam-3636	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3636	2	18	published	publish	VERB
ejpam-3636	2	19	by	by	ADP
ejpam-3636	2	20	new	new	PROPN
ejpam-3636	2	21	york	york	PROPN
ejpam-3636	2	22	business	business	PROPN
ejpam-3636	2	23	global	global	ADJ
ejpam-3636	2	24	coefficients	coefficient	NOUN
ejpam-3636	2	25	characterization	characterization	NOUN
ejpam-3636	2	26	of	of	ADP
ejpam-3636	2	27	entire	entire	ADJ
ejpam-3636	2	28	harmonic	harmonic	ADJ
ejpam-3636	2	29	functions	function	NOUN
ejpam-3636	2	30	in	in	ADP
ejpam-3636	2	31	terms	term	NOUN
ejpam-3636	2	32	of	of	ADP
ejpam-3636	2	33	norm	norm	NOUN
ejpam-3636	2	34	of	of	ADP
ejpam-3636	2	35	gradients	gradient	NOUN
ejpam-3636	2	36	at	at	ADP
ejpam-3636	2	37	origin	origin	NOUN
ejpam-3636	2	38	in	in	ADP
ejpam-3636	2	39	rn	rn	PROPN
ejpam-3636	2	40	,	,	PUNCT
ejpam-3636	2	41	n	n	PRON
ejpam-3636	2	42	≥	≥	NOUN
ejpam-3636	2	43	3	3	NUM
ejpam-3636	2	44	devendra	devendra	PROPN
ejpam-3636	2	45	kumar1,2	kumar1,2	PROPN
ejpam-3636	2	46	,	,	PUNCT
ejpam-3636	2	47	rajeev	rajeev	PROPN
ejpam-3636	2	48	kumar	kumar	PROPN
ejpam-3636	2	49	vishnoi3,∗	vishnoi3,∗	VERB
ejpam-3636	2	50	1	1	NUM
ejpam-3636	2	51	department	department	NOUN
ejpam-3636	2	52	of	of	ADP
ejpam-3636	2	53	mathematics	mathematic	NOUN
ejpam-3636	2	54	,	,	PUNCT
ejpam-3636	2	55	faculty	faculty	NOUN
ejpam-3636	2	56	of	of	ADP
ejpam-3636	2	57	sciences	sciences	PROPN
ejpam-3636	2	58	al	al	PROPN
ejpam-3636	2	59	-	-	PUNCT
ejpam-3636	2	60	baha	baha	PROPN
ejpam-3636	2	61	university	university	PROPN
ejpam-3636	2	62	,	,	PUNCT
ejpam-3636	2	63	p.o.box-1988	p.o.box-1988	PROPN
ejpam-3636	2	64	,	,	PUNCT
ejpam-3636	2	65	alaqiq	alaqiq	PROPN
ejpam-3636	2	66	,	,	PUNCT
ejpam-3636	2	67	al	al	PROPN
ejpam-3636	2	68	-	-	PUNCT
ejpam-3636	2	69	baha-65431	baha-65431	NOUN
ejpam-3636	2	70	,	,	PUNCT
ejpam-3636	2	71	saudi	saudi	PROPN
ejpam-3636	2	72	arabia	arabia	PROPN
ejpam-3636	2	73	,	,	PUNCT
ejpam-3636	2	74	k.s.a	k.s.a	NOUN
ejpam-3636	2	75	.	.	NOUN
ejpam-3636	2	76	2	2	NUM
ejpam-3636	2	77	research	research	NOUN
ejpam-3636	2	78	and	and	CCONJ
ejpam-3636	2	79	post	post	VERB
ejpam-3636	2	80	graduate	graduate	ADJ
ejpam-3636	2	81	studies	study	NOUN
ejpam-3636	2	82	,	,	PUNCT
ejpam-3636	2	83	department	department	NOUN
ejpam-3636	2	84	of	of	ADP
ejpam-3636	2	85	mathematics	mathematic	NOUN
ejpam-3636	2	86	,	,	PUNCT
ejpam-3636	2	87	m.	m.	NOUN
ejpam-3636	2	88	m.	m.	PROPN
ejpam-3636	2	89	h.	h.	PROPN
ejpam-3636	2	90	college	college	PROPN
ejpam-3636	2	91	,	,	PUNCT
ejpam-3636	2	92	model	model	NOUN
ejpam-3636	2	93	town	town	NOUN
ejpam-3636	2	94	,	,	PUNCT
ejpam-3636	2	95	ghaziabad-201001	ghaziabad-201001	NOUN
ejpam-3636	2	96	,	,	PUNCT
ejpam-3636	2	97	u.p	u.p	PROPN
ejpam-3636	2	98	.	.	PROPN
ejpam-3636	2	99	,	,	PUNCT
ejpam-3636	2	100	india	india	PROPN
ejpam-3636	2	101	3	3	PROPN
ejpam-3636	2	102	department	department	PROPN
ejpam-3636	2	103	of	of	ADP
ejpam-3636	2	104	mathematics	mathematics	PROPN
ejpam-3636	2	105	,	,	PUNCT
ejpam-3636	2	106	vardhaman	vardhaman	NOUN
ejpam-3636	2	107	college	college	NOUN
ejpam-3636	2	108	bijnor-246701	bijnor-246701	NOUN
ejpam-3636	2	109	,	,	PUNCT
ejpam-3636	2	110	u.p	u.p	PROPN
ejpam-3636	2	111	.	.	PROPN
ejpam-3636	2	112	,	,	PUNCT
ejpam-3636	2	113	india	india	PROPN
ejpam-3636	2	114	abstract	abstract	PROPN
ejpam-3636	2	115	.	.	PUNCT
ejpam-3636	3	1	coefficient	coefficient	NOUN
ejpam-3636	3	2	characterizations	characterization	NOUN
ejpam-3636	3	3	of	of	ADP
ejpam-3636	3	4	generalized	generalized	ADJ
ejpam-3636	3	5	order	order	NOUN
ejpam-3636	3	6	,	,	PUNCT
ejpam-3636	3	7	lower	low	ADJ
ejpam-3636	3	8	order	order	NOUN
ejpam-3636	3	9	and	and	CCONJ
ejpam-3636	3	10	generalized	generalized	ADJ
ejpam-3636	3	11	type	type	NOUN
ejpam-3636	3	12	of	of	ADP
ejpam-3636	3	13	entire	entire	ADJ
ejpam-3636	3	14	harmonic	harmonic	ADJ
ejpam-3636	3	15	function	function	NOUN
ejpam-3636	3	16	having	have	VERB
ejpam-3636	3	17	the	the	DET
ejpam-3636	3	18	spherical	spherical	ADJ
ejpam-3636	3	19	harmonic	harmonic	ADJ
ejpam-3636	3	20	expansion	expansion	NOUN
ejpam-3636	3	21	throughout	throughout	ADP
ejpam-3636	3	22	a	a	DET
ejpam-3636	3	23	neighborhood	neighborhood	NOUN
ejpam-3636	3	24	of	of	ADP
ejpam-3636	3	25	the	the	DET
ejpam-3636	3	26	origin	origin	NOUN
ejpam-3636	3	27	in	in	ADP
ejpam-3636	3	28	rn	rn	PROPN
ejpam-3636	3	29	have	have	AUX
ejpam-3636	3	30	been	be	AUX
ejpam-3636	3	31	obtained	obtain	VERB
ejpam-3636	3	32	in	in	ADP
ejpam-3636	3	33	terms	term	NOUN
ejpam-3636	3	34	of	of	ADP
ejpam-3636	3	35	norm	norm	NOUN
ejpam-3636	3	36	of	of	ADP
ejpam-3636	3	37	gradients	gradient	NOUN
ejpam-3636	3	38	at	at	ADP
ejpam-3636	3	39	origin	origin	NOUN
ejpam-3636	3	40	.	.	PUNCT
ejpam-3636	4	1	2020	2020	NUM
ejpam-3636	4	2	mathematics	mathematic	NOUN
ejpam-3636	4	3	subject	subject	NOUN
ejpam-3636	4	4	classifications	classification	NOUN
ejpam-3636	4	5	:	:	PUNCT
ejpam-3636	4	6	31b05	31b05	NUM
ejpam-3636	4	7	,	,	PUNCT
ejpam-3636	4	8	42a16	42a16	PRON
ejpam-3636	4	9	key	key	ADJ
ejpam-3636	4	10	words	word	NOUN
ejpam-3636	4	11	and	and	CCONJ
ejpam-3636	4	12	phrases	phrase	NOUN
ejpam-3636	4	13	:	:	PUNCT
ejpam-3636	4	14	norm	norm	NOUN
ejpam-3636	4	15	of	of	ADP
ejpam-3636	4	16	gradient	gradient	NOUN
ejpam-3636	4	17	,	,	PUNCT
ejpam-3636	4	18	entire	entire	ADJ
ejpam-3636	4	19	harmonic	harmonic	ADJ
ejpam-3636	4	20	functions	function	NOUN
ejpam-3636	4	21	,	,	PUNCT
ejpam-3636	4	22	generalized	generalized	ADJ
ejpam-3636	4	23	orders	order	NOUN
ejpam-3636	4	24	,	,	PUNCT
ejpam-3636	4	25	generalized	generalized	ADJ
ejpam-3636	4	26	type	type	NOUN
ejpam-3636	4	27	and	and	CCONJ
ejpam-3636	4	28	growth	growth	NOUN
ejpam-3636	4	29	of	of	ADP
ejpam-3636	4	30	zero	zero	NUM
ejpam-3636	4	31	orders	order	NOUN
ejpam-3636	4	32	.	.	PUNCT
ejpam-3636	5	1	1	1	X
ejpam-3636	5	2	.	.	X
ejpam-3636	5	3	introduction	introduction	NOUN
ejpam-3636	5	4	in	in	ADP
ejpam-3636	5	5	the	the	DET
ejpam-3636	5	6	study	study	NOUN
ejpam-3636	5	7	of	of	ADP
ejpam-3636	5	8	entire	entire	ADJ
ejpam-3636	5	9	functions	function	NOUN
ejpam-3636	5	10	of	of	ADP
ejpam-3636	5	11	one	one	NUM
ejpam-3636	5	12	complex	complex	ADJ
ejpam-3636	5	13	variable	variable	NOUN
ejpam-3636	5	14	,	,	PUNCT
ejpam-3636	5	15	the	the	DET
ejpam-3636	5	16	main	main	ADJ
ejpam-3636	5	17	issues	issue	NOUN
ejpam-3636	5	18	are	be	AUX
ejpam-3636	5	19	the	the	DET
ejpam-3636	5	20	relationship	relationship	NOUN
ejpam-3636	5	21	between	between	ADP
ejpam-3636	5	22	the	the	DET
ejpam-3636	5	23	growth	growth	NOUN
ejpam-3636	5	24	of	of	ADP
ejpam-3636	5	25	such	such	ADJ
ejpam-3636	5	26	functions	function	NOUN
ejpam-3636	5	27	and	and	CCONJ
ejpam-3636	5	28	behavior	behavior	NOUN
ejpam-3636	5	29	of	of	ADP
ejpam-3636	5	30	taylor	taylor	PROPN
ejpam-3636	5	31	coefficients	coefficient	NOUN
ejpam-3636	5	32	.	.	PUNCT
ejpam-3636	6	1	several	several	ADJ
ejpam-3636	6	2	authors	author	NOUN
ejpam-3636	6	3	such	such	ADJ
ejpam-3636	6	4	as	as	ADP
ejpam-3636	6	5	srivastava	srivastava	PROPN
ejpam-3636	6	6	and	and	CCONJ
ejpam-3636	6	7	kumar	kumar	PROPN
ejpam-3636	6	8	[	[	X
ejpam-3636	6	9	20	20	NUM
ejpam-3636	6	10	]	]	PUNCT
ejpam-3636	6	11	,	,	PUNCT
ejpam-3636	6	12	kumar	kumar	PROPN
ejpam-3636	7	1	[	[	X
ejpam-3636	7	2	11,14	11,14	NUM
ejpam-3636	7	3	]	]	PUNCT
ejpam-3636	7	4	,	,	PUNCT
ejpam-3636	7	5	harfaoui	harfaoui	ADJ
ejpam-3636	8	1	[	[	X
ejpam-3636	8	2	8	8	NUM
ejpam-3636	8	3	]	]	PUNCT
ejpam-3636	8	4	and	and	CCONJ
ejpam-3636	8	5	others	other	NOUN
ejpam-3636	8	6	investigated	investigate	VERB
ejpam-3636	8	7	growth	growth	NOUN
ejpam-3636	8	8	parameters	parameter	NOUN
ejpam-3636	8	9	of	of	ADP
ejpam-3636	8	10	entire	entire	ADJ
ejpam-3636	8	11	functions	function	NOUN
ejpam-3636	8	12	in	in	ADP
ejpam-3636	8	13	terms	term	NOUN
ejpam-3636	8	14	of	of	ADP
ejpam-3636	8	15	taylor	taylor	PROPN
ejpam-3636	8	16	’s	’s	PART
ejpam-3636	8	17	series	series	PROPN
ejpam-3636	8	18	coefficients	coefficient	NOUN
ejpam-3636	8	19	and	and	CCONJ
ejpam-3636	8	20	polynomial	polynomial	ADJ
ejpam-3636	8	21	approximation	approximation	NOUN
ejpam-3636	8	22	errors	error	NOUN
ejpam-3636	8	23	in	in	ADP
ejpam-3636	8	24	different	different	ADJ
ejpam-3636	8	25	norms	norm	NOUN
ejpam-3636	8	26	.	.	PUNCT
ejpam-3636	9	1	similar	similar	ADJ
ejpam-3636	9	2	studies	study	NOUN
ejpam-3636	9	3	have	have	AUX
ejpam-3636	9	4	been	be	AUX
ejpam-3636	9	5	done	do	VERB
ejpam-3636	9	6	for	for	ADP
ejpam-3636	9	7	harmonic	harmonic	ADJ
ejpam-3636	9	8	functions	function	NOUN
ejpam-3636	9	9	by	by	ADP
ejpam-3636	9	10	kumar	kumar	PROPN
ejpam-3636	9	11	[	[	X
ejpam-3636	9	12	12,13	12,13	NUM
ejpam-3636	9	13	]	]	PUNCT
ejpam-3636	9	14	,	,	PUNCT
ejpam-3636	9	15	kumar	kumar	PROPN
ejpam-3636	9	16	and	and	CCONJ
ejpam-3636	9	17	kasana	kasana	PROPN
ejpam-3636	10	1	[	[	X
ejpam-3636	10	2	15	15	NUM
ejpam-3636	10	3	]	]	PUNCT
ejpam-3636	10	4	and	and	CCONJ
ejpam-3636	10	5	armitage	armitage	VERB
ejpam-3636	11	1	[	[	X
ejpam-3636	11	2	1	1	NUM
ejpam-3636	11	3	]	]	PUNCT
ejpam-3636	11	4	as	as	SCONJ
ejpam-3636	11	5	they	they	PRON
ejpam-3636	11	6	have	have	VERB
ejpam-3636	11	7	series	series	NOUN
ejpam-3636	11	8	expansion	expansion	NOUN
ejpam-3636	11	9	in	in	ADP
ejpam-3636	11	10	terms	term	NOUN
ejpam-3636	11	11	of	of	ADP
ejpam-3636	11	12	spherical	spherical	ADJ
ejpam-3636	11	13	harmonics	harmonic	NOUN
ejpam-3636	11	14	in	in	ADP
ejpam-3636	11	15	rn	rn	PROPN
ejpam-3636	11	16	.	.	PUNCT
ejpam-3636	12	1	some	some	DET
ejpam-3636	12	2	times	time	NOUN
ejpam-3636	12	3	it	it	PRON
ejpam-3636	12	4	is	be	AUX
ejpam-3636	12	5	useful	useful	ADJ
ejpam-3636	12	6	to	to	PART
ejpam-3636	12	7	study	study	VERB
ejpam-3636	12	8	the	the	DET
ejpam-3636	12	9	growth	growth	NOUN
ejpam-3636	12	10	of	of	ADP
ejpam-3636	12	11	harmonic	harmonic	ADJ
ejpam-3636	12	12	functions	function	NOUN
ejpam-3636	12	13	in	in	ADP
ejpam-3636	12	14	terms	term	NOUN
ejpam-3636	12	15	of	of	ADP
ejpam-3636	12	16	norm	norm	NOUN
ejpam-3636	12	17	of	of	ADP
ejpam-3636	12	18	their	their	PRON
ejpam-3636	12	19	gradient	gradient	NOUN
ejpam-3636	12	20	at	at	ADP
ejpam-3636	12	21	the	the	DET
ejpam-3636	12	22	origin	origin	NOUN
ejpam-3636	12	23	in	in	ADP
ejpam-3636	12	24	n	n	CCONJ
ejpam-3636	12	25	-	-	PUNCT
ejpam-3636	12	26	dimensional	dimensional	ADJ
ejpam-3636	12	27	space	space	NOUN
ejpam-3636	12	28	.	.	PUNCT
ejpam-3636	13	1	such	such	ADJ
ejpam-3636	13	2	results	result	NOUN
ejpam-3636	13	3	are	be	AUX
ejpam-3636	13	4	equivalent	equivalent	ADJ
ejpam-3636	13	5	to	to	ADP
ejpam-3636	13	6	characterization	characterization	NOUN
ejpam-3636	13	7	in	in	ADP
ejpam-3636	13	8	terms	term	NOUN
ejpam-3636	13	9	of	of	ADP
ejpam-3636	13	10	spherical	spherical	ADJ
ejpam-3636	13	11	harmonic	harmonic	ADJ
ejpam-3636	13	12	coefficients	coefficient	NOUN
ejpam-3636	13	13	.	.	PUNCT
ejpam-3636	14	1	results	result	NOUN
ejpam-3636	14	2	of	of	ADP
ejpam-3636	14	3	one	one	NUM
ejpam-3636	14	4	kind	kind	NOUN
ejpam-3636	14	5	can	can	AUX
ejpam-3636	14	6	not	not	PART
ejpam-3636	14	7	obtained	obtain	VERB
ejpam-3636	14	8	directly	directly	ADV
ejpam-3636	14	9	from	from	ADP
ejpam-3636	14	10	the	the	DET
ejpam-3636	14	11	other	other	ADJ
ejpam-3636	14	12	,	,	PUNCT
ejpam-3636	14	13	and	and	CCONJ
ejpam-3636	14	14	thus	thus	ADV
ejpam-3636	14	15	require	require	VERB
ejpam-3636	14	16	separate	separate	ADJ
ejpam-3636	14	17	study	study	NOUN
ejpam-3636	14	18	.	.	PUNCT
ejpam-3636	15	1	also	also	ADV
ejpam-3636	15	2	,	,	PUNCT
ejpam-3636	15	3	the	the	DET
ejpam-3636	15	4	problem	problem	NOUN
ejpam-3636	15	5	to	to	PART
ejpam-3636	15	6	investigate	investigate	VERB
ejpam-3636	15	7	the	the	DET
ejpam-3636	15	8	growth	growth	NOUN
ejpam-3636	15	9	characteristics	characteristic	NOUN
ejpam-3636	15	10	of	of	ADP
ejpam-3636	15	11	harmonic	harmonic	ADJ
ejpam-3636	15	12	functions	function	NOUN
ejpam-3636	15	13	in	in	ADP
ejpam-3636	15	14	terms	term	NOUN
ejpam-3636	15	15	that	that	PRON
ejpam-3636	15	16	are	be	AUX
ejpam-3636	15	17	not	not	PART
ejpam-3636	15	18	related	relate	VERB
ejpam-3636	15	19	to	to	ADP
ejpam-3636	15	20	series	series	NOUN
ejpam-3636	15	21	expansion	expansion	NOUN
ejpam-3636	15	22	coefficients	coefficient	NOUN
ejpam-3636	15	23	.	.	PUNCT
ejpam-3636	16	1	the	the	DET
ejpam-3636	16	2	∗corresponding	∗corresponde	VERB
ejpam-3636	16	3	author	author	NOUN
ejpam-3636	16	4	.	.	PUNCT
ejpam-3636	17	1	doi	doi	NOUN
ejpam-3636	17	2	:	:	PUNCT
ejpam-3636	17	3	https://doi.org/10.29020/nybg.ejpam.v13i2.3636	https://doi.org/10.29020/nybg.ejpam.v13i2.3636	PRON
ejpam-3636	17	4	email	email	NOUN
ejpam-3636	17	5	addresses	address	NOUN
ejpam-3636	17	6	:	:	PUNCT
ejpam-3636	17	7	d	d	X
ejpam-3636	17	8	kumar001@rediffmail.com	kumar001@rediffmail.com	X
ejpam-3636	17	9	(	(	PUNCT
ejpam-3636	17	10	devendra	devendra	PROPN
ejpam-3636	17	11	kumar	kumar	PROPN
ejpam-3636	17	12	)	)	PUNCT
ejpam-3636	17	13	,	,	PUNCT
ejpam-3636	17	14	rajeevvishnoi100@gmail.com	rajeevvishnoi100@gmail.com	X
ejpam-3636	17	15	(	(	PUNCT
ejpam-3636	17	16	rajeev	rajeev	PROPN
ejpam-3636	17	17	kumar	kumar	PROPN
ejpam-3636	17	18	vishnoi	vishnoi	PROPN
ejpam-3636	17	19	)	)	PUNCT
ejpam-3636	17	20	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3636	18	1	258	258	NUM
ejpam-3636	18	2	c	c	X
ejpam-3636	18	3	©	©	NOUN
ejpam-3636	18	4	2020	2020	NUM
ejpam-3636	18	5	ejpam	ejpam	VERB
ejpam-3636	18	6	all	all	DET
ejpam-3636	18	7	rights	right	NOUN
ejpam-3636	18	8	reserved	reserve	VERB
ejpam-3636	18	9	.	.	PUNCT
ejpam-3636	19	1	d.	d.	PROPN
ejpam-3636	19	2	kumar	kumar	PROPN
ejpam-3636	19	3	,	,	PUNCT
ejpam-3636	19	4	r.k	r.k	PROPN
ejpam-3636	19	5	.	.	PROPN
ejpam-3636	19	6	vishnoi	vishnoi	PROPN
ejpam-3636	19	7	/	/	SYM
ejpam-3636	19	8	eur	eur	PROPN
ejpam-3636	19	9	.	.	PUNCT
ejpam-3636	20	1	j.	j.	PROPN
ejpam-3636	20	2	pure	pure	PROPN
ejpam-3636	20	3	appl	appl	PROPN
ejpam-3636	20	4	.	.	PROPN
ejpam-3636	20	5	math	math	PROPN
ejpam-3636	20	6	,	,	PUNCT
ejpam-3636	20	7	13	13	NUM
ejpam-3636	20	8	(	(	PUNCT
ejpam-3636	20	9	2	2	NUM
ejpam-3636	20	10	)	)	PUNCT
ejpam-3636	20	11	(	(	PUNCT
ejpam-3636	20	12	2020	2020	NUM
ejpam-3636	20	13	)	)	PUNCT
ejpam-3636	20	14	,	,	PUNCT
ejpam-3636	20	15	258	258	NUM
ejpam-3636	20	16	-	-	SYM
ejpam-3636	20	17	268	268	NUM
ejpam-3636	20	18	259	259	NUM
ejpam-3636	20	19	derivatives	derivative	NOUN
ejpam-3636	20	20	of	of	ADP
ejpam-3636	20	21	a	a	DET
ejpam-3636	20	22	harmonic	harmonic	ADJ
ejpam-3636	20	23	functions	function	NOUN
ejpam-3636	20	24	at	at	ADP
ejpam-3636	20	25	the	the	DET
ejpam-3636	20	26	origin	origin	NOUN
ejpam-3636	20	27	are	be	AUX
ejpam-3636	20	28	equal	equal	ADJ
ejpam-3636	20	29	to	to	ADP
ejpam-3636	20	30	complicated	complicated	ADJ
ejpam-3636	20	31	linear	linear	ADJ
ejpam-3636	20	32	combinations	combination	NOUN
ejpam-3636	20	33	of	of	ADP
ejpam-3636	20	34	the	the	DET
ejpam-3636	20	35	spherical	spherical	ADJ
ejpam-3636	20	36	harmonic	harmonic	ADJ
ejpam-3636	20	37	coefficients	coefficient	NOUN
ejpam-3636	20	38	.	.	PUNCT
ejpam-3636	21	1	the	the	DET
ejpam-3636	21	2	relevance	relevance	NOUN
ejpam-3636	21	3	of	of	ADP
ejpam-3636	21	4	this	this	DET
ejpam-3636	21	5	study	study	NOUN
ejpam-3636	21	6	is	be	AUX
ejpam-3636	21	7	due	due	ADJ
ejpam-3636	21	8	to	to	ADP
ejpam-3636	21	9	the	the	DET
ejpam-3636	21	10	fact	fact	NOUN
ejpam-3636	21	11	that	that	SCONJ
ejpam-3636	21	12	the	the	DET
ejpam-3636	21	13	harmonic	harmonic	ADJ
ejpam-3636	21	14	functions	function	NOUN
ejpam-3636	21	15	play	play	VERB
ejpam-3636	21	16	very	very	ADV
ejpam-3636	21	17	important	important	ADJ
ejpam-3636	21	18	role	role	NOUN
ejpam-3636	21	19	in	in	ADP
ejpam-3636	21	20	theoretical	theoretical	ADJ
ejpam-3636	21	21	mathematical	mathematical	ADJ
ejpam-3636	21	22	research	research	NOUN
ejpam-3636	21	23	,	,	PUNCT
ejpam-3636	21	24	physics	physics	NOUN
ejpam-3636	21	25	and	and	CCONJ
ejpam-3636	21	26	mechanics	mechanic	NOUN
ejpam-3636	21	27	to	to	PART
ejpam-3636	21	28	express	express	VERB
ejpam-3636	21	29	stationary	stationary	ADJ
ejpam-3636	21	30	processes	process	NOUN
ejpam-3636	21	31	.	.	PUNCT
ejpam-3636	22	1	therefore	therefore	ADV
ejpam-3636	22	2	,	,	PUNCT
ejpam-3636	22	3	the	the	DET
ejpam-3636	22	4	aim	aim	NOUN
ejpam-3636	22	5	of	of	ADP
ejpam-3636	22	6	this	this	DET
ejpam-3636	22	7	paper	paper	NOUN
ejpam-3636	22	8	is	be	AUX
ejpam-3636	22	9	to	to	PART
ejpam-3636	22	10	characterize	characterize	VERB
ejpam-3636	22	11	the	the	DET
ejpam-3636	22	12	generalized	generalized	ADJ
ejpam-3636	22	13	growth	growth	NOUN
ejpam-3636	22	14	parameters	parameter	NOUN
ejpam-3636	22	15	(	(	PUNCT
ejpam-3636	22	16	generalized	generalized	ADJ
ejpam-3636	22	17	order	order	NOUN
ejpam-3636	22	18	,	,	PUNCT
ejpam-3636	22	19	lower	low	ADJ
ejpam-3636	22	20	order	order	NOUN
ejpam-3636	22	21	and	and	CCONJ
ejpam-3636	22	22	generalized	generalized	ADJ
ejpam-3636	22	23	type	type	NOUN
ejpam-3636	22	24	)	)	PUNCT
ejpam-3636	22	25	in	in	ADP
ejpam-3636	22	26	the	the	DET
ejpam-3636	22	27	sense	sense	NOUN
ejpam-3636	22	28	of	of	ADP
ejpam-3636	22	29	sheremeta	sheremeta	NOUN
ejpam-3636	23	1	[	[	X
ejpam-3636	23	2	18	18	NUM
ejpam-3636	23	3	]	]	PUNCT
ejpam-3636	23	4	of	of	ADP
ejpam-3636	23	5	entire	entire	ADJ
ejpam-3636	23	6	harmonic	harmonic	ADJ
ejpam-3636	23	7	functions	function	NOUN
ejpam-3636	23	8	in	in	ADP
ejpam-3636	23	9	terms	term	NOUN
ejpam-3636	23	10	of	of	ADP
ejpam-3636	23	11	norm	norm	NOUN
ejpam-3636	23	12	of	of	ADP
ejpam-3636	23	13	gradient	gradient	NOUN
ejpam-3636	23	14	at	at	ADP
ejpam-3636	23	15	origin	origin	NOUN
ejpam-3636	23	16	.	.	PUNCT
ejpam-3636	24	1	it	it	PRON
ejpam-3636	24	2	is	be	AUX
ejpam-3636	24	3	significant	significant	ADJ
ejpam-3636	24	4	to	to	PART
ejpam-3636	24	5	mention	mention	VERB
ejpam-3636	24	6	here	here	ADV
ejpam-3636	24	7	that	that	DET
ejpam-3636	24	8	time	time	NOUN
ejpam-3636	24	9	dependent	dependent	ADJ
ejpam-3636	24	10	problems	problem	NOUN
ejpam-3636	24	11	in	in	ADP
ejpam-3636	24	12	r3	r3	PROPN
ejpam-3636	24	13	leads	lead	VERB
ejpam-3636	24	14	to	to	ADP
ejpam-3636	24	15	the	the	DET
ejpam-3636	24	16	study	study	NOUN
ejpam-3636	24	17	of	of	ADP
ejpam-3636	24	18	entire	entire	ADJ
ejpam-3636	24	19	harmonic	harmonic	ADJ
ejpam-3636	24	20	functions	function	NOUN
ejpam-3636	24	21	in	in	ADP
ejpam-3636	24	22	r4	r4	NOUN
ejpam-3636	24	23	.	.	PUNCT
ejpam-3636	25	1	a	a	DET
ejpam-3636	25	2	function	function	NOUN
ejpam-3636	25	3	h(x	h(x	PROPN
ejpam-3636	25	4	)	)	PUNCT
ejpam-3636	25	5	,	,	PUNCT
ejpam-3636	25	6	x	x	PUNCT
ejpam-3636	25	7	∈	∈	PROPN
ejpam-3636	25	8	rn	rn	PROPN
ejpam-3636	25	9	which	which	PRON
ejpam-3636	25	10	has	have	VERB
ejpam-3636	25	11	continuous	continuous	ADJ
ejpam-3636	25	12	partial	partial	ADJ
ejpam-3636	25	13	derivatives	derivative	NOUN
ejpam-3636	25	14	of	of	ADP
ejpam-3636	25	15	second	second	ADJ
ejpam-3636	25	16	order	order	NOUN
ejpam-3636	25	17	and	and	CCONJ
ejpam-3636	25	18	satisfies	satisfy	VERB
ejpam-3636	25	19	laplace	laplace	NOUN
ejpam-3636	25	20	,	,	PUNCT
ejpam-3636	25	21	s	s	NOUN
ejpam-3636	25	22	differential	differential	ADJ
ejpam-3636	25	23	equation	equation	NOUN
ejpam-3636	25	24	n∑	n∑	PROPN
ejpam-3636	25	25	i=1	i=1	PROPN
ejpam-3636	25	26	∂2h	∂2h	VERB
ejpam-3636	25	27	∂x2	∂x2	NOUN
ejpam-3636	25	28	i	i	NOUN
ejpam-3636	25	29	=	=	NOUN
ejpam-3636	25	30	0	0	NUM
ejpam-3636	25	31	is	be	AUX
ejpam-3636	25	32	said	say	VERB
ejpam-3636	25	33	to	to	PART
ejpam-3636	25	34	be	be	AUX
ejpam-3636	25	35	harmonic	harmonic	ADJ
ejpam-3636	25	36	in	in	ADP
ejpam-3636	25	37	n	n	ADV
ejpam-3636	25	38	-	-	PUNCT
ejpam-3636	25	39	dimensional	dimensional	ADJ
ejpam-3636	25	40	space	space	NOUN
ejpam-3636	25	41	rn	rn	PROPN
ejpam-3636	25	42	.	.	PUNCT
ejpam-3636	26	1	the	the	DET
ejpam-3636	26	2	function	function	NOUN
ejpam-3636	26	3	h	h	NOUN
ejpam-3636	26	4	has	have	VERB
ejpam-3636	26	5	the	the	DET
ejpam-3636	26	6	spherical	spherical	ADJ
ejpam-3636	26	7	harmonic	harmonic	ADJ
ejpam-3636	26	8	expansion	expansion	NOUN
ejpam-3636	26	9	throughout	throughout	ADP
ejpam-3636	26	10	a	a	DET
ejpam-3636	26	11	neighborhood	neighborhood	NOUN
ejpam-3636	26	12	of	of	ADP
ejpam-3636	26	13	the	the	DET
ejpam-3636	26	14	origin	origin	NOUN
ejpam-3636	26	15	in	in	ADP
ejpam-3636	26	16	rn	rn	PROPN
ejpam-3636	26	17	as	as	ADP
ejpam-3636	26	18	h(x	h(x	PROPN
ejpam-3636	26	19	)	)	PUNCT
ejpam-3636	27	1	=	=	PUNCT
ejpam-3636	28	1	∞∑	∞∑	NUM
ejpam-3636	28	2	k=0	k=0	PROPN
ejpam-3636	28	3	hk(x	hk(x	NOUN
ejpam-3636	28	4	)	)	PUNCT
ejpam-3636	28	5	,	,	PUNCT
ejpam-3636	28	6	(	(	PUNCT
ejpam-3636	28	7	1.1	1.1	NUM
ejpam-3636	28	8	)	)	PUNCT
ejpam-3636	28	9	where	where	SCONJ
ejpam-3636	28	10	hk(x	hk(x	NOUN
ejpam-3636	28	11	)	)	PUNCT
ejpam-3636	28	12	is	be	AUX
ejpam-3636	28	13	a	a	DET
ejpam-3636	28	14	harmonic	harmonic	ADJ
ejpam-3636	28	15	homogeneous	homogeneous	ADJ
ejpam-3636	28	16	polynomial	polynomial	NOUN
ejpam-3636	28	17	of	of	ADP
ejpam-3636	28	18	degree	degree	NOUN
ejpam-3636	28	19	k	k	PROPN
ejpam-3636	28	20	in	in	ADP
ejpam-3636	28	21	x1	x1	PROPN
ejpam-3636	28	22	,	,	PUNCT
ejpam-3636	28	23	x2	x2	PROPN
ejpam-3636	28	24	,	,	PUNCT
ejpam-3636	28	25	.	.	PUNCT
ejpam-3636	28	26	.	.	PUNCT
ejpam-3636	28	27	.	.	PUNCT
ejpam-3636	29	1	xn	xn	PUNCT
ejpam-3636	30	1	having	have	VERB
ejpam-3636	30	2	real	real	ADJ
ejpam-3636	30	3	coefficients	coefficient	NOUN
ejpam-3636	30	4	[	[	X
ejpam-3636	30	5	3	3	NUM
ejpam-3636	30	6	,	,	PUNCT
ejpam-3636	30	7	pp	pp	ADJ
ejpam-3636	30	8	.	.	PUNCT
ejpam-3636	31	1	47	47	NUM
ejpam-3636	31	2	]	]	PUNCT
ejpam-3636	31	3	.	.	PUNCT
ejpam-3636	32	1	these	these	DET
ejpam-3636	32	2	polynomials	polynomial	NOUN
ejpam-3636	32	3	are	be	AUX
ejpam-3636	32	4	known	know	VERB
ejpam-3636	32	5	as	as	ADP
ejpam-3636	32	6	spherical	spherical	ADJ
ejpam-3636	32	7	harmonics	harmonic	NOUN
ejpam-3636	32	8	.	.	PUNCT
ejpam-3636	33	1	let	let	VERB
ejpam-3636	33	2	sn	sn	PROPN
ejpam-3636	33	3	=	=	PUNCT
ejpam-3636	33	4	{	{	PUNCT
ejpam-3636	33	5	x	x	PUNCT
ejpam-3636	33	6	∈	∈	PROPN
ejpam-3636	33	7	rn	rn	NOUN
ejpam-3636	33	8	:	:	PUNCT
ejpam-3636	34	1	|x|	|x|	PROPN
ejpam-3636	34	2	=	=	SYM
ejpam-3636	34	3	1	1	X
ejpam-3636	34	4	}	}	PUNCT
ejpam-3636	34	5	be	be	AUX
ejpam-3636	34	6	a	a	DET
ejpam-3636	34	7	unit	unit	NOUN
ejpam-3636	34	8	sphere	sphere	ADV
ejpam-3636	34	9	in	in	ADP
ejpam-3636	34	10	rn	rn	PROPN
ejpam-3636	34	11	.	.	PUNCT
ejpam-3636	35	1	the	the	DET
ejpam-3636	35	2	series	series	NOUN
ejpam-3636	35	3	(	(	PUNCT
ejpam-3636	35	4	1.1	1.1	NUM
ejpam-3636	35	5	)	)	PUNCT
ejpam-3636	35	6	also	also	ADV
ejpam-3636	35	7	can	can	AUX
ejpam-3636	35	8	be	be	AUX
ejpam-3636	35	9	expressed	express	VERB
ejpam-3636	35	10	as	as	ADP
ejpam-3636	35	11	h(x	h(x	PROPN
ejpam-3636	35	12	)	)	PUNCT
ejpam-3636	36	1	=	=	PUNCT
ejpam-3636	37	1	∞∑	∞∑	PRON
ejpam-3636	37	2	k=0	k=0	PROPN
ejpam-3636	37	3	dk∑	dk∑	VERB
ejpam-3636	37	4	j=1	j=1	PROPN
ejpam-3636	37	5	ajkq	ajkq	NOUN
ejpam-3636	37	6	j	j	PROPN
ejpam-3636	37	7	k	k	PROPN
ejpam-3636	37	8	(	(	PUNCT
ejpam-3636	37	9	x	x	SYM
ejpam-3636	37	10	r	r	NOUN
ejpam-3636	37	11	)	)	PUNCT
ejpam-3636	37	12	rk	rk	NOUN
ejpam-3636	37	13	,	,	PUNCT
ejpam-3636	37	14	|x|	|x|	PROPN
ejpam-3636	37	15	=	=	SYM
ejpam-3636	37	16	r	r	PROPN
ejpam-3636	37	17	,	,	PUNCT
ejpam-3636	37	18	(	(	PUNCT
ejpam-3636	37	19	1.2	1.2	NUM
ejpam-3636	37	20	)	)	PUNCT
ejpam-3636	37	21	where	where	SCONJ
ejpam-3636	37	22	{	{	PUNCT
ejpam-3636	37	23	qjk	qjk	ADJ
ejpam-3636	37	24	}	}	PUNCT
ejpam-3636	37	25	dk	dk	NOUN
ejpam-3636	37	26	j=1	j=1	NOUN
ejpam-3636	37	27	be	be	AUX
ejpam-3636	37	28	an	an	DET
ejpam-3636	37	29	orthonormal	orthonormal	ADJ
ejpam-3636	37	30	basis	basis	NOUN
ejpam-3636	37	31	for	for	ADP
ejpam-3636	37	32	hk	hk	PROPN
ejpam-3636	37	33	with	with	ADP
ejpam-3636	37	34	respect	respect	NOUN
ejpam-3636	37	35	to	to	ADP
ejpam-3636	37	36	the	the	DET
ejpam-3636	37	37	scalar	scalar	ADJ
ejpam-3636	37	38	product	product	NOUN
ejpam-3636	37	39	<	<	X
ejpam-3636	37	40	f	f	X
ejpam-3636	37	41	,	,	PUNCT
ejpam-3636	37	42	g	g	PROPN
ejpam-3636	37	43	>	>	X
ejpam-3636	37	44	=	=	SYM
ejpam-3636	37	45	1	1	NUM
ejpam-3636	37	46	wn	wn	PROPN
ejpam-3636	37	47	∫	∫	PROPN
ejpam-3636	37	48	sn	sn	PROPN
ejpam-3636	37	49	f(x)g(x)dσ1	f(x)g(x)dσ1	PROPN
ejpam-3636	37	50	,	,	PUNCT
ejpam-3636	37	51	while	while	SCONJ
ejpam-3636	37	52	wn	wn	PROPN
ejpam-3636	37	53	=	=	PROPN
ejpam-3636	37	54	2πn/2	2πn/2	PROPN
ejpam-3636	37	55	γ(n/2	γ(n/2	PROPN
ejpam-3636	37	56	)	)	PUNCT
ejpam-3636	37	57	denotes	denote	VERB
ejpam-3636	37	58	the	the	DET
ejpam-3636	37	59	area	area	NOUN
ejpam-3636	37	60	of	of	ADP
ejpam-3636	37	61	sn	sn	PROPN
ejpam-3636	37	62	and	and	CCONJ
ejpam-3636	37	63	dσ1	dσ1	NOUN
ejpam-3636	37	64	is	be	AUX
ejpam-3636	37	65	the	the	DET
ejpam-3636	37	66	element	element	NOUN
ejpam-3636	37	67	of	of	ADP
ejpam-3636	37	68	surface	surface	NOUN
ejpam-3636	37	69	area	area	NOUN
ejpam-3636	37	70	on	on	ADP
ejpam-3636	37	71	sn	sn	PROPN
ejpam-3636	37	72	.	.	PUNCT
ejpam-3636	38	1	d.	d.	PROPN
ejpam-3636	38	2	kumar	kumar	PROPN
ejpam-3636	38	3	,	,	PUNCT
ejpam-3636	38	4	r.k	r.k	PROPN
ejpam-3636	38	5	.	.	PROPN
ejpam-3636	38	6	vishnoi	vishnoi	PROPN
ejpam-3636	38	7	/	/	SYM
ejpam-3636	38	8	eur	eur	PROPN
ejpam-3636	38	9	.	.	PUNCT
ejpam-3636	39	1	j.	j.	PROPN
ejpam-3636	39	2	pure	pure	PROPN
ejpam-3636	39	3	appl	appl	PROPN
ejpam-3636	39	4	.	.	PROPN
ejpam-3636	39	5	math	math	PROPN
ejpam-3636	39	6	,	,	PUNCT
ejpam-3636	39	7	13	13	NUM
ejpam-3636	39	8	(	(	PUNCT
ejpam-3636	39	9	2	2	NUM
ejpam-3636	39	10	)	)	PUNCT
ejpam-3636	39	11	(	(	PUNCT
ejpam-3636	39	12	2020	2020	NUM
ejpam-3636	39	13	)	)	PUNCT
ejpam-3636	39	14	,	,	PUNCT
ejpam-3636	39	15	258	258	NUM
ejpam-3636	39	16	-	-	SYM
ejpam-3636	39	17	268	268	NUM
ejpam-3636	39	18	260	260	NUM
ejpam-3636	39	19	also	also	ADV
ejpam-3636	39	20	(	(	PUNCT
ejpam-3636	39	21	see	see	VERB
ejpam-3636	39	22	[	[	X
ejpam-3636	39	23	21	21	NUM
ejpam-3636	39	24	,	,	PUNCT
ejpam-3636	39	25	pp.145	pp.145	NOUN
ejpam-3636	39	26	]	]	PUNCT
ejpam-3636	39	27	)	)	PUNCT
ejpam-3636	40	1	dk	dk	X
ejpam-3636	40	2	=	=	PUNCT
ejpam-3636	40	3	(	(	PUNCT
ejpam-3636	40	4	n+	n+	NUM
ejpam-3636	40	5	2k	2k	NOUN
ejpam-3636	40	6	−	−	PROPN
ejpam-3636	40	7	2)(n+	2)(n+	NUM
ejpam-3636	40	8	k	k	NOUN
ejpam-3636	40	9	−	−	NOUN
ejpam-3636	40	10	3	3	NUM
ejpam-3636	40	11	)	)	PUNCT
ejpam-3636	40	12	!	!	PUNCT
ejpam-3636	41	1	k!(n−	k!(n−	PROPN
ejpam-3636	41	2	2	2	NUM
ejpam-3636	41	3	)	)	PUNCT
ejpam-3636	41	4	!	!	PUNCT
ejpam-3636	42	1	is	be	AUX
ejpam-3636	42	2	the	the	DET
ejpam-3636	42	3	dimension	dimension	NOUN
ejpam-3636	42	4	of	of	ADP
ejpam-3636	42	5	vector	vector	NOUN
ejpam-3636	42	6	space	space	NOUN
ejpam-3636	42	7	hk	hk	PROPN
ejpam-3636	42	8	and	and	CCONJ
ejpam-3636	42	9	ajk	ajk	PROPN
ejpam-3636	43	1	=	=	NOUN
ejpam-3636	43	2	1	1	NUM
ejpam-3636	43	3	wn	wn	PROPN
ejpam-3636	43	4	∫	∫	PROPN
ejpam-3636	43	5	sn	sn	PROPN
ejpam-3636	43	6	h(x)qjk(x)dσ1	h(x)qjk(x)dσ1	PROPN
ejpam-3636	43	7	.	.	PUNCT
ejpam-3636	44	1	if	if	SCONJ
ejpam-3636	44	2	the	the	DET
ejpam-3636	44	3	series	series	NOUN
ejpam-3636	44	4	(	(	PUNCT
ejpam-3636	44	5	1.2	1.2	NUM
ejpam-3636	44	6	)	)	PUNCT
ejpam-3636	44	7	converges	converge	VERB
ejpam-3636	44	8	uniformly	uniformly	ADV
ejpam-3636	44	9	on	on	ADP
ejpam-3636	44	10	the	the	DET
ejpam-3636	44	11	sphere	sphere	NOUN
ejpam-3636	44	12	|x|	|x|	PROPN
ejpam-3636	44	13	=	=	PUNCT
ejpam-3636	45	1	(	(	PUNCT
ejpam-3636	45	2	∑n	∑n	PROPN
ejpam-3636	45	3	i=1	i=1	PROPN
ejpam-3636	45	4	x	x	SYM
ejpam-3636	45	5	2	2	NUM
ejpam-3636	45	6	i	i	NOUN
ejpam-3636	45	7	)	)	PUNCT
ejpam-3636	45	8	1	1	NUM
ejpam-3636	45	9	2	2	NUM
ejpam-3636	45	10	=	=	SYM
ejpam-3636	45	11	δ	δ	PROPN
ejpam-3636	45	12	,	,	PUNCT
ejpam-3636	45	13	then	then	ADV
ejpam-3636	45	14	we	we	PRON
ejpam-3636	45	15	have	have	VERB
ejpam-3636	45	16	ajk	ajk	PROPN
ejpam-3636	45	17	=	=	SYM
ejpam-3636	45	18	1	1	NUM
ejpam-3636	45	19	δ2k+n−1wn	δ2k+n−1wn	PROPN
ejpam-3636	45	20	∫	∫	PROPN
ejpam-3636	45	21	|x|=δ	|x|=δ	PROPN
ejpam-3636	45	22	h(x)qjk(x)dσ	h(x)qjk(x)dσ	NOUN
ejpam-3636	45	23	,	,	PUNCT
ejpam-3636	45	24	where	where	SCONJ
ejpam-3636	45	25	dσ	dσ	PROPN
ejpam-3636	45	26	=	=	PROPN
ejpam-3636	45	27	δn−1dσ1	δn−1dσ1	PROPN
ejpam-3636	45	28	is	be	AUX
ejpam-3636	45	29	the	the	DET
ejpam-3636	45	30	element	element	NOUN
ejpam-3636	45	31	of	of	ADP
ejpam-3636	45	32	surface	surface	NOUN
ejpam-3636	45	33	area	area	NOUN
ejpam-3636	45	34	on	on	ADP
ejpam-3636	45	35	the	the	DET
ejpam-3636	45	36	sphere	sphere	NOUN
ejpam-3636	45	37	|x|	|x|	PROPN
ejpam-3636	45	38	=	=	SYM
ejpam-3636	45	39	δ	δ	PROPN
ejpam-3636	45	40	.	.	PUNCT
ejpam-3636	46	1	for	for	ADP
ejpam-3636	46	2	each	each	DET
ejpam-3636	46	3	n	n	CCONJ
ejpam-3636	46	4	-	-	PUNCT
ejpam-3636	46	5	tuple	tuple	NOUN
ejpam-3636	46	6	a	a	PRON
ejpam-3636	46	7	=	=	SYM
ejpam-3636	46	8	(	(	PUNCT
ejpam-3636	46	9	a1	a1	PROPN
ejpam-3636	46	10	,	,	PUNCT
ejpam-3636	46	11	a2	a2	PROPN
ejpam-3636	46	12	,	,	PUNCT
ejpam-3636	46	13	.	.	PUNCT
ejpam-3636	46	14	.	.	PUNCT
ejpam-3636	46	15	.	.	PUNCT
ejpam-3636	47	1	,	,	PUNCT
ejpam-3636	47	2	an	an	X
ejpam-3636	47	3	)	)	PUNCT
ejpam-3636	47	4	of	of	ADP
ejpam-3636	47	5	non	non	ADJ
ejpam-3636	47	6	-	-	ADJ
ejpam-3636	47	7	negative	negative	ADJ
ejpam-3636	47	8	integers	integer	NOUN
ejpam-3636	47	9	,	,	PUNCT
ejpam-3636	47	10	we	we	PRON
ejpam-3636	47	11	define	define	VERB
ejpam-3636	47	12	|a|	|a|	NOUN
ejpam-3636	47	13	=	=	NOUN
ejpam-3636	47	14	a1	a1	PROPN
ejpam-3636	47	15	+	+	PROPN
ejpam-3636	47	16	a2	a2	PROPN
ejpam-3636	47	17	+	+	X
ejpam-3636	47	18	·	·	PUNCT
ejpam-3636	47	19	·	·	PUNCT
ejpam-3636	47	20	·	·	PUNCT
ejpam-3636	48	1	+	+	CCONJ
ejpam-3636	48	2	an	an	X
ejpam-3636	48	3	,	,	PUNCT
ejpam-3636	48	4	a	a	NOUN
ejpam-3636	48	5	!	!	PUNCT
ejpam-3636	48	6	=	=	SYM
ejpam-3636	48	7	a1!a2	a1!a2	PROPN
ejpam-3636	48	8	!	!	PUNCT
ejpam-3636	48	9	.	.	PUNCT
ejpam-3636	48	10	.	.	PUNCT
ejpam-3636	48	11	.	.	PUNCT
ejpam-3636	49	1	an	an	PRON
ejpam-3636	49	2	!	!	PUNCT
ejpam-3636	50	1	and	and	CCONJ
ejpam-3636	50	2	da	da	PROPN
ejpam-3636	50	3	=	=	SYM
ejpam-3636	50	4	∂|a|	∂|a|	PROPN
ejpam-3636	50	5	∂	∂	NOUN
ejpam-3636	50	6	a1	a1	NOUN
ejpam-3636	50	7	x1	x1	PROPN
ejpam-3636	50	8	∂	∂	NUM
ejpam-3636	50	9	a2	a2	PROPN
ejpam-3636	50	10	x2	x2	PROPN
ejpam-3636	50	11	...	...	PUNCT
ejpam-3636	50	12	∂anxn	∂anxn	ADJ
ejpam-3636	50	13	.	.	PUNCT
ejpam-3636	51	1	in	in	ADP
ejpam-3636	51	2	view	view	NOUN
ejpam-3636	51	3	of	of	ADP
ejpam-3636	51	4	[	[	X
ejpam-3636	51	5	2	2	NUM
ejpam-3636	51	6	]	]	PUNCT
ejpam-3636	51	7	for	for	ADP
ejpam-3636	51	8	each	each	DET
ejpam-3636	51	9	ξ	ξ	PROPN
ejpam-3636	51	10	∈	∈	PROPN
ejpam-3636	51	11	c∞(rn	c∞(rn	PROPN
ejpam-3636	51	12	)	)	PUNCT
ejpam-3636	51	13	and	and	CCONJ
ejpam-3636	51	14	non	non	ADJ
ejpam-3636	51	15	-	-	ADJ
ejpam-3636	51	16	negative	negative	ADJ
ejpam-3636	51	17	integer	integer	NOUN
ejpam-3636	51	18	k	k	NOUN
ejpam-3636	51	19	,	,	PUNCT
ejpam-3636	51	20	we	we	PRON
ejpam-3636	51	21	define	define	VERB
ejpam-3636	51	22	the	the	DET
ejpam-3636	51	23	norm	norm	NOUN
ejpam-3636	51	24	of	of	ADP
ejpam-3636	51	25	the	the	DET
ejpam-3636	51	26	kth	kth	PROPN
ejpam-3636	51	27	gradients	gradient	NOUN
ejpam-3636	51	28	of	of	ADP
ejpam-3636	51	29	h	h	NOUN
ejpam-3636	51	30	at	at	ADP
ejpam-3636	51	31	origin	origin	NOUN
ejpam-3636	51	32	by	by	ADP
ejpam-3636	51	33	|∇kh(0)|	|∇kh(0)|	NOUN
ejpam-3636	51	34	=	=	SYM
ejpam-3636	51	35	(	(	PUNCT
ejpam-3636	51	36	k	k	X
ejpam-3636	51	37	!	!	PUNCT
ejpam-3636	51	38	2k	2k	NOUN
ejpam-3636	51	39	∑	∑	PUNCT
ejpam-3636	51	40	|a|=k	|a|=k	PROPN
ejpam-3636	52	1	[	[	X
ejpam-3636	52	2	dah(0)]2	dah(0)]2	NOUN
ejpam-3636	52	3	a	a	X
ejpam-3636	52	4	!	!	PUNCT
ejpam-3636	52	5	)	)	PUNCT
ejpam-3636	52	6	1	1	NUM
ejpam-3636	52	7	2	2	NUM
ejpam-3636	52	8	.	.	PUNCT
ejpam-3636	53	1	(	(	PUNCT
ejpam-3636	53	2	1.3	1.3	NUM
ejpam-3636	53	3	)	)	PUNCT
ejpam-3636	53	4	it	it	PRON
ejpam-3636	53	5	has	have	AUX
ejpam-3636	53	6	been	be	AUX
ejpam-3636	53	7	proved	prove	VERB
ejpam-3636	53	8	[	[	X
ejpam-3636	53	9	5	5	NUM
ejpam-3636	53	10	]	]	PUNCT
ejpam-3636	53	11	that	that	SCONJ
ejpam-3636	53	12	the	the	DET
ejpam-3636	53	13	series	series	NOUN
ejpam-3636	53	14	(	(	PUNCT
ejpam-3636	53	15	1.1	1.1	NUM
ejpam-3636	53	16	)	)	PUNCT
ejpam-3636	53	17	converges	converge	VERB
ejpam-3636	53	18	absolutely	absolutely	ADV
ejpam-3636	53	19	and	and	CCONJ
ejpam-3636	53	20	uniformly	uniformly	ADV
ejpam-3636	53	21	on	on	ADP
ejpam-3636	53	22	compact	compact	ADJ
ejpam-3636	53	23	subsets	subset	NOUN
ejpam-3636	53	24	of	of	ADP
ejpam-3636	53	25	the	the	DET
ejpam-3636	53	26	open	open	ADJ
ejpam-3636	53	27	ball	ball	NOUN
ejpam-3636	53	28	|x|	|x|	PROPN
ejpam-3636	53	29	<	<	X
ejpam-3636	53	30	r	r	NOUN
ejpam-3636	53	31	,	,	PUNCT
ejpam-3636	53	32	where	where	SCONJ
ejpam-3636	53	33	r−1	r−1	PROPN
ejpam-3636	53	34	=	=	PUNCT
ejpam-3636	53	35	√	√	PROPN
ejpam-3636	53	36	2	2	NUM
ejpam-3636	53	37	lim	lim	NOUN
ejpam-3636	53	38	sup	sup	PROPN
ejpam-3636	53	39	k→∞	k→∞	NOUN
ejpam-3636	53	40	(	(	PUNCT
ejpam-3636	53	41	|∇kh(0)|	|∇kh(0)|	NOUN
ejpam-3636	53	42	k	k	PROPN
ejpam-3636	53	43	!	!	PUNCT
ejpam-3636	53	44	)	)	PUNCT
ejpam-3636	54	1	1	1	NUM
ejpam-3636	55	1	k	k	NOUN
ejpam-3636	55	2	.	.	PUNCT
ejpam-3636	56	1	(	(	PUNCT
ejpam-3636	56	2	1.4	1.4	NUM
ejpam-3636	56	3	)	)	PUNCT
ejpam-3636	56	4	definition	definition	NOUN
ejpam-3636	56	5	(	(	PUNCT
ejpam-3636	56	6	1.3	1.3	NUM
ejpam-3636	56	7	)	)	PUNCT
ejpam-3636	56	8	and	and	CCONJ
ejpam-3636	56	9	equality	equality	NOUN
ejpam-3636	56	10	(	(	PUNCT
ejpam-3636	56	11	1.4	1.4	NUM
ejpam-3636	56	12	)	)	PUNCT
ejpam-3636	56	13	immediately	immediately	ADV
ejpam-3636	56	14	show	show	VERB
ejpam-3636	56	15	that	that	SCONJ
ejpam-3636	56	16	the	the	DET
ejpam-3636	56	17	series	series	NOUN
ejpam-3636	56	18	(	(	PUNCT
ejpam-3636	56	19	1.1	1.1	NUM
ejpam-3636	56	20	)	)	PUNCT
ejpam-3636	56	21	converges	converge	VERB
ejpam-3636	56	22	absolutely	absolutely	ADV
ejpam-3636	56	23	and	and	CCONJ
ejpam-3636	56	24	uniformly	uniformly	ADV
ejpam-3636	56	25	on	on	ADP
ejpam-3636	56	26	compact	compact	ADJ
ejpam-3636	56	27	subsets	subset	NOUN
ejpam-3636	56	28	of	of	ADP
ejpam-3636	56	29	open	open	ADJ
ejpam-3636	56	30	ball	ball	NOUN
ejpam-3636	56	31	|x|	|x|	PROPN
ejpam-3636	56	32	<	<	X
ejpam-3636	56	33	r	r	NOUN
ejpam-3636	56	34	,	,	PUNCT
ejpam-3636	56	35	where	where	SCONJ
ejpam-3636	56	36	r−1	r−1	PROPN
ejpam-3636	56	37	=	=	SYM
ejpam-3636	56	38	lim	lim	PROPN
ejpam-3636	56	39	sup	sup	PROPN
ejpam-3636	56	40	k→∞	k→∞	NOUN
ejpam-3636	56	41	(	(	PUNCT
ejpam-3636	56	42	|∇kh(0)|	|∇kh(0)|	NOUN
ejpam-3636	56	43	k	k	PROPN
ejpam-3636	56	44	!	!	PUNCT
ejpam-3636	56	45	)	)	PUNCT
ejpam-3636	57	1	1	1	NUM
ejpam-3636	57	2	k	k	NOUN
ejpam-3636	57	3	,	,	PUNCT
ejpam-3636	57	4	(	(	PUNCT
ejpam-3636	57	5	1.5	1.5	NUM
ejpam-3636	57	6	)	)	PUNCT
ejpam-3636	57	7	and	and	CCONJ
ejpam-3636	57	8	such	such	ADJ
ejpam-3636	57	9	convergence	convergence	NOUN
ejpam-3636	57	10	can	can	AUX
ejpam-3636	57	11	not	not	PART
ejpam-3636	57	12	obtain	obtain	VERB
ejpam-3636	57	13	within	within	ADP
ejpam-3636	57	14	any	any	DET
ejpam-3636	57	15	larger	large	ADJ
ejpam-3636	57	16	ball	ball	NOUN
ejpam-3636	57	17	centered	center	VERB
ejpam-3636	57	18	at	at	ADP
ejpam-3636	57	19	origin	origin	NOUN
ejpam-3636	57	20	.	.	PUNCT
ejpam-3636	58	1	fryant	fryant	PROPN
ejpam-3636	58	2	and	and	CCONJ
ejpam-3636	58	3	shankar	shankar	PROPN
ejpam-3636	59	1	[	[	X
ejpam-3636	59	2	4	4	NUM
ejpam-3636	59	3	]	]	PUNCT
ejpam-3636	59	4	proved	prove	VERB
ejpam-3636	59	5	the	the	DET
ejpam-3636	59	6	following	follow	VERB
ejpam-3636	59	7	lemma	lemma	PROPN
ejpam-3636	59	8	.	.	PUNCT
ejpam-3636	60	1	lemma	lemma	PROPN
ejpam-3636	60	2	a.	a.	PROPN
ejpam-3636	60	3	let	let	VERB
ejpam-3636	60	4	h(x	h(x	PROPN
ejpam-3636	60	5	)	)	PUNCT
ejpam-3636	61	1	=	=	NOUN
ejpam-3636	61	2	∑∞	∑∞	NOUN
ejpam-3636	61	3	k=0hk(x	k=0hk(x	PROPN
ejpam-3636	61	4	)	)	PUNCT
ejpam-3636	61	5	is	be	AUX
ejpam-3636	61	6	uniformly	uniformly	ADV
ejpam-3636	61	7	convergent	convergent	NOUN
ejpam-3636	61	8	in	in	ADP
ejpam-3636	61	9	a	a	DET
ejpam-3636	61	10	neighborhood	neighborhood	NOUN
ejpam-3636	61	11	of	of	ADP
ejpam-3636	61	12	the	the	DET
ejpam-3636	61	13	origin	origin	NOUN
ejpam-3636	61	14	in	in	ADP
ejpam-3636	61	15	rn	rn	PROPN
ejpam-3636	61	16	.	.	PUNCT
ejpam-3636	62	1	then	then	ADV
ejpam-3636	62	2	for	for	ADP
ejpam-3636	62	3	all	all	DET
ejpam-3636	62	4	r	r	NOUN
ejpam-3636	62	5	<	<	X
ejpam-3636	62	6	r	r	NOUN
ejpam-3636	62	7	,	,	PUNCT
ejpam-3636	62	8	m2(r	m2(r	PROPN
ejpam-3636	62	9	,	,	PUNCT
ejpam-3636	62	10	h	h	NOUN
ejpam-3636	62	11	)	)	PUNCT
ejpam-3636	62	12	≤m(r	≤m(r	NOUN
ejpam-3636	62	13	,	,	PUNCT
ejpam-3636	62	14	h	h	NOUN
ejpam-3636	62	15	)	)	PUNCT
ejpam-3636	62	16	≤	≤	NOUN
ejpam-3636	62	17	n(r	n(r	NOUN
ejpam-3636	62	18	,	,	PUNCT
ejpam-3636	62	19	h	h	NOUN
ejpam-3636	62	20	)	)	PUNCT
ejpam-3636	62	21	,	,	PUNCT
ejpam-3636	62	22	d.	d.	PROPN
ejpam-3636	62	23	kumar	kumar	PROPN
ejpam-3636	62	24	,	,	PUNCT
ejpam-3636	62	25	r.k	r.k	PROPN
ejpam-3636	62	26	.	.	PROPN
ejpam-3636	62	27	vishnoi	vishnoi	PROPN
ejpam-3636	62	28	/	/	SYM
ejpam-3636	62	29	eur	eur	PROPN
ejpam-3636	62	30	.	.	PUNCT
ejpam-3636	63	1	j.	j.	PROPN
ejpam-3636	63	2	pure	pure	PROPN
ejpam-3636	63	3	appl	appl	PROPN
ejpam-3636	63	4	.	.	PROPN
ejpam-3636	63	5	math	math	PROPN
ejpam-3636	63	6	,	,	PUNCT
ejpam-3636	63	7	13	13	NUM
ejpam-3636	63	8	(	(	PUNCT
ejpam-3636	63	9	2	2	NUM
ejpam-3636	63	10	)	)	PUNCT
ejpam-3636	63	11	(	(	PUNCT
ejpam-3636	63	12	2020	2020	NUM
ejpam-3636	63	13	)	)	PUNCT
ejpam-3636	63	14	,	,	PUNCT
ejpam-3636	63	15	258	258	NUM
ejpam-3636	63	16	-	-	SYM
ejpam-3636	63	17	268	268	NUM
ejpam-3636	63	18	261	261	NUM
ejpam-3636	64	1	where	where	SCONJ
ejpam-3636	64	2	m(r	m(r	NOUN
ejpam-3636	64	3	,	,	PUNCT
ejpam-3636	64	4	h	h	NOUN
ejpam-3636	64	5	)	)	PUNCT
ejpam-3636	64	6	=	=	PUNCT
ejpam-3636	64	7	max|x|=r	max|x|=r	ADJ
ejpam-3636	64	8	|h(x)|	|h(x)|	PROPN
ejpam-3636	64	9	,	,	PUNCT
ejpam-3636	64	10	m2(r	m2(r	NOUN
ejpam-3636	64	11	,	,	PUNCT
ejpam-3636	64	12	h	h	NOUN
ejpam-3636	64	13	)	)	PUNCT
ejpam-3636	65	1	=	=	PUNCT
ejpam-3636	66	1	[	[	X
ejpam-3636	66	2	γ(n/2	γ(n/2	NOUN
ejpam-3636	66	3	)	)	PUNCT
ejpam-3636	66	4	∞∑	∞∑	PROPN
ejpam-3636	66	5	k=0	k=0	PUNCT
ejpam-3636	66	6	|∇kh(0)|2	|∇kh(0)|2	X
ejpam-3636	67	1	k!γ(k	k!γ(k	PROPN
ejpam-3636	67	2	+	+	CCONJ
ejpam-3636	67	3	n/2	n/2	X
ejpam-3636	67	4	)	)	PUNCT
ejpam-3636	67	5	r2k	r2k	NOUN
ejpam-3636	67	6	]	]	X
ejpam-3636	67	7	1	1	NUM
ejpam-3636	67	8	2	2	NUM
ejpam-3636	67	9	,	,	PUNCT
ejpam-3636	67	10	and	and	CCONJ
ejpam-3636	67	11	n(r	n(r	NOUN
ejpam-3636	67	12	,	,	PUNCT
ejpam-3636	67	13	h	h	NOUN
ejpam-3636	67	14	)	)	PUNCT
ejpam-3636	67	15	=	=	SYM
ejpam-3636	67	16	√	√	NUM
ejpam-3636	67	17	γ(n/2	γ(n/2	NOUN
ejpam-3636	67	18	)	)	PUNCT
ejpam-3636	68	1	∞∑	∞∑	NUM
ejpam-3636	68	2	k=1	k=1	ADJ
ejpam-3636	68	3	√	√	PUNCT
ejpam-3636	69	1	dk	dk	INTJ
ejpam-3636	69	2	|∇kh(0)|√	|∇kh(0)|√	PUNCT
ejpam-3636	69	3	k!γ(k	k!γ(k	PROPN
ejpam-3636	69	4	+	+	CCONJ
ejpam-3636	69	5	n/2	n/2	NOUN
ejpam-3636	69	6	)	)	PUNCT
ejpam-3636	69	7	rk	rk	VERB
ejpam-3636	69	8	.	.	PUNCT
ejpam-3636	70	1	here	here	ADV
ejpam-3636	70	2	the	the	DET
ejpam-3636	70	3	upper	upper	ADJ
ejpam-3636	70	4	bound	bound	NOUN
ejpam-3636	70	5	of	of	ADP
ejpam-3636	70	6	m(r	m(r	PROPN
ejpam-3636	70	7	,	,	PUNCT
ejpam-3636	70	8	h	h	NOUN
ejpam-3636	70	9	)	)	PUNCT
ejpam-3636	70	10	holds	hold	VERB
ejpam-3636	70	11	for	for	ADP
ejpam-3636	70	12	all	all	DET
ejpam-3636	70	13	r	r	NOUN
ejpam-3636	70	14	≥	≥	NOUN
ejpam-3636	70	15	0	0	NUM
ejpam-3636	70	16	,	,	PUNCT
ejpam-3636	70	17	and	and	CCONJ
ejpam-3636	70	18	the	the	DET
ejpam-3636	70	19	lower	lower	ADV
ejpam-3636	70	20	bound	bind	VERB
ejpam-3636	70	21	of	of	ADP
ejpam-3636	70	22	m(r	m(r	PROPN
ejpam-3636	70	23	,	,	PUNCT
ejpam-3636	70	24	h	h	NOUN
ejpam-3636	70	25	)	)	PUNCT
ejpam-3636	70	26	obtains	obtain	VERB
ejpam-3636	70	27	for	for	ADP
ejpam-3636	70	28	all	all	DET
ejpam-3636	70	29	r	r	NOUN
ejpam-3636	70	30	such	such	ADJ
ejpam-3636	70	31	that	that	SCONJ
ejpam-3636	70	32	the	the	DET
ejpam-3636	70	33	spherical	spherical	ADJ
ejpam-3636	70	34	harmonic	harmonic	ADJ
ejpam-3636	70	35	series	series	PROPN
ejpam-3636	70	36	h	h	PROPN
ejpam-3636	70	37	is	be	AUX
ejpam-3636	70	38	uniformly	uniformly	ADV
ejpam-3636	70	39	convergent	convergent	NOUN
ejpam-3636	70	40	on	on	ADP
ejpam-3636	70	41	the	the	DET
ejpam-3636	70	42	sphere	sphere	NOUN
ejpam-3636	70	43	|x|	|x|	PROPN
ejpam-3636	70	44	=	=	PUNCT
ejpam-3636	70	45	r.	r.	PROPN
ejpam-3636	70	46	we	we	PRON
ejpam-3636	70	47	define	define	VERB
ejpam-3636	70	48	the	the	DET
ejpam-3636	70	49	order	order	NOUN
ejpam-3636	70	50	ρ	ρ	NOUN
ejpam-3636	70	51	of	of	ADP
ejpam-3636	70	52	h	h	NOUN
ejpam-3636	70	53	as	as	ADP
ejpam-3636	70	54	ρ	ρ	PROPN
ejpam-3636	70	55	=	=	PROPN
ejpam-3636	70	56	lim	lim	PROPN
ejpam-3636	70	57	sup	sup	PROPN
ejpam-3636	70	58	r→∞	r→∞	NUM
ejpam-3636	70	59	log	log	NOUN
ejpam-3636	70	60	logm(r	logm(r	NOUN
ejpam-3636	70	61	,	,	PUNCT
ejpam-3636	70	62	h	h	NOUN
ejpam-3636	70	63	)	)	PUNCT
ejpam-3636	70	64	log	log	NOUN
ejpam-3636	70	65	r	r	NOUN
ejpam-3636	70	66	,	,	PUNCT
ejpam-3636	70	67	0	0	NUM
ejpam-3636	70	68	≤	≤	NUM
ejpam-3636	70	69	ρ	ρ	NUM
ejpam-3636	70	70	≤	≤	NUM
ejpam-3636	70	71	∞	∞	PROPN
ejpam-3636	70	72	,	,	PUNCT
ejpam-3636	70	73	and	and	CCONJ
ejpam-3636	70	74	when	when	SCONJ
ejpam-3636	70	75	0	0	NUM
ejpam-3636	70	76	<	<	X
ejpam-3636	70	77	ρ	ρ	X
ejpam-3636	70	78	<	<	X
ejpam-3636	70	79	∞	∞	PROPN
ejpam-3636	70	80	,	,	PUNCT
ejpam-3636	70	81	the	the	DET
ejpam-3636	70	82	type	type	NOUN
ejpam-3636	70	83	t	t	PROPN
ejpam-3636	70	84	is	be	AUX
ejpam-3636	70	85	defined	define	VERB
ejpam-3636	70	86	as	as	ADP
ejpam-3636	70	87	t	t	PROPN
ejpam-3636	70	88	=	=	SYM
ejpam-3636	70	89	lim	lim	PROPN
ejpam-3636	70	90	sup	sup	PROPN
ejpam-3636	70	91	r→∞	r→∞	NUM
ejpam-3636	70	92	logm(r	logm(r	NOUN
ejpam-3636	70	93	,	,	PUNCT
ejpam-3636	70	94	h	h	NOUN
ejpam-3636	70	95	)	)	PUNCT
ejpam-3636	70	96	rρ	rρ	NOUN
ejpam-3636	70	97	,	,	PUNCT
ejpam-3636	70	98	0	0	NUM
ejpam-3636	70	99	≤	≤	NUM
ejpam-3636	70	100	t	t	PROPN
ejpam-3636	70	101	≤	≤	NUM
ejpam-3636	70	102	∞.	∞.	PROPN
ejpam-3636	70	103	fugard	fugard	NOUN
ejpam-3636	70	104	[	[	X
ejpam-3636	70	105	6	6	NUM
ejpam-3636	70	106	]	]	PUNCT
ejpam-3636	70	107	characterized	characterize	VERB
ejpam-3636	70	108	the	the	DET
ejpam-3636	70	109	order	order	NOUN
ejpam-3636	70	110	and	and	CCONJ
ejpam-3636	70	111	type	type	NOUN
ejpam-3636	70	112	of	of	ADP
ejpam-3636	70	113	an	an	DET
ejpam-3636	70	114	entire	entire	ADJ
ejpam-3636	70	115	harmonic	harmonic	ADJ
ejpam-3636	70	116	function	function	NOUN
ejpam-3636	70	117	in	in	ADP
ejpam-3636	70	118	terms	term	NOUN
ejpam-3636	70	119	of	of	ADP
ejpam-3636	70	120	the	the	DET
ejpam-3636	70	121	mth	mth	NOUN
ejpam-3636	70	122	gradient	gradient	NOUN
ejpam-3636	70	123	defined	define	VERB
ejpam-3636	70	124	above	above	ADV
ejpam-3636	70	125	.	.	PUNCT
ejpam-3636	71	1	also	also	ADV
ejpam-3636	71	2	,	,	PUNCT
ejpam-3636	71	3	kumar	kumar	PROPN
ejpam-3636	71	4	and	and	CCONJ
ejpam-3636	71	5	singh	singh	PROPN
ejpam-3636	72	1	[	[	X
ejpam-3636	72	2	16	16	NUM
ejpam-3636	72	3	]	]	PUNCT
ejpam-3636	72	4	investigated	investigate	VERB
ejpam-3636	72	5	these	these	DET
ejpam-3636	72	6	results	result	NOUN
ejpam-3636	72	7	for	for	ADP
ejpam-3636	72	8	non	non	PRON
ejpam-3636	72	9	entire	entire	ADJ
ejpam-3636	72	10	case	case	NOUN
ejpam-3636	72	11	.	.	PUNCT
ejpam-3636	73	1	srivastava	srivastava	PROPN
ejpam-3636	74	1	[	[	X
ejpam-3636	74	2	19	19	NUM
ejpam-3636	74	3	]	]	PUNCT
ejpam-3636	74	4	improved	improve	VERB
ejpam-3636	74	5	fugard	fugard	NOUN
ejpam-3636	74	6	’s	’s	PART
ejpam-3636	74	7	results	result	NOUN
ejpam-3636	74	8	and	and	CCONJ
ejpam-3636	74	9	obtained	obtain	VERB
ejpam-3636	74	10	generalized	generalized	ADJ
ejpam-3636	74	11	order	order	NOUN
ejpam-3636	74	12	and	and	CCONJ
ejpam-3636	74	13	generalized	generalized	ADJ
ejpam-3636	74	14	type	type	NOUN
ejpam-3636	74	15	.	.	PUNCT
ejpam-3636	75	1	in	in	ADP
ejpam-3636	75	2	this	this	DET
ejpam-3636	75	3	paper	paper	NOUN
ejpam-3636	75	4	,	,	PUNCT
ejpam-3636	75	5	we	we	PRON
ejpam-3636	75	6	extend	extend	VERB
ejpam-3636	75	7	the	the	DET
ejpam-3636	75	8	results	result	NOUN
ejpam-3636	75	9	of	of	ADP
ejpam-3636	75	10	srivastava	srivastava	PROPN
ejpam-3636	75	11	[	[	X
ejpam-3636	75	12	19	19	NUM
ejpam-3636	75	13	]	]	PUNCT
ejpam-3636	75	14	.	.	PUNCT
ejpam-3636	76	1	2	2	X
ejpam-3636	76	2	.	.	NUM
ejpam-3636	76	3	generalized	generalized	ADJ
ejpam-3636	76	4	growth	growth	NOUN
ejpam-3636	76	5	let	let	VERB
ejpam-3636	76	6	ξ	ξ	NOUN
ejpam-3636	76	7	:	:	PUNCT
ejpam-3636	77	1	[	[	X
ejpam-3636	77	2	a,∞	a,∞	PROPN
ejpam-3636	77	3	)	)	PUNCT
ejpam-3636	77	4	→	→	SYM
ejpam-3636	77	5	r	r	NOUN
ejpam-3636	77	6	for	for	ADP
ejpam-3636	77	7	some	some	DET
ejpam-3636	77	8	a	a	DET
ejpam-3636	77	9	≥	≥	NOUN
ejpam-3636	77	10	0	0	NUM
ejpam-3636	77	11	,	,	PUNCT
ejpam-3636	77	12	such	such	ADJ
ejpam-3636	77	13	that	that	DET
ejpam-3636	77	14	ξ(x	ξ(x	NOUN
ejpam-3636	77	15	)	)	PUNCT
ejpam-3636	77	16	is	be	AUX
ejpam-3636	77	17	positive	positive	ADJ
ejpam-3636	77	18	,	,	PUNCT
ejpam-3636	77	19	strictly	strictly	ADV
ejpam-3636	77	20	increasing	increase	VERB
ejpam-3636	77	21	and	and	CCONJ
ejpam-3636	77	22	differentiable	differentiable	ADJ
ejpam-3636	77	23	and	and	CCONJ
ejpam-3636	77	24	tends	tend	VERB
ejpam-3636	77	25	to	to	ADP
ejpam-3636	77	26	∞	∞	PROPN
ejpam-3636	77	27	as	as	ADP
ejpam-3636	77	28	x	x	X
ejpam-3636	77	29	→	→	SYM
ejpam-3636	77	30	∞.	∞.	PROPN
ejpam-3636	77	31	then	then	ADV
ejpam-3636	77	32	ξ	ξ	PROPN
ejpam-3636	77	33	is	be	AUX
ejpam-3636	77	34	said	say	VERB
ejpam-3636	77	35	to	to	PART
ejpam-3636	77	36	belong	belong	VERB
ejpam-3636	77	37	to	to	ADP
ejpam-3636	77	38	the	the	DET
ejpam-3636	77	39	class	class	NOUN
ejpam-3636	77	40	l0	l0	PROPN
ejpam-3636	77	41	if	if	SCONJ
ejpam-3636	77	42	for	for	ADP
ejpam-3636	77	43	every	every	DET
ejpam-3636	77	44	real	real	ADV
ejpam-3636	77	45	valued	value	VERB
ejpam-3636	77	46	function	function	NOUN
ejpam-3636	77	47	φ(x	φ(x	NOUN
ejpam-3636	77	48	)	)	PUNCT
ejpam-3636	77	49	such	such	ADJ
ejpam-3636	77	50	that	that	SCONJ
ejpam-3636	77	51	φ(x)→	φ(x)→	NUM
ejpam-3636	77	52	0	0	PUNCT
ejpam-3636	77	53	as	as	ADP
ejpam-3636	77	54	x→∞	x→∞	NUM
ejpam-3636	77	55	,	,	PUNCT
ejpam-3636	77	56	ξ	ξ	PROPN
ejpam-3636	77	57	satisfies	satisfie	NOUN
ejpam-3636	77	58	lim	lim	PROPN
ejpam-3636	77	59	x→∞	x→∞	NUM
ejpam-3636	78	1	ξ[(1	ξ[(1	PROPN
ejpam-3636	78	2	+	+	PUNCT
ejpam-3636	78	3	φ(x))x	φ(x))x	PROPN
ejpam-3636	78	4	]	]	X
ejpam-3636	78	5	ξ(x	ξ(x	NOUN
ejpam-3636	78	6	)	)	PUNCT
ejpam-3636	78	7	=	=	SYM
ejpam-3636	79	1	1	1	NUM
ejpam-3636	79	2	,	,	PUNCT
ejpam-3636	79	3	and	and	CCONJ
ejpam-3636	79	4	belongs	belong	VERB
ejpam-3636	79	5	to	to	ADP
ejpam-3636	79	6	the	the	DET
ejpam-3636	79	7	class	class	NOUN
ejpam-3636	79	8	λ	λ	PROPN
ejpam-3636	79	9	if	if	SCONJ
ejpam-3636	79	10	for	for	ADP
ejpam-3636	79	11	all	all	DET
ejpam-3636	79	12	c	c	NOUN
ejpam-3636	79	13	,	,	PUNCT
ejpam-3636	79	14	0	0	PUNCT
ejpam-3636	79	15	<	<	X
ejpam-3636	79	16	c	c	X
ejpam-3636	79	17	<	<	X
ejpam-3636	79	18	∞	∞	PROPN
ejpam-3636	79	19	,	,	PUNCT
ejpam-3636	79	20	we	we	PRON
ejpam-3636	79	21	have	have	VERB
ejpam-3636	79	22	the	the	DET
ejpam-3636	79	23	stronger	strong	ADJ
ejpam-3636	79	24	condition	condition	NOUN
ejpam-3636	79	25	lim	lim	NOUN
ejpam-3636	79	26	x→∞	x→∞	NUM
ejpam-3636	79	27	ξ(cx	ξ(cx	PROPN
ejpam-3636	79	28	)	)	PUNCT
ejpam-3636	79	29	ξ(x	ξ(x	NOUN
ejpam-3636	79	30	)	)	PUNCT
ejpam-3636	80	1	=	=	SYM
ejpam-3636	81	1	1	1	X
ejpam-3636	81	2	.	.	PUNCT
ejpam-3636	81	3	let	let	VERB
ejpam-3636	81	4	α	α	PRON
ejpam-3636	81	5	,	,	PUNCT
ejpam-3636	81	6	β	β	PROPN
ejpam-3636	81	7	∈	∈	PROPN
ejpam-3636	81	8	l0,λ	l0,λ	PROPN
ejpam-3636	81	9	,	,	PUNCT
ejpam-3636	81	10	following	follow	VERB
ejpam-3636	81	11	the	the	DET
ejpam-3636	81	12	analogy	analogy	NOUN
ejpam-3636	81	13	with	with	ADP
ejpam-3636	81	14	[	[	X
ejpam-3636	81	15	18	18	NUM
ejpam-3636	81	16	]	]	PUNCT
ejpam-3636	81	17	,	,	PUNCT
ejpam-3636	81	18	we	we	PRON
ejpam-3636	81	19	define	define	VERB
ejpam-3636	81	20	generalized	generalized	ADJ
ejpam-3636	81	21	and	and	CCONJ
ejpam-3636	81	22	lower	low	ADJ
ejpam-3636	81	23	generalized	generalized	ADJ
ejpam-3636	81	24	order	order	NOUN
ejpam-3636	81	25	of	of	ADP
ejpam-3636	81	26	the	the	DET
ejpam-3636	81	27	entire	entire	ADJ
ejpam-3636	81	28	harmonic	harmonic	ADJ
ejpam-3636	81	29	function	function	NOUN
ejpam-3636	81	30	h	h	PROPN
ejpam-3636	81	31	∈	∈	PROPN
ejpam-3636	81	32	rn	rn	PROPN
ejpam-3636	81	33	by	by	ADP
ejpam-3636	81	34	d.	d.	PROPN
ejpam-3636	81	35	kumar	kumar	PROPN
ejpam-3636	81	36	,	,	PUNCT
ejpam-3636	81	37	r.k	r.k	PROPN
ejpam-3636	81	38	.	.	PROPN
ejpam-3636	81	39	vishnoi	vishnoi	PROPN
ejpam-3636	81	40	/	/	SYM
ejpam-3636	81	41	eur	eur	PROPN
ejpam-3636	81	42	.	.	PUNCT
ejpam-3636	82	1	j.	j.	PROPN
ejpam-3636	82	2	pure	pure	PROPN
ejpam-3636	82	3	appl	appl	PROPN
ejpam-3636	82	4	.	.	PROPN
ejpam-3636	82	5	math	math	PROPN
ejpam-3636	82	6	,	,	PUNCT
ejpam-3636	82	7	13	13	NUM
ejpam-3636	82	8	(	(	PUNCT
ejpam-3636	82	9	2	2	NUM
ejpam-3636	82	10	)	)	PUNCT
ejpam-3636	82	11	(	(	PUNCT
ejpam-3636	82	12	2020	2020	NUM
ejpam-3636	82	13	)	)	PUNCT
ejpam-3636	82	14	,	,	PUNCT
ejpam-3636	82	15	258	258	NUM
ejpam-3636	82	16	-	-	SYM
ejpam-3636	82	17	268	268	NUM
ejpam-3636	82	18	262	262	NUM
ejpam-3636	82	19	ρ(α	ρ(α	NOUN
ejpam-3636	82	20	,	,	PUNCT
ejpam-3636	82	21	β	β	X
ejpam-3636	82	22	,	,	PUNCT
ejpam-3636	82	23	h	h	NOUN
ejpam-3636	82	24	)	)	PUNCT
ejpam-3636	82	25	=	=	SYM
ejpam-3636	82	26	lim	lim	PROPN
ejpam-3636	82	27	sup	sup	PROPN
ejpam-3636	82	28	r→∞	r→∞	X
ejpam-3636	82	29	α(logm(r	α(logm(r	NOUN
ejpam-3636	82	30	,	,	PUNCT
ejpam-3636	82	31	h	h	NOUN
ejpam-3636	82	32	)	)	PUNCT
ejpam-3636	82	33	)	)	PUNCT
ejpam-3636	83	1	β(r	β(r	NOUN
ejpam-3636	83	2	)	)	PUNCT
ejpam-3636	83	3	,	,	PUNCT
ejpam-3636	83	4	λ(α	λ(α	PROPN
ejpam-3636	83	5	,	,	PUNCT
ejpam-3636	83	6	β	β	X
ejpam-3636	83	7	,	,	PUNCT
ejpam-3636	83	8	h	h	NOUN
ejpam-3636	83	9	)	)	PUNCT
ejpam-3636	83	10	=	=	SYM
ejpam-3636	83	11	lim	lim	PROPN
ejpam-3636	83	12	inf	inf	PROPN
ejpam-3636	83	13	r→∞	r→∞	PUNCT
ejpam-3636	83	14	α(logm(r	α(logm(r	NOUN
ejpam-3636	83	15	,	,	PUNCT
ejpam-3636	83	16	h	h	NOUN
ejpam-3636	83	17	)	)	PUNCT
ejpam-3636	83	18	)	)	PUNCT
ejpam-3636	84	1	β(r	β(r	NOUN
ejpam-3636	84	2	)	)	PUNCT
ejpam-3636	84	3	.	.	PUNCT
ejpam-3636	85	1	now	now	ADV
ejpam-3636	85	2	we	we	PRON
ejpam-3636	85	3	prove	prove	VERB
ejpam-3636	85	4	theorem	theorem	ADJ
ejpam-3636	85	5	2.1	2.1	NUM
ejpam-3636	85	6	.	.	PUNCT
ejpam-3636	86	1	let	let	VERB
ejpam-3636	86	2	h	h	PRON
ejpam-3636	86	3	be	be	AUX
ejpam-3636	86	4	a	a	DET
ejpam-3636	86	5	harmonic	harmonic	ADJ
ejpam-3636	86	6	function	function	NOUN
ejpam-3636	86	7	in	in	ADP
ejpam-3636	86	8	a	a	DET
ejpam-3636	86	9	neighborhood	neighborhood	NOUN
ejpam-3636	86	10	of	of	ADP
ejpam-3636	86	11	the	the	DET
ejpam-3636	86	12	origin	origin	NOUN
ejpam-3636	86	13	in	in	ADP
ejpam-3636	86	14	rn	rn	PROPN
ejpam-3636	86	15	,	,	PUNCT
ejpam-3636	86	16	satisfying	satisfy	VERB
ejpam-3636	86	17	one	one	NUM
ejpam-3636	86	18	of	of	ADP
ejpam-3636	86	19	the	the	DET
ejpam-3636	86	20	following	following	ADJ
ejpam-3636	86	21	conditions	condition	NOUN
ejpam-3636	86	22	:	:	PUNCT
ejpam-3636	86	23	(	(	PUNCT
ejpam-3636	86	24	i	i	NOUN
ejpam-3636	86	25	)	)	PUNCT
ejpam-3636	86	26	.	.	PUNCT
ejpam-3636	87	1	for	for	ADP
ejpam-3636	87	2	α	α	NOUN
ejpam-3636	87	3	,	,	PUNCT
ejpam-3636	87	4	β	β	X
ejpam-3636	87	5	∈	∈	PROPN
ejpam-3636	87	6	λ	λ	PROPN
ejpam-3636	87	7	,	,	PUNCT
ejpam-3636	87	8	f	f	PROPN
ejpam-3636	87	9	(	(	PUNCT
ejpam-3636	87	10	t	t	PROPN
ejpam-3636	87	11	,	,	PUNCT
ejpam-3636	87	12	c	c	NOUN
ejpam-3636	87	13	)	)	PUNCT
ejpam-3636	87	14	=	=	SYM
ejpam-3636	87	15	β−1(cα(t	β−1(cα(t	ADJ
ejpam-3636	87	16	)	)	PUNCT
ejpam-3636	87	17	)	)	PUNCT
ejpam-3636	87	18	,	,	PUNCT
ejpam-3636	87	19	0	0	PUNCT
ejpam-3636	87	20	<	<	X
ejpam-3636	87	21	c	c	X
ejpam-3636	87	22	<	<	X
ejpam-3636	87	23	∞	∞	PROPN
ejpam-3636	87	24	,	,	PUNCT
ejpam-3636	87	25	lim	lim	PROPN
ejpam-3636	87	26	t→∞	t→∞	PRON
ejpam-3636	87	27	d(logf	d(logf	NOUN
ejpam-3636	87	28	(	(	PUNCT
ejpam-3636	87	29	t	t	PROPN
ejpam-3636	87	30	,	,	PUNCT
ejpam-3636	87	31	c	c	NOUN
ejpam-3636	87	32	)	)	PUNCT
ejpam-3636	87	33	)	)	PUNCT
ejpam-3636	88	1	d(log	d(log	PROPN
ejpam-3636	88	2	t	t	PROPN
ejpam-3636	88	3	)	)	PUNCT
ejpam-3636	88	4	=	=	SYM
ejpam-3636	88	5	o(1	o(1	NOUN
ejpam-3636	88	6	)	)	PUNCT
ejpam-3636	88	7	.	.	PUNCT
ejpam-3636	89	1	(	(	PUNCT
ejpam-3636	89	2	ii	ii	NOUN
ejpam-3636	89	3	)	)	PUNCT
ejpam-3636	89	4	.	.	PUNCT
ejpam-3636	90	1	for	for	ADP
ejpam-3636	90	2	α	α	NOUN
ejpam-3636	90	3	,	,	PUNCT
ejpam-3636	90	4	β	β	PROPN
ejpam-3636	90	5	∈	∈	PROPN
ejpam-3636	90	6	l0	l0	PROPN
ejpam-3636	90	7	,	,	PUNCT
ejpam-3636	90	8	lim	lim	PROPN
ejpam-3636	90	9	t→∞	t→∞	PRON
ejpam-3636	90	10	d(logf	d(logf	NOUN
ejpam-3636	90	11	(	(	PUNCT
ejpam-3636	90	12	t	t	PROPN
ejpam-3636	90	13	,	,	PUNCT
ejpam-3636	90	14	c	c	NOUN
ejpam-3636	90	15	)	)	PUNCT
ejpam-3636	90	16	)	)	PUNCT
ejpam-3636	90	17	d(log	d(log	PROPN
ejpam-3636	90	18	t	t	PROPN
ejpam-3636	90	19	)	)	PUNCT
ejpam-3636	91	1	=	=	SYM
ejpam-3636	92	1	p	p	NOUN
ejpam-3636	92	2	,	,	PUNCT
ejpam-3636	92	3	0	0	PUNCT
ejpam-3636	92	4	<	<	X
ejpam-3636	92	5	p	p	X
ejpam-3636	92	6	<	<	X
ejpam-3636	92	7	∞	∞	PROPN
ejpam-3636	92	8	,	,	PUNCT
ejpam-3636	92	9	then	then	ADV
ejpam-3636	92	10	the	the	DET
ejpam-3636	92	11	generalized	generalized	ADJ
ejpam-3636	92	12	order	order	NOUN
ejpam-3636	92	13	ρ(α	ρ(α	NOUN
ejpam-3636	92	14	,	,	PUNCT
ejpam-3636	92	15	β	β	X
ejpam-3636	92	16	,	,	PUNCT
ejpam-3636	92	17	h	h	NOUN
ejpam-3636	92	18	)	)	PUNCT
ejpam-3636	92	19	of	of	ADP
ejpam-3636	92	20	entire	entire	ADJ
ejpam-3636	92	21	harmonic	harmonic	ADJ
ejpam-3636	92	22	function	function	NOUN
ejpam-3636	92	23	h	h	NOUN
ejpam-3636	92	24	is	be	AUX
ejpam-3636	92	25	determined	determine	VERB
ejpam-3636	92	26	by	by	ADP
ejpam-3636	92	27	ρ(α	ρ(α	NOUN
ejpam-3636	92	28	,	,	PUNCT
ejpam-3636	92	29	β	β	X
ejpam-3636	92	30	,	,	PUNCT
ejpam-3636	92	31	h	h	NOUN
ejpam-3636	92	32	)	)	PUNCT
ejpam-3636	93	1	=	=	SYM
ejpam-3636	93	2	lim	lim	PROPN
ejpam-3636	93	3	sup	sup	PROPN
ejpam-3636	93	4	k→∞	k→∞	NOUN
ejpam-3636	93	5	α(pk	α(pk	ADV
ejpam-3636	93	6	)	)	PUNCT
ejpam-3636	93	7	β(epr	β(epr	PROPN
ejpam-3636	93	8	[	[	PUNCT
ejpam-3636	93	9	|∇kh(0)|	|∇kh(0)|	NOUN
ejpam-3636	93	10	k	k	NOUN
ejpam-3636	93	11	!	!	PUNCT
ejpam-3636	93	12	]	]	PUNCT
ejpam-3636	94	1	−1	−1	NOUN
ejpam-3636	94	2	k	k	PROPN
ejpam-3636	94	3	)	)	PUNCT
ejpam-3636	94	4	.	.	PUNCT
ejpam-3636	95	1	proof	proof	NOUN
ejpam-3636	95	2	.	.	PUNCT
ejpam-3636	96	1	consider	consider	VERB
ejpam-3636	96	2	the	the	DET
ejpam-3636	96	3	entire	entire	ADJ
ejpam-3636	96	4	functions	function	NOUN
ejpam-3636	96	5	of	of	ADP
ejpam-3636	96	6	single	single	ADJ
ejpam-3636	96	7	complex	complex	ADJ
ejpam-3636	96	8	variable	variable	ADJ
ejpam-3636	96	9	z	z	NOUN
ejpam-3636	96	10	:	:	PUNCT
ejpam-3636	96	11	f1(z	f1(z	ADJ
ejpam-3636	96	12	)	)	PUNCT
ejpam-3636	96	13	=	=	SYM
ejpam-3636	96	14	√	√	NUM
ejpam-3636	96	15	γ(n/2	γ(n/2	NOUN
ejpam-3636	96	16	)	)	PUNCT
ejpam-3636	97	1	∞∑	∞∑	NUM
ejpam-3636	97	2	k=1	k=1	ADP
ejpam-3636	97	3	|∇kh(0)|√	|∇kh(0)|√	PUNCT
ejpam-3636	98	1	k!γ(k	k!γ(k	PROPN
ejpam-3636	98	2	+	+	CCONJ
ejpam-3636	98	3	n/2	n/2	PROPN
ejpam-3636	98	4	)	)	PUNCT
ejpam-3636	98	5	(	(	PUNCT
ejpam-3636	98	6	z	z	NOUN
ejpam-3636	98	7	r	r	NOUN
ejpam-3636	98	8	)	)	PUNCT
ejpam-3636	99	1	k	k	NOUN
ejpam-3636	99	2	,	,	PUNCT
ejpam-3636	99	3	and	and	CCONJ
ejpam-3636	99	4	f2(z	f2(z	X
ejpam-3636	99	5	)	)	PUNCT
ejpam-3636	99	6	=	=	SYM
ejpam-3636	99	7	√	√	NUM
ejpam-3636	99	8	γ(n/2	γ(n/2	NOUN
ejpam-3636	99	9	)	)	PUNCT
ejpam-3636	100	1	∞∑	∞∑	NUM
ejpam-3636	100	2	k=1	k=1	ADJ
ejpam-3636	100	3	√	√	PUNCT
ejpam-3636	101	1	dk	dk	INTJ
ejpam-3636	101	2	|∇kh(0)|√	|∇kh(0)|√	PUNCT
ejpam-3636	101	3	k!γ(k	k!γ(k	PROPN
ejpam-3636	101	4	+	+	CCONJ
ejpam-3636	101	5	n/2	n/2	PROPN
ejpam-3636	101	6	)	)	PUNCT
ejpam-3636	101	7	(	(	PUNCT
ejpam-3636	101	8	z	z	NOUN
ejpam-3636	101	9	r	r	NOUN
ejpam-3636	101	10	)	)	PUNCT
ejpam-3636	101	11	k.	k.	PROPN
ejpam-3636	102	1	since	since	SCONJ
ejpam-3636	102	2	γ(k	γ(k	PROPN
ejpam-3636	102	3	+	+	CCONJ
ejpam-3636	102	4	n/2	n/2	X
ejpam-3636	102	5	)	)	PUNCT
ejpam-3636	102	6	γ(k	γ(k	NOUN
ejpam-3636	102	7	+	+	CCONJ
ejpam-3636	102	8	1	1	X
ejpam-3636	102	9	)	)	PUNCT
ejpam-3636	102	10	=	=	SYM
ejpam-3636	103	1	k	k	PROPN
ejpam-3636	103	2	n	n	PROPN
ejpam-3636	103	3	2	2	NUM
ejpam-3636	103	4	−1	−1	NOUN
ejpam-3636	103	5	,	,	PUNCT
ejpam-3636	103	6	we	we	PRON
ejpam-3636	103	7	have	have	VERB
ejpam-3636	103	8	√	√	NUM
ejpam-3636	103	9	dk	dk	PRON
ejpam-3636	103	10	√	√	PROPN
ejpam-3636	103	11	γ(n/2)|∇kh(0)|√	γ(n/2)|∇kh(0)|√	VERB
ejpam-3636	103	12	k!γ(k	k!γ(k	PROPN
ejpam-3636	103	13	+	+	CCONJ
ejpam-3636	103	14	n/2	n/2	PROPN
ejpam-3636	103	15	)	)	PUNCT
ejpam-3636	103	16	'	'	PART
ejpam-3636	103	17	√	√	NOUN
ejpam-3636	103	18	dk	dk	PROPN
ejpam-3636	103	19	√	√	PROPN
ejpam-3636	103	20	γ(n/2)|∇kh(0)|	γ(n/2)|∇kh(0)|	NOUN
ejpam-3636	103	21	k!k(n−2)/4	k!k(n−2)/4	NOUN
ejpam-3636	103	22	,	,	PUNCT
ejpam-3636	103	23	as	as	ADP
ejpam-3636	103	24	(	(	PUNCT
ejpam-3636	103	25	dk	dk	NOUN
ejpam-3636	103	26	)	)	PUNCT
ejpam-3636	103	27	1	1	NUM
ejpam-3636	103	28	2	2	NUM
ejpam-3636	103	29	=	=	SYM
ejpam-3636	103	30	[	[	PUNCT
ejpam-3636	103	31	(	(	PUNCT
ejpam-3636	103	32	n+	n+	NUM
ejpam-3636	103	33	2k	2k	NOUN
ejpam-3636	103	34	−	−	PROPN
ejpam-3636	103	35	2)(n+	2)(n+	NUM
ejpam-3636	104	1	k	k	NOUN
ejpam-3636	104	2	−	−	NOUN
ejpam-3636	104	3	3	3	NUM
ejpam-3636	104	4	)	)	PUNCT
ejpam-3636	104	5	!	!	PUNCT
ejpam-3636	105	1	k!(n−	k!(n−	PROPN
ejpam-3636	105	2	2	2	NUM
ejpam-3636	105	3	)	)	PUNCT
ejpam-3636	105	4	!	!	PUNCT
ejpam-3636	106	1	]	]	PUNCT
ejpam-3636	107	1	1	1	NUM
ejpam-3636	107	2	2	2	NUM
ejpam-3636	107	3	=	=	SYM
ejpam-3636	107	4	[	[	PUNCT
ejpam-3636	107	5	(	(	PUNCT
ejpam-3636	107	6	n+	n+	NUM
ejpam-3636	107	7	k	k	NOUN
ejpam-3636	107	8	−	−	NOUN
ejpam-3636	108	1	3	3	NUM
ejpam-3636	108	2	)	)	PUNCT
ejpam-3636	108	3	!	!	PUNCT
ejpam-3636	109	1	(	(	PUNCT
ejpam-3636	109	2	k	k	X
ejpam-3636	109	3	−	−	NOUN
ejpam-3636	109	4	1	1	NUM
ejpam-3636	109	5	)	)	PUNCT
ejpam-3636	109	6	!	!	PUNCT
ejpam-3636	109	7	]	]	PUNCT
ejpam-3636	110	1	1	1	NUM
ejpam-3636	110	2	2	2	NUM
ejpam-3636	110	3	=	=	SYM
ejpam-3636	110	4	k	k	X
ejpam-3636	110	5	(	(	PUNCT
ejpam-3636	110	6	n−2	n−2	PROPN
ejpam-3636	110	7	)	)	PUNCT
ejpam-3636	110	8	2	2	NUM
ejpam-3636	110	9	.	.	PUNCT
ejpam-3636	111	1	d.	d.	PROPN
ejpam-3636	111	2	kumar	kumar	PROPN
ejpam-3636	111	3	,	,	PUNCT
ejpam-3636	111	4	r.k	r.k	PROPN
ejpam-3636	111	5	.	.	PROPN
ejpam-3636	111	6	vishnoi	vishnoi	PROPN
ejpam-3636	111	7	/	/	SYM
ejpam-3636	111	8	eur	eur	PROPN
ejpam-3636	111	9	.	.	PUNCT
ejpam-3636	112	1	j.	j.	PROPN
ejpam-3636	112	2	pure	pure	PROPN
ejpam-3636	112	3	appl	appl	PROPN
ejpam-3636	112	4	.	.	PROPN
ejpam-3636	112	5	math	math	PROPN
ejpam-3636	112	6	,	,	PUNCT
ejpam-3636	112	7	13	13	NUM
ejpam-3636	112	8	(	(	PUNCT
ejpam-3636	112	9	2	2	NUM
ejpam-3636	112	10	)	)	PUNCT
ejpam-3636	112	11	(	(	PUNCT
ejpam-3636	112	12	2020	2020	NUM
ejpam-3636	112	13	)	)	PUNCT
ejpam-3636	112	14	,	,	PUNCT
ejpam-3636	112	15	258	258	NUM
ejpam-3636	112	16	-	-	SYM
ejpam-3636	112	17	268	268	NUM
ejpam-3636	112	18	263	263	NUM
ejpam-3636	112	19	therefore	therefore	ADV
ejpam-3636	112	20	,	,	PUNCT
ejpam-3636	112	21	√	√	PROPN
ejpam-3636	112	22	dk	dk	PROPN
ejpam-3636	112	23	√	√	PROPN
ejpam-3636	112	24	γ(n/2)|∇kh(0)|√	γ(n/2)|∇kh(0)|√	VERB
ejpam-3636	112	25	k!γ(k	k!γ(k	PROPN
ejpam-3636	112	26	+	+	CCONJ
ejpam-3636	112	27	n/2	n/2	PROPN
ejpam-3636	112	28	)	)	PUNCT
ejpam-3636	112	29	'	'	PART
ejpam-3636	112	30	√	√	PROPN
ejpam-3636	112	31	γ(n/2)|∇kh(0)|k(n−2)/4	γ(n/2)|∇kh(0)|k(n−2)/4	PROPN
ejpam-3636	112	32	k	k	NOUN
ejpam-3636	112	33	!	!	PROPN
ejpam-3636	112	34	,	,	PUNCT
ejpam-3636	112	35	or	or	CCONJ
ejpam-3636	112	36	lim	lim	PROPN
ejpam-3636	112	37	k→∞	k→∞	NOUN
ejpam-3636	113	1	[	[	PUNCT
ejpam-3636	113	2	√	√	INTJ
ejpam-3636	113	3	dk	dk	PROPN
ejpam-3636	113	4	√	√	PROPN
ejpam-3636	113	5	γ(n/2)|∇kh(0)|√	γ(n/2)|∇kh(0)|√	VERB
ejpam-3636	113	6	k!γ(k	k!γ(k	PROPN
ejpam-3636	113	7	+	+	CCONJ
ejpam-3636	113	8	n/2	n/2	PROPN
ejpam-3636	113	9	)	)	PUNCT
ejpam-3636	113	10	]	]	PUNCT
ejpam-3636	113	11	−	−	PROPN
ejpam-3636	113	12	1	1	NUM
ejpam-3636	113	13	k	k	NOUN
ejpam-3636	113	14	'	'	PUNCT
ejpam-3636	113	15	[	[	PUNCT
ejpam-3636	113	16	|∇kh(0)|	|∇kh(0)|	NOUN
ejpam-3636	113	17	k	k	NOUN
ejpam-3636	113	18	!	!	PUNCT
ejpam-3636	114	1	]	]	X
ejpam-3636	114	2	−	−	PROPN
ejpam-3636	114	3	1	1	NUM
ejpam-3636	114	4	k	k	NOUN
ejpam-3636	114	5	.	.	PUNCT
ejpam-3636	115	1	hence	hence	ADV
ejpam-3636	115	2	f1(z	f1(z	PROPN
ejpam-3636	115	3	)	)	PUNCT
ejpam-3636	115	4	and	and	CCONJ
ejpam-3636	115	5	f2(z	f2(z	NOUN
ejpam-3636	115	6	)	)	PUNCT
ejpam-3636	115	7	defined	define	VERB
ejpam-3636	115	8	above	above	ADV
ejpam-3636	115	9	are	be	AUX
ejpam-3636	115	10	entire	entire	ADJ
ejpam-3636	115	11	functions	function	NOUN
ejpam-3636	115	12	in	in	ADP
ejpam-3636	115	13	view	view	NOUN
ejpam-3636	115	14	of	of	ADP
ejpam-3636	115	15	(	(	PUNCT
ejpam-3636	115	16	1.5	1.5	NUM
ejpam-3636	115	17	)	)	PUNCT
ejpam-3636	115	18	.	.	PUNCT
ejpam-3636	116	1	using	use	VERB
ejpam-3636	116	2	lemma	lemma	PROPN
ejpam-3636	116	3	a	a	PROPN
ejpam-3636	116	4	,	,	PUNCT
ejpam-3636	116	5	we	we	PRON
ejpam-3636	116	6	obtain	obtain	VERB
ejpam-3636	116	7	µ(r	µ(r	NOUN
ejpam-3636	116	8	,	,	PUNCT
ejpam-3636	116	9	f1	f1	NOUN
ejpam-3636	116	10	)	)	PUNCT
ejpam-3636	116	11	≤m(r	≤m(r	NOUN
ejpam-3636	116	12	,	,	PUNCT
ejpam-3636	116	13	h	h	NOUN
ejpam-3636	116	14	)	)	PUNCT
ejpam-3636	116	15	≤m(r	≤m(r	PROPN
ejpam-3636	116	16	,	,	PUNCT
ejpam-3636	116	17	f2	f2	PROPN
ejpam-3636	116	18	)	)	PUNCT
ejpam-3636	116	19	,	,	PUNCT
ejpam-3636	116	20	(	(	PUNCT
ejpam-3636	116	21	2.1	2.1	NUM
ejpam-3636	116	22	)	)	PUNCT
ejpam-3636	116	23	where	where	SCONJ
ejpam-3636	116	24	µ(r	µ(r	NOUN
ejpam-3636	116	25	,	,	PUNCT
ejpam-3636	116	26	f1	f1	NOUN
ejpam-3636	116	27	)	)	PUNCT
ejpam-3636	116	28	is	be	AUX
ejpam-3636	116	29	the	the	DET
ejpam-3636	116	30	maximum	maximum	ADJ
ejpam-3636	116	31	term	term	NOUN
ejpam-3636	116	32	of	of	ADP
ejpam-3636	116	33	the	the	DET
ejpam-3636	116	34	power	power	NOUN
ejpam-3636	116	35	series	series	PROPN
ejpam-3636	116	36	expansion	expansion	NOUN
ejpam-3636	116	37	of	of	ADP
ejpam-3636	116	38	function	function	NOUN
ejpam-3636	116	39	f1(z	f1(z	PROPN
ejpam-3636	116	40	)	)	PUNCT
ejpam-3636	116	41	on	on	ADP
ejpam-3636	116	42	the	the	DET
ejpam-3636	116	43	circle	circle	NOUN
ejpam-3636	116	44	|z|	|z|	NOUN
ejpam-3636	116	45	=	=	SYM
ejpam-3636	116	46	r	r	NOUN
ejpam-3636	116	47	and	and	CCONJ
ejpam-3636	116	48	m(r	m(r	PROPN
ejpam-3636	116	49	,	,	PUNCT
ejpam-3636	116	50	f2	f2	PROPN
ejpam-3636	116	51	)	)	PUNCT
ejpam-3636	116	52	=	=	SYM
ejpam-3636	116	53	max|z|=r	max|z|=r	PROPN
ejpam-3636	116	54	|f2(z)|	|f2(z)|	NOUN
ejpam-3636	116	55	.	.	PUNCT
ejpam-3636	117	1	we	we	PRON
ejpam-3636	117	2	see	see	VERB
ejpam-3636	117	3	that	that	PRON
ejpam-3636	117	4	|f1(z)|2	|f1(z)|2	NOUN
ejpam-3636	117	5	=	=	PUNCT
ejpam-3636	118	1	∞∑	∞∑	NUM
ejpam-3636	118	2	k=0	k=0	PROPN
ejpam-3636	118	3	{	{	PUNCT
ejpam-3636	118	4	√	√	PUNCT
ejpam-3636	118	5	γ(n/2)|∇kh(0)|√	γ(n/2)|∇kh(0)|√	VERB
ejpam-3636	118	6	k!γ(k	k!γ(k	PROPN
ejpam-3636	118	7	+	+	CCONJ
ejpam-3636	118	8	n/2	n/2	PROPN
ejpam-3636	118	9	)	)	PUNCT
ejpam-3636	118	10	}	}	PUNCT
ejpam-3636	118	11	2	2	NUM
ejpam-3636	118	12	(	(	PUNCT
ejpam-3636	118	13	r	r	NOUN
ejpam-3636	118	14	r	r	NOUN
ejpam-3636	118	15	)	)	PUNCT
ejpam-3636	118	16	2k	2k	NOUN
ejpam-3636	119	1	+	+	CCONJ
ejpam-3636	119	2	∑	∑	PROPN
ejpam-3636	119	3	k	k	PROPN
ejpam-3636	119	4	6	6	NUM
ejpam-3636	119	5	=	=	NOUN
ejpam-3636	119	6	m	m	NOUN
ejpam-3636	119	7	{	{	PUNCT
ejpam-3636	119	8	√	√	PROPN
ejpam-3636	119	9	γ(n/2)|∇kh(0)||∇m|h(0)|√	γ(n/2)|∇kh(0)||∇m|h(0)|√	PROPN
ejpam-3636	119	10	k!m!γ(k	k!m!γ(k	PROPN
ejpam-3636	120	1	+	+	CCONJ
ejpam-3636	120	2	n/2)γ(m+	n/2)γ(m+	X
ejpam-3636	120	3	n/2	n/2	NOUN
ejpam-3636	120	4	)	)	PUNCT
ejpam-3636	120	5	}	}	PUNCT
ejpam-3636	120	6	(	(	PUNCT
ejpam-3636	120	7	z	z	NOUN
ejpam-3636	120	8	r	r	NOUN
ejpam-3636	120	9	)	)	PUNCT
ejpam-3636	120	10	k	k	NOUN
ejpam-3636	120	11	(	(	PUNCT
ejpam-3636	120	12	z	z	NOUN
ejpam-3636	120	13	r	r	NOUN
ejpam-3636	120	14	)	)	PUNCT
ejpam-3636	120	15	m.	m.	NOUN
ejpam-3636	120	16	(	(	PUNCT
ejpam-3636	120	17	2.2	2.2	NUM
ejpam-3636	120	18	)	)	PUNCT
ejpam-3636	120	19	using	use	VERB
ejpam-3636	120	20	(	(	PUNCT
ejpam-3636	120	21	2.2	2.2	NUM
ejpam-3636	120	22	)	)	PUNCT
ejpam-3636	120	23	with	with	ADP
ejpam-3636	120	24	the	the	DET
ejpam-3636	120	25	estimate	estimate	NOUN
ejpam-3636	121	1	[	[	X
ejpam-3636	121	2	6	6	NUM
ejpam-3636	121	3	,	,	PUNCT
ejpam-3636	121	4	p.290	p.290	NOUN
ejpam-3636	121	5	]	]	PUNCT
ejpam-3636	121	6	of	of	ADP
ejpam-3636	121	7	m2(r	m2(r	PROPN
ejpam-3636	121	8	,	,	PUNCT
ejpam-3636	121	9	h	h	NOUN
ejpam-3636	121	10	)	)	PUNCT
ejpam-3636	121	11	,	,	PUNCT
ejpam-3636	121	12	we	we	PRON
ejpam-3636	121	13	get	get	VERB
ejpam-3636	121	14	m(r	m(r	PROPN
ejpam-3636	121	15	,	,	PUNCT
ejpam-3636	121	16	f1	f1	NOUN
ejpam-3636	121	17	≥m2(r	≥m2(r	NOUN
ejpam-3636	121	18	,	,	PUNCT
ejpam-3636	121	19	h	h	NOUN
ejpam-3636	121	20	)	)	PUNCT
ejpam-3636	121	21	≥	≥	PROPN
ejpam-3636	122	1	b	b	NOUN
ejpam-3636	122	2	(	(	PUNCT
ejpam-3636	122	3	r	r	NOUN
ejpam-3636	122	4	r	r	NOUN
ejpam-3636	122	5	)	)	PUNCT
ejpam-3636	122	6	k	k	PROPN
ejpam-3636	122	7	|∇kh(0)|	|∇kh(0)|	PROPN
ejpam-3636	122	8	k	k	PROPN
ejpam-3636	122	9	!	!	PROPN
ejpam-3636	122	10	,	,	PUNCT
ejpam-3636	122	11	(	(	PUNCT
ejpam-3636	122	12	2.3	2.3	NUM
ejpam-3636	122	13	)	)	PUNCT
ejpam-3636	122	14	where	where	SCONJ
ejpam-3636	122	15	b	b	NOUN
ejpam-3636	122	16	is	be	AUX
ejpam-3636	122	17	a	a	DET
ejpam-3636	122	18	finite	finite	NOUN
ejpam-3636	122	19	constant	constant	ADJ
ejpam-3636	122	20	.	.	PUNCT
ejpam-3636	123	1	since	since	SCONJ
ejpam-3636	123	2	µ(r	µ(r	NOUN
ejpam-3636	123	3	,	,	PUNCT
ejpam-3636	123	4	f1	f1	NOUN
ejpam-3636	123	5	)	)	PUNCT
ejpam-3636	123	6	is	be	AUX
ejpam-3636	123	7	the	the	DET
ejpam-3636	123	8	maximum	maximum	ADJ
ejpam-3636	123	9	term	term	NOUN
ejpam-3636	123	10	of	of	ADP
ejpam-3636	123	11	f1(z	f1(z	NOUN
ejpam-3636	123	12	)	)	PUNCT
ejpam-3636	123	13	then	then	ADV
ejpam-3636	123	14	by	by	ADP
ejpam-3636	123	15	a	a	DET
ejpam-3636	123	16	result	result	NOUN
ejpam-3636	123	17	of	of	ADP
ejpam-3636	123	18	valiron	valiron	NOUN
ejpam-3636	123	19	[	[	X
ejpam-3636	123	20	22	22	NUM
ejpam-3636	123	21	,	,	PUNCT
ejpam-3636	123	22	p.34	p.34	PROPN
ejpam-3636	123	23	]	]	X
ejpam-3636	123	24	,	,	PUNCT
ejpam-3636	123	25	we	we	PRON
ejpam-3636	123	26	obtain	obtain	VERB
ejpam-3636	123	27	logm(r	logm(r	NOUN
ejpam-3636	123	28	,	,	PUNCT
ejpam-3636	123	29	f1	f1	NOUN
ejpam-3636	123	30	)	)	PUNCT
ejpam-3636	123	31	'	'	PUNCT
ejpam-3636	123	32	logµ(r	logµ(r	NOUN
ejpam-3636	123	33	,	,	PUNCT
ejpam-3636	123	34	f1	f1	NOUN
ejpam-3636	123	35	)	)	PUNCT
ejpam-3636	123	36	as	as	SCONJ
ejpam-3636	123	37	r	r	NOUN
ejpam-3636	123	38	→∞.	→∞.	X
ejpam-3636	123	39	(	(	PUNCT
ejpam-3636	123	40	2.4	2.4	NUM
ejpam-3636	123	41	)	)	PUNCT
ejpam-3636	123	42	now	now	ADV
ejpam-3636	123	43	taking	take	VERB
ejpam-3636	123	44	into	into	ADP
ejpam-3636	123	45	account	account	NOUN
ejpam-3636	123	46	the	the	DET
ejpam-3636	123	47	definition	definition	NOUN
ejpam-3636	123	48	of	of	ADP
ejpam-3636	123	49	ρ(α	ρ(α	NOUN
ejpam-3636	123	50	,	,	PUNCT
ejpam-3636	123	51	β	β	X
ejpam-3636	123	52	,	,	PUNCT
ejpam-3636	123	53	h	h	NOUN
ejpam-3636	123	54	)	)	PUNCT
ejpam-3636	123	55	with	with	ADP
ejpam-3636	123	56	(	(	PUNCT
ejpam-3636	123	57	2.1	2.1	NUM
ejpam-3636	123	58	)	)	PUNCT
ejpam-3636	123	59	and	and	CCONJ
ejpam-3636	123	60	(	(	PUNCT
ejpam-3636	123	61	2.4	2.4	NUM
ejpam-3636	123	62	)	)	PUNCT
ejpam-3636	123	63	we	we	PRON
ejpam-3636	123	64	get	get	VERB
ejpam-3636	123	65	ρ(α	ρ(α	NOUN
ejpam-3636	123	66	,	,	PUNCT
ejpam-3636	123	67	β	β	NOUN
ejpam-3636	123	68	,	,	PUNCT
ejpam-3636	123	69	f1	f1	NOUN
ejpam-3636	123	70	)	)	PUNCT
ejpam-3636	123	71	≤	≤	NOUN
ejpam-3636	123	72	ρ(α	ρ(α	NOUN
ejpam-3636	123	73	,	,	PUNCT
ejpam-3636	123	74	β	β	X
ejpam-3636	123	75	,	,	PUNCT
ejpam-3636	123	76	h	h	NOUN
ejpam-3636	123	77	)	)	PUNCT
ejpam-3636	123	78	≤	≤	NOUN
ejpam-3636	123	79	ρ(α	ρ(α	NOUN
ejpam-3636	123	80	,	,	PUNCT
ejpam-3636	123	81	β	β	X
ejpam-3636	123	82	,	,	PUNCT
ejpam-3636	123	83	f2	f2	PROPN
ejpam-3636	123	84	)	)	PUNCT
ejpam-3636	123	85	.	.	PUNCT
ejpam-3636	124	1	applying	apply	VERB
ejpam-3636	124	2	the	the	DET
ejpam-3636	124	3	coefficient	coefficient	NOUN
ejpam-3636	124	4	formula	formula	NOUN
ejpam-3636	124	5	of	of	ADP
ejpam-3636	124	6	generalized	generalized	ADJ
ejpam-3636	124	7	order	order	NOUN
ejpam-3636	124	8	of	of	ADP
ejpam-3636	124	9	an	an	DET
ejpam-3636	124	10	entire	entire	ADJ
ejpam-3636	124	11	function	function	NOUN
ejpam-3636	124	12	of	of	ADP
ejpam-3636	124	13	one	one	NUM
ejpam-3636	124	14	complex	complex	ADJ
ejpam-3636	124	15	variable	variable	NOUN
ejpam-3636	124	16	[	[	X
ejpam-3636	124	17	18	18	NUM
ejpam-3636	124	18	]	]	PUNCT
ejpam-3636	124	19	and	and	CCONJ
ejpam-3636	124	20	bearing	bear	VERB
ejpam-3636	124	21	in	in	ADP
ejpam-3636	124	22	mind	mind	NOUN
ejpam-3636	124	23	that	that	SCONJ
ejpam-3636	124	24	β	β	X
ejpam-3636	124	25	∈	∈	PROPN
ejpam-3636	124	26	λ	λ	PROPN
ejpam-3636	124	27	or	or	CCONJ
ejpam-3636	124	28	l0	l0	PROPN
ejpam-3636	124	29	,	,	PUNCT
ejpam-3636	124	30	we	we	PRON
ejpam-3636	124	31	obtain	obtain	VERB
ejpam-3636	124	32	ρ(α	ρ(α	NOUN
ejpam-3636	124	33	,	,	PUNCT
ejpam-3636	124	34	β	β	NOUN
ejpam-3636	124	35	,	,	PUNCT
ejpam-3636	124	36	f1	f1	NOUN
ejpam-3636	124	37	)	)	PUNCT
ejpam-3636	124	38	=	=	SYM
ejpam-3636	124	39	ρ(α	ρ(α	NOUN
ejpam-3636	124	40	,	,	PUNCT
ejpam-3636	124	41	β	β	X
ejpam-3636	124	42	,	,	PUNCT
ejpam-3636	124	43	f2	f2	PROPN
ejpam-3636	124	44	=	=	PROPN
ejpam-3636	124	45	lim	lim	PROPN
ejpam-3636	124	46	sup	sup	PROPN
ejpam-3636	124	47	k→∞	k→∞	NOUN
ejpam-3636	124	48	α(pk	α(pk	ADV
ejpam-3636	124	49	)	)	PUNCT
ejpam-3636	124	50	β(epr	β(epr	PROPN
ejpam-3636	124	51	[	[	PUNCT
ejpam-3636	124	52	|∇kh(0)|	|∇kh(0)|	NOUN
ejpam-3636	124	53	k	k	NOUN
ejpam-3636	124	54	!	!	PUNCT
ejpam-3636	125	1	]	]	X
ejpam-3636	125	2	−	−	PROPN
ejpam-3636	125	3	1	1	NUM
ejpam-3636	125	4	k	k	NOUN
ejpam-3636	125	5	)	)	PUNCT
ejpam-3636	125	6	.	.	PUNCT
ejpam-3636	126	1	(	(	PUNCT
ejpam-3636	126	2	2.5	2.5	NUM
ejpam-3636	126	3	)	)	PUNCT
ejpam-3636	126	4	d.	d.	PROPN
ejpam-3636	126	5	kumar	kumar	PROPN
ejpam-3636	126	6	,	,	PUNCT
ejpam-3636	126	7	r.k	r.k	PROPN
ejpam-3636	126	8	.	.	PROPN
ejpam-3636	126	9	vishnoi	vishnoi	PROPN
ejpam-3636	126	10	/	/	SYM
ejpam-3636	126	11	eur	eur	PROPN
ejpam-3636	126	12	.	.	PUNCT
ejpam-3636	127	1	j.	j.	PROPN
ejpam-3636	127	2	pure	pure	PROPN
ejpam-3636	127	3	appl	appl	PROPN
ejpam-3636	127	4	.	.	PROPN
ejpam-3636	127	5	math	math	PROPN
ejpam-3636	127	6	,	,	PUNCT
ejpam-3636	127	7	13	13	NUM
ejpam-3636	127	8	(	(	PUNCT
ejpam-3636	127	9	2	2	NUM
ejpam-3636	127	10	)	)	PUNCT
ejpam-3636	127	11	(	(	PUNCT
ejpam-3636	127	12	2020	2020	NUM
ejpam-3636	127	13	)	)	PUNCT
ejpam-3636	127	14	,	,	PUNCT
ejpam-3636	127	15	258	258	NUM
ejpam-3636	127	16	-	-	SYM
ejpam-3636	127	17	268	268	NUM
ejpam-3636	127	18	264	264	NUM
ejpam-3636	127	19	remark	remark	NOUN
ejpam-3636	127	20	2.1	2.1	NUM
ejpam-3636	127	21	.	.	PUNCT
ejpam-3636	128	1	if	if	SCONJ
ejpam-3636	128	2	α(x	α(x	NOUN
ejpam-3636	128	3	)	)	PUNCT
ejpam-3636	128	4	=	=	SYM
ejpam-3636	129	1	β(x	β(x	PROPN
ejpam-3636	129	2	)	)	PUNCT
ejpam-3636	129	3	=	=	SYM
ejpam-3636	130	1	log	log	NOUN
ejpam-3636	130	2	x	x	NOUN
ejpam-3636	130	3	,	,	PUNCT
ejpam-3636	130	4	we	we	PRON
ejpam-3636	130	5	get	get	VERB
ejpam-3636	130	6	the	the	DET
ejpam-3636	130	7	classical	classical	ADJ
ejpam-3636	130	8	order	order	NOUN
ejpam-3636	130	9	ρ(h	ρ(h	NOUN
ejpam-3636	130	10	)	)	PUNCT
ejpam-3636	130	11	in	in	ADP
ejpam-3636	130	12	terms	term	NOUN
ejpam-3636	130	13	of	of	ADP
ejpam-3636	130	14	norm	norm	NOUN
ejpam-3636	130	15	of	of	ADP
ejpam-3636	130	16	gradient	gradient	NOUN
ejpam-3636	130	17	at	at	ADP
ejpam-3636	130	18	the	the	DET
ejpam-3636	130	19	origin	origin	NOUN
ejpam-3636	130	20	studied	study	VERB
ejpam-3636	130	21	by	by	ADP
ejpam-3636	130	22	fugard	fugard	NOUN
ejpam-3636	130	23	[	[	X
ejpam-3636	130	24	6	6	NUM
ejpam-3636	130	25	,	,	PUNCT
ejpam-3636	130	26	thm.2.1	thm.2.1	NOUN
ejpam-3636	130	27	]	]	PUNCT
ejpam-3636	130	28	,	,	PUNCT
ejpam-3636	130	29	ρ(h	ρ(h	X
ejpam-3636	130	30	)	)	PUNCT
ejpam-3636	131	1	=	=	SYM
ejpam-3636	131	2	lim	lim	PROPN
ejpam-3636	131	3	sup	sup	PROPN
ejpam-3636	131	4	k→∞	k→∞	NOUN
ejpam-3636	131	5	log	log	NOUN
ejpam-3636	131	6	k	k	PROPN
ejpam-3636	131	7	[	[	PUNCT
ejpam-3636	131	8	|∇kh(0)|	|∇kh(0)|	NOUN
ejpam-3636	131	9	k	k	NOUN
ejpam-3636	131	10	!	!	PUNCT
ejpam-3636	132	1	]	]	X
ejpam-3636	132	2	−	−	PROPN
ejpam-3636	132	3	1	1	NUM
ejpam-3636	132	4	k	k	PROPN
ejpam-3636	132	5	,	,	PUNCT
ejpam-3636	132	6	ρ(h	ρ(h	X
ejpam-3636	132	7	)	)	PUNCT
ejpam-3636	132	8	=	=	SYM
ejpam-3636	132	9	ρ	ρ	PROPN
ejpam-3636	132	10	.	.	PUNCT
ejpam-3636	132	11	remark	remark	PROPN
ejpam-3636	132	12	2.2	2.2	NUM
ejpam-3636	132	13	.	.	PUNCT
ejpam-3636	133	1	if	if	SCONJ
ejpam-3636	133	2	α(x	α(x	NOUN
ejpam-3636	133	3	)	)	PUNCT
ejpam-3636	133	4	=	=	SYM
ejpam-3636	134	1	x	x	NOUN
ejpam-3636	134	2	,	,	PUNCT
ejpam-3636	134	3	β(x	β(x	NOUN
ejpam-3636	134	4	)	)	PUNCT
ejpam-3636	134	5	=	=	SYM
ejpam-3636	134	6	xρ	xρ	PROPN
ejpam-3636	134	7	,	,	PUNCT
ejpam-3636	134	8	p	p	NOUN
ejpam-3636	134	9	=	=	SYM
ejpam-3636	134	10	1	1	NUM
ejpam-3636	134	11	ρ	ρ	NOUN
ejpam-3636	134	12	,	,	PUNCT
ejpam-3636	134	13	then	then	ADV
ejpam-3636	134	14	(	(	PUNCT
ejpam-3636	134	15	2.5	2.5	NUM
ejpam-3636	134	16	)	)	PUNCT
ejpam-3636	134	17	gives	give	VERB
ejpam-3636	134	18	the	the	DET
ejpam-3636	134	19	formula	formula	NOUN
ejpam-3636	134	20	for	for	ADP
ejpam-3636	134	21	the	the	DET
ejpam-3636	134	22	classical	classical	ADJ
ejpam-3636	134	23	type	type	NOUN
ejpam-3636	134	24	t	t	PROPN
ejpam-3636	134	25	(	(	PUNCT
ejpam-3636	134	26	h	h	NOUN
ejpam-3636	134	27	)	)	PUNCT
ejpam-3636	134	28	obtained	obtain	VERB
ejpam-3636	134	29	by	by	ADP
ejpam-3636	134	30	fugard	fugard	NOUN
ejpam-3636	134	31	[	[	X
ejpam-3636	134	32	6	6	NUM
ejpam-3636	134	33	,	,	PUNCT
ejpam-3636	134	34	thm.2.6	thm.2.6	PROPN
ejpam-3636	134	35	]	]	X
ejpam-3636	134	36	,	,	PUNCT
ejpam-3636	134	37	r(t	r(t	NOUN
ejpam-3636	134	38	(	(	PUNCT
ejpam-3636	134	39	h)ρe	h)ρe	PROPN
ejpam-3636	134	40	)	)	PUNCT
ejpam-3636	134	41	1	1	NUM
ejpam-3636	134	42	ρ	ρ	NOUN
ejpam-3636	134	43	=	=	SYM
ejpam-3636	134	44	lim	lim	PROPN
ejpam-3636	134	45	sup	sup	PROPN
ejpam-3636	134	46	k→∞	k→∞	NOUN
ejpam-3636	134	47	k	k	PROPN
ejpam-3636	134	48	1	1	NUM
ejpam-3636	134	49	ρ	ρ	NOUN
ejpam-3636	134	50	(	(	PUNCT
ejpam-3636	134	51	|∇kh(0)|	|∇kh(0)|	NOUN
ejpam-3636	134	52	k	k	PROPN
ejpam-3636	134	53	!	!	PUNCT
ejpam-3636	134	54	)	)	PUNCT
ejpam-3636	135	1	1	1	NUM
ejpam-3636	135	2	k	k	X
ejpam-3636	135	3	.	.	PUNCT
ejpam-3636	136	1	remark	remark	VERB
ejpam-3636	136	2	2.3	2.3	NUM
ejpam-3636	136	3	.	.	PUNCT
ejpam-3636	137	1	if	if	SCONJ
ejpam-3636	137	2	α(x	α(x	NOUN
ejpam-3636	137	3	)	)	PUNCT
ejpam-3636	137	4	=	=	SYM
ejpam-3636	138	1	x	x	NOUN
ejpam-3636	138	2	,	,	PUNCT
ejpam-3636	138	3	β(x	β(x	NOUN
ejpam-3636	138	4	)	)	PUNCT
ejpam-3636	138	5	=	=	SYM
ejpam-3636	139	1	xρ(x	xρ(x	NUM
ejpam-3636	139	2	)	)	PUNCT
ejpam-3636	139	3	,	,	PUNCT
ejpam-3636	139	4	where	where	SCONJ
ejpam-3636	139	5	ρ(x	ρ(x	NOUN
ejpam-3636	139	6	)	)	PUNCT
ejpam-3636	139	7	is	be	AUX
ejpam-3636	139	8	the	the	DET
ejpam-3636	139	9	proximate	proximate	NOUN
ejpam-3636	139	10	order	order	NOUN
ejpam-3636	139	11	of	of	ADP
ejpam-3636	139	12	the	the	DET
ejpam-3636	139	13	entire	entire	ADJ
ejpam-3636	139	14	function	function	NOUN
ejpam-3636	139	15	h	h	NOUN
ejpam-3636	139	16	,	,	PUNCT
ejpam-3636	139	17	then	then	ADV
ejpam-3636	139	18	the	the	DET
ejpam-3636	139	19	formula	formula	NOUN
ejpam-3636	139	20	for	for	ADP
ejpam-3636	139	21	the	the	DET
ejpam-3636	139	22	generalized	generalized	ADJ
ejpam-3636	139	23	type	type	NOUN
ejpam-3636	139	24	t	t	PROPN
ejpam-3636	139	25	∗(h	∗(h	PROPN
ejpam-3636	139	26	)	)	PUNCT
ejpam-3636	139	27	with	with	ADP
ejpam-3636	139	28	respect	respect	NOUN
ejpam-3636	139	29	to	to	PART
ejpam-3636	139	30	proximate	proximate	VERB
ejpam-3636	139	31	order	order	NOUN
ejpam-3636	139	32	ρ(x	ρ(x	NOUN
ejpam-3636	139	33	)	)	PUNCT
ejpam-3636	139	34	is	be	AUX
ejpam-3636	139	35	given	give	VERB
ejpam-3636	139	36	by	by	ADP
ejpam-3636	139	37	r(t	r(t	NOUN
ejpam-3636	139	38	∗(h)ρe	∗(h)ρe	NUM
ejpam-3636	139	39	)	)	PUNCT
ejpam-3636	139	40	1	1	NUM
ejpam-3636	139	41	ρ	ρ	NOUN
ejpam-3636	139	42	=	=	SYM
ejpam-3636	139	43	lim	lim	PROPN
ejpam-3636	139	44	sup	sup	PROPN
ejpam-3636	139	45	k→∞	k→∞	X
ejpam-3636	139	46	θ(k	θ(k	ADJ
ejpam-3636	139	47	)	)	PUNCT
ejpam-3636	139	48	(	(	PUNCT
ejpam-3636	139	49	|∇kh(0)|	|∇kh(0)|	NOUN
ejpam-3636	139	50	k	k	PROPN
ejpam-3636	139	51	!	!	PUNCT
ejpam-3636	139	52	)	)	PUNCT
ejpam-3636	140	1	1	1	NUM
ejpam-3636	140	2	k	k	NOUN
ejpam-3636	140	3	,	,	PUNCT
ejpam-3636	140	4	where	where	SCONJ
ejpam-3636	140	5	x	x	X
ejpam-3636	140	6	=	=	SYM
ejpam-3636	140	7	θ(k)⇔	θ(k)⇔	PROPN
ejpam-3636	140	8	k	k	X
ejpam-3636	140	9	=	=	PUNCT
ejpam-3636	140	10	xρ(x	xρ(x	NUM
ejpam-3636	140	11	)	)	PUNCT
ejpam-3636	140	12	.	.	PUNCT
ejpam-3636	141	1	theorem	theorem	VERB
ejpam-3636	141	2	2.2	2.2	NUM
ejpam-3636	141	3	.	.	PUNCT
ejpam-3636	142	1	let	let	VERB
ejpam-3636	142	2	h	h	PRON
ejpam-3636	142	3	be	be	AUX
ejpam-3636	142	4	a	a	DET
ejpam-3636	142	5	harmonic	harmonic	ADJ
ejpam-3636	142	6	function	function	NOUN
ejpam-3636	142	7	in	in	ADP
ejpam-3636	142	8	a	a	DET
ejpam-3636	142	9	neighborhood	neighborhood	NOUN
ejpam-3636	142	10	of	of	ADP
ejpam-3636	142	11	the	the	DET
ejpam-3636	142	12	origin	origin	NOUN
ejpam-3636	142	13	in	in	ADP
ejpam-3636	142	14	rn	rn	PROPN
ejpam-3636	142	15	,	,	PUNCT
ejpam-3636	142	16	n	n	PRON
ejpam-3636	142	17	≥	≥	NOUN
ejpam-3636	142	18	3	3	NUM
ejpam-3636	142	19	,	,	PUNCT
ejpam-3636	142	20	for	for	ADP
ejpam-3636	142	21	which	which	PRON
ejpam-3636	142	22	λ(α	λ(α	PROPN
ejpam-3636	142	23	,	,	PUNCT
ejpam-3636	142	24	β	β	X
ejpam-3636	142	25	,	,	PUNCT
ejpam-3636	142	26	h	h	NOUN
ejpam-3636	142	27	)	)	PUNCT
ejpam-3636	142	28	≥	≥	PROPN
ejpam-3636	142	29	lim	lim	PROPN
ejpam-3636	142	30	inf	inf	PROPN
ejpam-3636	142	31	k→∞	k→∞	NOUN
ejpam-3636	142	32	α(pk	α(pk	ADV
ejpam-3636	142	33	)	)	PUNCT
ejpam-3636	143	1	β(epr	β(epr	PROPN
ejpam-3636	143	2	[	[	PUNCT
ejpam-3636	143	3	|∇kh(0)|	|∇kh(0)|	NOUN
ejpam-3636	143	4	k	k	NOUN
ejpam-3636	143	5	!	!	PUNCT
ejpam-3636	144	1	]	]	X
ejpam-3636	144	2	−	−	PROPN
ejpam-3636	144	3	1	1	NUM
ejpam-3636	144	4	k	k	NOUN
ejpam-3636	144	5	)	)	PUNCT
ejpam-3636	144	6	.	.	PUNCT
ejpam-3636	145	1	(	(	PUNCT
ejpam-3636	145	2	2.6	2.6	NUM
ejpam-3636	145	3	)	)	PUNCT
ejpam-3636	145	4	if	if	SCONJ
ejpam-3636	145	5	the	the	DET
ejpam-3636	145	6	function	function	NOUN
ejpam-3636	145	7	µ(k	µ(k	NOUN
ejpam-3636	145	8	)	)	PUNCT
ejpam-3636	145	9	=	=	PRON
ejpam-3636	145	10	{	{	PUNCT
ejpam-3636	145	11	|∇kh(0)|	|∇kh(0)|	NOUN
ejpam-3636	145	12	|∇k+1h(0)|	|∇k+1h(0)|	NUM
ejpam-3636	145	13	}	}	PUNCT
ejpam-3636	145	14	√	√	PROPN
ejpam-3636	145	15	(	(	PUNCT
ejpam-3636	145	16	k	k	PROPN
ejpam-3636	145	17	+	+	PROPN
ejpam-3636	145	18	1)(k	1)(k	NUM
ejpam-3636	145	19	+	+	CCONJ
ejpam-3636	145	20	n/2	n/2	NOUN
ejpam-3636	145	21	)	)	PUNCT
ejpam-3636	145	22	be	be	VERB
ejpam-3636	145	23	a	a	DET
ejpam-3636	145	24	nondecreasing	nondecrease	VERB
ejpam-3636	145	25	function	function	NOUN
ejpam-3636	145	26	of	of	ADP
ejpam-3636	145	27	k	k	PROPN
ejpam-3636	145	28	for	for	ADP
ejpam-3636	145	29	all	all	DET
ejpam-3636	145	30	large	large	ADJ
ejpam-3636	145	31	values	value	NOUN
ejpam-3636	145	32	of	of	ADP
ejpam-3636	145	33	k	k	PROPN
ejpam-3636	145	34	and	and	CCONJ
ejpam-3636	145	35	one	one	NUM
ejpam-3636	145	36	of	of	ADP
ejpam-3636	145	37	the	the	DET
ejpam-3636	145	38	(	(	PUNCT
ejpam-3636	145	39	i),(ii	i),(ii	PROPN
ejpam-3636	145	40	)	)	PUNCT
ejpam-3636	145	41	conditions	condition	NOUN
ejpam-3636	145	42	of	of	ADP
ejpam-3636	145	43	theorem	theorem	ADJ
ejpam-3636	145	44	2.1	2.1	NUM
ejpam-3636	145	45	is	be	AUX
ejpam-3636	145	46	satisfied	satisfied	ADJ
ejpam-3636	145	47	,	,	PUNCT
ejpam-3636	145	48	then	then	ADV
ejpam-3636	145	49	inequality	inequality	NOUN
ejpam-3636	145	50	in	in	ADP
ejpam-3636	145	51	(	(	PUNCT
ejpam-3636	145	52	2.6	2.6	NUM
ejpam-3636	145	53	)	)	PUNCT
ejpam-3636	145	54	converts	convert	NOUN
ejpam-3636	145	55	in	in	ADP
ejpam-3636	145	56	equality	equality	NOUN
ejpam-3636	145	57	.	.	PUNCT
ejpam-3636	146	1	proof	proof	NOUN
ejpam-3636	146	2	.	.	PUNCT
ejpam-3636	147	1	as	as	ADP
ejpam-3636	147	2	f1(z	f1(z	PROPN
ejpam-3636	147	3	)	)	PUNCT
ejpam-3636	147	4	is	be	AUX
ejpam-3636	147	5	defined	define	VERB
ejpam-3636	147	6	above	above	ADV
ejpam-3636	147	7	is	be	AUX
ejpam-3636	147	8	an	an	DET
ejpam-3636	147	9	entire	entire	ADJ
ejpam-3636	147	10	function	function	NOUN
ejpam-3636	147	11	and	and	CCONJ
ejpam-3636	147	12	logm(r	logm(r	NOUN
ejpam-3636	147	13	,	,	PUNCT
ejpam-3636	147	14	f1	f1	NOUN
ejpam-3636	147	15	)	)	PUNCT
ejpam-3636	147	16	'	'	PUNCT
ejpam-3636	147	17	logm(r	logm(r	NOUN
ejpam-3636	147	18	,	,	PUNCT
ejpam-3636	147	19	h	h	NOUN
ejpam-3636	147	20	)	)	PUNCT
ejpam-3636	147	21	as	as	ADP
ejpam-3636	147	22	r	r	NOUN
ejpam-3636	147	23	→∞.	→∞.	X
ejpam-3636	147	24	hence	hence	ADV
ejpam-3636	147	25	f1(z	f1(z	PROPN
ejpam-3636	147	26	)	)	PUNCT
ejpam-3636	147	27	is	be	AUX
ejpam-3636	147	28	also	also	ADV
ejpam-3636	147	29	of	of	ADP
ejpam-3636	147	30	generalized	generalize	VERB
ejpam-3636	147	31	lower	low	ADJ
ejpam-3636	147	32	order	order	NOUN
ejpam-3636	147	33	λ(α	λ(α	PROPN
ejpam-3636	147	34	,	,	PUNCT
ejpam-3636	147	35	β	β	NOUN
ejpam-3636	147	36	,	,	PUNCT
ejpam-3636	147	37	f1	f1	NOUN
ejpam-3636	147	38	)	)	PUNCT
ejpam-3636	147	39	.	.	PUNCT
ejpam-3636	148	1	since	since	SCONJ
ejpam-3636	148	2	under	under	ADP
ejpam-3636	148	3	the	the	DET
ejpam-3636	148	4	assumption	assumption	NOUN
ejpam-3636	148	5	√	√	PROPN
ejpam-3636	148	6	γ(n/2)|∇kh(0)|√	γ(n/2)|∇kh(0)|√	PROPN
ejpam-3636	148	7	k!γ(k+n/2)√	k!γ(k+n/2)√	PROPN
ejpam-3636	148	8	γ(n/2)|∇k+1h(0)|√	γ(n/2)|∇k+1h(0)|√	X
ejpam-3636	148	9	(	(	PUNCT
ejpam-3636	148	10	k+1)!γ(k+1+n/2	k+1)!γ(k+1+n/2	PROPN
ejpam-3636	148	11	)	)	PUNCT
ejpam-3636	148	12	'	'	PART
ejpam-3636	148	13	|∇kh(0)|	|∇kh(0)|	NOUN
ejpam-3636	148	14	|∇k+1h(0)|	|∇k+1h(0)|	NUM
ejpam-3636	148	15	√	√	NUM
ejpam-3636	148	16	(	(	PUNCT
ejpam-3636	148	17	k	k	PROPN
ejpam-3636	148	18	+	+	PROPN
ejpam-3636	148	19	1)(k	1)(k	NUM
ejpam-3636	148	20	+	+	CCONJ
ejpam-3636	148	21	n/2	n/2	NOUN
ejpam-3636	148	22	)	)	PUNCT
ejpam-3636	148	23	is	be	AUX
ejpam-3636	148	24	non	non	ADJ
ejpam-3636	148	25	-	-	ADJ
ejpam-3636	148	26	decreasing	decrease	VERB
ejpam-3636	148	27	function	function	NOUN
ejpam-3636	148	28	of	of	ADP
ejpam-3636	148	29	k.	k.	PROPN
ejpam-3636	148	30	now	now	ADV
ejpam-3636	148	31	applying	apply	VERB
ejpam-3636	148	32	[	[	X
ejpam-3636	148	33	17	17	NUM
ejpam-3636	148	34	,	,	PUNCT
ejpam-3636	148	35	thm.2	thm.2	PROPN
ejpam-3636	148	36	]	]	PUNCT
ejpam-3636	148	37	with	with	ADP
ejpam-3636	148	38	(	(	PUNCT
ejpam-3636	148	39	2.1	2.1	NUM
ejpam-3636	148	40	)	)	PUNCT
ejpam-3636	148	41	,	,	PUNCT
ejpam-3636	148	42	for	for	ADP
ejpam-3636	148	43	the	the	DET
ejpam-3636	148	44	function	function	NOUN
ejpam-3636	148	45	f1(z	f1(z	PROPN
ejpam-3636	148	46	)	)	PUNCT
ejpam-3636	148	47	and	and	CCONJ
ejpam-3636	148	48	f2(z	f2(z	NOUN
ejpam-3636	148	49	)	)	PUNCT
ejpam-3636	148	50	we	we	PRON
ejpam-3636	148	51	get	get	VERB
ejpam-3636	148	52	the	the	DET
ejpam-3636	148	53	required	require	VERB
ejpam-3636	148	54	result	result	NOUN
ejpam-3636	148	55	.	.	PUNCT
ejpam-3636	149	1	d.	d.	PROPN
ejpam-3636	149	2	kumar	kumar	PROPN
ejpam-3636	149	3	,	,	PUNCT
ejpam-3636	149	4	r.k	r.k	PROPN
ejpam-3636	149	5	.	.	PROPN
ejpam-3636	149	6	vishnoi	vishnoi	PROPN
ejpam-3636	149	7	/	/	SYM
ejpam-3636	149	8	eur	eur	PROPN
ejpam-3636	149	9	.	.	PUNCT
ejpam-3636	150	1	j.	j.	PROPN
ejpam-3636	150	2	pure	pure	PROPN
ejpam-3636	150	3	appl	appl	PROPN
ejpam-3636	150	4	.	.	PROPN
ejpam-3636	150	5	math	math	PROPN
ejpam-3636	150	6	,	,	PUNCT
ejpam-3636	150	7	13	13	NUM
ejpam-3636	150	8	(	(	PUNCT
ejpam-3636	150	9	2	2	NUM
ejpam-3636	150	10	)	)	PUNCT
ejpam-3636	150	11	(	(	PUNCT
ejpam-3636	150	12	2020	2020	NUM
ejpam-3636	150	13	)	)	PUNCT
ejpam-3636	150	14	,	,	PUNCT
ejpam-3636	150	15	258	258	NUM
ejpam-3636	150	16	-	-	SYM
ejpam-3636	150	17	268	268	NUM
ejpam-3636	150	18	265	265	NUM
ejpam-3636	150	19	3	3	NUM
ejpam-3636	150	20	.	.	PUNCT
ejpam-3636	151	1	growth	growth	NOUN
ejpam-3636	151	2	of	of	ADP
ejpam-3636	151	3	entire	entire	ADJ
ejpam-3636	151	4	harmonic	harmonic	ADJ
ejpam-3636	151	5	functions	function	NOUN
ejpam-3636	151	6	of	of	ADP
ejpam-3636	151	7	zero	zero	NUM
ejpam-3636	151	8	order	order	NOUN
ejpam-3636	151	9	to	to	PART
ejpam-3636	151	10	study	study	VERB
ejpam-3636	151	11	the	the	DET
ejpam-3636	151	12	growth	growth	NOUN
ejpam-3636	151	13	of	of	ADP
ejpam-3636	151	14	entire	entire	ADJ
ejpam-3636	151	15	functions	function	NOUN
ejpam-3636	151	16	of	of	ADP
ejpam-3636	151	17	zero	zero	NUM
ejpam-3636	151	18	order	order	NOUN
ejpam-3636	151	19	,	,	PUNCT
ejpam-3636	151	20	kapoor	kapoor	NOUN
ejpam-3636	151	21	and	and	CCONJ
ejpam-3636	151	22	nautiyal	nautiyal	NOUN
ejpam-3636	151	23	[	[	X
ejpam-3636	151	24	10	10	NUM
ejpam-3636	151	25	]	]	PUNCT
ejpam-3636	151	26	defined	define	VERB
ejpam-3636	151	27	a	a	DET
ejpam-3636	151	28	new	new	ADJ
ejpam-3636	151	29	class	class	NOUN
ejpam-3636	151	30	of	of	ADP
ejpam-3636	151	31	functions	function	NOUN
ejpam-3636	151	32	as	as	SCONJ
ejpam-3636	151	33	follows	follow	VERB
ejpam-3636	151	34	:	:	PUNCT
ejpam-3636	151	35	the	the	DET
ejpam-3636	151	36	class	class	NOUN
ejpam-3636	151	37	of	of	ADP
ejpam-3636	151	38	functions	function	NOUN
ejpam-3636	151	39	ξ(x	ξ(x	NOUN
ejpam-3636	151	40	)	)	PUNCT
ejpam-3636	151	41	denoted	denote	VERB
ejpam-3636	151	42	by	by	ADP
ejpam-3636	151	43	ω	ω	NUM
ejpam-3636	151	44	which	which	PRON
ejpam-3636	151	45	satisfies	satisfy	VERB
ejpam-3636	151	46	:	:	PUNCT
ejpam-3636	151	47	(	(	PUNCT
ejpam-3636	151	48	i	i	NOUN
ejpam-3636	151	49	)	)	PUNCT
ejpam-3636	151	50	.	.	PUNCT
ejpam-3636	152	1	ξ(x	ξ(x	NOUN
ejpam-3636	152	2	)	)	PUNCT
ejpam-3636	152	3	is	be	AUX
ejpam-3636	152	4	positive	positive	ADJ
ejpam-3636	152	5	,	,	PUNCT
ejpam-3636	152	6	defined	define	VERB
ejpam-3636	152	7	on	on	ADP
ejpam-3636	152	8	[	[	X
ejpam-3636	152	9	a,∞	a,∞	PROPN
ejpam-3636	152	10	)	)	PUNCT
ejpam-3636	152	11	,	,	PUNCT
ejpam-3636	152	12	differentiable	differentiable	ADJ
ejpam-3636	152	13	,	,	PUNCT
ejpam-3636	152	14	strictly	strictly	ADV
ejpam-3636	152	15	increasing	increase	VERB
ejpam-3636	152	16	and	and	CCONJ
ejpam-3636	152	17	tends	tend	VERB
ejpam-3636	152	18	to	to	ADP
ejpam-3636	152	19	∞	∞	PROPN
ejpam-3636	152	20	as	as	ADP
ejpam-3636	152	21	x→∞.	x→∞.	PROPN
ejpam-3636	152	22	(	(	PUNCT
ejpam-3636	152	23	ii	ii	NOUN
ejpam-3636	152	24	)	)	PUNCT
ejpam-3636	152	25	.	.	PUNCT
ejpam-3636	153	1	ξ(x	ξ(x	NOUN
ejpam-3636	153	2	)	)	PUNCT
ejpam-3636	154	1	such	such	ADJ
ejpam-3636	154	2	that	that	SCONJ
ejpam-3636	154	3	lim	lim	PROPN
ejpam-3636	154	4	x→∞	x→∞	PUNCT
ejpam-3636	154	5	d(ξ(x	d(ξ(x	NOUN
ejpam-3636	154	6	)	)	PUNCT
ejpam-3636	154	7	)	)	PUNCT
ejpam-3636	155	1	d(log	d(log	PROPN
ejpam-3636	155	2	x	x	X
ejpam-3636	155	3	)	)	PUNCT
ejpam-3636	155	4	=	=	SYM
ejpam-3636	156	1	k	k	NOUN
ejpam-3636	156	2	,	,	PUNCT
ejpam-3636	156	3	0	0	PUNCT
ejpam-3636	156	4	<	<	X
ejpam-3636	156	5	k	k	X
ejpam-3636	156	6	<	<	X
ejpam-3636	156	7	∞.	∞.	PROPN
ejpam-3636	156	8	the	the	DET
ejpam-3636	156	9	generalized	generalized	ADJ
ejpam-3636	156	10	order	order	NOUN
ejpam-3636	156	11	ρ(α	ρ(α	NOUN
ejpam-3636	156	12	,	,	PUNCT
ejpam-3636	156	13	α	α	X
ejpam-3636	156	14	,	,	PUNCT
ejpam-3636	156	15	f	f	NOUN
ejpam-3636	156	16	)	)	PUNCT
ejpam-3636	156	17	,	,	PUNCT
ejpam-3636	156	18	generalized	generalize	VERB
ejpam-3636	156	19	lower	low	ADJ
ejpam-3636	156	20	order	order	NOUN
ejpam-3636	156	21	λ(α	λ(α	PROPN
ejpam-3636	156	22	,	,	PUNCT
ejpam-3636	156	23	α	α	X
ejpam-3636	156	24	,	,	PUNCT
ejpam-3636	156	25	f	f	NOUN
ejpam-3636	156	26	)	)	PUNCT
ejpam-3636	156	27	and	and	CCONJ
ejpam-3636	156	28	generalized	generalized	ADJ
ejpam-3636	156	29	type	type	NOUN
ejpam-3636	156	30	of	of	ADP
ejpam-3636	156	31	the	the	DET
ejpam-3636	156	32	entire	entire	ADJ
ejpam-3636	156	33	function	function	NOUN
ejpam-3636	156	34	f(z	f(z	PROPN
ejpam-3636	156	35	)	)	PUNCT
ejpam-3636	156	36	were	be	AUX
ejpam-3636	156	37	defined	define	VERB
ejpam-3636	156	38	as	as	ADP
ejpam-3636	156	39	:	:	PUNCT
ejpam-3636	156	40	ρ(α	ρ(α	NOUN
ejpam-3636	156	41	,	,	PUNCT
ejpam-3636	156	42	α	α	NOUN
ejpam-3636	156	43	,	,	PUNCT
ejpam-3636	156	44	h	h	NOUN
ejpam-3636	156	45	)	)	PUNCT
ejpam-3636	157	1	=	=	SYM
ejpam-3636	157	2	lim	lim	PROPN
ejpam-3636	157	3	sup	sup	PROPN
ejpam-3636	157	4	r→∞	r→∞	X
ejpam-3636	157	5	α(logm(r	α(logm(r	NOUN
ejpam-3636	157	6	,	,	PUNCT
ejpam-3636	157	7	f	f	NOUN
ejpam-3636	157	8	)	)	PUNCT
ejpam-3636	157	9	)	)	PUNCT
ejpam-3636	158	1	α(log	α(log	PROPN
ejpam-3636	158	2	r	r	NOUN
ejpam-3636	158	3	)	)	PUNCT
ejpam-3636	158	4	,	,	PUNCT
ejpam-3636	158	5	λ(α	λ(α	PROPN
ejpam-3636	158	6	,	,	PUNCT
ejpam-3636	158	7	α	α	X
ejpam-3636	158	8	,	,	PUNCT
ejpam-3636	158	9	f	f	NOUN
ejpam-3636	158	10	)	)	PUNCT
ejpam-3636	158	11	=	=	SYM
ejpam-3636	158	12	lim	lim	PROPN
ejpam-3636	158	13	inf	inf	PROPN
ejpam-3636	158	14	r→∞	r→∞	PUNCT
ejpam-3636	158	15	α(logm(r	α(logm(r	NOUN
ejpam-3636	158	16	,	,	PUNCT
ejpam-3636	158	17	f	f	NOUN
ejpam-3636	158	18	)	)	PUNCT
ejpam-3636	158	19	)	)	PUNCT
ejpam-3636	158	20	α(log	α(log	PROPN
ejpam-3636	158	21	r	r	NOUN
ejpam-3636	158	22	)	)	PUNCT
ejpam-3636	158	23	,	,	PUNCT
ejpam-3636	158	24	t	t	PROPN
ejpam-3636	158	25	(	(	PUNCT
ejpam-3636	158	26	α	α	PROPN
ejpam-3636	158	27	,	,	PUNCT
ejpam-3636	158	28	α	α	NOUN
ejpam-3636	158	29	,	,	PUNCT
ejpam-3636	158	30	f	f	NOUN
ejpam-3636	158	31	)	)	PUNCT
ejpam-3636	159	1	=	=	SYM
ejpam-3636	159	2	lim	lim	PROPN
ejpam-3636	159	3	sup	sup	PROPN
ejpam-3636	159	4	r→∞	r→∞	X
ejpam-3636	159	5	α(logm(r	α(logm(r	NOUN
ejpam-3636	159	6	,	,	PUNCT
ejpam-3636	159	7	f	f	NOUN
ejpam-3636	159	8	)	)	PUNCT
ejpam-3636	159	9	)	)	PUNCT
ejpam-3636	160	1	[	[	X
ejpam-3636	160	2	α(log	α(log	NUM
ejpam-3636	160	3	r)]ρ	r)]ρ	NOUN
ejpam-3636	160	4	,	,	PUNCT
ejpam-3636	160	5	where	where	SCONJ
ejpam-3636	160	6	α(x	α(x	NOUN
ejpam-3636	160	7	)	)	PUNCT
ejpam-3636	160	8	∈	∈	PROPN
ejpam-3636	160	9	ω	ω	PROPN
ejpam-3636	160	10	and	and	CCONJ
ejpam-3636	160	11	1	1	NUM
ejpam-3636	160	12	≤	≤	NOUN
ejpam-3636	160	13	λ(α	λ(α	PROPN
ejpam-3636	160	14	,	,	PUNCT
ejpam-3636	160	15	α	α	X
ejpam-3636	160	16	,	,	PUNCT
ejpam-3636	160	17	f	f	NOUN
ejpam-3636	160	18	)	)	PUNCT
ejpam-3636	160	19	≤	≤	NOUN
ejpam-3636	160	20	ρ(α	ρ(α	NOUN
ejpam-3636	160	21	,	,	PUNCT
ejpam-3636	160	22	α	α	X
ejpam-3636	160	23	,	,	PUNCT
ejpam-3636	160	24	f	f	NOUN
ejpam-3636	160	25	)	)	PUNCT
ejpam-3636	160	26	≤	≤	NOUN
ejpam-3636	160	27	∞.	∞.	PROPN
ejpam-3636	161	1	the	the	DET
ejpam-3636	161	2	coefficient	coefficient	NOUN
ejpam-3636	161	3	characterizations	characterization	NOUN
ejpam-3636	161	4	of	of	ADP
ejpam-3636	161	5	entire	entire	ADJ
ejpam-3636	161	6	function	function	NOUN
ejpam-3636	161	7	f(z	f(z	NOUN
ejpam-3636	161	8	)	)	PUNCT
ejpam-3636	162	1	=	=	PUNCT
ejpam-3636	162	2	∑∞	∑∞	NOUN
ejpam-3636	162	3	n=0	n=0	NUM
ejpam-3636	162	4	akz	akz	NOUN
ejpam-3636	163	1	k	k	PROPN
ejpam-3636	163	2	were	be	AUX
ejpam-3636	163	3	also	also	ADV
ejpam-3636	163	4	obtained	obtain	VERB
ejpam-3636	163	5	as	as	ADP
ejpam-3636	163	6	follows	follow	VERB
ejpam-3636	163	7	:	:	PUNCT
ejpam-3636	163	8	ρ(α	ρ(α	NOUN
ejpam-3636	163	9	,	,	PUNCT
ejpam-3636	163	10	α	α	X
ejpam-3636	163	11	,	,	PUNCT
ejpam-3636	163	12	f	f	NOUN
ejpam-3636	163	13	)	)	PUNCT
ejpam-3636	164	1	=	=	SYM
ejpam-3636	164	2	1	1	NUM
ejpam-3636	164	3	+	+	NUM
ejpam-3636	164	4	lim	lim	PROPN
ejpam-3636	164	5	sup	sup	PROPN
ejpam-3636	164	6	k→∞	k→∞	NOUN
ejpam-3636	164	7	α(k	α(k	PROPN
ejpam-3636	164	8	)	)	PUNCT
ejpam-3636	164	9	α(log	α(log	NOUN
ejpam-3636	164	10	|ak|−	|ak|−	PROPN
ejpam-3636	164	11	1	1	NUM
ejpam-3636	164	12	k	k	PROPN
ejpam-3636	164	13	)	)	PUNCT
ejpam-3636	164	14	.	.	PUNCT
ejpam-3636	165	1	(	(	PUNCT
ejpam-3636	165	2	3.1	3.1	NUM
ejpam-3636	165	3	)	)	PUNCT
ejpam-3636	165	4	if	if	SCONJ
ejpam-3636	165	5	|	|	NOUN
ejpam-3636	165	6	akak+1	akak+1	VERB
ejpam-3636	165	7	|	|	ADV
ejpam-3636	165	8	be	be	AUX
ejpam-3636	165	9	a	a	DET
ejpam-3636	165	10	non	non	ADJ
ejpam-3636	165	11	-	-	ADJ
ejpam-3636	165	12	decreasing	decrease	VERB
ejpam-3636	165	13	function	function	NOUN
ejpam-3636	165	14	of	of	ADP
ejpam-3636	165	15	k	k	NOUN
ejpam-3636	165	16	,	,	PUNCT
ejpam-3636	165	17	then	then	ADV
ejpam-3636	165	18	λ(α	λ(α	PROPN
ejpam-3636	165	19	,	,	PUNCT
ejpam-3636	165	20	α	α	X
ejpam-3636	165	21	,	,	PUNCT
ejpam-3636	165	22	f	f	NOUN
ejpam-3636	165	23	)	)	PUNCT
ejpam-3636	165	24	=	=	SYM
ejpam-3636	165	25	1	1	NUM
ejpam-3636	166	1	+	+	NUM
ejpam-3636	166	2	lim	lim	PROPN
ejpam-3636	166	3	inf	inf	PROPN
ejpam-3636	166	4	k→∞	k→∞	NOUN
ejpam-3636	166	5	α(k	α(k	PROPN
ejpam-3636	166	6	)	)	PUNCT
ejpam-3636	166	7	α(log	α(log	NOUN
ejpam-3636	166	8	|ak|−	|ak|−	PROPN
ejpam-3636	166	9	1	1	NUM
ejpam-3636	166	10	k	k	PROPN
ejpam-3636	166	11	)	)	PUNCT
ejpam-3636	166	12	.	.	PUNCT
ejpam-3636	167	1	(	(	PUNCT
ejpam-3636	167	2	3.2	3.2	NUM
ejpam-3636	167	3	)	)	PUNCT
ejpam-3636	167	4	also	also	ADV
ejpam-3636	167	5	,	,	PUNCT
ejpam-3636	167	6	for	for	ADP
ejpam-3636	167	7	α(x	α(x	NOUN
ejpam-3636	167	8	)	)	PUNCT
ejpam-3636	167	9	∈	∈	PROPN
ejpam-3636	167	10	ω	ω	PROPN
ejpam-3636	167	11	,	,	PUNCT
ejpam-3636	167	12	ganti	ganti	NOUN
ejpam-3636	167	13	and	and	CCONJ
ejpam-3636	167	14	srivastava	srivastava	PROPN
ejpam-3636	168	1	[	[	X
ejpam-3636	168	2	7	7	NUM
ejpam-3636	168	3	]	]	PUNCT
ejpam-3636	168	4	obtained	obtain	VERB
ejpam-3636	168	5	t	t	PROPN
ejpam-3636	168	6	(	(	PUNCT
ejpam-3636	168	7	α	α	PROPN
ejpam-3636	168	8	,	,	PUNCT
ejpam-3636	168	9	α	α	NOUN
ejpam-3636	168	10	,	,	PUNCT
ejpam-3636	168	11	f	f	NOUN
ejpam-3636	168	12	)	)	PUNCT
ejpam-3636	169	1	=	=	SYM
ejpam-3636	169	2	lim	lim	PROPN
ejpam-3636	169	3	sup	sup	PROPN
ejpam-3636	169	4	k→∞	k→∞	PROPN
ejpam-3636	169	5	α(kρ	α(kρ	PROPN
ejpam-3636	169	6	)	)	PUNCT
ejpam-3636	169	7	{	{	PUNCT
ejpam-3636	169	8	α	α	X
ejpam-3636	169	9	(	(	PUNCT
ejpam-3636	169	10	ρ	ρ	PROPN
ejpam-3636	169	11	ρ−1	ρ−1	PROPN
ejpam-3636	169	12	log	log	NOUN
ejpam-3636	169	13	|ak|−	|ak|−	PROPN
ejpam-3636	169	14	1	1	NUM
ejpam-3636	169	15	k	k	NOUN
ejpam-3636	169	16	)	)	PUNCT
ejpam-3636	169	17	}	}	PUNCT
ejpam-3636	169	18	ρ−1	ρ−1	PROPN
ejpam-3636	169	19	,	,	PUNCT
ejpam-3636	169	20	provided	provide	VERB
ejpam-3636	169	21	df	df	PROPN
ejpam-3636	169	22	(	(	PUNCT
ejpam-3636	169	23	k;t	k;t	PROPN
ejpam-3636	169	24	,	,	PUNCT
ejpam-3636	169	25	ρ	ρ	NOUN
ejpam-3636	169	26	)	)	PUNCT
ejpam-3636	169	27	d(log	d(log	NOUN
ejpam-3636	169	28	x	x	X
ejpam-3636	169	29	)	)	PUNCT
ejpam-3636	169	30	=	=	SYM
ejpam-3636	169	31	o(1	o(1	NOUN
ejpam-3636	169	32	)	)	PUNCT
ejpam-3636	169	33	as	as	ADP
ejpam-3636	169	34	x→∞	x→∞	NUM
ejpam-3636	169	35	for	for	ADP
ejpam-3636	169	36	all	all	DET
ejpam-3636	169	37	t	t	PROPN
ejpam-3636	169	38	,	,	PUNCT
ejpam-3636	169	39	0	0	PUNCT
ejpam-3636	169	40	<	<	X
ejpam-3636	169	41	t	t	X
ejpam-3636	169	42	<	<	X
ejpam-3636	169	43	∞.	∞.	PROPN
ejpam-3636	169	44	ning	ning	NOUN
ejpam-3636	169	45	juhong	juhong	PROPN
ejpam-3636	169	46	and	and	CCONJ
ejpam-3636	169	47	chen	chen	PROPN
ejpam-3636	169	48	qing	qing	PROPN
ejpam-3636	170	1	[	[	X
ejpam-3636	170	2	9	9	NUM
ejpam-3636	170	3	]	]	PUNCT
ejpam-3636	170	4	improved	improve	VERB
ejpam-3636	170	5	above	above	ADP
ejpam-3636	170	6	results	result	NOUN
ejpam-3636	170	7	by	by	ADP
ejpam-3636	170	8	introducing	introduce	VERB
ejpam-3636	170	9	a	a	DET
ejpam-3636	170	10	new	new	ADJ
ejpam-3636	170	11	class	class	NOUN
ejpam-3636	170	12	ω∗	ω∗	NOUN
ejpam-3636	170	13	(	(	PUNCT
ejpam-3636	170	14	the	the	DET
ejpam-3636	170	15	extension	extension	NOUN
ejpam-3636	170	16	of	of	ADP
ejpam-3636	170	17	ω	ω	NUM
ejpam-3636	170	18	)	)	PUNCT
ejpam-3636	170	19	.	.	PUNCT
ejpam-3636	171	1	d.	d.	PROPN
ejpam-3636	171	2	kumar	kumar	PROPN
ejpam-3636	171	3	,	,	PUNCT
ejpam-3636	171	4	r.k	r.k	PROPN
ejpam-3636	171	5	.	.	PROPN
ejpam-3636	171	6	vishnoi	vishnoi	PROPN
ejpam-3636	171	7	/	/	SYM
ejpam-3636	171	8	eur	eur	PROPN
ejpam-3636	171	9	.	.	PUNCT
ejpam-3636	172	1	j.	j.	PROPN
ejpam-3636	172	2	pure	pure	PROPN
ejpam-3636	172	3	appl	appl	PROPN
ejpam-3636	172	4	.	.	PROPN
ejpam-3636	172	5	math	math	PROPN
ejpam-3636	172	6	,	,	PUNCT
ejpam-3636	172	7	13	13	NUM
ejpam-3636	172	8	(	(	PUNCT
ejpam-3636	172	9	2	2	NUM
ejpam-3636	172	10	)	)	PUNCT
ejpam-3636	172	11	(	(	PUNCT
ejpam-3636	172	12	2020	2020	NUM
ejpam-3636	172	13	)	)	PUNCT
ejpam-3636	172	14	,	,	PUNCT
ejpam-3636	172	15	258	258	NUM
ejpam-3636	172	16	-	-	SYM
ejpam-3636	172	17	268	268	NUM
ejpam-3636	172	18	266	266	NUM
ejpam-3636	172	19	the	the	DET
ejpam-3636	172	20	class	class	NOUN
ejpam-3636	172	21	of	of	ADP
ejpam-3636	172	22	functions	function	NOUN
ejpam-3636	172	23	ξ(x	ξ(x	NOUN
ejpam-3636	172	24	)	)	PUNCT
ejpam-3636	172	25	∈	∈	NOUN
ejpam-3636	172	26	ω∗	ω∗	NOUN
ejpam-3636	172	27	satisfies	satisfie	NOUN
ejpam-3636	172	28	(	(	PUNCT
ejpam-3636	172	29	i	i	NOUN
ejpam-3636	172	30	)	)	PUNCT
ejpam-3636	172	31	and	and	CCONJ
ejpam-3636	172	32	(	(	PUNCT
ejpam-3636	172	33	iii	iii	NOUN
ejpam-3636	172	34	)	)	PUNCT
ejpam-3636	172	35	(	(	PUNCT
ejpam-3636	172	36	iii).limx→∞	iii).limx→∞	PROPN
ejpam-3636	172	37	d(ξ(x	d(ξ(x	PROPN
ejpam-3636	172	38	)	)	PUNCT
ejpam-3636	172	39	)	)	PUNCT
ejpam-3636	173	1	d(log[q	d(log[q	ADP
ejpam-3636	173	2	]	]	X
ejpam-3636	173	3	x	x	X
ejpam-3636	173	4	)	)	PUNCT
ejpam-3636	173	5	=	=	SYM
ejpam-3636	173	6	k	k	NOUN
ejpam-3636	173	7	,	,	PUNCT
ejpam-3636	173	8	0	0	PUNCT
ejpam-3636	173	9	<	<	X
ejpam-3636	173	10	k	k	X
ejpam-3636	173	11	<	<	X
ejpam-3636	173	12	∞	∞	PROPN
ejpam-3636	173	13	,	,	PUNCT
ejpam-3636	173	14	q	q	X
ejpam-3636	173	15	≥	≥	NOUN
ejpam-3636	173	16	1	1	NUM
ejpam-3636	173	17	,	,	PUNCT
ejpam-3636	173	18	q	q	PROPN
ejpam-3636	173	19	∈	∈	PROPN
ejpam-3636	173	20	n+	n+	ADP
ejpam-3636	173	21	,	,	PUNCT
ejpam-3636	173	22	where	where	SCONJ
ejpam-3636	173	23	log[q	log[q	NOUN
ejpam-3636	173	24	]	]	X
ejpam-3636	173	25	x	x	SYM
ejpam-3636	173	26	=	=	SYM
ejpam-3636	173	27	log[q−1	log[q−1	X
ejpam-3636	173	28	]	]	PUNCT
ejpam-3636	173	29	log	log	NOUN
ejpam-3636	173	30	x	x	NOUN
ejpam-3636	173	31	,	,	PUNCT
ejpam-3636	173	32	log[0	log[0	X
ejpam-3636	173	33	]	]	PUNCT
ejpam-3636	173	34	=	=	PUNCT
ejpam-3636	173	35	x.	x.	NOUN
ejpam-3636	173	36	the	the	DET
ejpam-3636	173	37	class	class	NOUN
ejpam-3636	173	38	ξ(x	ξ(x	NOUN
ejpam-3636	173	39	)	)	PUNCT
ejpam-3636	173	40	also	also	ADV
ejpam-3636	173	41	satisfies	satisfy	VERB
ejpam-3636	173	42	l0	l0	PROPN
ejpam-3636	173	43	and	and	CCONJ
ejpam-3636	173	44	λ	λ	NOUN
ejpam-3636	173	45	.	.	PUNCT
ejpam-3636	174	1	it	it	PRON
ejpam-3636	174	2	is	be	AUX
ejpam-3636	174	3	clear	clear	ADJ
ejpam-3636	174	4	that	that	SCONJ
ejpam-3636	174	5	α(x	α(x	NOUN
ejpam-3636	174	6	)	)	PUNCT
ejpam-3636	174	7	∈	∈	PROPN
ejpam-3636	174	8	ω	ω	PROPN
ejpam-3636	174	9	is	be	AUX
ejpam-3636	174	10	a	a	DET
ejpam-3636	174	11	particular	particular	ADJ
ejpam-3636	174	12	case	case	NOUN
ejpam-3636	174	13	of	of	ADP
ejpam-3636	174	14	α(x	α(x	NOUN
ejpam-3636	174	15	)	)	PUNCT
ejpam-3636	174	16	∈	∈	PROPN
ejpam-3636	174	17	ω∗.	ω∗.	PROPN
ejpam-3636	174	18	for	for	ADP
ejpam-3636	174	19	q	q	NOUN
ejpam-3636	174	20	=	=	SYM
ejpam-3636	174	21	1	1	X
ejpam-3636	174	22	.	.	PUNCT
ejpam-3636	175	1	ning	ning	PROPN
ejpam-3636	175	2	juhong	juhong	PROPN
ejpam-3636	175	3	and	and	CCONJ
ejpam-3636	175	4	chen	chen	PROPN
ejpam-3636	175	5	qing	qing	PROPN
ejpam-3636	176	1	[	[	X
ejpam-3636	176	2	9	9	NUM
ejpam-3636	176	3	]	]	PUNCT
ejpam-3636	176	4	obtained	obtain	VERB
ejpam-3636	176	5	the	the	DET
ejpam-3636	176	6	following	follow	VERB
ejpam-3636	176	7	coefficient	coefficient	NOUN
ejpam-3636	176	8	characterization	characterization	NOUN
ejpam-3636	176	9	:	:	PUNCT
ejpam-3636	176	10	let	let	VERB
ejpam-3636	176	11	α(x	α(x	NUM
ejpam-3636	176	12	)	)	PUNCT
ejpam-3636	176	13	∈	∈	PROPN
ejpam-3636	176	14	ω∗	ω∗	NOUN
ejpam-3636	176	15	,	,	PUNCT
ejpam-3636	176	16	then	then	ADV
ejpam-3636	176	17	some	some	DET
ejpam-3636	176	18	necessary	necessary	ADJ
ejpam-3636	176	19	and	and	CCONJ
ejpam-3636	176	20	sufficient	sufficient	ADJ
ejpam-3636	176	21	conditions	condition	NOUN
ejpam-3636	176	22	of	of	ADP
ejpam-3636	176	23	the	the	DET
ejpam-3636	176	24	entire	entire	ADJ
ejpam-3636	176	25	function	function	NOUN
ejpam-3636	176	26	f(z	f(z	NOUN
ejpam-3636	176	27	)	)	PUNCT
ejpam-3636	176	28	having	have	VERB
ejpam-3636	176	29	generalized	generalize	VERB
ejpam-3636	176	30	order	order	NOUN
ejpam-3636	176	31	ρ	ρ	NOUN
ejpam-3636	176	32	is	be	AUX
ejpam-3636	176	33	lim	lim	NOUN
ejpam-3636	176	34	sup	sup	PROPN
ejpam-3636	176	35	r→∞	r→∞	X
ejpam-3636	176	36	α(logm(r	α(logm(r	NOUN
ejpam-3636	176	37	,	,	PUNCT
ejpam-3636	176	38	f	f	NOUN
ejpam-3636	176	39	)	)	PUNCT
ejpam-3636	176	40	)	)	PUNCT
ejpam-3636	177	1	α(log	α(log	PROPN
ejpam-3636	177	2	r	r	NOUN
ejpam-3636	177	3	)	)	PUNCT
ejpam-3636	177	4	−	−	PROPN
ejpam-3636	177	5	1	1	NUM
ejpam-3636	177	6	=	=	SYM
ejpam-3636	177	7	lim	lim	PROPN
ejpam-3636	177	8	sup	sup	PROPN
ejpam-3636	177	9	k→∞	k→∞	NOUN
ejpam-3636	177	10	α(k	α(k	PROPN
ejpam-3636	177	11	)	)	PUNCT
ejpam-3636	177	12	α(log	α(log	NOUN
ejpam-3636	177	13	|ak|−	|ak|−	PROPN
ejpam-3636	177	14	1	1	NUM
ejpam-3636	177	15	k	k	NOUN
ejpam-3636	177	16	)	)	PUNCT
ejpam-3636	177	17	for	for	ADP
ejpam-3636	177	18	q	q	NOUN
ejpam-3636	177	19	=	=	SYM
ejpam-3636	177	20	1	1	NUM
ejpam-3636	177	21	,	,	PUNCT
ejpam-3636	177	22	(	(	PUNCT
ejpam-3636	177	23	3.3	3.3	NUM
ejpam-3636	177	24	)	)	PUNCT
ejpam-3636	177	25	lim	lim	PROPN
ejpam-3636	177	26	sup	sup	PROPN
ejpam-3636	177	27	k→∞	k→∞	NOUN
ejpam-3636	177	28	α(k	α(k	PROPN
ejpam-3636	177	29	)	)	PUNCT
ejpam-3636	177	30	α(log	α(log	NOUN
ejpam-3636	177	31	|ak|−	|ak|−	PROPN
ejpam-3636	177	32	1	1	NUM
ejpam-3636	177	33	k	k	PROPN
ejpam-3636	177	34	)	)	PUNCT
ejpam-3636	177	35	≤	≤	NOUN
ejpam-3636	177	36	lim	lim	PROPN
ejpam-3636	177	37	sup	sup	PROPN
ejpam-3636	177	38	r→∞	r→∞	X
ejpam-3636	177	39	α(logm(r	α(logm(r	NOUN
ejpam-3636	177	40	,	,	PUNCT
ejpam-3636	177	41	f	f	NOUN
ejpam-3636	177	42	)	)	PUNCT
ejpam-3636	177	43	)	)	PUNCT
ejpam-3636	177	44	α(log	α(log	PROPN
ejpam-3636	177	45	r	r	NOUN
ejpam-3636	177	46	)	)	PUNCT
ejpam-3636	177	47	≤	≤	NOUN
ejpam-3636	178	1	lim	lim	PROPN
ejpam-3636	178	2	sup	sup	PROPN
ejpam-3636	178	3	k→∞	k→∞	NOUN
ejpam-3636	178	4	α(k	α(k	PROPN
ejpam-3636	178	5	)	)	PUNCT
ejpam-3636	178	6	α(log	α(log	NOUN
ejpam-3636	178	7	|ak|−	|ak|−	PROPN
ejpam-3636	178	8	1	1	NUM
ejpam-3636	178	9	k	k	PROPN
ejpam-3636	178	10	)	)	PUNCT
ejpam-3636	179	1	+	+	CCONJ
ejpam-3636	179	2	1	1	NUM
ejpam-3636	179	3	,	,	PUNCT
ejpam-3636	179	4	for	for	ADP
ejpam-3636	179	5	q	q	NOUN
ejpam-3636	179	6	=	=	SYM
ejpam-3636	179	7	2	2	NUM
ejpam-3636	179	8	,	,	PUNCT
ejpam-3636	179	9	3	3	NUM
ejpam-3636	179	10	,	,	PUNCT
ejpam-3636	179	11	.	.	PUNCT
ejpam-3636	179	12	.	.	PUNCT
ejpam-3636	179	13	.	.	PUNCT
ejpam-3636	180	1	,	,	PUNCT
ejpam-3636	180	2	.	.	PUNCT
ejpam-3636	181	1	(	(	PUNCT
ejpam-3636	181	2	3.4	3.4	NUM
ejpam-3636	181	3	)	)	PUNCT
ejpam-3636	181	4	for	for	ADP
ejpam-3636	181	5	α(x	α(x	NOUN
ejpam-3636	181	6	)	)	PUNCT
ejpam-3636	181	7	∈	∈	PROPN
ejpam-3636	181	8	ω∗	ω∗	PROPN
ejpam-3636	181	9	,	,	PUNCT
ejpam-3636	181	10	the	the	DET
ejpam-3636	181	11	entire	entire	ADJ
ejpam-3636	181	12	function	function	NOUN
ejpam-3636	181	13	f(z	f(z	PROPN
ejpam-3636	181	14	)	)	PUNCT
ejpam-3636	181	15	of	of	ADP
ejpam-3636	181	16	generalized	generalized	ADJ
ejpam-3636	181	17	order	order	NOUN
ejpam-3636	181	18	ρ	ρ	NOUN
ejpam-3636	181	19	,	,	PUNCT
ejpam-3636	181	20	1	1	NUM
ejpam-3636	181	21	<	<	X
ejpam-3636	181	22	ρ	ρ	X
ejpam-3636	181	23	<	<	X
ejpam-3636	181	24	∞	∞	NUM
ejpam-3636	181	25	having	have	VERB
ejpam-3636	181	26	the	the	DET
ejpam-3636	181	27	generalized	generalized	ADJ
ejpam-3636	181	28	type	type	NOUN
ejpam-3636	181	29	t	t	NOUN
ejpam-3636	181	30	if	if	SCONJ
ejpam-3636	182	1	and	and	CCONJ
ejpam-3636	182	2	only	only	ADV
ejpam-3636	182	3	if	if	SCONJ
ejpam-3636	182	4	lim	lim	PROPN
ejpam-3636	182	5	sup	sup	PROPN
ejpam-3636	182	6	r→∞	r→∞	X
ejpam-3636	182	7	α(logm(r	α(logm(r	NOUN
ejpam-3636	182	8	,	,	PUNCT
ejpam-3636	182	9	f	f	NOUN
ejpam-3636	182	10	)	)	PUNCT
ejpam-3636	182	11	)	)	PUNCT
ejpam-3636	183	1	[	[	X
ejpam-3636	183	2	α(log	α(log	NUM
ejpam-3636	183	3	r)]ρ	r)]ρ	NOUN
ejpam-3636	183	4	=	=	PUNCT
ejpam-3636	183	5	lim	lim	PROPN
ejpam-3636	183	6	sup	sup	PROPN
ejpam-3636	183	7	k→∞	k→∞	PROPN
ejpam-3636	183	8	α(kρ	α(kρ	PROPN
ejpam-3636	183	9	)	)	PUNCT
ejpam-3636	183	10	{	{	PUNCT
ejpam-3636	183	11	α(log	α(log	PROPN
ejpam-3636	183	12	|ak|−	|ak|−	PROPN
ejpam-3636	183	13	1	1	NUM
ejpam-3636	183	14	k	k	NOUN
ejpam-3636	183	15	)	)	PUNCT
ejpam-3636	183	16	}	}	PUNCT
ejpam-3636	183	17	ρ−1	ρ−1	PROPN
ejpam-3636	183	18	for	for	ADP
ejpam-3636	183	19	q	q	NOUN
ejpam-3636	183	20	=	=	SYM
ejpam-3636	183	21	1	1	NUM
ejpam-3636	183	22	,	,	PUNCT
ejpam-3636	183	23	(	(	PUNCT
ejpam-3636	183	24	3.5	3.5	NUM
ejpam-3636	183	25	)	)	PUNCT
ejpam-3636	183	26	lim	lim	PROPN
ejpam-3636	183	27	sup	sup	PROPN
ejpam-3636	183	28	r→∞	r→∞	X
ejpam-3636	183	29	α(logm(r	α(logm(r	NOUN
ejpam-3636	183	30	,	,	PUNCT
ejpam-3636	183	31	f	f	NOUN
ejpam-3636	183	32	)	)	PUNCT
ejpam-3636	183	33	)	)	PUNCT
ejpam-3636	184	1	[	[	X
ejpam-3636	184	2	α(log	α(log	NUM
ejpam-3636	184	3	r)]ρ	r)]ρ	NOUN
ejpam-3636	184	4	=	=	PUNCT
ejpam-3636	184	5	lim	lim	PROPN
ejpam-3636	184	6	sup	sup	PROPN
ejpam-3636	184	7	k→∞	k→∞	PROPN
ejpam-3636	184	8	α(kρ	α(kρ	PROPN
ejpam-3636	184	9	)	)	PUNCT
ejpam-3636	184	10	{	{	PUNCT
ejpam-3636	184	11	α(log	α(log	PROPN
ejpam-3636	184	12	|ak|−	|ak|−	PROPN
ejpam-3636	184	13	1	1	NUM
ejpam-3636	184	14	k	k	NOUN
ejpam-3636	184	15	)	)	PUNCT
ejpam-3636	184	16	}	}	PUNCT
ejpam-3636	184	17	ρ	ρ	NOUN
ejpam-3636	184	18	for	for	ADP
ejpam-3636	184	19	q	q	NOUN
ejpam-3636	184	20	=	=	SYM
ejpam-3636	184	21	2	2	NUM
ejpam-3636	184	22	,	,	PUNCT
ejpam-3636	184	23	3	3	NUM
ejpam-3636	184	24	,	,	PUNCT
ejpam-3636	184	25	.	.	PUNCT
ejpam-3636	184	26	.	.	PUNCT
ejpam-3636	184	27	.	.	PUNCT
ejpam-3636	184	28	.	.	PUNCT
ejpam-3636	185	1	(	(	PUNCT
ejpam-3636	185	2	3.6	3.6	NUM
ejpam-3636	185	3	)	)	PUNCT
ejpam-3636	185	4	now	now	ADV
ejpam-3636	185	5	we	we	PRON
ejpam-3636	185	6	prove	prove	VERB
ejpam-3636	185	7	theorem	theorem	ADJ
ejpam-3636	185	8	3.1	3.1	NUM
ejpam-3636	185	9	.	.	PUNCT
ejpam-3636	186	1	let	let	VERB
ejpam-3636	186	2	α(x	α(x	NUM
ejpam-3636	186	3	)	)	PUNCT
ejpam-3636	186	4	∈	∈	PROPN
ejpam-3636	186	5	ω∗	ω∗	NOUN
ejpam-3636	186	6	,	,	PUNCT
ejpam-3636	186	7	then	then	ADV
ejpam-3636	186	8	necessary	necessary	ADJ
ejpam-3636	186	9	and	and	CCONJ
ejpam-3636	186	10	sufficient	sufficient	ADJ
ejpam-3636	186	11	conditions	condition	NOUN
ejpam-3636	186	12	for	for	SCONJ
ejpam-3636	186	13	h	h	NOUN
ejpam-3636	186	14	to	to	PART
ejpam-3636	186	15	be	be	AUX
ejpam-3636	186	16	continued	continue	VERB
ejpam-3636	186	17	to	to	ADP
ejpam-3636	186	18	the	the	DET
ejpam-3636	186	19	entire	entire	ADJ
ejpam-3636	186	20	harmonic	harmonic	ADJ
ejpam-3636	186	21	function	function	NOUN
ejpam-3636	186	22	in	in	ADP
ejpam-3636	186	23	space	space	PROPN
ejpam-3636	186	24	rn	rn	PROPN
ejpam-3636	186	25	,	,	PUNCT
ejpam-3636	186	26	n	n	PRON
ejpam-3636	186	27	≥	≥	NOUN
ejpam-3636	186	28	3	3	NUM
ejpam-3636	186	29	having	have	VERB
ejpam-3636	186	30	generalized	generalize	VERB
ejpam-3636	186	31	order	order	NOUN
ejpam-3636	186	32	ρ1(α	ρ1(α	SYM
ejpam-3636	186	33	,	,	PUNCT
ejpam-3636	186	34	α	α	NOUN
ejpam-3636	186	35	,	,	PUNCT
ejpam-3636	186	36	h	h	NOUN
ejpam-3636	186	37	)	)	PUNCT
ejpam-3636	186	38	is	be	AUX
ejpam-3636	186	39	lim	lim	PROPN
ejpam-3636	186	40	sup	sup	PROPN
ejpam-3636	186	41	k→∞	k→∞	NOUN
ejpam-3636	186	42	α(k	α(k	NOUN
ejpam-3636	186	43	)	)	PUNCT
ejpam-3636	186	44	α(log	α(log	PROPN
ejpam-3636	186	45	[	[	PUNCT
ejpam-3636	186	46	|∇kh(0)|	|∇kh(0)|	NOUN
ejpam-3636	186	47	k	k	NOUN
ejpam-3636	186	48	!	!	PUNCT
ejpam-3636	187	1	]	]	X
ejpam-3636	187	2	−	−	PROPN
ejpam-3636	187	3	1	1	NUM
ejpam-3636	187	4	k	k	NOUN
ejpam-3636	187	5	)	)	PUNCT
ejpam-3636	187	6	≤	≤	NOUN
ejpam-3636	187	7	lim	lim	PROPN
ejpam-3636	187	8	sup	sup	PROPN
ejpam-3636	187	9	r→∞	r→∞	NUM
ejpam-3636	187	10	α(logm(r	α(logm(r	NOUN
ejpam-3636	187	11	,	,	PUNCT
ejpam-3636	187	12	h	h	NOUN
ejpam-3636	187	13	)	)	PUNCT
ejpam-3636	187	14	)	)	PUNCT
ejpam-3636	187	15	α(log	α(log	PROPN
ejpam-3636	187	16	r	r	NOUN
ejpam-3636	187	17	)	)	PUNCT
ejpam-3636	187	18	≤	≤	NOUN
ejpam-3636	188	1	lim	lim	PROPN
ejpam-3636	188	2	sup	sup	PROPN
ejpam-3636	188	3	k→∞	k→∞	NOUN
ejpam-3636	188	4	α(k	α(k	NOUN
ejpam-3636	188	5	)	)	PUNCT
ejpam-3636	188	6	α(log	α(log	PROPN
ejpam-3636	188	7	[	[	PUNCT
ejpam-3636	188	8	|∇kh(0)|	|∇kh(0)|	NOUN
ejpam-3636	188	9	k	k	NOUN
ejpam-3636	188	10	!	!	PUNCT
ejpam-3636	189	1	]	]	X
ejpam-3636	189	2	−	−	PROPN
ejpam-3636	189	3	1	1	NUM
ejpam-3636	189	4	k	k	NOUN
ejpam-3636	189	5	)	)	PUNCT
ejpam-3636	190	1	+	+	CCONJ
ejpam-3636	190	2	1	1	NUM
ejpam-3636	190	3	for	for	ADP
ejpam-3636	190	4	q	q	NOUN
ejpam-3636	190	5	=	=	SYM
ejpam-3636	190	6	2	2	NUM
ejpam-3636	190	7	,	,	PUNCT
ejpam-3636	190	8	3	3	NUM
ejpam-3636	190	9	,	,	PUNCT
ejpam-3636	190	10	.	.	PUNCT
ejpam-3636	190	11	.	.	PUNCT
ejpam-3636	190	12	.	.	PUNCT
ejpam-3636	190	13	.	.	PUNCT
ejpam-3636	191	1	(	(	PUNCT
ejpam-3636	191	2	3.7	3.7	NUM
ejpam-3636	191	3	)	)	PUNCT
ejpam-3636	191	4	proof	proof	NOUN
ejpam-3636	191	5	.	.	PUNCT
ejpam-3636	192	1	applying	apply	VERB
ejpam-3636	192	2	the	the	DET
ejpam-3636	192	3	method	method	NOUN
ejpam-3636	192	4	of	of	ADP
ejpam-3636	192	5	proving	prove	VERB
ejpam-3636	192	6	theorem	theorem	ADJ
ejpam-3636	192	7	2.1	2.1	NUM
ejpam-3636	192	8	and	and	CCONJ
ejpam-3636	192	9	taking	take	VERB
ejpam-3636	192	10	(	(	PUNCT
ejpam-3636	192	11	3.4	3.4	NUM
ejpam-3636	192	12	)	)	PUNCT
ejpam-3636	192	13	into	into	ADP
ejpam-3636	192	14	account	account	NOUN
ejpam-3636	192	15	with	with	ADP
ejpam-3636	192	16	properties	property	NOUN
ejpam-3636	192	17	of	of	ADP
ejpam-3636	192	18	α(x	α(x	NOUN
ejpam-3636	192	19	)	)	PUNCT
ejpam-3636	192	20	,	,	PUNCT
ejpam-3636	192	21	we	we	PRON
ejpam-3636	192	22	obtain	obtain	VERB
ejpam-3636	192	23	the	the	DET
ejpam-3636	192	24	required	require	VERB
ejpam-3636	192	25	result	result	NOUN
ejpam-3636	192	26	(	(	PUNCT
ejpam-3636	192	27	3.7	3.7	NUM
ejpam-3636	192	28	)	)	PUNCT
ejpam-3636	192	29	.	.	PUNCT
ejpam-3636	193	1	references	reference	NOUN
ejpam-3636	193	2	267	267	NUM
ejpam-3636	193	3	theorem	theorem	NOUN
ejpam-3636	193	4	3.2	3.2	NUM
ejpam-3636	193	5	.	.	PUNCT
ejpam-3636	194	1	let	let	VERB
ejpam-3636	194	2	α(x	α(x	NOUN
ejpam-3636	194	3	)	)	PUNCT
ejpam-3636	194	4	∈	∈	PROPN
ejpam-3636	194	5	ω∗	ω∗	NOUN
ejpam-3636	194	6	,	,	PUNCT
ejpam-3636	194	7	then	then	ADV
ejpam-3636	194	8	the	the	DET
ejpam-3636	194	9	function	function	NOUN
ejpam-3636	194	10	h	h	NOUN
ejpam-3636	194	11	can	can	AUX
ejpam-3636	194	12	be	be	AUX
ejpam-3636	194	13	continued	continue	VERB
ejpam-3636	194	14	to	to	ADP
ejpam-3636	194	15	the	the	DET
ejpam-3636	194	16	entire	entire	ADJ
ejpam-3636	194	17	harmonic	harmonic	ADJ
ejpam-3636	194	18	function	function	NOUN
ejpam-3636	194	19	in	in	ADP
ejpam-3636	194	20	space	space	PROPN
ejpam-3636	194	21	rn	rn	PROPN
ejpam-3636	194	22	,	,	PUNCT
ejpam-3636	194	23	n	n	PRON
ejpam-3636	194	24	≥	≥	NOUN
ejpam-3636	194	25	3	3	NUM
ejpam-3636	194	26	,	,	PUNCT
ejpam-3636	194	27	having	have	VERB
ejpam-3636	194	28	generalized	generalize	VERB
ejpam-3636	194	29	order	order	NOUN
ejpam-3636	194	30	ρ1(α	ρ1(α	SYM
ejpam-3636	194	31	,	,	PUNCT
ejpam-3636	194	32	α	α	NOUN
ejpam-3636	194	33	,	,	PUNCT
ejpam-3636	194	34	h	h	NOUN
ejpam-3636	194	35	)	)	PUNCT
ejpam-3636	194	36	,	,	PUNCT
ejpam-3636	194	37	1	1	NUM
ejpam-3636	194	38	<	<	X
ejpam-3636	194	39	ρ1(α	ρ1(α	PROPN
ejpam-3636	194	40	,	,	PUNCT
ejpam-3636	194	41	α	α	NOUN
ejpam-3636	194	42	,	,	PUNCT
ejpam-3636	194	43	h	h	NOUN
ejpam-3636	194	44	)	)	PUNCT
ejpam-3636	194	45	<	<	X
ejpam-3636	195	1	∞	∞	PROPN
ejpam-3636	195	2	,	,	PUNCT
ejpam-3636	195	3	is	be	AUX
ejpam-3636	195	4	of	of	ADP
ejpam-3636	195	5	generalized	generalized	ADJ
ejpam-3636	195	6	type	type	NOUN
ejpam-3636	195	7	t1(α	t1(α	PROPN
ejpam-3636	195	8	,	,	PUNCT
ejpam-3636	195	9	α	α	NOUN
ejpam-3636	195	10	,	,	PUNCT
ejpam-3636	195	11	h	h	NOUN
ejpam-3636	195	12	)	)	PUNCT
ejpam-3636	195	13	if	if	SCONJ
ejpam-3636	195	14	,	,	PUNCT
ejpam-3636	195	15	and	and	CCONJ
ejpam-3636	195	16	only	only	ADV
ejpam-3636	195	17	if	if	SCONJ
ejpam-3636	195	18	lim	lim	PROPN
ejpam-3636	195	19	sup	sup	PROPN
ejpam-3636	195	20	r→∞	r→∞	X
ejpam-3636	195	21	α(logm(r	α(logm(r	NOUN
ejpam-3636	195	22	,	,	PUNCT
ejpam-3636	195	23	h	h	NOUN
ejpam-3636	195	24	)	)	PUNCT
ejpam-3636	195	25	)	)	PUNCT
ejpam-3636	196	1	[	[	X
ejpam-3636	196	2	α(log	α(log	NOUN
ejpam-3636	196	3	r)]ρ1	r)]ρ1	X
ejpam-3636	196	4	=	=	SYM
ejpam-3636	196	5	lim	lim	PROPN
ejpam-3636	196	6	sup	sup	PROPN
ejpam-3636	196	7	k→∞	k→∞	ADV
ejpam-3636	196	8	α(k	α(k	PROPN
ejpam-3636	196	9	)	)	PUNCT
ejpam-3636	197	1	[	[	X
ejpam-3636	197	2	α(log	α(log	X
ejpam-3636	197	3	[	[	PUNCT
ejpam-3636	197	4	|∇kh(0)|	|∇kh(0)|	NOUN
ejpam-3636	197	5	k	k	NOUN
ejpam-3636	197	6	!	!	PUNCT
ejpam-3636	198	1	]	]	X
ejpam-3636	198	2	−	−	PROPN
ejpam-3636	198	3	1	1	NUM
ejpam-3636	198	4	k	k	NOUN
ejpam-3636	198	5	)	)	PUNCT
ejpam-3636	198	6	]	]	PUNCT
ejpam-3636	198	7	ρ1	ρ1	NOUN
ejpam-3636	198	8	for	for	ADP
ejpam-3636	198	9	q	q	NOUN
ejpam-3636	198	10	=	=	SYM
ejpam-3636	198	11	2	2	NUM
ejpam-3636	198	12	,	,	PUNCT
ejpam-3636	198	13	3	3	NUM
ejpam-3636	198	14	,	,	PUNCT
ejpam-3636	198	15	.	.	PUNCT
ejpam-3636	198	16	.	.	PUNCT
ejpam-3636	198	17	.	.	PUNCT
ejpam-3636	198	18	.	.	PUNCT
ejpam-3636	199	1	proof	proof	NOUN
ejpam-3636	199	2	.	.	PUNCT
ejpam-3636	200	1	the	the	DET
ejpam-3636	200	2	result	result	NOUN
ejpam-3636	200	3	follows	follow	VERB
ejpam-3636	200	4	on	on	ADP
ejpam-3636	200	5	using	use	VERB
ejpam-3636	200	6	(	(	PUNCT
ejpam-3636	200	7	3.6	3.6	NUM
ejpam-3636	200	8	)	)	PUNCT
ejpam-3636	200	9	for	for	ADP
ejpam-3636	200	10	the	the	DET
ejpam-3636	200	11	entire	entire	ADJ
ejpam-3636	200	12	function	function	NOUN
ejpam-3636	200	13	f1(z	f1(z	NOUN
ejpam-3636	200	14	)	)	PUNCT
ejpam-3636	200	15	.	.	PUNCT
ejpam-3636	201	1	remark	remark	PROPN
ejpam-3636	201	2	3.1	3.1	NUM
ejpam-3636	201	3	.	.	PUNCT
ejpam-3636	202	1	theorems	theorem	NOUN
ejpam-3636	202	2	3.1	3.1	NUM
ejpam-3636	202	3	and	and	CCONJ
ejpam-3636	202	4	3.2	3.2	NUM
ejpam-3636	202	5	have	have	AUX
ejpam-3636	202	6	been	be	AUX
ejpam-3636	202	7	proved	prove	VERB
ejpam-3636	202	8	by	by	ADP
ejpam-3636	202	9	srivastava	srivastava	PROPN
ejpam-3636	203	1	[	[	X
ejpam-3636	203	2	19	19	NUM
ejpam-3636	203	3	]	]	X
ejpam-3636	203	4	for	for	ADP
ejpam-3636	203	5	q	q	NOUN
ejpam-3636	203	6	=	=	SYM
ejpam-3636	203	7	1	1	X
ejpam-3636	203	8	.	.	PUNCT
ejpam-3636	203	9	acknowledgements	acknowledgement	NOUN
ejpam-3636	203	10	the	the	DET
ejpam-3636	203	11	authors	author	NOUN
ejpam-3636	203	12	are	be	AUX
ejpam-3636	203	13	thankful	thankful	ADJ
ejpam-3636	203	14	to	to	ADP
ejpam-3636	203	15	the	the	DET
ejpam-3636	203	16	editor	editor	NOUN
ejpam-3636	203	17	for	for	ADP
ejpam-3636	203	18	his	his	PRON
ejpam-3636	203	19	useful	useful	ADJ
ejpam-3636	203	20	comments	comment	NOUN
ejpam-3636	203	21	,	,	PUNCT
ejpam-3636	203	22	and	and	CCONJ
ejpam-3636	203	23	the	the	DET
ejpam-3636	203	24	referees	referee	NOUN
ejpam-3636	203	25	for	for	ADP
ejpam-3636	203	26	their	their	PRON
ejpam-3636	203	27	valuable	valuable	ADJ
ejpam-3636	203	28	suggestions	suggestion	NOUN
ejpam-3636	203	29	which	which	PRON
ejpam-3636	203	30	improved	improve	VERB
ejpam-3636	203	31	the	the	DET
ejpam-3636	203	32	paper	paper	NOUN
ejpam-3636	203	33	.	.	PUNCT
ejpam-3636	204	1	references	reference	NOUN
ejpam-3636	204	2	[	[	X
ejpam-3636	204	3	1	1	NUM
ejpam-3636	204	4	]	]	X
ejpam-3636	204	5	d.h	d.h	PROPN
ejpam-3636	204	6	.	.	PROPN
ejpam-3636	204	7	armitage	armitage	PROPN
ejpam-3636	204	8	,	,	PUNCT
ejpam-3636	204	9	on	on	ADP
ejpam-3636	204	10	the	the	DET
ejpam-3636	204	11	derivatives	derivative	NOUN
ejpam-3636	204	12	at	at	ADP
ejpam-3636	204	13	the	the	DET
ejpam-3636	204	14	origin	origin	NOUN
ejpam-3636	204	15	of	of	ADP
ejpam-3636	204	16	entire	entire	ADJ
ejpam-3636	204	17	harmonic	harmonic	ADJ
ejpam-3636	204	18	functions	function	NOUN
ejpam-3636	204	19	,	,	PUNCT
ejpam-3636	204	20	glasgow	glasgow	PROPN
ejpam-3636	204	21	math	math	NOUN
ejpam-3636	204	22	.	.	PUNCT
ejpam-3636	205	1	j.	j.	PROPN
ejpam-3636	205	2	,	,	PUNCT
ejpam-3636	205	3	20	20	NUM
ejpam-3636	205	4	(	(	PUNCT
ejpam-3636	205	5	1979),147	1979),147	NUM
ejpam-3636	205	6	-	-	SYM
ejpam-3636	205	7	154	154	NUM
ejpam-3636	205	8	.	.	PUNCT
ejpam-3636	206	1	[	[	X
ejpam-3636	206	2	2	2	NUM
ejpam-3636	206	3	]	]	X
ejpam-3636	206	4	a.p	a.p	PROPN
ejpam-3636	206	5	.	.	PROPN
ejpam-3636	206	6	calderon	calderon	PROPN
ejpam-3636	206	7	and	and	CCONJ
ejpam-3636	206	8	a.	a.	NOUN
ejpam-3636	206	9	zygmund	zygmund	PROPN
ejpam-3636	206	10	,	,	PUNCT
ejpam-3636	206	11	on	on	ADP
ejpam-3636	206	12	higher	high	ADJ
ejpam-3636	206	13	gradients	gradient	NOUN
ejpam-3636	206	14	of	of	ADP
ejpam-3636	206	15	harmonic	harmonic	ADJ
ejpam-3636	206	16	functions	function	NOUN
ejpam-3636	206	17	,	,	PUNCT
ejpam-3636	206	18	studia	studia	PROPN
ejpam-3636	206	19	math	math	NOUN
ejpam-3636	206	20	.	.	PUNCT
ejpam-3636	206	21	,	,	PUNCT
ejpam-3636	206	22	24	24	NUM
ejpam-3636	206	23	(	(	PUNCT
ejpam-3636	206	24	1964	1964	NUM
ejpam-3636	206	25	)	)	PUNCT
ejpam-3636	206	26	,	,	PUNCT
ejpam-3636	206	27	211	211	NUM
ejpam-3636	206	28	-	-	SYM
ejpam-3636	206	29	226	226	NUM
ejpam-3636	206	30	.	.	PUNCT
ejpam-3636	207	1	[	[	X
ejpam-3636	207	2	3	3	X
ejpam-3636	207	3	]	]	X
ejpam-3636	207	4	n.	n.	NOUN
ejpam-3636	207	5	du	du	PROPN
ejpam-3636	207	6	plessis	plessis	PROPN
ejpam-3636	207	7	,	,	PUNCT
ejpam-3636	207	8	an	an	DET
ejpam-3636	207	9	introduction	introduction	NOUN
ejpam-3636	207	10	to	to	ADP
ejpam-3636	207	11	potential	potential	ADJ
ejpam-3636	207	12	theory	theory	NOUN
ejpam-3636	207	13	,	,	PUNCT
ejpam-3636	207	14	oliver	oliver	PROPN
ejpam-3636	207	15	and	and	CCONJ
ejpam-3636	207	16	boyd	boyd	PROPN
ejpam-3636	207	17	edinburg	edinburg	PROPN
ejpam-3636	207	18	,	,	PUNCT
ejpam-3636	207	19	1970	1970	NUM
ejpam-3636	207	20	.	.	PUNCT
ejpam-3636	208	1	[	[	X
ejpam-3636	208	2	4	4	NUM
ejpam-3636	208	3	]	]	X
ejpam-3636	208	4	a.j	a.j	PROPN
ejpam-3636	208	5	.	.	PROPN
ejpam-3636	208	6	fryant	fryant	PROPN
ejpam-3636	208	7	and	and	CCONJ
ejpam-3636	208	8	h.	h.	PROPN
ejpam-3636	208	9	shankar	shankar	PROPN
ejpam-3636	208	10	,	,	PUNCT
ejpam-3636	208	11	growth	growth	NOUN
ejpam-3636	208	12	of	of	ADP
ejpam-3636	208	13	harmonic	harmonic	ADJ
ejpam-3636	208	14	functions	function	NOUN
ejpam-3636	208	15	in	in	ADP
ejpam-3636	208	16	hyperspheres	hypersphere	NOUN
ejpam-3636	208	17	,	,	PUNCT
ejpam-3636	208	18	j.	j.	PROPN
ejpam-3636	208	19	math	math	PROPN
ejpam-3636	208	20	.	.	PUNCT
ejpam-3636	209	1	anal	anal	PROPN
ejpam-3636	209	2	.	.	PUNCT
ejpam-3636	210	1	appl	appl	PROPN
ejpam-3636	210	2	.	.	PROPN
ejpam-3636	210	3	,	,	PUNCT
ejpam-3636	210	4	122	122	NUM
ejpam-3636	210	5	(	(	PUNCT
ejpam-3636	210	6	1987	1987	NUM
ejpam-3636	210	7	)	)	PUNCT
ejpam-3636	210	8	,	,	PUNCT
ejpam-3636	210	9	453	453	NUM
ejpam-3636	210	10	-	-	SYM
ejpam-3636	210	11	462	462	NUM
ejpam-3636	210	12	.	.	PUNCT
ejpam-3636	211	1	[	[	X
ejpam-3636	211	2	5	5	NUM
ejpam-3636	211	3	]	]	X
ejpam-3636	211	4	t.b	t.b	PROPN
ejpam-3636	211	5	.	.	PROPN
ejpam-3636	211	6	fugard	fugard	PROPN
ejpam-3636	211	7	,	,	PUNCT
ejpam-3636	211	8	on	on	ADP
ejpam-3636	211	9	the	the	DET
ejpam-3636	211	10	largest	large	ADJ
ejpam-3636	211	11	ball	ball	NOUN
ejpam-3636	211	12	of	of	ADP
ejpam-3636	211	13	harmonic	harmonic	ADJ
ejpam-3636	211	14	continuation	continuation	NOUN
ejpam-3636	211	15	,	,	PUNCT
ejpam-3636	211	16	j.	j.	PROPN
ejpam-3636	211	17	math	math	PROPN
ejpam-3636	211	18	.	.	PUNCT
ejpam-3636	212	1	anal	anal	PROPN
ejpam-3636	212	2	.	.	PUNCT
ejpam-3636	213	1	appl	appl	PROPN
ejpam-3636	213	2	.	.	PROPN
ejpam-3636	213	3	,	,	PUNCT
ejpam-3636	213	4	90	90	NUM
ejpam-3636	213	5	(	(	PUNCT
ejpam-3636	213	6	1982	1982	NUM
ejpam-3636	213	7	)	)	PUNCT
ejpam-3636	213	8	,	,	PUNCT
ejpam-3636	213	9	548	548	NUM
ejpam-3636	213	10	-	-	SYM
ejpam-3636	213	11	554	554	NUM
ejpam-3636	213	12	.	.	PUNCT
ejpam-3636	214	1	[	[	X
ejpam-3636	214	2	6	6	NUM
ejpam-3636	214	3	]	]	X
ejpam-3636	214	4	t.b	t.b	PROPN
ejpam-3636	214	5	.	.	PROPN
ejpam-3636	214	6	fugard	fugard	PROPN
ejpam-3636	214	7	,	,	PUNCT
ejpam-3636	214	8	growth	growth	NOUN
ejpam-3636	214	9	of	of	ADP
ejpam-3636	214	10	harmonic	harmonic	ADJ
ejpam-3636	214	11	functions	function	NOUN
ejpam-3636	214	12	in	in	ADP
ejpam-3636	214	13	rn	rn	PROPN
ejpam-3636	214	14	,	,	PUNCT
ejpam-3636	214	15	j.	j.	PROPN
ejpam-3636	214	16	math	math	PROPN
ejpam-3636	214	17	.	.	PUNCT
ejpam-3636	215	1	anal	anal	PROPN
ejpam-3636	215	2	.	.	PUNCT
ejpam-3636	216	1	appl	appl	PROPN
ejpam-3636	216	2	.	.	PROPN
ejpam-3636	216	3	,	,	PUNCT
ejpam-3636	216	4	74	74	NUM
ejpam-3636	216	5	(	(	PUNCT
ejpam-3636	216	6	1980	1980	NUM
ejpam-3636	216	7	)	)	PUNCT
ejpam-3636	216	8	,	,	PUNCT
ejpam-3636	216	9	286	286	NUM
ejpam-3636	216	10	-	-	SYM
ejpam-3636	216	11	291	291	NUM
ejpam-3636	216	12	.	.	PUNCT
ejpam-3636	217	1	[	[	X
ejpam-3636	217	2	7	7	X
ejpam-3636	217	3	]	]	X
ejpam-3636	217	4	r.	r.	PROPN
ejpam-3636	217	5	ganti	ganti	PROPN
ejpam-3636	217	6	and	and	CCONJ
ejpam-3636	217	7	g.s	g.s	PROPN
ejpam-3636	217	8	.	.	PROPN
ejpam-3636	217	9	srivastava	srivastava	PROPN
ejpam-3636	217	10	,	,	PUNCT
ejpam-3636	217	11	approximation	approximation	NOUN
ejpam-3636	217	12	of	of	ADP
ejpam-3636	217	13	entire	entire	ADJ
ejpam-3636	217	14	function	function	NOUN
ejpam-3636	217	15	of	of	ADP
ejpam-3636	217	16	slow	slow	ADJ
ejpam-3636	217	17	growth	growth	NOUN
ejpam-3636	217	18	,	,	PUNCT
ejpam-3636	217	19	general	general	ADJ
ejpam-3636	217	20	mathematics	mathematic	NOUN
ejpam-3636	217	21	,	,	PUNCT
ejpam-3636	217	22	14	14	NUM
ejpam-3636	217	23	(	(	PUNCT
ejpam-3636	217	24	2006	2006	NUM
ejpam-3636	217	25	)	)	PUNCT
ejpam-3636	217	26	,	,	PUNCT
ejpam-3636	217	27	59	59	NUM
ejpam-3636	217	28	-	-	SYM
ejpam-3636	217	29	76	76	NUM
ejpam-3636	217	30	.	.	PUNCT
ejpam-3636	218	1	[	[	X
ejpam-3636	218	2	8	8	NUM
ejpam-3636	218	3	]	]	X
ejpam-3636	218	4	m.	m.	NOUN
ejpam-3636	218	5	harfaoui	harfaoui	PROPN
ejpam-3636	218	6	,	,	PUNCT
ejpam-3636	218	7	generalized	generalized	ADJ
ejpam-3636	218	8	order	order	NOUN
ejpam-3636	218	9	and	and	CCONJ
ejpam-3636	218	10	best	good	ADJ
ejpam-3636	218	11	approximation	approximation	NOUN
ejpam-3636	218	12	of	of	ADP
ejpam-3636	218	13	entire	entire	ADJ
ejpam-3636	218	14	function	function	NOUN
ejpam-3636	218	15	in	in	ADP
ejpam-3636	218	16	lp	lp	ADJ
ejpam-3636	218	17	-	-	PUNCT
ejpam-3636	218	18	norm	norm	NOUN
ejpam-3636	218	19	,	,	PUNCT
ejpam-3636	218	20	internat	internat	PROPN
ejpam-3636	218	21	.	.	PUNCT
ejpam-3636	219	1	j.	j.	PROPN
ejpam-3636	219	2	math	math	PROPN
ejpam-3636	219	3	.	.	PUNCT
ejpam-3636	220	1	and	and	CCONJ
ejpam-3636	220	2	math	math	NOUN
ejpam-3636	220	3	.	.	PUNCT
ejpam-3636	221	1	sci	sci	PROPN
ejpam-3636	221	2	.	.	PROPN
ejpam-3636	221	3	,	,	PUNCT
ejpam-3636	221	4	2010	2010	NUM
ejpam-3636	221	5	(	(	PUNCT
ejpam-3636	221	6	2010	2010	NUM
ejpam-3636	221	7	)	)	PUNCT
ejpam-3636	221	8	,	,	PUNCT
ejpam-3636	221	9	1	1	NUM
ejpam-3636	221	10	-	-	SYM
ejpam-3636	221	11	15	15	NUM
ejpam-3636	221	12	[	[	X
ejpam-3636	221	13	9	9	NUM
ejpam-3636	221	14	]	]	SYM
ejpam-3636	221	15	ning	ning	NOUN
ejpam-3636	221	16	juhong	juhong	PROPN
ejpam-3636	221	17	and	and	CCONJ
ejpam-3636	221	18	chen	chen	PROPN
ejpam-3636	221	19	qing	qing	PROPN
ejpam-3636	221	20	,	,	PUNCT
ejpam-3636	221	21	approximation	approximation	NOUN
ejpam-3636	221	22	of	of	ADP
ejpam-3636	221	23	entire	entire	ADJ
ejpam-3636	221	24	functions	function	NOUN
ejpam-3636	221	25	of	of	ADP
ejpam-3636	221	26	slow	slow	ADJ
ejpam-3636	221	27	growth	growth	NOUN
ejpam-3636	221	28	,	,	PUNCT
ejpam-3636	221	29	intern	intern	NOUN
ejpam-3636	221	30	.	.	PUNCT
ejpam-3636	222	1	j.	j.	PROPN
ejpam-3636	222	2	pure	pure	PROPN
ejpam-3636	222	3	appl	appl	PROPN
ejpam-3636	222	4	.	.	PUNCT
ejpam-3636	222	5	math	math	PROPN
ejpam-3636	222	6	.	.	PUNCT
ejpam-3636	222	7	,	,	PUNCT
ejpam-3636	222	8	113	113	NUM
ejpam-3636	222	9	,	,	PUNCT
ejpam-3636	222	10	no.3	no.3	X
ejpam-3636	222	11	(	(	PUNCT
ejpam-3636	222	12	2017	2017	NUM
ejpam-3636	222	13	)	)	PUNCT
ejpam-3636	222	14	,	,	PUNCT
ejpam-3636	222	15	399	399	NUM
ejpam-3636	222	16	-	-	SYM
ejpam-3636	222	17	413	413	NUM
ejpam-3636	222	18	.	.	PUNCT
ejpam-3636	223	1	[	[	X
ejpam-3636	223	2	10	10	NUM
ejpam-3636	223	3	]	]	X
ejpam-3636	223	4	g.p	g.p	PROPN
ejpam-3636	223	5	.	.	PROPN
ejpam-3636	223	6	kapoor	kapoor	PROPN
ejpam-3636	223	7	and	and	CCONJ
ejpam-3636	223	8	a.	a.	PROPN
ejpam-3636	223	9	nautiyal	nautiyal	PROPN
ejpam-3636	223	10	,	,	PUNCT
ejpam-3636	223	11	polynomial	polynomial	ADJ
ejpam-3636	223	12	approximation	approximation	NOUN
ejpam-3636	223	13	of	of	ADP
ejpam-3636	223	14	an	an	DET
ejpam-3636	223	15	entire	entire	ADJ
ejpam-3636	223	16	function	function	NOUN
ejpam-3636	223	17	of	of	ADP
ejpam-3636	223	18	slow	slow	ADJ
ejpam-3636	223	19	growth	growth	NOUN
ejpam-3636	223	20	,	,	PUNCT
ejpam-3636	223	21	j.	j.	PROPN
ejpam-3636	223	22	approx	approx	PROPN
ejpam-3636	223	23	.	.	PUNCT
ejpam-3636	224	1	theory	theory	NOUN
ejpam-3636	224	2	,	,	PUNCT
ejpam-3636	224	3	32	32	NUM
ejpam-3636	224	4	(	(	PUNCT
ejpam-3636	224	5	1981	1981	NUM
ejpam-3636	224	6	)	)	PUNCT
ejpam-3636	224	7	,	,	PUNCT
ejpam-3636	224	8	64	64	NUM
ejpam-3636	224	9	-	-	SYM
ejpam-3636	224	10	75	75	NUM
ejpam-3636	224	11	.	.	PUNCT
ejpam-3636	225	1	references	reference	NOUN
ejpam-3636	225	2	268	268	NUM
ejpam-3636	225	3	[	[	X
ejpam-3636	225	4	11	11	NUM
ejpam-3636	225	5	]	]	X
ejpam-3636	225	6	d.	d.	PROPN
ejpam-3636	225	7	kumar	kumar	PROPN
ejpam-3636	225	8	,	,	PUNCT
ejpam-3636	225	9	generalized	generalized	ADJ
ejpam-3636	225	10	growth	growth	NOUN
ejpam-3636	225	11	and	and	CCONJ
ejpam-3636	225	12	best	good	ADJ
ejpam-3636	225	13	approximation	approximation	NOUN
ejpam-3636	225	14	of	of	ADP
ejpam-3636	225	15	entire	entire	ADJ
ejpam-3636	225	16	functions	function	NOUN
ejpam-3636	225	17	in	in	ADP
ejpam-3636	225	18	lp	lp	NOUN
ejpam-3636	225	19	-	-	NOUN
ejpam-3636	225	20	norm	norm	NOUN
ejpam-3636	225	21	in	in	ADP
ejpam-3636	225	22	several	several	ADJ
ejpam-3636	225	23	complex	complex	ADJ
ejpam-3636	225	24	variables	variable	NOUN
ejpam-3636	225	25	,	,	PUNCT
ejpam-3636	225	26	annali	annali	X
ejpam-3636	225	27	dell’universita	dell’universita	ADJ
ejpam-3636	225	28	’	'	PUNCT
ejpam-3636	225	29	de	de	ADJ
ejpam-3636	225	30	ferrara	ferrara	NOUN
ejpam-3636	225	31	,	,	PUNCT
ejpam-3636	225	32	57	57	NUM
ejpam-3636	225	33	,	,	PUNCT
ejpam-3636	225	34	issue-2	issue-2	PROPN
ejpam-3636	225	35	(	(	PUNCT
ejpam-3636	225	36	2011	2011	NUM
ejpam-3636	225	37	)	)	PUNCT
ejpam-3636	225	38	,	,	PUNCT
ejpam-3636	225	39	353	353	NUM
ejpam-3636	225	40	-	-	SYM
ejpam-3636	225	41	372	372	NUM
ejpam-3636	225	42	.	.	PUNCT
ejpam-3636	226	1	[	[	X
ejpam-3636	226	2	12	12	NUM
ejpam-3636	226	3	]	]	X
ejpam-3636	226	4	d.	d.	PROPN
ejpam-3636	226	5	kumar	kumar	PROPN
ejpam-3636	226	6	,	,	PUNCT
ejpam-3636	226	7	the	the	DET
ejpam-3636	226	8	growth	growth	NOUN
ejpam-3636	226	9	of	of	ADP
ejpam-3636	226	10	harmonic	harmonic	ADJ
ejpam-3636	226	11	functions	function	NOUN
ejpam-3636	226	12	in	in	ADP
ejpam-3636	226	13	hyper	hyper	ADJ
ejpam-3636	226	14	spheres	sphere	NOUN
ejpam-3636	226	15	,	,	PUNCT
ejpam-3636	226	16	demonstrat	demonstrat	PROPN
ejpam-3636	226	17	.	.	PROPN
ejpam-3636	226	18	math	math	PROPN
ejpam-3636	226	19	.	.	PUNCT
ejpam-3636	226	20	,	,	PUNCT
ejpam-3636	226	21	32	32	NUM
ejpam-3636	226	22	,	,	PUNCT
ejpam-3636	226	23	no	no	INTJ
ejpam-3636	226	24	.	.	NOUN
ejpam-3636	226	25	4	4	NUM
ejpam-3636	226	26	(	(	PUNCT
ejpam-3636	226	27	1999	1999	NUM
ejpam-3636	226	28	)	)	PUNCT
ejpam-3636	226	29	,	,	PUNCT
ejpam-3636	226	30	717	717	NUM
ejpam-3636	226	31	-	-	SYM
ejpam-3636	226	32	724	724	NUM
ejpam-3636	226	33	.	.	PUNCT
ejpam-3636	227	1	[	[	X
ejpam-3636	227	2	13	13	NUM
ejpam-3636	227	3	]	]	X
ejpam-3636	227	4	d.	d.	PROPN
ejpam-3636	227	5	kumar	kumar	PROPN
ejpam-3636	227	6	,	,	PUNCT
ejpam-3636	227	7	growth	growth	NOUN
ejpam-3636	227	8	and	and	CCONJ
ejpam-3636	227	9	approximation	approximation	NOUN
ejpam-3636	227	10	of	of	ADP
ejpam-3636	227	11	entire	entire	ADJ
ejpam-3636	227	12	harmonic	harmonic	ADJ
ejpam-3636	227	13	functions	function	NOUN
ejpam-3636	227	14	in	in	ADP
ejpam-3636	227	15	rn	rn	PROPN
ejpam-3636	227	16	,	,	PUNCT
ejpam-3636	227	17	n	n	PROPN
ejpam-3636	227	18	>	>	X
ejpam-3636	227	19	3	3	NUM
ejpam-3636	227	20	,	,	PUNCT
ejpam-3636	227	21	georgian	georgian	ADJ
ejpam-3636	227	22	math	math	NOUN
ejpam-3636	227	23	.	.	PUNCT
ejpam-3636	228	1	j.	j.	PROPN
ejpam-3636	228	2	,	,	PUNCT
ejpam-3636	228	3	15	15	NUM
ejpam-3636	228	4	,	,	PUNCT
ejpam-3636	228	5	no.1	no.1	NUM
ejpam-3636	228	6	(	(	PUNCT
ejpam-3636	228	7	2008	2008	NUM
ejpam-3636	228	8	)	)	PUNCT
ejpam-3636	228	9	,	,	PUNCT
ejpam-3636	228	10	1	1	NUM
ejpam-3636	228	11	-	-	SYM
ejpam-3636	228	12	12	12	NUM
ejpam-3636	228	13	.	.	PUNCT
ejpam-3636	229	1	[	[	X
ejpam-3636	229	2	14	14	NUM
ejpam-3636	229	3	]	]	X
ejpam-3636	229	4	d.	d.	PROPN
ejpam-3636	229	5	kumar	kumar	PROPN
ejpam-3636	229	6	,	,	PUNCT
ejpam-3636	229	7	growth	growth	NOUN
ejpam-3636	229	8	and	and	CCONJ
ejpam-3636	229	9	approximation	approximation	NOUN
ejpam-3636	229	10	of	of	ADP
ejpam-3636	229	11	solutions	solution	NOUN
ejpam-3636	229	12	to	to	ADP
ejpam-3636	229	13	a	a	DET
ejpam-3636	229	14	class	class	NOUN
ejpam-3636	229	15	of	of	ADP
ejpam-3636	229	16	certain	certain	ADJ
ejpam-3636	229	17	linear	linear	ADJ
ejpam-3636	229	18	partial	partial	ADJ
ejpam-3636	229	19	differential	differential	NOUN
ejpam-3636	229	20	equations	equation	NOUN
ejpam-3636	229	21	in	in	ADP
ejpam-3636	229	22	rn	rn	PROPN
ejpam-3636	229	23	,	,	PUNCT
ejpam-3636	229	24	mathematica	mathematica	PROPN
ejpam-3636	229	25	slovaca	slovaca	PROPN
ejpam-3636	229	26	,	,	PUNCT
ejpam-3636	229	27	64	64	NUM
ejpam-3636	229	28	,	,	PUNCT
ejpam-3636	229	29	issue-1	issue-1	NUM
ejpam-3636	229	30	(	(	PUNCT
ejpam-3636	229	31	2014	2014	NUM
ejpam-3636	229	32	)	)	PUNCT
ejpam-3636	229	33	,	,	PUNCT
ejpam-3636	229	34	139	139	NUM
ejpam-3636	229	35	-	-	SYM
ejpam-3636	229	36	154	154	NUM
ejpam-3636	229	37	.	.	PUNCT
ejpam-3636	230	1	[	[	X
ejpam-3636	230	2	15	15	NUM
ejpam-3636	230	3	]	]	X
ejpam-3636	230	4	d.	d.	PROPN
ejpam-3636	230	5	kumar	kumar	PROPN
ejpam-3636	230	6	and	and	CCONJ
ejpam-3636	230	7	h.s	h.s	PROPN
ejpam-3636	230	8	.	.	PROPN
ejpam-3636	230	9	kasana	kasana	PROPN
ejpam-3636	230	10	,	,	PUNCT
ejpam-3636	230	11	on	on	ADP
ejpam-3636	230	12	maximum	maximum	ADJ
ejpam-3636	230	13	term	term	NOUN
ejpam-3636	230	14	,	,	PUNCT
ejpam-3636	230	15	maximum	maximum	ADJ
ejpam-3636	230	16	modulus	modulus	NOUN
ejpam-3636	230	17	and	and	CCONJ
ejpam-3636	230	18	approximation	approximation	NOUN
ejpam-3636	230	19	error	error	NOUN
ejpam-3636	230	20	of	of	ADP
ejpam-3636	230	21	an	an	DET
ejpam-3636	230	22	entire	entire	ADJ
ejpam-3636	230	23	harmonic	harmonic	ADJ
ejpam-3636	230	24	function	function	NOUN
ejpam-3636	230	25	in	in	ADP
ejpam-3636	230	26	r3	r3	PROPN
ejpam-3636	230	27	,	,	PUNCT
ejpam-3636	230	28	riv	riv	PROPN
ejpam-3636	230	29	.	.	PROPN
ejpam-3636	230	30	mat	mat	PROPN
ejpam-3636	230	31	.	.	PROPN
ejpam-3636	230	32	univ	univ	PROPN
ejpam-3636	230	33	.	.	PUNCT
ejpam-3636	231	1	parma	parma	PROPN
ejpam-3636	231	2	,	,	PUNCT
ejpam-3636	231	3	6(1	6(1	NUM
ejpam-3636	231	4	)	)	PUNCT
ejpam-3636	231	5	(	(	PUNCT
ejpam-3636	231	6	1998	1998	NUM
ejpam-3636	231	7	)	)	PUNCT
ejpam-3636	231	8	,	,	PUNCT
ejpam-3636	231	9	215	215	NUM
ejpam-3636	231	10	-	-	SYM
ejpam-3636	231	11	223	223	NUM
ejpam-3636	231	12	.	.	PUNCT
ejpam-3636	232	1	[	[	X
ejpam-3636	232	2	16	16	NUM
ejpam-3636	232	3	]	]	X
ejpam-3636	232	4	d.	d.	PROPN
ejpam-3636	232	5	kumar	kumar	PROPN
ejpam-3636	232	6	and	and	CCONJ
ejpam-3636	232	7	rajbir	rajbir	PROPN
ejpam-3636	232	8	singh	singh	PROPN
ejpam-3636	232	9	,	,	PUNCT
ejpam-3636	232	10	generalized	generalized	ADJ
ejpam-3636	232	11	growth	growth	NOUN
ejpam-3636	232	12	of	of	ADP
ejpam-3636	232	13	harmonic	harmonic	ADJ
ejpam-3636	232	14	functions	function	NOUN
ejpam-3636	232	15	in	in	ADP
ejpam-3636	232	16	hyperspheres	hypersphere	NOUN
ejpam-3636	232	17	,	,	PUNCT
ejpam-3636	232	18	tjmm	tjmm	NOUN
ejpam-3636	232	19	,	,	PUNCT
ejpam-3636	232	20	5	5	NUM
ejpam-3636	232	21	,	,	PUNCT
ejpam-3636	232	22	no.1	no.1	X
ejpam-3636	232	23	(	(	PUNCT
ejpam-3636	232	24	2013	2013	NUM
ejpam-3636	232	25	)	)	PUNCT
ejpam-3636	232	26	,	,	PUNCT
ejpam-3636	232	27	45	45	NUM
ejpam-3636	232	28	-	-	SYM
ejpam-3636	232	29	57	57	NUM
ejpam-3636	232	30	.	.	PUNCT
ejpam-3636	233	1	[	[	X
ejpam-3636	233	2	17	17	NUM
ejpam-3636	233	3	]	]	X
ejpam-3636	233	4	s.m	s.m	PROPN
ejpam-3636	233	5	.	.	PROPN
ejpam-3636	233	6	shah	shah	PROPN
ejpam-3636	233	7	,	,	PUNCT
ejpam-3636	233	8	polynomial	polynomial	ADJ
ejpam-3636	233	9	approximation	approximation	NOUN
ejpam-3636	233	10	of	of	ADP
ejpam-3636	233	11	an	an	DET
ejpam-3636	233	12	entire	entire	ADJ
ejpam-3636	233	13	function	function	NOUN
ejpam-3636	233	14	and	and	CCONJ
ejpam-3636	233	15	generalized	generalized	ADJ
ejpam-3636	233	16	orders	order	NOUN
ejpam-3636	233	17	,	,	PUNCT
ejpam-3636	233	18	j.	j.	PROPN
ejpam-3636	233	19	approx	approx	PROPN
ejpam-3636	233	20	.	.	PUNCT
ejpam-3636	234	1	theory	theory	NOUN
ejpam-3636	234	2	,	,	PUNCT
ejpam-3636	234	3	19(1977	19(1977	NUM
ejpam-3636	234	4	)	)	PUNCT
ejpam-3636	234	5	,	,	PUNCT
ejpam-3636	234	6	315	315	NUM
ejpam-3636	234	7	-	-	SYM
ejpam-3636	234	8	324	324	NUM
ejpam-3636	234	9	.	.	PUNCT
ejpam-3636	235	1	[	[	X
ejpam-3636	235	2	18	18	NUM
ejpam-3636	235	3	]	]	X
ejpam-3636	235	4	m.n	m.n	PROPN
ejpam-3636	235	5	.	.	PROPN
ejpam-3636	235	6	sheremeta	sheremeta	PROPN
ejpam-3636	235	7	,	,	PUNCT
ejpam-3636	235	8	on	on	ADP
ejpam-3636	235	9	the	the	DET
ejpam-3636	235	10	connection	connection	NOUN
ejpam-3636	235	11	between	between	ADP
ejpam-3636	235	12	the	the	DET
ejpam-3636	235	13	growth	growth	NOUN
ejpam-3636	235	14	of	of	ADP
ejpam-3636	235	15	the	the	DET
ejpam-3636	235	16	maximum	maximum	ADJ
ejpam-3636	235	17	modulus	modulus	NOUN
ejpam-3636	235	18	of	of	ADP
ejpam-3636	235	19	of	of	ADP
ejpam-3636	235	20	an	an	DET
ejpam-3636	235	21	entire	entire	ADJ
ejpam-3636	235	22	function	function	NOUN
ejpam-3636	235	23	and	and	CCONJ
ejpam-3636	235	24	the	the	DET
ejpam-3636	235	25	moduli	modulus	NOUN
ejpam-3636	235	26	of	of	ADP
ejpam-3636	235	27	the	the	DET
ejpam-3636	235	28	coefficients	coefficient	NOUN
ejpam-3636	235	29	of	of	ADP
ejpam-3636	235	30	its	its	PRON
ejpam-3636	235	31	power	power	NOUN
ejpam-3636	235	32	series	series	NOUN
ejpam-3636	235	33	expansion	expansion	NOUN
ejpam-3636	235	34	,	,	PUNCT
ejpam-3636	235	35	amer	amer	PROPN
ejpam-3636	235	36	.	.	PROPN
ejpam-3636	235	37	math	math	PROPN
ejpam-3636	235	38	.	.	PUNCT
ejpam-3636	236	1	soc	soc	PROPN
ejpam-3636	236	2	.	.	PUNCT
ejpam-3636	236	3	,	,	PUNCT
ejpam-3636	236	4	translation	translation	NOUN
ejpam-3636	236	5	,	,	PUNCT
ejpam-3636	236	6	88	88	NUM
ejpam-3636	236	7	(	(	PUNCT
ejpam-3636	236	8	1970	1970	NUM
ejpam-3636	236	9	)	)	PUNCT
ejpam-3636	236	10	,	,	PUNCT
ejpam-3636	236	11	291	291	NUM
ejpam-3636	236	12	-	-	SYM
ejpam-3636	236	13	301	301	NUM
ejpam-3636	236	14	.	.	PUNCT
ejpam-3636	237	1	[	[	X
ejpam-3636	237	2	19	19	NUM
ejpam-3636	237	3	]	]	X
ejpam-3636	237	4	g.s	g.s	PROPN
ejpam-3636	237	5	.	.	PROPN
ejpam-3636	237	6	srivastava	srivastava	PROPN
ejpam-3636	237	7	,	,	PUNCT
ejpam-3636	237	8	growth	growth	NOUN
ejpam-3636	237	9	of	of	ADP
ejpam-3636	237	10	entire	entire	ADJ
ejpam-3636	237	11	harmonic	harmonic	ADJ
ejpam-3636	237	12	functions	function	NOUN
ejpam-3636	237	13	in	in	ADP
ejpam-3636	237	14	rn	rn	PROPN
ejpam-3636	237	15	,	,	PUNCT
ejpam-3636	237	16	n	n	PRON
ejpam-3636	237	17	≥	≥	NOUN
ejpam-3636	237	18	2	2	NUM
ejpam-3636	237	19	and	and	CCONJ
ejpam-3636	237	20	generalized	generalized	ADJ
ejpam-3636	237	21	orders	order	NOUN
ejpam-3636	237	22	,	,	PUNCT
ejpam-3636	237	23	bull	bull	NOUN
ejpam-3636	237	24	.	.	PUNCT
ejpam-3636	238	1	greek	greek	ADJ
ejpam-3636	238	2	math	math	NOUN
ejpam-3636	238	3	.	.	PUNCT
ejpam-3636	239	1	soc	soc	PROPN
ejpam-3636	239	2	.	.	PUNCT
ejpam-3636	239	3	,	,	PUNCT
ejpam-3636	239	4	55(2008	55(2008	PROPN
ejpam-3636	239	5	)	)	PUNCT
ejpam-3636	239	6	,	,	PUNCT
ejpam-3636	239	7	49	49	NUM
ejpam-3636	239	8	-	-	SYM
ejpam-3636	239	9	58	58	NUM
ejpam-3636	239	10	.	.	PUNCT
ejpam-3636	240	1	[	[	X
ejpam-3636	240	2	20	20	NUM
ejpam-3636	240	3	]	]	X
ejpam-3636	240	4	g.s	g.s	PROPN
ejpam-3636	240	5	.	.	PROPN
ejpam-3636	240	6	srivastava	srivastava	PROPN
ejpam-3636	240	7	and	and	CCONJ
ejpam-3636	240	8	s.	s.	PROPN
ejpam-3636	240	9	kumar	kumar	PROPN
ejpam-3636	240	10	,	,	PUNCT
ejpam-3636	240	11	uniform	uniform	ADJ
ejpam-3636	240	12	approximation	approximation	NOUN
ejpam-3636	240	13	of	of	ADP
ejpam-3636	240	14	entire	entire	ADJ
ejpam-3636	240	15	functions	function	NOUN
ejpam-3636	240	16	on	on	ADP
ejpam-3636	240	17	compact	compact	ADJ
ejpam-3636	240	18	sets	set	NOUN
ejpam-3636	240	19	and	and	CCONJ
ejpam-3636	240	20	their	their	PRON
ejpam-3636	240	21	generalized	generalized	ADJ
ejpam-3636	240	22	growth	growth	NOUN
ejpam-3636	240	23	,	,	PUNCT
ejpam-3636	240	24	new	new	PROPN
ejpam-3636	240	25	zeland	zeland	PROPN
ejpam-3636	240	26	j.	j.	PROPN
ejpam-3636	240	27	math	math	PROPN
ejpam-3636	240	28	.	.	PUNCT
ejpam-3636	241	1	,	,	PUNCT
ejpam-3636	241	2	39	39	NUM
ejpam-3636	241	3	(	(	PUNCT
ejpam-3636	241	4	2009	2009	NUM
ejpam-3636	241	5	)	)	PUNCT
ejpam-3636	241	6	,	,	PUNCT
ejpam-3636	241	7	33	33	NUM
ejpam-3636	241	8	-	-	SYM
ejpam-3636	241	9	43	43	NUM
ejpam-3636	241	10	.	.	PUNCT
ejpam-3636	242	1	[	[	X
ejpam-3636	242	2	21	21	NUM
ejpam-3636	242	3	]	]	X
ejpam-3636	242	4	e.m	e.m	PROPN
ejpam-3636	242	5	.	.	PROPN
ejpam-3636	242	6	stein	stein	PROPN
ejpam-3636	242	7	and	and	CCONJ
ejpam-3636	242	8	g.	g.	PROPN
ejpam-3636	242	9	weiss	weiss	PROPN
ejpam-3636	242	10	,	,	PUNCT
ejpam-3636	242	11	introduction	introduction	NOUN
ejpam-3636	242	12	to	to	ADP
ejpam-3636	242	13	fourier	fourier	ADJ
ejpam-3636	242	14	analysis	analysis	NOUN
ejpam-3636	242	15	of	of	ADP
ejpam-3636	242	16	euclidean	euclidean	ADJ
ejpam-3636	242	17	spaces	space	NOUN
ejpam-3636	242	18	[	[	X
ejpam-3636	242	19	russisn	russisn	NOUN
ejpam-3636	242	20	translation	translation	NOUN
ejpam-3636	242	21	]	]	X
ejpam-3636	242	22	,	,	PUNCT
ejpam-3636	242	23	mir	mir	PROPN
ejpam-3636	242	24	,	,	PUNCT
ejpam-3636	242	25	moscow	moscow	PROPN
ejpam-3636	242	26	,	,	PUNCT
ejpam-3636	242	27	1974	1974	NUM
ejpam-3636	242	28	.	.	PUNCT
ejpam-3636	243	1	[	[	X
ejpam-3636	243	2	22	22	NUM
ejpam-3636	243	3	]	]	X
ejpam-3636	243	4	g.	g.	PROPN
ejpam-3636	243	5	valiron	valiron	PROPN
ejpam-3636	243	6	,	,	PUNCT
ejpam-3636	243	7	lectures	lecture	VERB
ejpam-3636	243	8	on	on	ADP
ejpam-3636	243	9	the	the	DET
ejpam-3636	243	10	general	general	ADJ
ejpam-3636	243	11	theory	theory	NOUN
ejpam-3636	243	12	of	of	ADP
ejpam-3636	243	13	integral	integral	ADJ
ejpam-3636	243	14	functions	function	NOUN
ejpam-3636	243	15	,	,	PUNCT
ejpam-3636	243	16	chelsea	chelsea	PROPN
ejpam-3636	243	17	publ	publ	PROPN
ejpam-3636	243	18	.	.	PUNCT
ejpam-3636	244	1	co.	co.	PROPN
ejpam-3636	244	2	,	,	PUNCT
ejpam-3636	244	3	new	new	PROPN
ejpam-3636	244	4	york	york	PROPN
ejpam-3636	244	5	,	,	PUNCT
ejpam-3636	244	6	1949	1949	NUM
ejpam-3636	244	7	.	.	PUNCT