id	sid	tid	token	lemma	pos
ejpam-3547	1	1	european	european	PROPN
ejpam-3547	1	2	journal	journal	PROPN
ejpam-3547	1	3	of	of	ADP
ejpam-3547	1	4	pure	pure	ADJ
ejpam-3547	1	5	and	and	CCONJ
ejpam-3547	1	6	applied	apply	VERB
ejpam-3547	1	7	mathematics	mathematic	NOUN
ejpam-3547	1	8	vol	vol	NOUN
ejpam-3547	1	9	.	.	PROPN
ejpam-3547	2	1	12	12	NUM
ejpam-3547	2	2	,	,	PUNCT
ejpam-3547	2	3	no	no	INTJ
ejpam-3547	2	4	.	.	NOUN
ejpam-3547	2	5	4	4	NUM
ejpam-3547	2	6	,	,	PUNCT
ejpam-3547	2	7	2019	2019	NUM
ejpam-3547	2	8	,	,	PUNCT
ejpam-3547	2	9	1508	1508	NUM
ejpam-3547	2	10	-	-	SYM
ejpam-3547	2	11	1523	1523	NUM
ejpam-3547	2	12	issn	issn	PROPN
ejpam-3547	2	13	1307	1307	NUM
ejpam-3547	2	14	-	-	SYM
ejpam-3547	2	15	5543	5543	NUM
ejpam-3547	2	16	–	–	PUNCT
ejpam-3547	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3547	2	18	published	publish	VERB
ejpam-3547	2	19	by	by	ADP
ejpam-3547	2	20	new	new	PROPN
ejpam-3547	2	21	york	york	PROPN
ejpam-3547	2	22	business	business	PROPN
ejpam-3547	2	23	global	global	ADJ
ejpam-3547	2	24	simultaneous	simultaneous	ADJ
ejpam-3547	2	25	approximation	approximation	NOUN
ejpam-3547	2	26	of	of	ADP
ejpam-3547	2	27	new	new	ADJ
ejpam-3547	2	28	sequence	sequence	NOUN
ejpam-3547	2	29	of	of	ADP
ejpam-3547	2	30	integral	integral	ADJ
ejpam-3547	2	31	type	type	NOUN
ejpam-3547	2	32	operators	operator	NOUN
ejpam-3547	2	33	with	with	ADP
ejpam-3547	2	34	parameter	parameter	PROPN
ejpam-3547	2	35	δ0	δ0	PROPN
ejpam-3547	2	36	ali	ali	PROPN
ejpam-3547	2	37	jassim	jassim	PROPN
ejpam-3547	2	38	mohammad1	mohammad1	PROPN
ejpam-3547	2	39	,	,	PUNCT
ejpam-3547	2	40	hadeel	hadeel	PROPN
ejpam-3547	2	41	omar	omar	PROPN
ejpam-3547	2	42	muslim2,∗	muslim2,∗	VERB
ejpam-3547	2	43	1	1	NUM
ejpam-3547	2	44	department	department	NOUN
ejpam-3547	2	45	of	of	ADP
ejpam-3547	2	46	mathematics	mathematic	NOUN
ejpam-3547	2	47	,	,	PUNCT
ejpam-3547	2	48	faculty	faculty	NOUN
ejpam-3547	2	49	of	of	ADP
ejpam-3547	2	50	education	education	NOUN
ejpam-3547	2	51	for	for	ADP
ejpam-3547	2	52	pure	pure	ADJ
ejpam-3547	2	53	sciences	science	NOUN
ejpam-3547	2	54	,	,	PUNCT
ejpam-3547	2	55	university	university	NOUN
ejpam-3547	2	56	of	of	ADP
ejpam-3547	2	57	basra	basra	PROPN
ejpam-3547	2	58	,	,	PUNCT
ejpam-3547	2	59	basra	basra	PROPN
ejpam-3547	2	60	,	,	PUNCT
ejpam-3547	2	61	iraq	iraq	PROPN
ejpam-3547	2	62	.	.	PUNCT
ejpam-3547	3	1	2	2	NUM
ejpam-3547	3	2	department	department	NOUN
ejpam-3547	3	3	of	of	ADP
ejpam-3547	3	4	thermal	thermal	ADJ
ejpam-3547	3	5	mechanical	mechanical	ADJ
ejpam-3547	3	6	engineering	engineering	NOUN
ejpam-3547	3	7	,	,	PUNCT
ejpam-3547	3	8	faculty	faculty	NOUN
ejpam-3547	3	9	of	of	ADP
ejpam-3547	3	10	engineering	engineering	NOUN
ejpam-3547	3	11	technology	technology	NOUN
ejpam-3547	3	12	,	,	PUNCT
ejpam-3547	3	13	southern	southern	PROPN
ejpam-3547	3	14	technical	technical	PROPN
ejpam-3547	3	15	university	university	PROPN
ejpam-3547	3	16	,	,	PUNCT
ejpam-3547	3	17	basra	basra	PROPN
ejpam-3547	3	18	,	,	PUNCT
ejpam-3547	3	19	iraq	iraq	PROPN
ejpam-3547	3	20	.	.	PUNCT
ejpam-3547	4	1	abstract	abstract	ADJ
ejpam-3547	4	2	.	.	PUNCT
ejpam-3547	5	1	in	in	ADP
ejpam-3547	5	2	this	this	DET
ejpam-3547	5	3	paper	paper	NOUN
ejpam-3547	5	4	,	,	PUNCT
ejpam-3547	5	5	we	we	PRON
ejpam-3547	5	6	define	define	VERB
ejpam-3547	5	7	a	a	DET
ejpam-3547	5	8	new	new	ADJ
ejpam-3547	5	9	sequence	sequence	NOUN
ejpam-3547	5	10	of	of	ADP
ejpam-3547	5	11	linear	linear	ADJ
ejpam-3547	5	12	positive	positive	ADJ
ejpam-3547	5	13	operators	operator	NOUN
ejpam-3547	5	14	of	of	ADP
ejpam-3547	5	15	integral	integral	ADJ
ejpam-3547	5	16	type	type	NOUN
ejpam-3547	5	17	wn(f	wn(f	PUNCT
ejpam-3547	5	18	;	;	PUNCT
ejpam-3547	5	19	x	x	X
ejpam-3547	5	20	)	)	PUNCT
ejpam-3547	5	21	to	to	PART
ejpam-3547	5	22	approximate	approximate	ADJ
ejpam-3547	5	23	functions	function	NOUN
ejpam-3547	5	24	in	in	ADP
ejpam-3547	5	25	the	the	DET
ejpam-3547	5	26	space	space	NOUN
ejpam-3547	5	27	cα[0,∞	cα[0,∞	PROPN
ejpam-3547	5	28	)	)	PUNCT
ejpam-3547	5	29	,	,	PUNCT
ejpam-3547	5	30	α	α	X
ejpam-3547	5	31	>	>	X
ejpam-3547	5	32	0	0	X
ejpam-3547	5	33	.	.	PUNCT
ejpam-3547	6	1	first	first	ADV
ejpam-3547	6	2	,	,	PUNCT
ejpam-3547	6	3	we	we	PRON
ejpam-3547	6	4	study	study	VERB
ejpam-3547	6	5	the	the	DET
ejpam-3547	6	6	basic	basic	ADJ
ejpam-3547	6	7	convergence	convergence	NOUN
ejpam-3547	6	8	theorem	theorem	VERB
ejpam-3547	6	9	in	in	ADP
ejpam-3547	6	10	simultaneous	simultaneous	ADJ
ejpam-3547	6	11	approximation	approximation	NOUN
ejpam-3547	6	12	and	and	CCONJ
ejpam-3547	6	13	then	then	ADV
ejpam-3547	6	14	study	study	VERB
ejpam-3547	6	15	voronovskaja	voronovskaja	ADJ
ejpam-3547	6	16	-	-	PUNCT
ejpam-3547	6	17	type	type	NOUN
ejpam-3547	6	18	asymptotic	asymptotic	ADJ
ejpam-3547	6	19	formula	formula	NOUN
ejpam-3547	6	20	.	.	PUNCT
ejpam-3547	7	1	then	then	ADV
ejpam-3547	7	2	,	,	PUNCT
ejpam-3547	7	3	we	we	PRON
ejpam-3547	7	4	estimate	estimate	VERB
ejpam-3547	7	5	an	an	DET
ejpam-3547	7	6	error	error	NOUN
ejpam-3547	7	7	occurs	occur	VERB
ejpam-3547	7	8	by	by	ADP
ejpam-3547	7	9	this	this	DET
ejpam-3547	7	10	approximation	approximation	NOUN
ejpam-3547	7	11	in	in	ADP
ejpam-3547	7	12	the	the	DET
ejpam-3547	7	13	terms	term	NOUN
ejpam-3547	7	14	of	of	ADP
ejpam-3547	7	15	the	the	DET
ejpam-3547	7	16	modulus	modulus	NOUN
ejpam-3547	7	17	of	of	ADP
ejpam-3547	7	18	continuity	continuity	NOUN
ejpam-3547	7	19	.	.	PUNCT
ejpam-3547	8	1	next	next	ADV
ejpam-3547	8	2	,	,	PUNCT
ejpam-3547	8	3	we	we	PRON
ejpam-3547	8	4	give	give	VERB
ejpam-3547	8	5	numerical	numerical	ADJ
ejpam-3547	8	6	examples	example	NOUN
ejpam-3547	8	7	to	to	PART
ejpam-3547	8	8	approximate	approximate	VERB
ejpam-3547	8	9	two	two	NUM
ejpam-3547	8	10	test	test	NOUN
ejpam-3547	8	11	functions	function	NOUN
ejpam-3547	8	12	in	in	ADP
ejpam-3547	8	13	the	the	DET
ejpam-3547	8	14	space	space	NOUN
ejpam-3547	8	15	cα[0,∞	cα[0,∞	PROPN
ejpam-3547	8	16	)	)	PUNCT
ejpam-3547	8	17	by	by	ADP
ejpam-3547	8	18	the	the	DET
ejpam-3547	8	19	sequence	sequence	NOUN
ejpam-3547	8	20	wn(f	wn(f	PUNCT
ejpam-3547	8	21	;	;	PUNCT
ejpam-3547	8	22	x	x	X
ejpam-3547	8	23	)	)	PUNCT
ejpam-3547	8	24	.	.	PUNCT
ejpam-3547	9	1	finally	finally	ADV
ejpam-3547	9	2	,	,	PUNCT
ejpam-3547	9	3	we	we	PRON
ejpam-3547	9	4	compare	compare	VERB
ejpam-3547	9	5	the	the	DET
ejpam-3547	9	6	results	result	NOUN
ejpam-3547	9	7	with	with	ADP
ejpam-3547	9	8	the	the	DET
ejpam-3547	9	9	classical	classical	ADJ
ejpam-3547	9	10	sequence	sequence	NOUN
ejpam-3547	9	11	of	of	ADP
ejpam-3547	9	12	szãsz	szãsz	PROPN
ejpam-3547	9	13	operators	operator	NOUN
ejpam-3547	9	14	sn(f	sn(f	ADP
ejpam-3547	9	15	;	;	PUNCT
ejpam-3547	9	16	x	x	X
ejpam-3547	9	17	)	)	PUNCT
ejpam-3547	9	18	on	on	ADP
ejpam-3547	9	19	the	the	DET
ejpam-3547	9	20	interval	interval	NOUN
ejpam-3547	9	21	[	[	X
ejpam-3547	9	22	a	a	X
ejpam-3547	9	23	,	,	PUNCT
ejpam-3547	9	24	b	b	NOUN
ejpam-3547	9	25	]	]	X
ejpam-3547	9	26	.	.	PUNCT
ejpam-3547	10	1	it	it	PRON
ejpam-3547	10	2	turns	turn	VERB
ejpam-3547	10	3	out	out	ADP
ejpam-3547	10	4	that	that	SCONJ
ejpam-3547	10	5	,	,	PUNCT
ejpam-3547	10	6	the	the	DET
ejpam-3547	10	7	sequence	sequence	NOUN
ejpam-3547	10	8	wn(f	wn(f	PUNCT
ejpam-3547	10	9	;	;	PUNCT
ejpam-3547	10	10	x	x	X
ejpam-3547	10	11	)	)	PUNCT
ejpam-3547	10	12	gives	give	VERB
ejpam-3547	10	13	better	well	ADJ
ejpam-3547	10	14	results	result	NOUN
ejpam-3547	10	15	than	than	ADP
ejpam-3547	10	16	the	the	DET
ejpam-3547	10	17	results	result	NOUN
ejpam-3547	10	18	of	of	ADP
ejpam-3547	10	19	the	the	DET
ejpam-3547	10	20	sequence	sequence	NOUN
ejpam-3547	10	21	sn(f	sn(f	ADP
ejpam-3547	10	22	;	;	PUNCT
ejpam-3547	10	23	x	x	X
ejpam-3547	10	24	)	)	PUNCT
ejpam-3547	10	25	for	for	ADP
ejpam-3547	10	26	the	the	DET
ejpam-3547	10	27	two	two	NUM
ejpam-3547	10	28	test	test	NOUN
ejpam-3547	10	29	functions	function	NOUN
ejpam-3547	10	30	using	use	VERB
ejpam-3547	10	31	in	in	ADP
ejpam-3547	10	32	the	the	DET
ejpam-3547	10	33	numerical	numerical	ADJ
ejpam-3547	10	34	examples	example	NOUN
ejpam-3547	10	35	.	.	PUNCT
ejpam-3547	11	1	2010	2010	NUM
ejpam-3547	11	2	mathematics	mathematic	NOUN
ejpam-3547	11	3	subject	subject	NOUN
ejpam-3547	11	4	classifications	classification	NOUN
ejpam-3547	11	5	:	:	PUNCT
ejpam-3547	11	6	41a10	41a10	NUM
ejpam-3547	11	7	,	,	PUNCT
ejpam-3547	11	8	41a25,41a36	41a25,41a36	NOUN
ejpam-3547	11	9	key	key	ADJ
ejpam-3547	11	10	words	word	NOUN
ejpam-3547	11	11	and	and	CCONJ
ejpam-3547	11	12	phrases	phrase	NOUN
ejpam-3547	11	13	:	:	PUNCT
ejpam-3547	11	14	linear	linear	ADJ
ejpam-3547	11	15	positive	positive	ADJ
ejpam-3547	11	16	operators	operator	NOUN
ejpam-3547	11	17	,	,	PUNCT
ejpam-3547	11	18	simultaneous	simultaneous	ADJ
ejpam-3547	11	19	approximation	approximation	NOUN
ejpam-3547	11	20	,	,	PUNCT
ejpam-3547	11	21	voronovskajatype	voronovskajatype	NOUN
ejpam-3547	11	22	asymptotic	asymptotic	ADJ
ejpam-3547	11	23	formula	formula	NOUN
ejpam-3547	11	24	,	,	PUNCT
ejpam-3547	11	25	modulus	modulus	NOUN
ejpam-3547	11	26	of	of	ADP
ejpam-3547	11	27	continuity	continuity	NOUN
ejpam-3547	11	28	1	1	NUM
ejpam-3547	11	29	.	.	PUNCT
ejpam-3547	12	1	introduction	introduction	NOUN
ejpam-3547	12	2	bernstein	bernstein	PROPN
ejpam-3547	12	3	in	in	ADP
ejpam-3547	12	4	1912	1912	NUM
ejpam-3547	12	5	,	,	PUNCT
ejpam-3547	12	6	using	use	VERB
ejpam-3547	12	7	a	a	DET
ejpam-3547	12	8	sequence	sequence	NOUN
ejpam-3547	12	9	known	know	VERB
ejpam-3547	12	10	by	by	ADP
ejpam-3547	12	11	his	his	PRON
ejpam-3547	12	12	name	name	NOUN
ejpam-3547	12	13	,	,	PUNCT
ejpam-3547	12	14	bernstein	bernstein	PROPN
ejpam-3547	12	15	sequence	sequence	PROPN
ejpam-3547	12	16	,	,	PUNCT
ejpam-3547	12	17	which	which	PRON
ejpam-3547	12	18	is	be	AUX
ejpam-3547	12	19	defined	define	VERB
ejpam-3547	12	20	as:[1	as:[1	X
ejpam-3547	12	21	]	]	PUNCT
ejpam-3547	12	22	bn(f	bn(f	PUNCT
ejpam-3547	12	23	;	;	PUNCT
ejpam-3547	12	24	x	x	X
ejpam-3547	12	25	)	)	PUNCT
ejpam-3547	13	1	=	=	SYM
ejpam-3547	13	2	n∑	n∑	PROPN
ejpam-3547	13	3	k=0	k=0	PROPN
ejpam-3547	13	4	bn	bn	PROPN
ejpam-3547	13	5	,	,	PUNCT
ejpam-3547	13	6	k(x)f	k(x)f	PROPN
ejpam-3547	13	7	(	(	PUNCT
ejpam-3547	13	8	k	k	NOUN
ejpam-3547	13	9	n	n	PROPN
ejpam-3547	13	10	)	)	PUNCT
ejpam-3547	13	11	(	(	PUNCT
ejpam-3547	13	12	1.1	1.1	NUM
ejpam-3547	13	13	)	)	PUNCT
ejpam-3547	13	14	where	where	SCONJ
ejpam-3547	13	15	,	,	PUNCT
ejpam-3547	13	16	bn	bn	PROPN
ejpam-3547	13	17	,	,	PUNCT
ejpam-3547	13	18	k	k	PROPN
ejpam-3547	13	19	(	(	PUNCT
ejpam-3547	13	20	x	x	X
ejpam-3547	13	21	)	)	PUNCT
ejpam-3547	13	22	=	=	SYM
ejpam-3547	13	23	(	(	PUNCT
ejpam-3547	13	24	n	n	X
ejpam-3547	13	25	k	k	NOUN
ejpam-3547	13	26	)	)	PUNCT
ejpam-3547	14	1	xk(1−	xk(1−	PROPN
ejpam-3547	15	1	x)n−k	x)n−k	PROPN
ejpam-3547	16	1	and	and	CCONJ
ejpam-3547	16	2	f	f	PROPN
ejpam-3547	16	3	∈	∈	PROPN
ejpam-3547	16	4	c[0	c[0	PROPN
ejpam-3547	16	5	,	,	PUNCT
ejpam-3547	16	6	1	1	NUM
ejpam-3547	16	7	]	]	PUNCT
ejpam-3547	16	8	.	.	PUNCT
ejpam-3547	17	1	next	next	ADJ
ejpam-3547	17	2	,	,	PUNCT
ejpam-3547	17	3	voronovskaja	voronovskaja	NOUN
ejpam-3547	17	4	in	in	ADP
ejpam-3547	17	5	1932	1932	NUM
ejpam-3547	17	6	shown	show	VERB
ejpam-3547	17	7	that	that	SCONJ
ejpam-3547	17	8	the	the	DET
ejpam-3547	17	9	order	order	NOUN
ejpam-3547	17	10	of	of	ADP
ejpam-3547	17	11	approximation	approximation	NOUN
ejpam-3547	17	12	is	be	AUX
ejpam-3547	17	13	o(n−1	o(n−1	ADJ
ejpam-3547	17	14	)	)	PUNCT
ejpam-3547	17	15	.	.	PUNCT
ejpam-3547	18	1	also	also	ADV
ejpam-3547	18	2	,	,	PUNCT
ejpam-3547	18	3	she	she	PRON
ejpam-3547	18	4	showed	show	VERB
ejpam-3547	18	5	that	that	SCONJ
ejpam-3547	18	6	this	this	DET
ejpam-3547	18	7	order	order	NOUN
ejpam-3547	18	8	of	of	ADP
ejpam-3547	18	9	approximation	approximation	NOUN
ejpam-3547	18	10	by	by	ADP
ejpam-3547	18	11	bernstein	bernstein	PROPN
ejpam-3547	18	12	sequence	sequence	NOUN
ejpam-3547	18	13	can	can	AUX
ejpam-3547	18	14	not	not	PART
ejpam-3547	18	15	be	be	AUX
ejpam-3547	18	16	improved	improve	VERB
ejpam-3547	18	17	beyond	beyond	ADP
ejpam-3547	18	18	o(n−1).[18	o(n−1).[18	NUM
ejpam-3547	18	19	]	]	PUNCT
ejpam-3547	18	20	.	.	PUNCT
ejpam-3547	19	1	many	many	ADJ
ejpam-3547	19	2	papers	paper	NOUN
ejpam-3547	19	3	interested	interested	ADJ
ejpam-3547	19	4	in	in	ADP
ejpam-3547	19	5	the	the	DET
ejpam-3547	19	6	classical	classical	ADJ
ejpam-3547	19	7	sequences	sequence	NOUN
ejpam-3547	19	8	of	of	ADP
ejpam-3547	19	9	bernstein	bernstein	PROPN
ejpam-3547	19	10	and	and	CCONJ
ejpam-3547	19	11	gave	give	VERB
ejpam-3547	19	12	some	some	DET
ejpam-3547	19	13	modifications	modification	NOUN
ejpam-3547	19	14	of	of	ADP
ejpam-3547	19	15	them	they	PRON
ejpam-3547	19	16	[	[	X
ejpam-3547	19	17	5	5	NUM
ejpam-3547	19	18	]	]	PUNCT
ejpam-3547	19	19	,	,	PUNCT
ejpam-3547	19	20	[	[	X
ejpam-3547	19	21	11	11	NUM
ejpam-3547	19	22	]	]	PUNCT
ejpam-3547	19	23	.	.	PUNCT
ejpam-3547	20	1	in	in	ADP
ejpam-3547	20	2	addition	addition	NOUN
ejpam-3547	20	3	,	,	PUNCT
ejpam-3547	20	4	the	the	DET
ejpam-3547	20	5	numerical	numerical	ADJ
ejpam-3547	20	6	application	application	NOUN
ejpam-3547	20	7	for	for	ADP
ejpam-3547	20	8	this	this	DET
ejpam-3547	20	9	∗corresponding	∗corresponde	VERB
ejpam-3547	20	10	author	author	NOUN
ejpam-3547	20	11	.	.	PUNCT
ejpam-3547	21	1	doi	doi	NOUN
ejpam-3547	21	2	:	:	PUNCT
ejpam-3547	21	3	https://doi.org/10.29020/nybg.ejpam.v12i4.3547	https://doi.org/10.29020/nybg.ejpam.v12i4.3547	PROPN
ejpam-3547	21	4	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3547	21	5	1508	1508	NUM
ejpam-3547	22	1	c	c	X
ejpam-3547	22	2	©	©	PROPN
ejpam-3547	22	3	2019	2019	NUM
ejpam-3547	22	4	ejpam	ejpam	NOUN
ejpam-3547	22	5	all	all	DET
ejpam-3547	22	6	rights	right	NOUN
ejpam-3547	22	7	reserved	reserve	VERB
ejpam-3547	22	8	.	.	PUNCT
ejpam-3547	23	1	a.	a.	PROPN
ejpam-3547	23	2	j.	j.	PROPN
ejpam-3547	23	3	mohammad	mohammad	PROPN
ejpam-3547	23	4	,	,	PUNCT
ejpam-3547	23	5	h.	h.	PROPN
ejpam-3547	23	6	o.	o.	PROPN
ejpam-3547	23	7	muslim	muslim	PROPN
ejpam-3547	23	8	/	/	SYM
ejpam-3547	23	9	eur	eur	PROPN
ejpam-3547	23	10	.	.	PUNCT
ejpam-3547	24	1	j.	j.	PROPN
ejpam-3547	24	2	pure	pure	PROPN
ejpam-3547	24	3	appl	appl	PROPN
ejpam-3547	24	4	.	.	PROPN
ejpam-3547	24	5	math	math	PROPN
ejpam-3547	24	6	,	,	PUNCT
ejpam-3547	24	7	12	12	NUM
ejpam-3547	24	8	(	(	PUNCT
ejpam-3547	24	9	4	4	NUM
ejpam-3547	24	10	)	)	PUNCT
ejpam-3547	24	11	(	(	PUNCT
ejpam-3547	24	12	2019	2019	NUM
ejpam-3547	24	13	)	)	PUNCT
ejpam-3547	24	14	,	,	PUNCT
ejpam-3547	24	15	1508	1508	NUM
ejpam-3547	24	16	-	-	SYM
ejpam-3547	24	17	1523	1523	NUM
ejpam-3547	24	18	1509	1509	NUM
ejpam-3547	24	19	sequence	sequence	NOUN
ejpam-3547	24	20	are	be	AUX
ejpam-3547	24	21	very	very	ADV
ejpam-3547	24	22	limited	limited	ADJ
ejpam-3547	24	23	[	[	X
ejpam-3547	24	24	3	3	NUM
ejpam-3547	24	25	]	]	PUNCT
ejpam-3547	24	26	,	,	PUNCT
ejpam-3547	24	27	[	[	X
ejpam-3547	24	28	13	13	NUM
ejpam-3547	24	29	]	]	PUNCT
ejpam-3547	24	30	.	.	PUNCT
ejpam-3547	25	1	szãsz	szãsz	ADV
ejpam-3547	25	2	in	in	ADP
ejpam-3547	25	3	1950	1950	NUM
ejpam-3547	25	4	,	,	PUNCT
ejpam-3547	25	5	generalized	generalize	VERB
ejpam-3547	25	6	the	the	DET
ejpam-3547	25	7	bernstein	bernstein	PROPN
ejpam-3547	25	8	sequence	sequence	NOUN
ejpam-3547	25	9	to	to	PART
ejpam-3547	25	10	approximate	approximate	VERB
ejpam-3547	25	11	the	the	DET
ejpam-3547	25	12	space	space	NOUN
ejpam-3547	25	13	of	of	ADP
ejpam-3547	25	14	continuous	continuous	ADJ
ejpam-3547	25	15	functions	function	NOUN
ejpam-3547	25	16	on	on	ADP
ejpam-3547	25	17	the	the	DET
ejpam-3547	25	18	interval	interval	NOUN
ejpam-3547	25	19	[	[	X
ejpam-3547	25	20	0,∞	0,∞	NOUN
ejpam-3547	25	21	)	)	PUNCT
ejpam-3547	25	22	as	as	ADP
ejpam-3547	25	23	[	[	X
ejpam-3547	25	24	16	16	NUM
ejpam-3547	25	25	]	]	PUNCT
ejpam-3547	25	26	sn(f	sn(f	ADJ
ejpam-3547	25	27	;	;	PUNCT
ejpam-3547	25	28	x	x	X
ejpam-3547	25	29	)	)	PUNCT
ejpam-3547	25	30	=	=	PUNCT
ejpam-3547	26	1	∞∑	∞∑	NUM
ejpam-3547	26	2	k=0	k=0	PUNCT
ejpam-3547	26	3	qn	qn	PROPN
ejpam-3547	26	4	,	,	PUNCT
ejpam-3547	26	5	k(x)f	k(x)f	PROPN
ejpam-3547	26	6	(	(	PUNCT
ejpam-3547	26	7	k	k	NOUN
ejpam-3547	26	8	n	n	PROPN
ejpam-3547	26	9	)	)	PUNCT
ejpam-3547	26	10	(	(	PUNCT
ejpam-3547	26	11	1.2	1.2	NUM
ejpam-3547	26	12	)	)	PUNCT
ejpam-3547	27	1	where	where	SCONJ
ejpam-3547	27	2	qn	qn	NOUN
ejpam-3547	27	3	,	,	PUNCT
ejpam-3547	27	4	k(x	k(x	PROPN
ejpam-3547	27	5	)	)	PUNCT
ejpam-3547	27	6	=	=	PUNCT
ejpam-3547	27	7	(	(	PUNCT
ejpam-3547	27	8	nx)k	nx)k	PROPN
ejpam-3547	27	9	k!enx	k!enx	PROPN
ejpam-3547	27	10	,	,	PUNCT
ejpam-3547	27	11	x	x	PUNCT
ejpam-3547	27	12	∈	∈	PROPN
ejpam-3547	28	1	[	[	X
ejpam-3547	28	2	0,∞	0,∞	NOUN
ejpam-3547	28	3	)	)	PUNCT
ejpam-3547	28	4	.	.	PUNCT
ejpam-3547	29	1	several	several	ADJ
ejpam-3547	29	2	new	new	ADJ
ejpam-3547	29	3	modifications	modification	NOUN
ejpam-3547	29	4	of	of	ADP
ejpam-3547	29	5	szãsz	szãsz	ADJ
ejpam-3547	29	6	sequence	sequence	NOUN
ejpam-3547	29	7	were	be	AUX
ejpam-3547	29	8	constructed	construct	VERB
ejpam-3547	29	9	and	and	CCONJ
ejpam-3547	29	10	studied	study	VERB
ejpam-3547	29	11	,	,	PUNCT
ejpam-3547	29	12	here	here	ADV
ejpam-3547	29	13	we	we	PRON
ejpam-3547	29	14	refer	refer	VERB
ejpam-3547	29	15	to	to	ADP
ejpam-3547	29	16	[	[	X
ejpam-3547	29	17	4	4	NUM
ejpam-3547	29	18	,	,	PUNCT
ejpam-3547	29	19	14	14	NUM
ejpam-3547	29	20	,	,	PUNCT
ejpam-3547	29	21	17	17	NUM
ejpam-3547	29	22	,	,	PUNCT
ejpam-3547	29	23	20	20	NUM
ejpam-3547	29	24	]	]	PUNCT
ejpam-3547	29	25	.	.	PUNCT
ejpam-3547	30	1	also	also	ADV
ejpam-3547	30	2	,	,	PUNCT
ejpam-3547	30	3	many	many	ADJ
ejpam-3547	30	4	authors	author	NOUN
ejpam-3547	30	5	have	have	AUX
ejpam-3547	30	6	discussed	discuss	VERB
ejpam-3547	30	7	the	the	DET
ejpam-3547	30	8	approximation	approximation	NOUN
ejpam-3547	30	9	behavior	behavior	NOUN
ejpam-3547	30	10	of	of	ADP
ejpam-3547	30	11	different	different	ADJ
ejpam-3547	30	12	summation	summation	NOUN
ejpam-3547	30	13	-	-	PUNCT
ejpam-3547	30	14	integral	integral	ADJ
ejpam-3547	30	15	type	type	NOUN
ejpam-3547	30	16	operators	operator	NOUN
ejpam-3547	30	17	(	(	PUNCT
ejpam-3547	30	18	see	see	VERB
ejpam-3547	30	19	[	[	X
ejpam-3547	30	20	6	6	NUM
ejpam-3547	30	21	,	,	PUNCT
ejpam-3547	30	22	7	7	NUM
ejpam-3547	30	23	,	,	PUNCT
ejpam-3547	30	24	10	10	NUM
ejpam-3547	30	25	,	,	PUNCT
ejpam-3547	30	26	12	12	NUM
ejpam-3547	30	27	]	]	PUNCT
ejpam-3547	30	28	)	)	PUNCT
ejpam-3547	30	29	the	the	DET
ejpam-3547	30	30	sequence	sequence	NOUN
ejpam-3547	30	31	of	of	ADP
ejpam-3547	30	32	integral	integral	ADJ
ejpam-3547	30	33	type	type	NOUN
ejpam-3547	30	34	operators	operator	NOUN
ejpam-3547	30	35	obviously	obviously	ADV
ejpam-3547	30	36	appeared	appear	VERB
ejpam-3547	30	37	in	in	ADP
ejpam-3547	30	38	the	the	DET
ejpam-3547	30	39	proof	proof	NOUN
ejpam-3547	30	40	of	of	ADP
ejpam-3547	30	41	weierstrass	weierstrass	PROPN
ejpam-3547	30	42	theorem	theorem	NOUN
ejpam-3547	30	43	(	(	PUNCT
ejpam-3547	30	44	the	the	DET
ejpam-3547	30	45	fundamental	fundamental	ADJ
ejpam-3547	30	46	theorem	theorem	NOUN
ejpam-3547	30	47	in	in	ADP
ejpam-3547	30	48	approximation	approximation	NOUN
ejpam-3547	30	49	theory	theory	NOUN
ejpam-3547	30	50	)	)	PUNCT
ejpam-3547	30	51	,	,	PUNCT
ejpam-3547	30	52	these	these	DET
ejpam-3547	30	53	sequences	sequence	NOUN
ejpam-3547	30	54	variety	variety	NOUN
ejpam-3547	30	55	via	via	ADP
ejpam-3547	30	56	the	the	DET
ejpam-3547	30	57	effort	effort	NOUN
ejpam-3547	30	58	of	of	ADP
ejpam-3547	30	59	some	some	PRON
ejpam-3547	30	60	of	of	ADP
ejpam-3547	30	61	the	the	DET
ejpam-3547	30	62	researchers	researcher	NOUN
ejpam-3547	30	63	who	who	PRON
ejpam-3547	30	64	re	re	VERB
ejpam-3547	30	65	-	-	VERB
ejpam-3547	30	66	proved	prove	VERB
ejpam-3547	30	67	the	the	DET
ejpam-3547	30	68	weierstrass	weierstrass	NOUN
ejpam-3547	30	69	theorem	theorem	VERB
ejpam-3547	30	70	by	by	ADP
ejpam-3547	30	71	using	use	VERB
ejpam-3547	30	72	different	different	ADJ
ejpam-3547	30	73	sequences	sequence	NOUN
ejpam-3547	30	74	of	of	ADP
ejpam-3547	30	75	integral	integral	ADJ
ejpam-3547	30	76	type	type	NOUN
ejpam-3547	30	77	[	[	X
ejpam-3547	30	78	8	8	NUM
ejpam-3547	30	79	,	,	PUNCT
ejpam-3547	30	80	9	9	NUM
ejpam-3547	30	81	,	,	PUNCT
ejpam-3547	30	82	19	19	NUM
ejpam-3547	30	83	]	]	PUNCT
ejpam-3547	30	84	.	.	PUNCT
ejpam-3547	31	1	in	in	ADP
ejpam-3547	31	2	the	the	DET
ejpam-3547	31	3	equation	equation	NOUN
ejpam-3547	31	4	(	(	PUNCT
ejpam-3547	31	5	1.1	1.1	NUM
ejpam-3547	31	6	)	)	PUNCT
ejpam-3547	31	7	bernstein	bernstein	PROPN
ejpam-3547	31	8	used	use	VERB
ejpam-3547	31	9	the	the	DET
ejpam-3547	31	10	finite	finite	ADJ
ejpam-3547	31	11	discrete	discrete	ADJ
ejpam-3547	31	12	sequence	sequence	NOUN
ejpam-3547	31	13	of	of	ADP
ejpam-3547	31	14	a	a	DET
ejpam-3547	31	15	linear	linear	ADJ
ejpam-3547	31	16	positive	positive	ADJ
ejpam-3547	31	17	operator	operator	NOUN
ejpam-3547	31	18	to	to	PART
ejpam-3547	31	19	give	give	VERB
ejpam-3547	31	20	another	another	DET
ejpam-3547	31	21	proof	proof	NOUN
ejpam-3547	31	22	of	of	ADP
ejpam-3547	31	23	weierstrass	weierstrass	NOUN
ejpam-3547	31	24	theorem	theorem	VERB
ejpam-3547	31	25	.	.	PUNCT
ejpam-3547	32	1	the	the	DET
ejpam-3547	32	2	bernstein	bernstein	PROPN
ejpam-3547	32	3	sequence	sequence	PROPN
ejpam-3547	32	4	gives	give	VERB
ejpam-3547	32	5	a	a	DET
ejpam-3547	32	6	better	well	ADJ
ejpam-3547	32	7	result	result	NOUN
ejpam-3547	32	8	than	than	ADP
ejpam-3547	32	9	the	the	DET
ejpam-3547	32	10	previous	previous	ADJ
ejpam-3547	32	11	sequences	sequence	NOUN
ejpam-3547	32	12	in	in	ADP
ejpam-3547	32	13	applications	application	NOUN
ejpam-3547	32	14	because	because	SCONJ
ejpam-3547	32	15	it	it	PRON
ejpam-3547	32	16	is	be	AUX
ejpam-3547	32	17	simplest	simple	ADJ
ejpam-3547	32	18	,	,	PUNCT
ejpam-3547	32	19	finite	finite	ADJ
ejpam-3547	32	20	and	and	CCONJ
ejpam-3547	32	21	discrete	discrete	ADJ
ejpam-3547	32	22	sequence	sequence	NOUN
ejpam-3547	32	23	[	[	X
ejpam-3547	32	24	3	3	NUM
ejpam-3547	32	25	]	]	PUNCT
ejpam-3547	32	26	,	,	PUNCT
ejpam-3547	32	27	[	[	X
ejpam-3547	32	28	13	13	NUM
ejpam-3547	32	29	]	]	PUNCT
ejpam-3547	32	30	.	.	PUNCT
ejpam-3547	33	1	we	we	PRON
ejpam-3547	33	2	believe	believe	VERB
ejpam-3547	33	3	that	that	SCONJ
ejpam-3547	33	4	the	the	DET
ejpam-3547	33	5	same	same	ADJ
ejpam-3547	33	6	case	case	NOUN
ejpam-3547	33	7	occurs	occur	VERB
ejpam-3547	33	8	when	when	SCONJ
ejpam-3547	33	9	we	we	PRON
ejpam-3547	33	10	replaced	replace	VERB
ejpam-3547	33	11	bernstein	bernstein	PROPN
ejpam-3547	33	12	by	by	ADP
ejpam-3547	33	13	szãsz	szãsz	ADJ
ejpam-3547	33	14	sequence	sequence	NOUN
ejpam-3547	33	15	so	so	ADV
ejpam-3547	33	16	,	,	PUNCT
ejpam-3547	33	17	we	we	PRON
ejpam-3547	33	18	will	will	AUX
ejpam-3547	33	19	use	use	VERB
ejpam-3547	33	20	the	the	DET
ejpam-3547	33	21	classical	classical	ADJ
ejpam-3547	33	22	szãsz	szãsz	ADJ
ejpam-3547	33	23	sequence	sequence	NOUN
ejpam-3547	33	24	to	to	PART
ejpam-3547	33	25	compare	compare	VERB
ejpam-3547	33	26	with	with	ADP
ejpam-3547	33	27	the	the	DET
ejpam-3547	33	28	numerical	numerical	ADJ
ejpam-3547	33	29	results	result	NOUN
ejpam-3547	33	30	of	of	ADP
ejpam-3547	33	31	our	our	PRON
ejpam-3547	33	32	sequence	sequence	NOUN
ejpam-3547	33	33	.	.	PUNCT
ejpam-3547	34	1	for	for	ADP
ejpam-3547	34	2	x	x	X
ejpam-3547	34	3	≥	≥	X
ejpam-3547	34	4	0	0	NUM
ejpam-3547	34	5	is	be	AUX
ejpam-3547	34	6	arbitrary	arbitrary	ADJ
ejpam-3547	34	7	but	but	CCONJ
ejpam-3547	34	8	fixed	fix	VERB
ejpam-3547	34	9	,	,	PUNCT
ejpam-3547	34	10	we	we	PRON
ejpam-3547	34	11	define	define	VERB
ejpam-3547	34	12	that	that	DET
ejpam-3547	34	13	cα[0,∞	cα[0,∞	NOUN
ejpam-3547	34	14	)	)	PUNCT
ejpam-3547	35	1	=	=	PRON
ejpam-3547	35	2	{	{	PUNCT
ejpam-3547	35	3	f	f	PROPN
ejpam-3547	35	4	∈	∈	PROPN
ejpam-3547	35	5	c[0,∞	c[0,∞	PROPN
ejpam-3547	35	6	)	)	PUNCT
ejpam-3547	35	7	:	:	PUNCT
ejpam-3547	36	1	|f(t)|	|f(t)|	PROPN
ejpam-3547	36	2	=	=	SYM
ejpam-3547	36	3	o(eαt	o(eαt	PROPN
ejpam-3547	36	4	)	)	PUNCT
ejpam-3547	36	5	,	,	PUNCT
ejpam-3547	36	6	for	for	ADP
ejpam-3547	36	7	some	some	DET
ejpam-3547	36	8	α	α	NOUN
ejpam-3547	36	9	>	>	X
ejpam-3547	36	10	0	0	PUNCT
ejpam-3547	36	11	}	}	PUNCT
ejpam-3547	36	12	and	and	CCONJ
ejpam-3547	36	13	the	the	DET
ejpam-3547	36	14	norm	norm	NOUN
ejpam-3547	36	15	‖f‖cα	‖f‖cα	PROPN
ejpam-3547	37	1	[	[	X
ejpam-3547	37	2	0,∞	0,∞	NUM
ejpam-3547	37	3	)	)	PUNCT
ejpam-3547	37	4	=	=	PUNCT
ejpam-3547	37	5	supt∈[0,∞	supt∈[0,∞	NOUN
ejpam-3547	37	6	)	)	PUNCT
ejpam-3547	38	1	|f(t)|e−αt	|f(t)|e−αt	PROPN
ejpam-3547	38	2	.	.	PROPN
ejpam-3547	38	3	for	for	ADP
ejpam-3547	38	4	f	f	PROPN
ejpam-3547	38	5	∈	∈	PROPN
ejpam-3547	38	6	cα[0,∞	cα[0,∞	PROPN
ejpam-3547	38	7	)	)	PUNCT
ejpam-3547	38	8	,	,	PUNCT
ejpam-3547	38	9	we	we	PRON
ejpam-3547	38	10	define	define	VERB
ejpam-3547	38	11	and	and	CCONJ
ejpam-3547	38	12	study	study	VERB
ejpam-3547	38	13	the	the	DET
ejpam-3547	38	14	following	follow	VERB
ejpam-3547	38	15	sequence	sequence	NOUN
ejpam-3547	38	16	of	of	ADP
ejpam-3547	38	17	linear	linear	ADJ
ejpam-3547	38	18	positive	positive	ADJ
ejpam-3547	38	19	operators	operator	NOUN
ejpam-3547	38	20	:	:	PUNCT
ejpam-3547	38	21	wn(f	wn(f	PUNCT
ejpam-3547	38	22	;	;	PUNCT
ejpam-3547	38	23	x	x	X
ejpam-3547	38	24	)	)	PUNCT
ejpam-3547	38	25	=	=	SYM
ejpam-3547	39	1	∫	∫	PROPN
ejpam-3547	39	2	x	x	SYM
ejpam-3547	39	3	0	0	NUM
ejpam-3547	39	4	kn(t;x)f(t)dt	kn(t;x)f(t)dt	PROPN
ejpam-3547	39	5	(	(	PUNCT
ejpam-3547	39	6	1.3	1.3	NUM
ejpam-3547	39	7	)	)	PUNCT
ejpam-3547	39	8	kn(t;x	kn(t;x	PROPN
ejpam-3547	39	9	)	)	PUNCT
ejpam-3547	39	10	is	be	AUX
ejpam-3547	39	11	the	the	DET
ejpam-3547	39	12	kernel	kernel	NOUN
ejpam-3547	39	13	of	of	ADP
ejpam-3547	39	14	wn(f	wn(f	PUNCT
ejpam-3547	39	15	;	;	PUNCT
ejpam-3547	39	16	x	x	X
ejpam-3547	39	17	)	)	PUNCT
ejpam-3547	39	18	which	which	PRON
ejpam-3547	39	19	is	be	AUX
ejpam-3547	39	20	define	define	ADJ
ejpam-3547	39	21	as	as	ADP
ejpam-3547	39	22	:	:	PUNCT
ejpam-3547	39	23	kn(t;x	kn(t;x	PROPN
ejpam-3547	39	24	)	)	PUNCT
ejpam-3547	39	25	=	=	SYM
ejpam-3547	39	26	ncosh(nt	ncosh(nt	ADJ
ejpam-3547	39	27	)	)	PUNCT
ejpam-3547	39	28	(	(	PUNCT
ejpam-3547	39	29	δ0	δ0	NOUN
ejpam-3547	39	30	+	+	CCONJ
ejpam-3547	39	31	sinh(nx	sinh(nx	NOUN
ejpam-3547	39	32	)	)	PUNCT
ejpam-3547	39	33	)	)	PUNCT
ejpam-3547	39	34	,	,	PUNCT
ejpam-3547	39	35	x	x	PUNCT
ejpam-3547	39	36	∈	∈	PROPN
ejpam-3547	40	1	[	[	X
ejpam-3547	40	2	0,∞	0,∞	NOUN
ejpam-3547	40	3	)	)	PUNCT
ejpam-3547	40	4	,	,	PUNCT
ejpam-3547	41	1	arbitrary	arbitrary	ADJ
ejpam-3547	41	2	but	but	CCONJ
ejpam-3547	41	3	fixed	fix	VERB
ejpam-3547	41	4	,	,	PUNCT
ejpam-3547	41	5	n	n	NOUN
ejpam-3547	41	6	∈	∈	NOUN
ejpam-3547	41	7	n	n	NOUN
ejpam-3547	41	8	:	:	PUNCT
ejpam-3547	41	9	=	=	SYM
ejpam-3547	41	10	1	1	NUM
ejpam-3547	41	11	,	,	PUNCT
ejpam-3547	41	12	2	2	NUM
ejpam-3547	41	13	,	,	PUNCT
ejpam-3547	41	14	3	3	NUM
ejpam-3547	41	15	,	,	PUNCT
ejpam-3547	41	16	...	...	PUNCT
ejpam-3547	41	17	and	and	CCONJ
ejpam-3547	41	18	δ0	δ0	VERB
ejpam-3547	41	19	positive	positive	ADJ
ejpam-3547	41	20	parameter	parameter	NOUN
ejpam-3547	41	21	.	.	PUNCT
ejpam-3547	42	1	firstly	firstly	ADV
ejpam-3547	42	2	,	,	PUNCT
ejpam-3547	42	3	we	we	PRON
ejpam-3547	42	4	introduce	introduce	VERB
ejpam-3547	42	5	some	some	DET
ejpam-3547	42	6	preliminary	preliminary	ADJ
ejpam-3547	42	7	results	result	NOUN
ejpam-3547	42	8	for	for	ADP
ejpam-3547	42	9	wn(f	wn(f	PUNCT
ejpam-3547	42	10	;	;	PUNCT
ejpam-3547	42	11	x	x	X
ejpam-3547	42	12	)	)	PUNCT
ejpam-3547	42	13	.	.	PUNCT
ejpam-3547	43	1	then	then	ADV
ejpam-3547	43	2	,	,	PUNCT
ejpam-3547	43	3	we	we	PRON
ejpam-3547	43	4	study	study	VERB
ejpam-3547	43	5	pointwise	pointwise	NOUN
ejpam-3547	43	6	convergence	convergence	NOUN
ejpam-3547	43	7	in	in	ADP
ejpam-3547	43	8	simultaneous	simultaneous	ADJ
ejpam-3547	43	9	approximation	approximation	NOUN
ejpam-3547	43	10	and	and	CCONJ
ejpam-3547	43	11	give	give	VERB
ejpam-3547	43	12	a	a	DET
ejpam-3547	43	13	voronovskaja	voronovskaja	NOUN
ejpam-3547	43	14	-	-	PUNCT
ejpam-3547	43	15	type	type	NOUN
ejpam-3547	43	16	asymptotic	asymptotic	ADJ
ejpam-3547	43	17	formula	formula	NOUN
ejpam-3547	43	18	for	for	ADP
ejpam-3547	43	19	the	the	DET
ejpam-3547	43	20	sequence	sequence	NOUN
ejpam-3547	43	21	wn(f	wn(f	PUNCT
ejpam-3547	43	22	;	;	PUNCT
ejpam-3547	43	23	x	x	X
ejpam-3547	43	24	)	)	PUNCT
ejpam-3547	43	25	.	.	PUNCT
ejpam-3547	44	1	after	after	ADP
ejpam-3547	44	2	that	that	PRON
ejpam-3547	44	3	,	,	PUNCT
ejpam-3547	44	4	we	we	PRON
ejpam-3547	44	5	proceed	proceed	VERB
ejpam-3547	44	6	to	to	PART
ejpam-3547	44	7	estimate	estimate	VERB
ejpam-3547	44	8	an	an	DET
ejpam-3547	44	9	error	error	NOUN
ejpam-3547	44	10	occurring	occur	VERB
ejpam-3547	44	11	by	by	ADP
ejpam-3547	44	12	the	the	DET
ejpam-3547	44	13	approximation	approximation	NOUN
ejpam-3547	44	14	by	by	ADP
ejpam-3547	44	15	this	this	DET
ejpam-3547	44	16	sequence	sequence	NOUN
ejpam-3547	44	17	in	in	ADP
ejpam-3547	44	18	terms	term	NOUN
ejpam-3547	44	19	of	of	ADP
ejpam-3547	44	20	the	the	DET
ejpam-3547	44	21	modulus	modulus	NOUN
ejpam-3547	44	22	of	of	ADP
ejpam-3547	44	23	continuity	continuity	NOUN
ejpam-3547	44	24	.	.	PUNCT
ejpam-3547	45	1	finally	finally	ADV
ejpam-3547	45	2	,	,	PUNCT
ejpam-3547	45	3	we	we	PRON
ejpam-3547	45	4	give	give	VERB
ejpam-3547	45	5	numerical	numerical	ADJ
ejpam-3547	45	6	examples	example	NOUN
ejpam-3547	45	7	for	for	SCONJ
ejpam-3547	45	8	our	our	PRON
ejpam-3547	45	9	sequence	sequence	NOUN
ejpam-3547	45	10	to	to	PART
ejpam-3547	45	11	approximate	approximate	VERB
ejpam-3547	45	12	two	two	NUM
ejpam-3547	45	13	test	test	NOUN
ejpam-3547	45	14	functions	function	NOUN
ejpam-3547	45	15	g1(t	g1(t	PART
ejpam-3547	45	16	)	)	PUNCT
ejpam-3547	45	17	=	=	SYM
ejpam-3547	45	18	sin(10t)e−2	sin(10t)e−2	PROPN
ejpam-3547	45	19	t	t	PROPN
ejpam-3547	45	20	,	,	PUNCT
ejpam-3547	45	21	g2(t	g2(t	PROPN
ejpam-3547	45	22	)	)	PUNCT
ejpam-3547	45	23	=	=	SYM
ejpam-3547	45	24	√	√	NUM
ejpam-3547	45	25	1−	1−	NUM
ejpam-3547	45	26	(	(	PUNCT
ejpam-3547	45	27	t−	t−	PROPN
ejpam-3547	45	28	1)2	1)2	NUM
ejpam-3547	45	29	and	and	CCONJ
ejpam-3547	45	30	evaluate	evaluate	VERB
ejpam-3547	45	31	the	the	DET
ejpam-3547	45	32	maximum	maximum	ADJ
ejpam-3547	45	33	errors	error	NOUN
ejpam-3547	45	34	occurring	occur	VERB
ejpam-3547	45	35	by	by	ADP
ejpam-3547	45	36	a.	a.	PROPN
ejpam-3547	45	37	j.	j.	PROPN
ejpam-3547	45	38	mohammad	mohammad	PROPN
ejpam-3547	45	39	,	,	PUNCT
ejpam-3547	45	40	h.	h.	PROPN
ejpam-3547	45	41	o.	o.	PROPN
ejpam-3547	45	42	muslim	muslim	PROPN
ejpam-3547	45	43	/	/	SYM
ejpam-3547	45	44	eur	eur	PROPN
ejpam-3547	45	45	.	.	PUNCT
ejpam-3547	46	1	j.	j.	PROPN
ejpam-3547	46	2	pure	pure	PROPN
ejpam-3547	46	3	appl	appl	PROPN
ejpam-3547	46	4	.	.	PROPN
ejpam-3547	46	5	math	math	PROPN
ejpam-3547	46	6	,	,	PUNCT
ejpam-3547	46	7	12	12	NUM
ejpam-3547	46	8	(	(	PUNCT
ejpam-3547	46	9	4	4	NUM
ejpam-3547	46	10	)	)	PUNCT
ejpam-3547	46	11	(	(	PUNCT
ejpam-3547	46	12	2019	2019	NUM
ejpam-3547	46	13	)	)	PUNCT
ejpam-3547	46	14	,	,	PUNCT
ejpam-3547	46	15	1508	1508	NUM
ejpam-3547	46	16	-	-	SYM
ejpam-3547	46	17	1523	1523	NUM
ejpam-3547	46	18	1510	1510	NUM
ejpam-3547	46	19	this	this	DET
ejpam-3547	46	20	approximation	approximation	NOUN
ejpam-3547	46	21	,	,	PUNCT
ejpam-3547	46	22	also	also	ADV
ejpam-3547	46	23	,	,	PUNCT
ejpam-3547	46	24	compare	compare	VERB
ejpam-3547	46	25	the	the	DET
ejpam-3547	46	26	results	result	NOUN
ejpam-3547	46	27	with	with	ADP
ejpam-3547	46	28	the	the	DET
ejpam-3547	46	29	sequence	sequence	NOUN
ejpam-3547	46	30	of	of	ADP
ejpam-3547	46	31	classical	classical	ADJ
ejpam-3547	46	32	szãsz	szãsz	PROPN
ejpam-3547	46	33	operators	operator	NOUN
ejpam-3547	46	34	sn(gi(t);x	sn(gi(t);x	PROPN
ejpam-3547	46	35	)	)	PUNCT
ejpam-3547	46	36	,	,	PUNCT
ejpam-3547	47	1	i	i	PRON
ejpam-3547	47	2	=	=	NOUN
ejpam-3547	47	3	1	1	NUM
ejpam-3547	47	4	,	,	PUNCT
ejpam-3547	47	5	2	2	NUM
ejpam-3547	47	6	on	on	ADP
ejpam-3547	47	7	the	the	DET
ejpam-3547	47	8	intrval	intrval	NOUN
ejpam-3547	47	9	[	[	X
ejpam-3547	47	10	a	a	X
ejpam-3547	47	11	,	,	PUNCT
ejpam-3547	47	12	b	b	NOUN
ejpam-3547	47	13	]	]	X
ejpam-3547	47	14	.	.	PUNCT
ejpam-3547	48	1	2	2	X
ejpam-3547	48	2	.	.	X
ejpam-3547	48	3	preliminary	preliminary	ADJ
ejpam-3547	48	4	results	result	NOUN
ejpam-3547	48	5	in	in	ADP
ejpam-3547	48	6	this	this	DET
ejpam-3547	48	7	section	section	NOUN
ejpam-3547	48	8	,	,	PUNCT
ejpam-3547	48	9	we	we	PRON
ejpam-3547	48	10	give	give	VERB
ejpam-3547	48	11	some	some	DET
ejpam-3547	48	12	preliminary	preliminary	ADJ
ejpam-3547	48	13	results	result	NOUN
ejpam-3547	48	14	for	for	ADP
ejpam-3547	48	15	the	the	DET
ejpam-3547	48	16	operators	operator	NOUN
ejpam-3547	48	17	wn(f	wn(f	PUNCT
ejpam-3547	48	18	;	;	PUNCT
ejpam-3547	48	19	x	x	X
ejpam-3547	48	20	)	)	PUNCT
ejpam-3547	48	21	which	which	PRON
ejpam-3547	48	22	we	we	PRON
ejpam-3547	48	23	need	need	VERB
ejpam-3547	48	24	in	in	ADP
ejpam-3547	48	25	our	our	PRON
ejpam-3547	48	26	study	study	NOUN
ejpam-3547	48	27	.	.	PUNCT
ejpam-3547	49	1	lemma	lemma	PROPN
ejpam-3547	49	2	2.1	2.1	NUM
ejpam-3547	49	3	.	.	PUNCT
ejpam-3547	50	1	for	for	ADP
ejpam-3547	50	2	x	x	PROPN
ejpam-3547	50	3	∈	∈	PROPN
ejpam-3547	50	4	[	[	X
ejpam-3547	50	5	0,∞	0,∞	NOUN
ejpam-3547	50	6	)	)	PUNCT
ejpam-3547	50	7	the	the	DET
ejpam-3547	50	8	following	follow	VERB
ejpam-3547	50	9	conditions	condition	NOUN
ejpam-3547	50	10	hold	hold	VERB
ejpam-3547	50	11	:	:	PUNCT
ejpam-3547	50	12	(	(	PUNCT
ejpam-3547	50	13	i	i	NOUN
ejpam-3547	50	14	)	)	PUNCT
ejpam-3547	50	15	wn(1;x	wn(1;x	PROPN
ejpam-3547	50	16	)	)	PUNCT
ejpam-3547	51	1	=	=	SYM
ejpam-3547	51	2	sinh(nx	sinh(nx	NOUN
ejpam-3547	51	3	)	)	PUNCT
ejpam-3547	51	4	(	(	PUNCT
ejpam-3547	51	5	δ0	δ0	NOUN
ejpam-3547	51	6	+	+	CCONJ
ejpam-3547	51	7	sinh(nx	sinh(nx	NOUN
ejpam-3547	51	8	)	)	PUNCT
ejpam-3547	51	9	)	)	PUNCT
ejpam-3547	51	10	→	→	SYM
ejpam-3547	51	11	1	1	NUM
ejpam-3547	51	12	as	as	ADP
ejpam-3547	51	13	n→∞	n→∞	NUM
ejpam-3547	51	14	;	;	PUNCT
ejpam-3547	51	15	(	(	PUNCT
ejpam-3547	51	16	ii	ii	NOUN
ejpam-3547	51	17	)	)	PUNCT
ejpam-3547	51	18	wn(t;x	wn(t;x	PROPN
ejpam-3547	51	19	)	)	PUNCT
ejpam-3547	51	20	=	=	SYM
ejpam-3547	52	1	xsinh(nx	xsinh(nx	PROPN
ejpam-3547	52	2	)	)	PUNCT
ejpam-3547	52	3	(	(	PUNCT
ejpam-3547	52	4	δ0	δ0	NOUN
ejpam-3547	52	5	+	+	CCONJ
ejpam-3547	52	6	sinh(nx	sinh(nx	NOUN
ejpam-3547	52	7	)	)	PUNCT
ejpam-3547	52	8	)	)	PUNCT
ejpam-3547	53	1	−	−	ADP
ejpam-3547	53	2	cosh(nx	cosh(nx	NOUN
ejpam-3547	53	3	)	)	PUNCT
ejpam-3547	53	4	n	n	CCONJ
ejpam-3547	53	5	(	(	PUNCT
ejpam-3547	53	6	δ0	δ0	NOUN
ejpam-3547	53	7	+	+	X
ejpam-3547	53	8	sinh(nx	sinh(nx	NOUN
ejpam-3547	53	9	)	)	PUNCT
ejpam-3547	53	10	)	)	PUNCT
ejpam-3547	54	1	+	+	CCONJ
ejpam-3547	54	2	1	1	NUM
ejpam-3547	54	3	n	n	NOUN
ejpam-3547	54	4	(	(	PUNCT
ejpam-3547	54	5	δ0	δ0	NOUN
ejpam-3547	54	6	+	+	X
ejpam-3547	54	7	sinh(nx	sinh(nx	NOUN
ejpam-3547	54	8	)	)	PUNCT
ejpam-3547	54	9	)	)	PUNCT
ejpam-3547	54	10	→	→	PUNCT
ejpam-3547	55	1	x	x	X
ejpam-3547	55	2	as	as	ADP
ejpam-3547	55	3	n→∞	n→∞	NUM
ejpam-3547	55	4	;	;	PUNCT
ejpam-3547	55	5	(	(	PUNCT
ejpam-3547	55	6	iii	iii	X
ejpam-3547	55	7	)	)	PUNCT
ejpam-3547	55	8	wn(t2;x	wn(t2;x	PROPN
ejpam-3547	55	9	)	)	PUNCT
ejpam-3547	55	10	=	=	SYM
ejpam-3547	55	11	x2sinh(nx	x2sinh(nx	NOUN
ejpam-3547	55	12	)	)	PUNCT
ejpam-3547	55	13	(	(	PUNCT
ejpam-3547	55	14	δ0	δ0	NOUN
ejpam-3547	55	15	+	+	CCONJ
ejpam-3547	55	16	sinh(nx	sinh(nx	NOUN
ejpam-3547	55	17	)	)	PUNCT
ejpam-3547	55	18	)	)	PUNCT
ejpam-3547	56	1	−	−	ADP
ejpam-3547	56	2	2xcosh(nx	2xcosh(nx	NUM
ejpam-3547	56	3	)	)	PUNCT
ejpam-3547	56	4	n	n	CCONJ
ejpam-3547	56	5	(	(	PUNCT
ejpam-3547	56	6	δ0	δ0	NOUN
ejpam-3547	56	7	+	+	X
ejpam-3547	56	8	sinh(nx	sinh(nx	NOUN
ejpam-3547	56	9	)	)	PUNCT
ejpam-3547	56	10	)	)	PUNCT
ejpam-3547	57	1	+	+	CCONJ
ejpam-3547	57	2	2sinh(nx	2sinh(nx	X
ejpam-3547	57	3	)	)	PUNCT
ejpam-3547	57	4	n2	n2	NOUN
ejpam-3547	57	5	(	(	PUNCT
ejpam-3547	57	6	δ0	δ0	NOUN
ejpam-3547	57	7	+	+	X
ejpam-3547	57	8	sinh(nx	sinh(nx	NOUN
ejpam-3547	57	9	)	)	PUNCT
ejpam-3547	57	10	)	)	PUNCT
ejpam-3547	58	1	→	→	SYM
ejpam-3547	58	2	x2	x2	NOUN
ejpam-3547	58	3	as	as	ADP
ejpam-3547	58	4	n→∞.	n→∞.	ADJ
ejpam-3547	58	5	proof	proof	NOUN
ejpam-3547	58	6	.	.	PUNCT
ejpam-3547	59	1	by	by	ADP
ejpam-3547	59	2	the	the	DET
ejpam-3547	59	3	direct	direct	ADJ
ejpam-3547	59	4	computation	computation	NOUN
ejpam-3547	59	5	,	,	PUNCT
ejpam-3547	59	6	the	the	DET
ejpam-3547	59	7	proof	proof	NOUN
ejpam-3547	59	8	of	of	ADP
ejpam-3547	59	9	this	this	DET
ejpam-3547	59	10	lemma	lemma	PROPN
ejpam-3547	59	11	follows	follow	VERB
ejpam-3547	59	12	immediate	immediate	ADJ
ejpam-3547	59	13	.	.	PUNCT
ejpam-3547	60	1	in	in	ADP
ejpam-3547	60	2	addition	addition	NOUN
ejpam-3547	60	3	,	,	PUNCT
ejpam-3547	60	4	from	from	ADP
ejpam-3547	60	5	the	the	DET
ejpam-3547	60	6	above	above	ADJ
ejpam-3547	60	7	lemma	lemma	PROPN
ejpam-3547	60	8	and	and	CCONJ
ejpam-3547	60	9	the	the	DET
ejpam-3547	60	10	korovkin	korovkin	NOUN
ejpam-3547	60	11	theorem	theorem	VERB
ejpam-3547	60	12	[	[	PUNCT
ejpam-3547	60	13	9	9	NUM
ejpam-3547	60	14	]	]	PUNCT
ejpam-3547	60	15	,	,	PUNCT
ejpam-3547	60	16	we	we	PRON
ejpam-3547	60	17	have	have	VERB
ejpam-3547	60	18	that	that	PRON
ejpam-3547	60	19	:	:	PUNCT
ejpam-3547	61	1	lim	lim	PROPN
ejpam-3547	61	2	n→∞	n→∞	X
ejpam-3547	61	3	wn(f(t);x	wn(f(t);x	PROPN
ejpam-3547	61	4	)	)	PUNCT
ejpam-3547	61	5	=	=	SYM
ejpam-3547	61	6	f(x	f(x	PROPN
ejpam-3547	61	7	)	)	PUNCT
ejpam-3547	61	8	.	.	PUNCT
ejpam-3547	62	1	(	(	PUNCT
ejpam-3547	62	2	2.1	2.1	NUM
ejpam-3547	62	3	)	)	PUNCT
ejpam-3547	62	4	further	far	ADV
ejpam-3547	62	5	,	,	PUNCT
ejpam-3547	62	6	if	if	SCONJ
ejpam-3547	62	7	f	f	PROPN
ejpam-3547	62	8	is	be	AUX
ejpam-3547	62	9	exists	exist	VERB
ejpam-3547	62	10	and	and	CCONJ
ejpam-3547	62	11	is	be	AUX
ejpam-3547	62	12	continuous	continuous	ADJ
ejpam-3547	62	13	on	on	ADP
ejpam-3547	62	14	(	(	PUNCT
ejpam-3547	62	15	a	a	DET
ejpam-3547	62	16	−	−	PROPN
ejpam-3547	62	17	η	η	PROPN
ejpam-3547	62	18	,	,	PUNCT
ejpam-3547	62	19	b	b	PROPN
ejpam-3547	62	20	+	+	CCONJ
ejpam-3547	62	21	η	η	PROPN
ejpam-3547	62	22	)	)	PUNCT
ejpam-3547	62	23	⊂	⊂	PROPN
ejpam-3547	62	24	(	(	PUNCT
ejpam-3547	62	25	0,∞	0,∞	NOUN
ejpam-3547	62	26	)	)	PUNCT
ejpam-3547	62	27	,	,	PUNCT
ejpam-3547	62	28	η	η	PROPN
ejpam-3547	62	29	>	>	X
ejpam-3547	62	30	0	0	PROPN
ejpam-3547	62	31	,	,	PUNCT
ejpam-3547	62	32	the	the	DET
ejpam-3547	62	33	limit	limit	NOUN
ejpam-3547	62	34	(	(	PUNCT
ejpam-3547	62	35	2.1	2.1	NUM
ejpam-3547	62	36	)	)	PUNCT
ejpam-3547	62	37	holds	hold	VERB
ejpam-3547	62	38	uniformly	uniformly	ADV
ejpam-3547	62	39	on	on	ADP
ejpam-3547	62	40	[	[	X
ejpam-3547	62	41	a	a	X
ejpam-3547	62	42	,	,	PUNCT
ejpam-3547	62	43	b	b	NOUN
ejpam-3547	62	44	]	]	X
ejpam-3547	62	45	.	.	PUNCT
ejpam-3547	63	1	our	our	PRON
ejpam-3547	63	2	next	next	ADJ
ejpam-3547	63	3	definition	definition	NOUN
ejpam-3547	63	4	is	be	AUX
ejpam-3547	63	5	the	the	DET
ejpam-3547	63	6	m−	m−	PROPN
ejpam-3547	63	7	th	th	NOUN
ejpam-3547	63	8	order	order	NOUN
ejpam-3547	63	9	moment	moment	NOUN
ejpam-3547	63	10	for	for	ADP
ejpam-3547	63	11	wn(f	wn(f	PUNCT
ejpam-3547	63	12	;	;	PUNCT
ejpam-3547	63	13	x	x	X
ejpam-3547	63	14	)	)	PUNCT
ejpam-3547	63	15	.	.	PUNCT
ejpam-3547	64	1	definition	definition	NOUN
ejpam-3547	64	2	2.1	2.1	NUM
ejpam-3547	64	3	.	.	PUNCT
ejpam-3547	65	1	for	for	ADP
ejpam-3547	65	2	m	m	PROPN
ejpam-3547	65	3	∈	∈	PROPN
ejpam-3547	65	4	n0	n0	NOUN
ejpam-3547	65	5	the	the	DET
ejpam-3547	65	6	m−th	m−th	PROPN
ejpam-3547	65	7	order	order	NOUN
ejpam-3547	65	8	moment	moment	NOUN
ejpam-3547	65	9	tn	tn	PROPN
ejpam-3547	65	10	,	,	PUNCT
ejpam-3547	65	11	m(x	m(x	PROPN
ejpam-3547	65	12	)	)	PUNCT
ejpam-3547	65	13	for	for	ADP
ejpam-3547	65	14	the	the	DET
ejpam-3547	65	15	operator	operator	NOUN
ejpam-3547	65	16	wn(f(t);x	wn(f(t);x	PROPN
ejpam-3547	65	17	)	)	PUNCT
ejpam-3547	65	18	is	be	AUX
ejpam-3547	65	19	define	define	VERB
ejpam-3547	65	20	as	as	ADP
ejpam-3547	65	21	:	:	PUNCT
ejpam-3547	65	22	tn	tn	PROPN
ejpam-3547	65	23	,	,	PUNCT
ejpam-3547	65	24	m(x	m(x	PROPN
ejpam-3547	65	25	)	)	PUNCT
ejpam-3547	66	1	=	=	SYM
ejpam-3547	66	2	wn((t−	wn((t−	PROPN
ejpam-3547	66	3	x)m;x	x)m;x	PROPN
ejpam-3547	66	4	)	)	PUNCT
ejpam-3547	67	1	=	=	PRON
ejpam-3547	67	2	(	(	PUNCT
ejpam-3547	67	3	−1)mwn((x−	−1)mwn((x−	NOUN
ejpam-3547	67	4	t)m;x	t)m;x	NOUN
ejpam-3547	67	5	)	)	PUNCT
ejpam-3547	68	1	=	=	SYM
ejpam-3547	68	2	n(−1)m	n(−1)m	PROPN
ejpam-3547	68	3	(	(	PUNCT
ejpam-3547	68	4	δ0	δ0	NOUN
ejpam-3547	68	5	+	+	X
ejpam-3547	68	6	sinh(nx	sinh(nx	NOUN
ejpam-3547	68	7	)	)	PUNCT
ejpam-3547	68	8	)	)	PUNCT
ejpam-3547	69	1	∫	∫	PROPN
ejpam-3547	70	1	x	x	SYM
ejpam-3547	70	2	0	0	NUM
ejpam-3547	70	3	cosh(nt)(x−t)mdt	cosh(nt)(x−t)mdt	ADJ
ejpam-3547	70	4	(	(	PUNCT
ejpam-3547	70	5	2.2	2.2	NUM
ejpam-3547	70	6	)	)	PUNCT
ejpam-3547	70	7	the	the	DET
ejpam-3547	70	8	recurrence	recurrence	NOUN
ejpam-3547	70	9	relations	relation	NOUN
ejpam-3547	70	10	for	for	ADP
ejpam-3547	70	11	tn	tn	PROPN
ejpam-3547	70	12	,	,	PUNCT
ejpam-3547	70	13	m(x	m(x	PROPN
ejpam-3547	70	14	)	)	PUNCT
ejpam-3547	70	15	are	be	AUX
ejpam-3547	70	16	given	give	VERB
ejpam-3547	70	17	in	in	ADP
ejpam-3547	70	18	the	the	DET
ejpam-3547	70	19	next	next	ADJ
ejpam-3547	70	20	lamma	lamma	PROPN
ejpam-3547	70	21	.	.	PUNCT
ejpam-3547	71	1	lemma	lemma	PROPN
ejpam-3547	71	2	2.2	2.2	NUM
ejpam-3547	71	3	.	.	PUNCT
ejpam-3547	72	1	for	for	ADP
ejpam-3547	72	2	the	the	DET
ejpam-3547	72	3	function	function	PROPN
ejpam-3547	72	4	tn	tn	PROPN
ejpam-3547	72	5	,	,	PUNCT
ejpam-3547	72	6	m(x	m(x	PROPN
ejpam-3547	72	7	)	)	PUNCT
ejpam-3547	72	8	,	,	PUNCT
ejpam-3547	72	9	we	we	PRON
ejpam-3547	72	10	have	have	VERB
ejpam-3547	72	11	:	:	PUNCT
ejpam-3547	72	12	(	(	PUNCT
ejpam-3547	72	13	i	i	NOUN
ejpam-3547	72	14	)	)	PUNCT
ejpam-3547	72	15	tn,0(x	tn,0(x	NOUN
ejpam-3547	72	16	)	)	PUNCT
ejpam-3547	73	1	=	=	SYM
ejpam-3547	73	2	sinh(nx	sinh(nx	NOUN
ejpam-3547	73	3	)	)	PUNCT
ejpam-3547	73	4	(	(	PUNCT
ejpam-3547	73	5	δ0	δ0	NOUN
ejpam-3547	73	6	+	+	CCONJ
ejpam-3547	73	7	sinh(nx	sinh(nx	NOUN
ejpam-3547	73	8	)	)	PUNCT
ejpam-3547	73	9	)	)	PUNCT
ejpam-3547	73	10	;	;	PUNCT
ejpam-3547	73	11	(	(	PUNCT
ejpam-3547	73	12	ii	ii	NOUN
ejpam-3547	73	13	)	)	PUNCT
ejpam-3547	73	14	tn,1(x	tn,1(x	PROPN
ejpam-3547	73	15	)	)	PUNCT
ejpam-3547	73	16	=	=	SYM
ejpam-3547	73	17	1	1	NUM
ejpam-3547	73	18	n	n	CCONJ
ejpam-3547	73	19	(	(	PUNCT
ejpam-3547	73	20	δ0	δ0	NOUN
ejpam-3547	73	21	+	+	X
ejpam-3547	73	22	sinh(nx	sinh(nx	NOUN
ejpam-3547	73	23	)	)	PUNCT
ejpam-3547	73	24	)	)	PUNCT
ejpam-3547	74	1	−	−	ADP
ejpam-3547	74	2	cosh(nx	cosh(nx	NOUN
ejpam-3547	74	3	)	)	PUNCT
ejpam-3547	74	4	n	n	CCONJ
ejpam-3547	74	5	(	(	PUNCT
ejpam-3547	74	6	δ0	δ0	NOUN
ejpam-3547	74	7	+	+	X
ejpam-3547	74	8	sinh(nx	sinh(nx	NOUN
ejpam-3547	74	9	)	)	PUNCT
ejpam-3547	74	10	)	)	PUNCT
ejpam-3547	74	11	;	;	PUNCT
ejpam-3547	74	12	a.	a.	PROPN
ejpam-3547	74	13	j.	j.	PROPN
ejpam-3547	74	14	mohammad	mohammad	PROPN
ejpam-3547	74	15	,	,	PUNCT
ejpam-3547	74	16	h.	h.	PROPN
ejpam-3547	74	17	o.	o.	PROPN
ejpam-3547	74	18	muslim	muslim	PROPN
ejpam-3547	74	19	/	/	SYM
ejpam-3547	74	20	eur	eur	PROPN
ejpam-3547	74	21	.	.	PUNCT
ejpam-3547	75	1	j.	j.	PROPN
ejpam-3547	75	2	pure	pure	PROPN
ejpam-3547	75	3	appl	appl	PROPN
ejpam-3547	75	4	.	.	PROPN
ejpam-3547	75	5	math	math	PROPN
ejpam-3547	75	6	,	,	PUNCT
ejpam-3547	75	7	12	12	NUM
ejpam-3547	75	8	(	(	PUNCT
ejpam-3547	75	9	4	4	NUM
ejpam-3547	75	10	)	)	PUNCT
ejpam-3547	75	11	(	(	PUNCT
ejpam-3547	75	12	2019	2019	NUM
ejpam-3547	75	13	)	)	PUNCT
ejpam-3547	75	14	,	,	PUNCT
ejpam-3547	75	15	1508	1508	NUM
ejpam-3547	75	16	-	-	SYM
ejpam-3547	75	17	1523	1523	NUM
ejpam-3547	75	18	1511	1511	NUM
ejpam-3547	75	19	(	(	PUNCT
ejpam-3547	75	20	iii	iii	NOUN
ejpam-3547	75	21	)	)	PUNCT
ejpam-3547	75	22	tn,2(x	tn,2(x	PROPN
ejpam-3547	75	23	)	)	PUNCT
ejpam-3547	75	24	=	=	SYM
ejpam-3547	75	25	2sinh(nx	2sinh(nx	NUM
ejpam-3547	75	26	)	)	PUNCT
ejpam-3547	75	27	n2	n2	NOUN
ejpam-3547	75	28	(	(	PUNCT
ejpam-3547	75	29	δ0	δ0	NOUN
ejpam-3547	75	30	+	+	X
ejpam-3547	75	31	sinh(nx	sinh(nx	NOUN
ejpam-3547	75	32	)	)	PUNCT
ejpam-3547	75	33	)	)	PUNCT
ejpam-3547	75	34	−	−	NOUN
ejpam-3547	76	1	2x	2x	NUM
ejpam-3547	76	2	n	n	CCONJ
ejpam-3547	76	3	(	(	PUNCT
ejpam-3547	76	4	δ0	δ0	NOUN
ejpam-3547	76	5	+	+	X
ejpam-3547	76	6	sinh(nx	sinh(nx	NOUN
ejpam-3547	76	7	)	)	PUNCT
ejpam-3547	76	8	)	)	PUNCT
ejpam-3547	76	9	.	.	PUNCT
ejpam-3547	77	1	then	then	ADV
ejpam-3547	77	2	,	,	PUNCT
ejpam-3547	77	3	we	we	PRON
ejpam-3547	77	4	have	have	VERB
ejpam-3547	77	5	the	the	DET
ejpam-3547	77	6	following	follow	VERB
ejpam-3547	77	7	recurrence	recurrence	NOUN
ejpam-3547	77	8	relation	relation	PROPN
ejpam-3547	77	9	:	:	PUNCT
ejpam-3547	77	10	tn	tn	PROPN
ejpam-3547	77	11	,	,	PUNCT
ejpam-3547	77	12	m(x	m(x	PROPN
ejpam-3547	77	13	)	)	PUNCT
ejpam-3547	77	14	=	=	SYM
ejpam-3547	77	15	m(m−	m(m−	PROPN
ejpam-3547	77	16	1	1	X
ejpam-3547	77	17	)	)	PUNCT
ejpam-3547	77	18	n2	n2	PROPN
ejpam-3547	77	19	tn	tn	PROPN
ejpam-3547	77	20	,	,	PUNCT
ejpam-3547	77	21	m−2(x)−	m−2(x)−	PROPN
ejpam-3547	77	22	m(−1)m	m(−1)m	PROPN
ejpam-3547	77	23	n	n	CCONJ
ejpam-3547	77	24	(	(	PUNCT
ejpam-3547	77	25	δ0	δ0	NOUN
ejpam-3547	77	26	+	+	X
ejpam-3547	77	27	sinh(nx	sinh(nx	NOUN
ejpam-3547	77	28	)	)	PUNCT
ejpam-3547	77	29	)	)	PUNCT
ejpam-3547	78	1	xm−1,m	xm−1,m	PROPN
ejpam-3547	78	2	>	>	X
ejpam-3547	79	1	2	2	X
ejpam-3547	79	2	.	.	PUNCT
ejpam-3547	79	3	(	(	PUNCT
ejpam-3547	79	4	2.3	2.3	NUM
ejpam-3547	79	5	)	)	PUNCT
ejpam-3547	79	6	further	far	ADV
ejpam-3547	79	7	,	,	PUNCT
ejpam-3547	79	8	we	we	PRON
ejpam-3547	79	9	have	have	AUX
ejpam-3547	79	10	:	:	PUNCT
ejpam-3547	79	11	(	(	PUNCT
ejpam-3547	79	12	1	1	X
ejpam-3547	79	13	)	)	PUNCT
ejpam-3547	79	14	tn	tn	PROPN
ejpam-3547	79	15	,	,	PUNCT
ejpam-3547	79	16	m(x	m(x	PROPN
ejpam-3547	79	17	)	)	PUNCT
ejpam-3547	79	18	approximate	approximate	VERB
ejpam-3547	79	19	a	a	DET
ejpam-3547	79	20	polynomial	polynomial	NOUN
ejpam-3547	79	21	in	in	ADP
ejpam-3547	79	22	x	x	PUNCT
ejpam-3547	79	23	of	of	ADP
ejpam-3547	79	24	degree	degree	NOUN
ejpam-3547	79	25	<	<	X
ejpam-3547	79	26	m	m	NOUN
ejpam-3547	79	27	,	,	PUNCT
ejpam-3547	79	28	whenever	whenever	SCONJ
ejpam-3547	79	29	n	n	PRON
ejpam-3547	79	30	is	be	AUX
ejpam-3547	79	31	sufficiently	sufficiently	ADV
ejpam-3547	79	32	large	large	ADJ
ejpam-3547	79	33	.	.	PUNCT
ejpam-3547	80	1	(	(	PUNCT
ejpam-3547	80	2	2	2	X
ejpam-3547	80	3	)	)	PUNCT
ejpam-3547	80	4	for	for	ADP
ejpam-3547	80	5	every	every	DET
ejpam-3547	80	6	x	x	SYM
ejpam-3547	80	7	∈	∈	PROPN
ejpam-3547	81	1	[	[	X
ejpam-3547	81	2	0,∞	0,∞	NOUN
ejpam-3547	81	3	)	)	PUNCT
ejpam-3547	81	4	,	,	PUNCT
ejpam-3547	81	5	tn	tn	PROPN
ejpam-3547	81	6	,	,	PUNCT
ejpam-3547	81	7	m(x	m(x	PROPN
ejpam-3547	81	8	)	)	PUNCT
ejpam-3547	82	1	=	=	SYM
ejpam-3547	82	2	o	o	NOUN
ejpam-3547	82	3	(	(	PUNCT
ejpam-3547	82	4	n−m	n−m	PROPN
ejpam-3547	82	5	)	)	PUNCT
ejpam-3547	82	6	.	.	PUNCT
ejpam-3547	83	1	proof	proof	NOUN
ejpam-3547	83	2	.	.	PUNCT
ejpam-3547	84	1	by	by	ADP
ejpam-3547	84	2	direct	direct	ADJ
ejpam-3547	84	3	computation	computation	NOUN
ejpam-3547	84	4	and	and	CCONJ
ejpam-3547	84	5	using	use	VERB
ejpam-3547	84	6	lemma	lemma	PROPN
ejpam-3547	84	7	(	(	PUNCT
ejpam-3547	84	8	2.1	2.1	NUM
ejpam-3547	84	9	)	)	PUNCT
ejpam-3547	84	10	,	,	PUNCT
ejpam-3547	84	11	we	we	PRON
ejpam-3547	84	12	have	have	VERB
ejpam-3547	84	13	(	(	PUNCT
ejpam-3547	84	14	i),(ii),(iii	i),(ii),(iii	NOUN
ejpam-3547	84	15	)	)	PUNCT
ejpam-3547	84	16	.	.	PUNCT
ejpam-3547	85	1	now	now	ADV
ejpam-3547	85	2	,	,	PUNCT
ejpam-3547	85	3	we	we	PRON
ejpam-3547	85	4	prove	prove	VERB
ejpam-3547	85	5	(	(	PUNCT
ejpam-3547	85	6	2.3	2.3	NUM
ejpam-3547	85	7	)	)	PUNCT
ejpam-3547	85	8	,	,	PUNCT
ejpam-3547	85	9	for	for	ADP
ejpam-3547	85	10	x	x	PROPN
ejpam-3547	85	11	∈	∈	PROPN
ejpam-3547	86	1	[	[	X
ejpam-3547	86	2	0,∞	0,∞	NOUN
ejpam-3547	86	3	)	)	PUNCT
ejpam-3547	86	4	,	,	PUNCT
ejpam-3547	86	5	and	and	CCONJ
ejpam-3547	86	6	all	all	PRON
ejpam-3547	86	7	m	m	VERB
ejpam-3547	86	8	>	>	X
ejpam-3547	86	9	2	2	NUM
ejpam-3547	86	10	,	,	PUNCT
ejpam-3547	86	11	we	we	PRON
ejpam-3547	86	12	have	have	VERB
ejpam-3547	86	13	:	:	PUNCT
ejpam-3547	86	14	tn	tn	PROPN
ejpam-3547	86	15	,	,	PUNCT
ejpam-3547	86	16	m(x	m(x	PROPN
ejpam-3547	86	17	)	)	PUNCT
ejpam-3547	87	1	=	=	SYM
ejpam-3547	87	2	n(−1)m	n(−1)m	PROPN
ejpam-3547	87	3	(	(	PUNCT
ejpam-3547	87	4	δ0	δ0	NOUN
ejpam-3547	87	5	+	+	X
ejpam-3547	87	6	sinh(nx	sinh(nx	NOUN
ejpam-3547	87	7	)	)	PUNCT
ejpam-3547	87	8	)	)	PUNCT
ejpam-3547	87	9	∫	∫	PROPN
ejpam-3547	88	1	x	x	SYM
ejpam-3547	88	2	0	0	PUNCT
ejpam-3547	88	3	cosh(nt)(x−	cosh(nt)(x−	CCONJ
ejpam-3547	88	4	t)mdt	t)mdt	NOUN
ejpam-3547	88	5	=	=	SYM
ejpam-3547	88	6	n(−1)m	n(−1)m	NOUN
ejpam-3547	88	7	(	(	PUNCT
ejpam-3547	88	8	δ0	δ0	NOUN
ejpam-3547	88	9	+	+	X
ejpam-3547	88	10	sinh(nx	sinh(nx	NOUN
ejpam-3547	88	11	)	)	PUNCT
ejpam-3547	88	12	)	)	PUNCT
ejpam-3547	89	1	[	[	PUNCT
ejpam-3547	89	2	m	m	VERB
ejpam-3547	89	3	n	n	PRON
ejpam-3547	89	4	∫	∫	PROPN
ejpam-3547	89	5	x	x	SYM
ejpam-3547	89	6	0	0	PROPN
ejpam-3547	89	7	sinh(nt)(x−	sinh(nt)(x−	ADJ
ejpam-3547	89	8	t)m−1dt	t)m−1dt	NOUN
ejpam-3547	89	9	]	]	PUNCT
ejpam-3547	90	1	=	=	SYM
ejpam-3547	90	2	n(−1)m	n(−1)m	PROPN
ejpam-3547	90	3	(	(	PUNCT
ejpam-3547	90	4	δ0	δ0	NOUN
ejpam-3547	90	5	+	+	X
ejpam-3547	90	6	sinh(nx	sinh(nx	NOUN
ejpam-3547	90	7	)	)	PUNCT
ejpam-3547	90	8	)	)	PUNCT
ejpam-3547	91	1	[	[	PUNCT
ejpam-3547	91	2	−m	−m	NOUN
ejpam-3547	91	3	n2	n2	ADJ
ejpam-3547	91	4	xm−1	xm−1	PROPN
ejpam-3547	91	5	+	+	CCONJ
ejpam-3547	91	6	m(m−	m(m−	PROPN
ejpam-3547	91	7	1	1	NUM
ejpam-3547	91	8	)	)	PUNCT
ejpam-3547	91	9	n2	n2	ADJ
ejpam-3547	91	10	∫	∫	PROPN
ejpam-3547	91	11	x	x	SYM
ejpam-3547	91	12	0	0	PROPN
ejpam-3547	91	13	cosh(nt)(x−	cosh(nt)(x−	PROPN
ejpam-3547	91	14	t)m−2dt	t)m−2dt	PROPN
ejpam-3547	91	15	]	]	PUNCT
ejpam-3547	92	1	=	=	PUNCT
ejpam-3547	92	2	m(m−	m(m−	PROPN
ejpam-3547	92	3	1	1	NUM
ejpam-3547	92	4	)	)	PUNCT
ejpam-3547	92	5	n2	n2	PROPN
ejpam-3547	92	6	tn	tn	PROPN
ejpam-3547	92	7	,	,	PUNCT
ejpam-3547	92	8	m−2(x)−	m−2(x)−	PROPN
ejpam-3547	92	9	m(−1)m	m(−1)m	PROPN
ejpam-3547	92	10	n	n	CCONJ
ejpam-3547	92	11	(	(	PUNCT
ejpam-3547	92	12	δ0	δ0	NOUN
ejpam-3547	92	13	+	+	X
ejpam-3547	92	14	sinh(nx	sinh(nx	NOUN
ejpam-3547	92	15	)	)	PUNCT
ejpam-3547	92	16	)	)	PUNCT
ejpam-3547	93	1	xm−1	xm−1	PROPN
ejpam-3547	93	2	.	.	PUNCT
ejpam-3547	94	1	therefore,(2.3	therefore,(2.3	NUM
ejpam-3547	94	2	)	)	PUNCT
ejpam-3547	94	3	satisfied	satisfied	ADJ
ejpam-3547	94	4	.	.	PUNCT
ejpam-3547	95	1	the	the	DET
ejpam-3547	95	2	consequence	consequence	NOUN
ejpam-3547	95	3	(	(	PUNCT
ejpam-3547	95	4	1	1	X
ejpam-3547	95	5	)	)	PUNCT
ejpam-3547	95	6	can	can	AUX
ejpam-3547	95	7	be	be	AUX
ejpam-3547	95	8	proved	prove	VERB
ejpam-3547	95	9	easily	easily	ADV
ejpam-3547	95	10	by	by	ADP
ejpam-3547	95	11	using	use	VERB
ejpam-3547	95	12	(	(	PUNCT
ejpam-3547	95	13	2.3	2.3	NUM
ejpam-3547	95	14	)	)	PUNCT
ejpam-3547	95	15	and	and	CCONJ
ejpam-3547	95	16	the	the	DET
ejpam-3547	95	17	induction	induction	NOUN
ejpam-3547	95	18	on	on	ADP
ejpam-3547	95	19	m	m	PROPN
ejpam-3547	95	20	,	,	PUNCT
ejpam-3547	95	21	so	so	ADV
ejpam-3547	95	22	the	the	DET
ejpam-3547	95	23	details	detail	NOUN
ejpam-3547	95	24	are	be	AUX
ejpam-3547	95	25	omitted	omit	VERB
ejpam-3547	95	26	.	.	PUNCT
ejpam-3547	96	1	lemma	lemma	PROPN
ejpam-3547	96	2	2.3	2.3	NUM
ejpam-3547	96	3	.	.	PUNCT
ejpam-3547	97	1	for	for	ADP
ejpam-3547	97	2	m	m	PROPN
ejpam-3547	97	3	>	>	X
ejpam-3547	97	4	1	1	NUM
ejpam-3547	97	5	,	,	PUNCT
ejpam-3547	97	6	we	we	PRON
ejpam-3547	97	7	have	have	VERB
ejpam-3547	97	8	:	:	PUNCT
ejpam-3547	97	9	wn(tm;x	wn(tm;x	PROPN
ejpam-3547	97	10	)	)	PUNCT
ejpam-3547	98	1	=	=	PRON
ejpam-3547	98	2	(	(	PUNCT
ejpam-3547	98	3	sinh(nx	sinh(nx	NOUN
ejpam-3547	98	4	)	)	PUNCT
ejpam-3547	98	5	(	(	PUNCT
ejpam-3547	98	6	δ0	δ0	NOUN
ejpam-3547	98	7	+	+	CCONJ
ejpam-3547	98	8	sinh(nx	sinh(nx	NOUN
ejpam-3547	98	9	)	)	PUNCT
ejpam-3547	98	10	)	)	PUNCT
ejpam-3547	98	11	)	)	PUNCT
ejpam-3547	99	1	xm	xm	PROPN
ejpam-3547	100	1	−	−	PROPN
ejpam-3547	100	2	(	(	PUNCT
ejpam-3547	100	3	mcosh(nx	mcosh(nx	NOUN
ejpam-3547	100	4	)	)	PUNCT
ejpam-3547	100	5	n	n	CCONJ
ejpam-3547	100	6	(	(	PUNCT
ejpam-3547	100	7	δ0	δ0	NOUN
ejpam-3547	100	8	+	+	X
ejpam-3547	100	9	sinh(nx	sinh(nx	NOUN
ejpam-3547	100	10	)	)	PUNCT
ejpam-3547	100	11	)	)	PUNCT
ejpam-3547	100	12	)	)	PUNCT
ejpam-3547	101	1	xm−1	xm−1	PROPN
ejpam-3547	102	1	+	+	PROPN
ejpam-3547	102	2	o	o	PROPN
ejpam-3547	102	3	(	(	PUNCT
ejpam-3547	102	4	n−2	n−2	PROPN
ejpam-3547	102	5	)	)	PUNCT
ejpam-3547	102	6	.	.	PUNCT
ejpam-3547	103	1	clearly	clearly	ADV
ejpam-3547	103	2	,	,	PUNCT
ejpam-3547	103	3	we	we	PRON
ejpam-3547	103	4	have	have	VERB
ejpam-3547	103	5	limn→∞wn(tm;x	limn→∞wn(tm;x	X
ejpam-3547	103	6	)	)	PUNCT
ejpam-3547	104	1	=	=	SYM
ejpam-3547	104	2	xm	xm	PROPN
ejpam-3547	104	3	.	.	PUNCT
ejpam-3547	105	1	proof	proof	NOUN
ejpam-3547	105	2	.	.	PUNCT
ejpam-3547	106	1	wn(tm;x	wn(tm;x	PROPN
ejpam-3547	106	2	)	)	PUNCT
ejpam-3547	107	1	=	=	SYM
ejpam-3547	108	1	n	n	CCONJ
ejpam-3547	108	2	(	(	PUNCT
ejpam-3547	108	3	δ0	δ0	NOUN
ejpam-3547	108	4	+	+	X
ejpam-3547	108	5	sinh(nx	sinh(nx	NOUN
ejpam-3547	108	6	)	)	PUNCT
ejpam-3547	108	7	)	)	PUNCT
ejpam-3547	108	8	∫	∫	PROPN
ejpam-3547	109	1	x	x	SYM
ejpam-3547	109	2	0	0	NUM
ejpam-3547	109	3	cosh(nt)tmdt	cosh(nt)tmdt	PROPN
ejpam-3547	109	4	=	=	SYM
ejpam-3547	109	5	n	n	CCONJ
ejpam-3547	109	6	(	(	PUNCT
ejpam-3547	109	7	δ0	δ0	NOUN
ejpam-3547	109	8	+	+	X
ejpam-3547	109	9	sinh(nx	sinh(nx	NOUN
ejpam-3547	109	10	)	)	PUNCT
ejpam-3547	109	11	)	)	PUNCT
ejpam-3547	110	1	[	[	X
ejpam-3547	110	2	(	(	PUNCT
ejpam-3547	110	3	1	1	NUM
ejpam-3547	110	4	n	n	PRON
ejpam-3547	110	5	sinh(nx	sinh(nx	NOUN
ejpam-3547	110	6	)	)	PUNCT
ejpam-3547	110	7	)	)	PUNCT
ejpam-3547	111	1	xm	xm	PROPN
ejpam-3547	112	1	−	−	PROPN
ejpam-3547	112	2	m	m	VERB
ejpam-3547	112	3	n	n	NUM
ejpam-3547	112	4	∫	∫	NOUN
ejpam-3547	112	5	x	x	SYM
ejpam-3547	112	6	0	0	NUM
ejpam-3547	112	7	sinh(nt)tm−1dt	sinh(nt)tm−1dt	NOUN
ejpam-3547	112	8	]	]	PUNCT
ejpam-3547	113	1	=	=	SYM
ejpam-3547	113	2	(	(	PUNCT
ejpam-3547	113	3	sinh(nx	sinh(nx	NOUN
ejpam-3547	113	4	)	)	PUNCT
ejpam-3547	113	5	(	(	PUNCT
ejpam-3547	113	6	δ0	δ0	NOUN
ejpam-3547	113	7	+	+	CCONJ
ejpam-3547	113	8	sinh(nx	sinh(nx	NOUN
ejpam-3547	113	9	)	)	PUNCT
ejpam-3547	113	10	)	)	PUNCT
ejpam-3547	113	11	)	)	PUNCT
ejpam-3547	114	1	xm	xm	PROPN
ejpam-3547	115	1	−	−	PROPN
ejpam-3547	115	2	(	(	PUNCT
ejpam-3547	115	3	mcosh(nx	mcosh(nx	NOUN
ejpam-3547	115	4	)	)	PUNCT
ejpam-3547	115	5	n	n	CCONJ
ejpam-3547	115	6	(	(	PUNCT
ejpam-3547	115	7	δ0	δ0	NOUN
ejpam-3547	115	8	+	+	X
ejpam-3547	115	9	sinh(nx	sinh(nx	NOUN
ejpam-3547	115	10	)	)	PUNCT
ejpam-3547	115	11	)	)	PUNCT
ejpam-3547	115	12	)	)	PUNCT
ejpam-3547	116	1	xm−1	xm−1	PROPN
ejpam-3547	116	2	a.	a.	PROPN
ejpam-3547	116	3	j.	j.	PROPN
ejpam-3547	116	4	mohammad	mohammad	PROPN
ejpam-3547	116	5	,	,	PUNCT
ejpam-3547	116	6	h.	h.	PROPN
ejpam-3547	116	7	o.	o.	PROPN
ejpam-3547	116	8	muslim	muslim	PROPN
ejpam-3547	116	9	/	/	SYM
ejpam-3547	116	10	eur	eur	PROPN
ejpam-3547	116	11	.	.	PUNCT
ejpam-3547	117	1	j.	j.	PROPN
ejpam-3547	117	2	pure	pure	PROPN
ejpam-3547	117	3	appl	appl	PROPN
ejpam-3547	117	4	.	.	PROPN
ejpam-3547	117	5	math	math	PROPN
ejpam-3547	117	6	,	,	PUNCT
ejpam-3547	117	7	12	12	NUM
ejpam-3547	117	8	(	(	PUNCT
ejpam-3547	117	9	4	4	NUM
ejpam-3547	117	10	)	)	PUNCT
ejpam-3547	117	11	(	(	PUNCT
ejpam-3547	117	12	2019	2019	NUM
ejpam-3547	117	13	)	)	PUNCT
ejpam-3547	117	14	,	,	PUNCT
ejpam-3547	117	15	1508	1508	NUM
ejpam-3547	117	16	-	-	SYM
ejpam-3547	117	17	1523	1523	NUM
ejpam-3547	117	18	1512	1512	NUM
ejpam-3547	117	19	+	+	CCONJ
ejpam-3547	117	20	(	(	PUNCT
ejpam-3547	117	21	m(m−	m(m−	PROPN
ejpam-3547	117	22	1	1	NUM
ejpam-3547	117	23	)	)	PUNCT
ejpam-3547	117	24	n	n	CCONJ
ejpam-3547	117	25	(	(	PUNCT
ejpam-3547	117	26	δ0	δ0	NOUN
ejpam-3547	117	27	+	+	X
ejpam-3547	117	28	sinh(nx	sinh(nx	NOUN
ejpam-3547	117	29	)	)	PUNCT
ejpam-3547	117	30	)	)	PUNCT
ejpam-3547	117	31	)	)	PUNCT
ejpam-3547	118	1	∫	∫	PROPN
ejpam-3547	118	2	x	x	SYM
ejpam-3547	118	3	0	0	NUM
ejpam-3547	118	4	cosh(nt)tm−2dt	cosh(nt)tm−2dt	NOUN
ejpam-3547	118	5	=	=	SYM
ejpam-3547	118	6	(	(	PUNCT
ejpam-3547	118	7	sinh(nx	sinh(nx	NOUN
ejpam-3547	118	8	)	)	PUNCT
ejpam-3547	118	9	(	(	PUNCT
ejpam-3547	118	10	δ0	δ0	NOUN
ejpam-3547	118	11	+	+	CCONJ
ejpam-3547	118	12	sinh(nx	sinh(nx	NOUN
ejpam-3547	118	13	)	)	PUNCT
ejpam-3547	118	14	)	)	PUNCT
ejpam-3547	118	15	)	)	PUNCT
ejpam-3547	119	1	xm	xm	PROPN
ejpam-3547	120	1	−	−	PROPN
ejpam-3547	120	2	(	(	PUNCT
ejpam-3547	120	3	mcosh(nx	mcosh(nx	NOUN
ejpam-3547	120	4	)	)	PUNCT
ejpam-3547	120	5	n	n	CCONJ
ejpam-3547	120	6	(	(	PUNCT
ejpam-3547	120	7	δ0	δ0	NOUN
ejpam-3547	120	8	+	+	X
ejpam-3547	120	9	sinh(nx	sinh(nx	NOUN
ejpam-3547	120	10	)	)	PUNCT
ejpam-3547	120	11	)	)	PUNCT
ejpam-3547	120	12	)	)	PUNCT
ejpam-3547	121	1	xm−1	xm−1	PROPN
ejpam-3547	122	1	+	+	PROPN
ejpam-3547	122	2	o	o	PROPN
ejpam-3547	122	3	(	(	PUNCT
ejpam-3547	122	4	n−2	n−2	PROPN
ejpam-3547	122	5	)	)	PUNCT
ejpam-3547	122	6	.	.	PUNCT
ejpam-3547	123	1	lemma	lemma	PROPN
ejpam-3547	123	2	2.4	2.4	NUM
ejpam-3547	123	3	.	.	PUNCT
ejpam-3547	124	1	let	let	VERB
ejpam-3547	124	2	δ	δ	PROPN
ejpam-3547	124	3	and	and	CCONJ
ejpam-3547	124	4	α	α	PRON
ejpam-3547	124	5	be	be	VERB
ejpam-3547	124	6	any	any	DET
ejpam-3547	124	7	two	two	NUM
ejpam-3547	124	8	positive	positive	ADJ
ejpam-3547	124	9	real	real	ADJ
ejpam-3547	124	10	numbers	number	NOUN
ejpam-3547	124	11	and	and	CCONJ
ejpam-3547	124	12	[	[	X
ejpam-3547	124	13	a	a	X
ejpam-3547	124	14	,	,	PUNCT
ejpam-3547	124	15	b	b	NOUN
ejpam-3547	124	16	]	]	X
ejpam-3547	124	17	⊂	⊂	X
ejpam-3547	124	18	(	(	PUNCT
ejpam-3547	124	19	0,∞	0,∞	NUM
ejpam-3547	124	20	)	)	PUNCT
ejpam-3547	124	21	.	.	PUNCT
ejpam-3547	125	1	then	then	ADV
ejpam-3547	125	2	for	for	ADP
ejpam-3547	125	3	λ	λ	PROPN
ejpam-3547	125	4	>	>	X
ejpam-3547	125	5	0	0	PROPN
ejpam-3547	125	6	,	,	PUNCT
ejpam-3547	125	7	we	we	PRON
ejpam-3547	125	8	have	have	VERB
ejpam-3547	125	9	:	:	PUNCT
ejpam-3547	125	10	sup	sup	NOUN
ejpam-3547	125	11	x∈[a	x∈[a	PROPN
ejpam-3547	125	12	,	,	PUNCT
ejpam-3547	125	13	b	b	X
ejpam-3547	125	14	]	]	X
ejpam-3547	125	15	∣∣∣∣∫	∣∣∣∣∫	PRON
ejpam-3547	125	16	x−t	x−t	PROPN
ejpam-3547	125	17	>	>	PROPN
ejpam-3547	125	18	δ	δ	PROPN
ejpam-3547	125	19	kn(t;x)eαtdt	kn(t;x)eαtdt	PROPN
ejpam-3547	125	20	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3547	126	1	=	=	PUNCT
ejpam-3547	126	2	o	o	X
ejpam-3547	126	3	(	(	PUNCT
ejpam-3547	126	4	n−λ	n−λ	NOUN
ejpam-3547	126	5	)	)	PUNCT
ejpam-3547	126	6	.	.	PUNCT
ejpam-3547	127	1	making	make	VERB
ejpam-3547	127	2	use	use	NOUN
ejpam-3547	127	3	of	of	ADP
ejpam-3547	127	4	taylor	taylor	PROPN
ejpam-3547	127	5	’s	’s	PART
ejpam-3547	127	6	expansion	expansion	NOUN
ejpam-3547	127	7	,	,	PUNCT
ejpam-3547	127	8	schwartz	schwartz	PROPN
ejpam-3547	127	9	inequality	inequality	PROPN
ejpam-3547	127	10	and	and	CCONJ
ejpam-3547	127	11	lemma	lemma	PROPN
ejpam-3547	127	12	2.2(2	2.2(2	NUM
ejpam-3547	127	13	)	)	PUNCT
ejpam-3547	127	14	,	,	PUNCT
ejpam-3547	127	15	the	the	DET
ejpam-3547	127	16	proof	proof	NOUN
ejpam-3547	127	17	of	of	ADP
ejpam-3547	127	18	this	this	DET
ejpam-3547	127	19	lemma	lemma	PROPN
ejpam-3547	127	20	easily	easily	ADV
ejpam-3547	127	21	follows	follow	VERB
ejpam-3547	127	22	.	.	PUNCT
ejpam-3547	128	1	lemma	lemma	PROPN
ejpam-3547	128	2	2.5	2.5	NUM
ejpam-3547	128	3	.	.	PUNCT
ejpam-3547	129	1	[	[	X
ejpam-3547	129	2	15	15	NUM
ejpam-3547	129	3	]	]	X
ejpam-3547	129	4	(	(	PUNCT
ejpam-3547	129	5	1	1	X
ejpam-3547	129	6	)	)	PUNCT
ejpam-3547	129	7	let	let	VERB
ejpam-3547	129	8	r	r	PRON
ejpam-3547	129	9	be	be	AUX
ejpam-3547	129	10	a	a	DET
ejpam-3547	129	11	nonnegative	nonnegative	ADJ
ejpam-3547	129	12	integer	integer	NOUN
ejpam-3547	129	13	and	and	CCONJ
ejpam-3547	129	14	assume	assume	VERB
ejpam-3547	129	15	f	f	PROPN
ejpam-3547	129	16	and	and	CCONJ
ejpam-3547	129	17	g	g	PROPN
ejpam-3547	129	18	are	be	AUX
ejpam-3547	129	19	r	r	NOUN
ejpam-3547	129	20	-	-	PUNCT
ejpam-3547	129	21	times	time	NOUN
ejpam-3547	129	22	differentiable	differentiable	ADJ
ejpam-3547	129	23	functions	function	NOUN
ejpam-3547	129	24	of	of	ADP
ejpam-3547	129	25	x	x	PUNCT
ejpam-3547	129	26	then	then	ADV
ejpam-3547	129	27	:	:	PUNCT
ejpam-3547	129	28	dr	dr	PROPN
ejpam-3547	129	29	dxr	dxr	PROPN
ejpam-3547	129	30	(	(	PUNCT
ejpam-3547	129	31	fg	fg	PROPN
ejpam-3547	129	32	)	)	PUNCT
ejpam-3547	129	33	=	=	PUNCT
ejpam-3547	130	1	∑r	∑r	PROPN
ejpam-3547	130	2	l=0	l=0	PROPN
ejpam-3547	130	3	(	(	PUNCT
ejpam-3547	130	4	r	r	NOUN
ejpam-3547	130	5	l	l	NOUN
ejpam-3547	130	6	)	)	PUNCT
ejpam-3547	130	7	dr−l	dr−l	NOUN
ejpam-3547	130	8	dxr−l	dxr−l	NOUN
ejpam-3547	130	9	(	(	PUNCT
ejpam-3547	130	10	f	f	X
ejpam-3547	130	11	)	)	PUNCT
ejpam-3547	130	12	dl	dl	PROPN
ejpam-3547	130	13	dxl	dxl	PROPN
ejpam-3547	130	14	(	(	PUNCT
ejpam-3547	130	15	g	g	NOUN
ejpam-3547	130	16	)	)	PUNCT
ejpam-3547	130	17	;	;	PUNCT
ejpam-3547	130	18	(	(	PUNCT
ejpam-3547	130	19	2	2	X
ejpam-3547	130	20	)	)	PUNCT
ejpam-3547	130	21	let	let	VERB
ejpam-3547	130	22	g(x	g(x	NOUN
ejpam-3547	130	23	)	)	PUNCT
ejpam-3547	130	24	be	be	AUX
ejpam-3547	130	25	a	a	DET
ejpam-3547	130	26	real	real	ADJ
ejpam-3547	130	27	or	or	CCONJ
ejpam-3547	130	28	complex	complex	ADJ
ejpam-3547	130	29	valued	value	VERB
ejpam-3547	130	30	function	function	NOUN
ejpam-3547	130	31	that	that	PRON
ejpam-3547	130	32	is	be	AUX
ejpam-3547	130	33	r	r	NOUN
ejpam-3547	130	34	-	-	PUNCT
ejpam-3547	130	35	times	time	NOUN
ejpam-3547	130	36	differentiable	differentiable	NOUN
ejpam-3547	130	37	then	then	ADV
ejpam-3547	130	38	:	:	PUNCT
ejpam-3547	130	39	dr	dr	PROPN
ejpam-3547	130	40	dxr	dxr	PROPN
ejpam-3547	130	41	(	(	PUNCT
ejpam-3547	130	42	1	1	NUM
ejpam-3547	130	43	g(x	g(x	NOUN
ejpam-3547	130	44	)	)	PUNCT
ejpam-3547	130	45	)	)	PUNCT
ejpam-3547	131	1	=	=	PUNCT
ejpam-3547	132	1	∑r	∑r	NOUN
ejpam-3547	132	2	l=0(−1)l	l=0(−1)l	NOUN
ejpam-3547	132	3	(	(	PUNCT
ejpam-3547	132	4	r+1	r+1	PROPN
ejpam-3547	132	5	l+1	l+1	PROPN
ejpam-3547	132	6	)	)	PUNCT
ejpam-3547	132	7	1	1	NUM
ejpam-3547	132	8	(	(	PUNCT
ejpam-3547	132	9	g(x))l+1	g(x))l+1	NOUN
ejpam-3547	132	10	(	(	PUNCT
ejpam-3547	132	11	f	f	X
ejpam-3547	132	12	)	)	PUNCT
ejpam-3547	132	13	dr	dr	PROPN
ejpam-3547	132	14	dxr	dxr	PROPN
ejpam-3547	132	15	(	(	PUNCT
ejpam-3547	132	16	g(x))l	g(x))l	PROPN
ejpam-3547	132	17	.	.	PUNCT
ejpam-3547	133	1	lemma	lemma	PROPN
ejpam-3547	133	2	2.6	2.6	NUM
ejpam-3547	133	3	.	.	PUNCT
ejpam-3547	134	1	for	for	ADP
ejpam-3547	134	2	r	r	PROPN
ejpam-3547	134	3	∈	∈	PROPN
ejpam-3547	134	4	n	n	CCONJ
ejpam-3547	134	5	,	,	PUNCT
ejpam-3547	134	6	we	we	PRON
ejpam-3547	134	7	have	have	VERB
ejpam-3547	134	8	:	:	PUNCT
ejpam-3547	134	9	(	(	PUNCT
ejpam-3547	134	10	i	i	NOUN
ejpam-3547	134	11	)	)	PUNCT
ejpam-3547	134	12	limn→∞	limn→∞	PROPN
ejpam-3547	134	13	sinh(nx	sinh(nx	NOUN
ejpam-3547	134	14	)	)	PUNCT
ejpam-3547	134	15	(	(	PUNCT
ejpam-3547	134	16	δ0	δ0	NOUN
ejpam-3547	134	17	+	+	CCONJ
ejpam-3547	134	18	sinh(nx	sinh(nx	NOUN
ejpam-3547	134	19	)	)	PUNCT
ejpam-3547	134	20	)	)	PUNCT
ejpam-3547	135	1	=	=	SYM
ejpam-3547	135	2	1	1	NUM
ejpam-3547	135	3	;	;	PUNCT
ejpam-3547	135	4	(	(	PUNCT
ejpam-3547	135	5	ii	ii	NOUN
ejpam-3547	135	6	)	)	PUNCT
ejpam-3547	135	7	limn→∞	limn→∞	PROPN
ejpam-3547	135	8	cosh(nx	cosh(nx	NOUN
ejpam-3547	135	9	)	)	PUNCT
ejpam-3547	135	10	(	(	PUNCT
ejpam-3547	135	11	δ0	δ0	NOUN
ejpam-3547	135	12	+	+	CCONJ
ejpam-3547	135	13	sinh(nx	sinh(nx	NOUN
ejpam-3547	135	14	)	)	PUNCT
ejpam-3547	135	15	)	)	PUNCT
ejpam-3547	136	1	=	=	SYM
ejpam-3547	136	2	1	1	NUM
ejpam-3547	136	3	;	;	PUNCT
ejpam-3547	136	4	(	(	PUNCT
ejpam-3547	136	5	iii	iii	X
ejpam-3547	136	6	)	)	PUNCT
ejpam-3547	136	7	limn→∞	limn→∞	PROPN
ejpam-3547	136	8	dr	dr	PROPN
ejpam-3547	136	9	dxr	dxr	PROPN
ejpam-3547	136	10	(	(	PUNCT
ejpam-3547	136	11	sinh(nx	sinh(nx	NOUN
ejpam-3547	136	12	)	)	PUNCT
ejpam-3547	136	13	(	(	PUNCT
ejpam-3547	136	14	δ0	δ0	NOUN
ejpam-3547	136	15	+	+	CCONJ
ejpam-3547	136	16	sinh(nx	sinh(nx	NOUN
ejpam-3547	136	17	)	)	PUNCT
ejpam-3547	136	18	)	)	PUNCT
ejpam-3547	136	19	)	)	PUNCT
ejpam-3547	137	1	=	=	PUNCT
ejpam-3547	137	2	0	0	NUM
ejpam-3547	137	3	;	;	PUNCT
ejpam-3547	137	4	(	(	PUNCT
ejpam-3547	137	5	iv	iv	X
ejpam-3547	137	6	)	)	PUNCT
ejpam-3547	137	7	limn→∞	limn→∞	PROPN
ejpam-3547	137	8	dr	dr	PROPN
ejpam-3547	137	9	dxr	dxr	PROPN
ejpam-3547	137	10	(	(	PUNCT
ejpam-3547	137	11	cosh(nx	cosh(nx	NOUN
ejpam-3547	137	12	)	)	PUNCT
ejpam-3547	137	13	(	(	PUNCT
ejpam-3547	137	14	δ0	δ0	NOUN
ejpam-3547	137	15	+	+	CCONJ
ejpam-3547	137	16	sinh(nx	sinh(nx	NOUN
ejpam-3547	137	17	)	)	PUNCT
ejpam-3547	137	18	)	)	PUNCT
ejpam-3547	137	19	)	)	PUNCT
ejpam-3547	138	1	=	=	PUNCT
ejpam-3547	138	2	0	0	NUM
ejpam-3547	138	3	;	;	PUNCT
ejpam-3547	138	4	(	(	PUNCT
ejpam-3547	138	5	v	v	NOUN
ejpam-3547	138	6	)	)	PUNCT
ejpam-3547	138	7	limn→∞	limn→∞	PROPN
ejpam-3547	138	8	dr	dr	PROPN
ejpam-3547	138	9	dxr	dxr	PROPN
ejpam-3547	138	10	(	(	PUNCT
ejpam-3547	138	11	1	1	NUM
ejpam-3547	138	12	(	(	PUNCT
ejpam-3547	138	13	δ0	δ0	NOUN
ejpam-3547	138	14	+	+	X
ejpam-3547	138	15	sinh(nx	sinh(nx	NOUN
ejpam-3547	138	16	)	)	PUNCT
ejpam-3547	138	17	)	)	PUNCT
ejpam-3547	138	18	)	)	PUNCT
ejpam-3547	139	1	=	=	PUNCT
ejpam-3547	139	2	0	0	NUM
ejpam-3547	139	3	;	;	PUNCT
ejpam-3547	139	4	(	(	PUNCT
ejpam-3547	139	5	vi	vi	NOUN
ejpam-3547	139	6	)	)	PUNCT
ejpam-3547	139	7	limn→∞	limn→∞	PROPN
ejpam-3547	139	8	dr	dr	PROPN
ejpam-3547	139	9	dxr	dxr	PROPN
ejpam-3547	139	10	(	(	PUNCT
ejpam-3547	139	11	xsinh(nx	xsinh(nx	PROPN
ejpam-3547	139	12	)	)	PUNCT
ejpam-3547	139	13	(	(	PUNCT
ejpam-3547	139	14	δ0	δ0	NOUN
ejpam-3547	139	15	+	+	CCONJ
ejpam-3547	139	16	sinh(nx	sinh(nx	NOUN
ejpam-3547	139	17	)	)	PUNCT
ejpam-3547	139	18	)	)	PUNCT
ejpam-3547	139	19	)	)	PUNCT
ejpam-3547	140	1	=	=	PUNCT
ejpam-3547	140	2	0	0	NUM
ejpam-3547	140	3	,	,	PUNCT
ejpam-3547	140	4	r	r	NOUN
ejpam-3547	140	5	>	>	X
ejpam-3547	140	6	1	1	NUM
ejpam-3547	140	7	.	.	PUNCT
ejpam-3547	140	8	a.	a.	PROPN
ejpam-3547	140	9	j.	j.	PROPN
ejpam-3547	140	10	mohammad	mohammad	PROPN
ejpam-3547	140	11	,	,	PUNCT
ejpam-3547	140	12	h.	h.	PROPN
ejpam-3547	140	13	o.	o.	PROPN
ejpam-3547	140	14	muslim	muslim	PROPN
ejpam-3547	140	15	/	/	SYM
ejpam-3547	140	16	eur	eur	PROPN
ejpam-3547	140	17	.	.	PUNCT
ejpam-3547	141	1	j.	j.	PROPN
ejpam-3547	141	2	pure	pure	PROPN
ejpam-3547	141	3	appl	appl	PROPN
ejpam-3547	141	4	.	.	PROPN
ejpam-3547	141	5	math	math	PROPN
ejpam-3547	141	6	,	,	PUNCT
ejpam-3547	141	7	12	12	NUM
ejpam-3547	141	8	(	(	PUNCT
ejpam-3547	141	9	4	4	NUM
ejpam-3547	141	10	)	)	PUNCT
ejpam-3547	141	11	(	(	PUNCT
ejpam-3547	141	12	2019	2019	NUM
ejpam-3547	141	13	)	)	PUNCT
ejpam-3547	141	14	,	,	PUNCT
ejpam-3547	141	15	1508	1508	NUM
ejpam-3547	141	16	-	-	SYM
ejpam-3547	141	17	1523	1523	NUM
ejpam-3547	141	18	1513	1513	NUM
ejpam-3547	141	19	lemma	lemma	PROPN
ejpam-3547	141	20	2.7	2.7	NUM
ejpam-3547	141	21	.	.	PUNCT
ejpam-3547	142	1	[	[	X
ejpam-3547	142	2	2	2	X
ejpam-3547	142	3	]	]	PUNCT
ejpam-3547	142	4	for	for	ADP
ejpam-3547	142	5	the	the	DET
ejpam-3547	142	6	function	function	NOUN
ejpam-3547	142	7	f	f	PROPN
ejpam-3547	142	8	(	(	PUNCT
ejpam-3547	142	9	x	x	NOUN
ejpam-3547	142	10	)	)	PUNCT
ejpam-3547	142	11	given	give	VERB
ejpam-3547	142	12	by	by	ADP
ejpam-3547	142	13	:	:	PUNCT
ejpam-3547	142	14	f	f	PROPN
ejpam-3547	142	15	(	(	PUNCT
ejpam-3547	142	16	x	x	X
ejpam-3547	142	17	)	)	PUNCT
ejpam-3547	142	18	=	=	SYM
ejpam-3547	142	19	∫	∫	NOUN
ejpam-3547	142	20	b(x	b(x	NOUN
ejpam-3547	142	21	)	)	PUNCT
ejpam-3547	142	22	a(x	a(x	PROPN
ejpam-3547	142	23	)	)	PUNCT
ejpam-3547	142	24	f(x	f(x	PROPN
ejpam-3547	142	25	,	,	PUNCT
ejpam-3547	142	26	y)dy	y)dy	PROPN
ejpam-3547	142	27	then	then	ADV
ejpam-3547	142	28	the	the	DET
ejpam-3547	142	29	chain	chain	NOUN
ejpam-3547	142	30	rule	rule	NOUN
ejpam-3547	142	31	of	of	ADP
ejpam-3547	142	32	differentiation	differentiation	NOUN
ejpam-3547	142	33	of	of	ADP
ejpam-3547	142	34	the	the	DET
ejpam-3547	142	35	function	function	NOUN
ejpam-3547	142	36	f	f	PROPN
ejpam-3547	142	37	(	(	PUNCT
ejpam-3547	142	38	x	x	X
ejpam-3547	142	39	)	)	PUNCT
ejpam-3547	142	40	gives	give	VERB
ejpam-3547	142	41	:	:	PUNCT
ejpam-3547	142	42	f	f	NUM
ejpam-3547	143	1	′	′	NUM
ejpam-3547	144	1	(	(	PUNCT
ejpam-3547	144	2	x	x	X
ejpam-3547	144	3	)	)	PUNCT
ejpam-3547	144	4	=	=	SYM
ejpam-3547	145	1	b	b	NOUN
ejpam-3547	145	2	′	′	NUM
ejpam-3547	145	3	(	(	PUNCT
ejpam-3547	145	4	x)f(x	x)f(x	PROPN
ejpam-3547	145	5	,	,	PUNCT
ejpam-3547	145	6	b(x))−	b(x))−	NOUN
ejpam-3547	145	7	a′(x)f(x	a′(x)f(x	PROPN
ejpam-3547	145	8	,	,	PUNCT
ejpam-3547	145	9	a(x	a(x	NOUN
ejpam-3547	145	10	)	)	PUNCT
ejpam-3547	145	11	)	)	PUNCT
ejpam-3547	146	1	+	+	CCONJ
ejpam-3547	146	2	∫	∫	PROPN
ejpam-3547	146	3	b(x	b(x	NOUN
ejpam-3547	146	4	)	)	PUNCT
ejpam-3547	146	5	a(x	a(x	PROPN
ejpam-3547	146	6	)	)	PUNCT
ejpam-3547	146	7	∂	∂	PUNCT
ejpam-3547	146	8	∂x	∂x	PROPN
ejpam-3547	146	9	f(x	f(x	PROPN
ejpam-3547	146	10	,	,	PUNCT
ejpam-3547	146	11	y)dy	y)dy	PROPN
ejpam-3547	146	12	3	3	NUM
ejpam-3547	146	13	.	.	PUNCT
ejpam-3547	147	1	the	the	DET
ejpam-3547	147	2	main	main	ADJ
ejpam-3547	147	3	results	result	NOUN
ejpam-3547	147	4	first	first	ADV
ejpam-3547	147	5	,	,	PUNCT
ejpam-3547	147	6	we	we	PRON
ejpam-3547	147	7	prove	prove	VERB
ejpam-3547	147	8	that	that	SCONJ
ejpam-3547	147	9	:	:	PUNCT
ejpam-3547	147	10	wn	wn	INTJ
ejpam-3547	147	11	(	(	PUNCT
ejpam-3547	147	12	r)(f(t);x)→	r)(f(t);x)→	PROPN
ejpam-3547	147	13	f	f	X
ejpam-3547	147	14	(	(	PUNCT
ejpam-3547	147	15	r)(x	r)(x	PROPN
ejpam-3547	147	16	)	)	PUNCT
ejpam-3547	147	17	,	,	PUNCT
ejpam-3547	147	18	as	as	ADP
ejpam-3547	147	19	n→∞	n→∞	NUM
ejpam-3547	147	20	,	,	PUNCT
ejpam-3547	147	21	r	r	NOUN
ejpam-3547	147	22	∈	∈	PROPN
ejpam-3547	147	23	n.	n.	NOUN
ejpam-3547	147	24	theorem	theorem	VERB
ejpam-3547	147	25	3.1	3.1	NUM
ejpam-3547	147	26	.	.	PUNCT
ejpam-3547	147	27	suppose	suppose	VERB
ejpam-3547	147	28	that	that	SCONJ
ejpam-3547	147	29	r	r	PROPN
ejpam-3547	147	30	∈	∈	PROPN
ejpam-3547	147	31	n	n	CCONJ
ejpam-3547	147	32	,	,	PUNCT
ejpam-3547	147	33	f	f	PROPN
ejpam-3547	147	34	∈	∈	PROPN
ejpam-3547	147	35	cα[0,∞	cα[0,∞	PROPN
ejpam-3547	147	36	)	)	PUNCT
ejpam-3547	147	37	and	and	CCONJ
ejpam-3547	147	38	f	f	PROPN
ejpam-3547	147	39	(	(	PUNCT
ejpam-3547	147	40	r+1)(x	r+1)(x	PROPN
ejpam-3547	147	41	)	)	PUNCT
ejpam-3547	147	42	exists	exist	VERB
ejpam-3547	147	43	at	at	ADP
ejpam-3547	147	44	a	a	DET
ejpam-3547	147	45	point	point	NOUN
ejpam-3547	147	46	x	x	X
ejpam-3547	147	47	∈	∈	NOUN
ejpam-3547	147	48	(	(	PUNCT
ejpam-3547	147	49	0,∞	0,∞	NOUN
ejpam-3547	147	50	)	)	PUNCT
ejpam-3547	147	51	,	,	PUNCT
ejpam-3547	147	52	then	then	ADV
ejpam-3547	147	53	:	:	PUNCT
ejpam-3547	147	54	lim	lim	PROPN
ejpam-3547	147	55	n→∞	n→∞	NUM
ejpam-3547	147	56	wn	wn	PROPN
ejpam-3547	147	57	(	(	PUNCT
ejpam-3547	147	58	r)(f(t);x)→	r)(f(t);x)→	PROPN
ejpam-3547	147	59	f	f	X
ejpam-3547	147	60	(	(	PUNCT
ejpam-3547	147	61	r)(x	r)(x	PROPN
ejpam-3547	147	62	)	)	PUNCT
ejpam-3547	147	63	.	.	PUNCT
ejpam-3547	148	1	(	(	PUNCT
ejpam-3547	148	2	3.1	3.1	NUM
ejpam-3547	148	3	)	)	PUNCT
ejpam-3547	148	4	further	far	ADV
ejpam-3547	148	5	,	,	PUNCT
ejpam-3547	148	6	if	if	SCONJ
ejpam-3547	148	7	f	f	PROPN
ejpam-3547	148	8	(	(	PUNCT
ejpam-3547	148	9	r+1)(x	r+1)(x	PROPN
ejpam-3547	148	10	)	)	PUNCT
ejpam-3547	148	11	exists	exist	VERB
ejpam-3547	148	12	and	and	CCONJ
ejpam-3547	148	13	is	be	AUX
ejpam-3547	148	14	continuous	continuous	ADJ
ejpam-3547	148	15	on	on	ADP
ejpam-3547	148	16	(	(	PUNCT
ejpam-3547	148	17	a	a	DET
ejpam-3547	148	18	−	−	PROPN
ejpam-3547	148	19	η	η	PROPN
ejpam-3547	148	20	,	,	PUNCT
ejpam-3547	148	21	b	b	PROPN
ejpam-3547	148	22	+	+	CCONJ
ejpam-3547	148	23	η	η	PROPN
ejpam-3547	148	24	)	)	PUNCT
ejpam-3547	148	25	⊂	⊂	PROPN
ejpam-3547	148	26	(	(	PUNCT
ejpam-3547	148	27	0,∞	0,∞	NOUN
ejpam-3547	148	28	)	)	PUNCT
ejpam-3547	148	29	,	,	PUNCT
ejpam-3547	148	30	η	η	PROPN
ejpam-3547	148	31	>	>	X
ejpam-3547	148	32	0	0	PROPN
ejpam-3547	148	33	,	,	PUNCT
ejpam-3547	148	34	the	the	DET
ejpam-3547	148	35	limit	limit	NOUN
ejpam-3547	148	36	(	(	PUNCT
ejpam-3547	148	37	3.1	3.1	NUM
ejpam-3547	148	38	)	)	PUNCT
ejpam-3547	148	39	holds	hold	VERB
ejpam-3547	148	40	uniformly	uniformly	ADV
ejpam-3547	148	41	on	on	ADP
ejpam-3547	148	42	[	[	X
ejpam-3547	148	43	a	a	X
ejpam-3547	148	44	,	,	PUNCT
ejpam-3547	148	45	b	b	NOUN
ejpam-3547	148	46	]	]	PUNCT
ejpam-3547	148	47	.	.	PUNCT
ejpam-3547	149	1	proof	proof	NOUN
ejpam-3547	149	2	.	.	PUNCT
ejpam-3547	150	1	by	by	ADP
ejpam-3547	150	2	using	use	VERB
ejpam-3547	150	3	taylor	taylor	PROPN
ejpam-3547	150	4	’s	’s	PART
ejpam-3547	150	5	expansion	expansion	NOUN
ejpam-3547	150	6	of	of	ADP
ejpam-3547	150	7	f	f	PROPN
ejpam-3547	150	8	,	,	PUNCT
ejpam-3547	150	9	when	when	SCONJ
ejpam-3547	150	10	ξ	ξ	PROPN
ejpam-3547	150	11	lies	lie	VERB
ejpam-3547	150	12	between	between	ADP
ejpam-3547	150	13	t	t	PROPN
ejpam-3547	150	14	and	and	CCONJ
ejpam-3547	150	15	x	x	X
ejpam-3547	150	16	,	,	PUNCT
ejpam-3547	150	17	we	we	PRON
ejpam-3547	150	18	get	get	VERB
ejpam-3547	150	19	:	:	PUNCT
ejpam-3547	150	20	f(t	f(t	NOUN
ejpam-3547	150	21	)	)	PUNCT
ejpam-3547	151	1	=	=	PUNCT
ejpam-3547	151	2	∑r	∑r	PROPN
ejpam-3547	151	3	i=0	i=0	PROPN
ejpam-3547	151	4	f	f	X
ejpam-3547	151	5	(	(	PUNCT
ejpam-3547	151	6	i)(x	i)(x	PROPN
ejpam-3547	151	7	)	)	PUNCT
ejpam-3547	151	8	i	i	PRON
ejpam-3547	151	9	!	!	PUNCT
ejpam-3547	152	1	(	(	PUNCT
ejpam-3547	152	2	t−	t−	PROPN
ejpam-3547	152	3	x)i	x)i	PUNCT
ejpam-3547	153	1	+	+	CCONJ
ejpam-3547	153	2	f	f	X
ejpam-3547	153	3	(	(	PUNCT
ejpam-3547	153	4	r+1)(ξ	r+1)(ξ	PROPN
ejpam-3547	153	5	)	)	PUNCT
ejpam-3547	153	6	(	(	PUNCT
ejpam-3547	153	7	r	r	NOUN
ejpam-3547	153	8	+	+	NOUN
ejpam-3547	153	9	1	1	NUM
ejpam-3547	153	10	)	)	PUNCT
ejpam-3547	153	11	!	!	PUNCT
ejpam-3547	154	1	(	(	PUNCT
ejpam-3547	154	2	t−	t−	PROPN
ejpam-3547	154	3	x)r+1	x)r+1	PROPN
ejpam-3547	154	4	,	,	PUNCT
ejpam-3547	154	5	operating	operate	VERB
ejpam-3547	154	6	by	by	ADP
ejpam-3547	154	7	the	the	DET
ejpam-3547	154	8	sequence	sequence	NOUN
ejpam-3547	154	9	w	w	PROPN
ejpam-3547	154	10	(	(	PUNCT
ejpam-3547	154	11	r	r	NOUN
ejpam-3547	154	12	)	)	PUNCT
ejpam-3547	154	13	n	n	NOUN
ejpam-3547	154	14	,	,	PUNCT
ejpam-3547	154	15	we	we	PRON
ejpam-3547	154	16	get	get	VERB
ejpam-3547	154	17	:	:	PUNCT
ejpam-3547	154	18	wn	wn	PROPN
ejpam-3547	154	19	(	(	PUNCT
ejpam-3547	154	20	r)(f(t);x	r)(f(t);x	PROPN
ejpam-3547	154	21	)	)	PUNCT
ejpam-3547	154	22	=	=	SYM
ejpam-3547	155	1	r∑	r∑	ADP
ejpam-3547	155	2	i=0	i=0	PROPN
ejpam-3547	155	3	f	f	X
ejpam-3547	155	4	(	(	PUNCT
ejpam-3547	155	5	i)(x	i)(x	PROPN
ejpam-3547	155	6	)	)	PUNCT
ejpam-3547	155	7	i	i	PRON
ejpam-3547	155	8	!	!	PUNCT
ejpam-3547	156	1	(	(	PUNCT
ejpam-3547	156	2	−1)iwn	−1)iwn	PROPN
ejpam-3547	156	3	(	(	PUNCT
ejpam-3547	156	4	r)((x−	r)((x−	PROPN
ejpam-3547	156	5	t)i;x	t)i;x	PROPN
ejpam-3547	156	6	)	)	PUNCT
ejpam-3547	157	1	+	+	NUM
ejpam-3547	157	2	f	f	X
ejpam-3547	157	3	(	(	PUNCT
ejpam-3547	157	4	r+1)(ξ	r+1)(ξ	PROPN
ejpam-3547	157	5	)	)	PUNCT
ejpam-3547	157	6	(	(	PUNCT
ejpam-3547	157	7	r	r	NOUN
ejpam-3547	157	8	+	+	NOUN
ejpam-3547	157	9	1	1	NUM
ejpam-3547	157	10	)	)	PUNCT
ejpam-3547	157	11	!	!	PUNCT
ejpam-3547	158	1	(	(	PUNCT
ejpam-3547	158	2	−1)r+1wn	−1)r+1wn	X
ejpam-3547	158	3	(	(	PUNCT
ejpam-3547	158	4	r)((x−	r)((x−	NOUN
ejpam-3547	158	5	t)r+1;x	t)r+1;x	PROPN
ejpam-3547	158	6	)	)	PUNCT
ejpam-3547	158	7	:	:	PUNCT
ejpam-3547	159	1	=	=	SYM
ejpam-3547	159	2	σ1	σ1	PROPN
ejpam-3547	159	3	+	+	CCONJ
ejpam-3547	159	4	σ2	σ2	PROPN
ejpam-3547	159	5	σ1	σ1	PROPN
ejpam-3547	159	6	:	:	PUNCT
ejpam-3547	159	7	=	=	SYM
ejpam-3547	159	8	r∑	r∑	X
ejpam-3547	159	9	i=0	i=0	PROPN
ejpam-3547	159	10	f	f	X
ejpam-3547	159	11	(	(	PUNCT
ejpam-3547	159	12	i)(x	i)(x	PROPN
ejpam-3547	159	13	)	)	PUNCT
ejpam-3547	159	14	i	i	PRON
ejpam-3547	159	15	!	!	PUNCT
ejpam-3547	160	1	(	(	PUNCT
ejpam-3547	160	2	−1)iwn	−1)iwn	PROPN
ejpam-3547	160	3	(	(	PUNCT
ejpam-3547	160	4	r)((x−	r)((x−	PROPN
ejpam-3547	160	5	t)i;x	t)i;x	PROPN
ejpam-3547	160	6	)	)	PUNCT
ejpam-3547	161	1	=	=	SYM
ejpam-3547	161	2	r∑	r∑	ADP
ejpam-3547	161	3	i=0	i=0	PROPN
ejpam-3547	161	4	f	f	X
ejpam-3547	161	5	(	(	PUNCT
ejpam-3547	161	6	i)(x	i)(x	PROPN
ejpam-3547	161	7	)	)	PUNCT
ejpam-3547	161	8	i	i	PRON
ejpam-3547	161	9	!	!	PUNCT
ejpam-3547	162	1	(	(	PUNCT
ejpam-3547	162	2	−1)i	−1)i	X
ejpam-3547	162	3	i∑	i∑	ADJ
ejpam-3547	162	4	j=0	j=0	PROPN
ejpam-3547	162	5	(	(	PUNCT
ejpam-3547	162	6	i	i	PRON
ejpam-3547	162	7	j	j	PROPN
ejpam-3547	162	8	)	)	PUNCT
ejpam-3547	162	9	x(i−j)(−1)jwn	x(i−j)(−1)jwn	PROPN
ejpam-3547	162	10	(	(	PUNCT
ejpam-3547	162	11	r)(tj	r)(tj	X
ejpam-3547	162	12	;	;	PUNCT
ejpam-3547	162	13	x	x	X
ejpam-3547	162	14	)	)	PUNCT
ejpam-3547	162	15	=	=	SYM
ejpam-3547	162	16	f	f	PROPN
ejpam-3547	162	17	(	(	PUNCT
ejpam-3547	162	18	r)(x	r)(x	PROPN
ejpam-3547	162	19	)	)	PUNCT
ejpam-3547	162	20	r	r	NOUN
ejpam-3547	162	21	!	!	PUNCT
ejpam-3547	162	22	wn	wn	PROPN
ejpam-3547	162	23	(	(	PUNCT
ejpam-3547	162	24	r)(tr;x	r)(tr;x	PROPN
ejpam-3547	162	25	)	)	PUNCT
ejpam-3547	162	26	when	when	SCONJ
ejpam-3547	162	27	j	j	PROPN
ejpam-3547	162	28	<	<	X
ejpam-3547	162	29	r	r	X
ejpam-3547	162	30	then	then	ADV
ejpam-3547	162	31	wn	wn	PROPN
ejpam-3547	162	32	(	(	PUNCT
ejpam-3547	162	33	r)(tj	r)(tj	NOUN
ejpam-3547	162	34	;	;	PUNCT
ejpam-3547	162	35	x	x	X
ejpam-3547	162	36	)	)	PUNCT
ejpam-3547	162	37	−→	−→	NOUN
ejpam-3547	162	38	0	0	NUM
ejpam-3547	162	39	as	as	ADP
ejpam-3547	162	40	n	n	NUM
ejpam-3547	162	41	−→∞.	−→∞.	PUNCT
ejpam-3547	162	42	a.	a.	PROPN
ejpam-3547	162	43	j.	j.	PROPN
ejpam-3547	162	44	mohammad	mohammad	PROPN
ejpam-3547	162	45	,	,	PUNCT
ejpam-3547	162	46	h.	h.	PROPN
ejpam-3547	162	47	o.	o.	PROPN
ejpam-3547	162	48	muslim	muslim	PROPN
ejpam-3547	162	49	/	/	SYM
ejpam-3547	162	50	eur	eur	PROPN
ejpam-3547	162	51	.	.	PUNCT
ejpam-3547	163	1	j.	j.	PROPN
ejpam-3547	163	2	pure	pure	PROPN
ejpam-3547	163	3	appl	appl	PROPN
ejpam-3547	163	4	.	.	PROPN
ejpam-3547	163	5	math	math	PROPN
ejpam-3547	163	6	,	,	PUNCT
ejpam-3547	163	7	12	12	NUM
ejpam-3547	163	8	(	(	PUNCT
ejpam-3547	163	9	4	4	NUM
ejpam-3547	163	10	)	)	PUNCT
ejpam-3547	163	11	(	(	PUNCT
ejpam-3547	163	12	2019	2019	NUM
ejpam-3547	163	13	)	)	PUNCT
ejpam-3547	163	14	,	,	PUNCT
ejpam-3547	163	15	1508	1508	NUM
ejpam-3547	163	16	-	-	SYM
ejpam-3547	163	17	1523	1523	NUM
ejpam-3547	163	18	1514	1514	NUM
ejpam-3547	163	19	using	use	VERB
ejpam-3547	163	20	lemma	lemma	PROPN
ejpam-3547	163	21	2.3	2.3	NUM
ejpam-3547	163	22	,	,	PUNCT
ejpam-3547	163	23	lemma	lemma	PROPN
ejpam-3547	163	24	2.5	2.5	NUM
ejpam-3547	163	25	,	,	PUNCT
ejpam-3547	163	26	and	and	CCONJ
ejpam-3547	163	27	lemma	lemma	PROPN
ejpam-3547	163	28	2.6	2.6	NUM
ejpam-3547	163	29	we	we	PRON
ejpam-3547	163	30	get	get	VERB
ejpam-3547	163	31	:	:	PUNCT
ejpam-3547	163	32	σ1	σ1	NOUN
ejpam-3547	163	33	=	=	SYM
ejpam-3547	163	34	f	f	PROPN
ejpam-3547	163	35	(	(	PUNCT
ejpam-3547	163	36	r)(x	r)(x	PROPN
ejpam-3547	163	37	)	)	PUNCT
ejpam-3547	164	1	r	r	NOUN
ejpam-3547	164	2	!	!	PUNCT
ejpam-3547	164	3	{	{	PUNCT
ejpam-3547	164	4	r	r	X
ejpam-3547	164	5	!	!	PUNCT
ejpam-3547	164	6	(	(	PUNCT
ejpam-3547	164	7	sinh(nx	sinh(nx	NOUN
ejpam-3547	164	8	)	)	PUNCT
ejpam-3547	164	9	(	(	PUNCT
ejpam-3547	164	10	δ0	δ0	NOUN
ejpam-3547	164	11	+	+	CCONJ
ejpam-3547	164	12	sinh(nx	sinh(nx	NOUN
ejpam-3547	164	13	)	)	PUNCT
ejpam-3547	164	14	)	)	PUNCT
ejpam-3547	164	15	)	)	PUNCT
ejpam-3547	165	1	+	+	CCONJ
ejpam-3547	165	2	rr!x	rr!x	PROPN
ejpam-3547	165	3	ncosh(nx	ncosh(nx	NOUN
ejpam-3547	165	4	)	)	PUNCT
ejpam-3547	165	5	(	(	PUNCT
ejpam-3547	165	6	δ0	δ0	NOUN
ejpam-3547	165	7	+	+	CCONJ
ejpam-3547	165	8	sinh(nx	sinh(nx	NOUN
ejpam-3547	165	9	)	)	PUNCT
ejpam-3547	165	10	)	)	PUNCT
ejpam-3547	166	1	(	(	PUNCT
ejpam-3547	166	2	1−	1−	NUM
ejpam-3547	166	3	sinh(nx	sinh(nx	NOUN
ejpam-3547	166	4	)	)	PUNCT
ejpam-3547	166	5	(	(	PUNCT
ejpam-3547	166	6	δ0	δ0	NOUN
ejpam-3547	166	7	+	+	CCONJ
ejpam-3547	166	8	sinh(nx	sinh(nx	NOUN
ejpam-3547	166	9	)	)	PUNCT
ejpam-3547	166	10	)	)	PUNCT
ejpam-3547	166	11	)	)	PUNCT
ejpam-3547	167	1	+	+	CCONJ
ejpam-3547	167	2	...	...	PUNCT
ejpam-3547	168	1	+	+	CCONJ
ejpam-3547	168	2	xr	xr	PROPN
ejpam-3547	168	3	dr	dr	PROPN
ejpam-3547	168	4	dxr	dxr	PROPN
ejpam-3547	168	5	(	(	PUNCT
ejpam-3547	168	6	sinh(nx	sinh(nx	NOUN
ejpam-3547	168	7	)	)	PUNCT
ejpam-3547	168	8	(	(	PUNCT
ejpam-3547	168	9	δ0	δ0	NOUN
ejpam-3547	168	10	+	+	CCONJ
ejpam-3547	168	11	sinh(nx	sinh(nx	NOUN
ejpam-3547	168	12	)	)	PUNCT
ejpam-3547	168	13	)	)	PUNCT
ejpam-3547	168	14	)	)	PUNCT
ejpam-3547	169	1	−	−	PROPN
ejpam-3547	169	2	rr	rr	NOUN
ejpam-3547	169	3	!	!	PUNCT
ejpam-3547	170	1	(	(	PUNCT
ejpam-3547	170	2	sinh(nx	sinh(nx	NOUN
ejpam-3547	170	3	)	)	PUNCT
ejpam-3547	170	4	(	(	PUNCT
ejpam-3547	170	5	δ0	δ0	NOUN
ejpam-3547	170	6	+	+	CCONJ
ejpam-3547	170	7	sinh(nx	sinh(nx	NOUN
ejpam-3547	170	8	)	)	PUNCT
ejpam-3547	170	9	)	)	PUNCT
ejpam-3547	170	10	−	−	PROPN
ejpam-3547	171	1	cosh2(nx	cosh2(nx	NOUN
ejpam-3547	171	2	)	)	PUNCT
ejpam-3547	171	3	(	(	PUNCT
ejpam-3547	171	4	δ0	δ0	NOUN
ejpam-3547	171	5	+	+	CCONJ
ejpam-3547	171	6	sinh(nx))2	sinh(nx))2	NOUN
ejpam-3547	171	7	)	)	PUNCT
ejpam-3547	171	8	−	−	PROPN
ejpam-3547	171	9	...	...	PUNCT
ejpam-3547	172	1	−	−	PUNCT
ejpam-3547	172	2	r	r	NOUN
ejpam-3547	173	1	n	n	PROPN
ejpam-3547	173	2	xr−1	xr−1	PROPN
ejpam-3547	173	3	dr	dr	PROPN
ejpam-3547	173	4	dxr	dxr	PROPN
ejpam-3547	173	5	(	(	PUNCT
ejpam-3547	173	6	cosh(nx	cosh(nx	NOUN
ejpam-3547	173	7	)	)	PUNCT
ejpam-3547	173	8	(	(	PUNCT
ejpam-3547	173	9	δ0	δ0	NOUN
ejpam-3547	173	10	+	+	CCONJ
ejpam-3547	173	11	sinh(nx	sinh(nx	NOUN
ejpam-3547	173	12	)	)	PUNCT
ejpam-3547	173	13	)	)	PUNCT
ejpam-3547	173	14	)	)	PUNCT
ejpam-3547	174	1	}	}	PUNCT
ejpam-3547	174	2	−→	−→	NOUN
ejpam-3547	174	3	f	f	X
ejpam-3547	174	4	(	(	PUNCT
ejpam-3547	174	5	r)(x	r)(x	PROPN
ejpam-3547	174	6	)	)	PUNCT
ejpam-3547	174	7	as	as	ADP
ejpam-3547	174	8	n	n	NUM
ejpam-3547	174	9	−→∞.	−→∞.	NOUN
ejpam-3547	174	10	σ2	σ2	PROPN
ejpam-3547	174	11	=	=	SYM
ejpam-3547	174	12	f	f	PROPN
ejpam-3547	174	13	(	(	PUNCT
ejpam-3547	174	14	r+1)(ξ	r+1)(ξ	PROPN
ejpam-3547	174	15	)	)	PUNCT
ejpam-3547	174	16	(	(	PUNCT
ejpam-3547	174	17	r	r	NOUN
ejpam-3547	174	18	+	+	NOUN
ejpam-3547	174	19	1	1	NUM
ejpam-3547	174	20	)	)	PUNCT
ejpam-3547	174	21	!	!	PUNCT
ejpam-3547	175	1	(	(	PUNCT
ejpam-3547	175	2	−1)r+1w	−1)r+1w	INTJ
ejpam-3547	175	3	(	(	PUNCT
ejpam-3547	175	4	r	r	NOUN
ejpam-3547	175	5	)	)	PUNCT
ejpam-3547	175	6	n	n	NOUN
ejpam-3547	175	7	(	(	PUNCT
ejpam-3547	175	8	(	(	PUNCT
ejpam-3547	175	9	x−	x−	PROPN
ejpam-3547	175	10	t)r+1	t)r+1	PROPN
ejpam-3547	175	11	;	;	PUNCT
ejpam-3547	175	12	x	x	X
ejpam-3547	175	13	)	)	PUNCT
ejpam-3547	175	14	=	=	SYM
ejpam-3547	175	15	f	f	PROPN
ejpam-3547	175	16	(	(	PUNCT
ejpam-3547	175	17	r+1)(ξ	r+1)(ξ	PROPN
ejpam-3547	175	18	)	)	PUNCT
ejpam-3547	175	19	(	(	PUNCT
ejpam-3547	175	20	r	r	NOUN
ejpam-3547	175	21	+	+	NOUN
ejpam-3547	175	22	1	1	NUM
ejpam-3547	175	23	)	)	PUNCT
ejpam-3547	175	24	!	!	PUNCT
ejpam-3547	176	1	(	(	PUNCT
ejpam-3547	176	2	−1)r+1	−1)r+1	INTJ
ejpam-3547	176	3	d	d	X
ejpam-3547	176	4	r	r	NOUN
ejpam-3547	176	5	dxr	dxr	ADJ
ejpam-3547	176	6	{	{	PUNCT
ejpam-3547	176	7	n	n	PROPN
ejpam-3547	176	8	(	(	PUNCT
ejpam-3547	176	9	δ0	δ0	NOUN
ejpam-3547	176	10	+	+	X
ejpam-3547	176	11	sinh(nx	sinh(nx	NOUN
ejpam-3547	176	12	)	)	PUNCT
ejpam-3547	176	13	)	)	PUNCT
ejpam-3547	176	14	∫	∫	PROPN
ejpam-3547	176	15	x	x	SYM
ejpam-3547	176	16	0	0	NUM
ejpam-3547	176	17	cosh(nt	cosh(nt	PROPN
ejpam-3547	176	18	)	)	PUNCT
ejpam-3547	176	19	(	(	PUNCT
ejpam-3547	176	20	x−	x−	PROPN
ejpam-3547	176	21	t)r+1	t)r+1	PROPN
ejpam-3547	176	22	dt	dt	PROPN
ejpam-3547	176	23	}	}	PUNCT
ejpam-3547	176	24	.	.	PUNCT
ejpam-3547	177	1	using	use	VERB
ejpam-3547	177	2	lemma	lemma	PROPN
ejpam-3547	177	3	2.5	2.5	NUM
ejpam-3547	177	4	,	,	PUNCT
ejpam-3547	177	5	lemma	lemma	PROPN
ejpam-3547	177	6	2.6	2.6	NUM
ejpam-3547	177	7	and	and	CCONJ
ejpam-3547	177	8	lemma	lemma	PROPN
ejpam-3547	177	9	2.7	2.7	NUM
ejpam-3547	177	10	,	,	PUNCT
ejpam-3547	177	11	we	we	PRON
ejpam-3547	177	12	obtain	obtain	VERB
ejpam-3547	177	13	:	:	PUNCT
ejpam-3547	177	14	σ2	σ2	PROPN
ejpam-3547	177	15	=	=	SYM
ejpam-3547	177	16	f	f	PROPN
ejpam-3547	177	17	(	(	PUNCT
ejpam-3547	177	18	r+1)(ξ	r+1)(ξ	PROPN
ejpam-3547	177	19	)	)	PUNCT
ejpam-3547	177	20	(	(	PUNCT
ejpam-3547	177	21	r	r	NOUN
ejpam-3547	177	22	+	+	NOUN
ejpam-3547	177	23	1	1	NUM
ejpam-3547	177	24	)	)	PUNCT
ejpam-3547	177	25	!	!	PUNCT
ejpam-3547	178	1	(	(	PUNCT
ejpam-3547	178	2	−1)r+1	−1)r+1	INTJ
ejpam-3547	178	3	r∑	r∑	X
ejpam-3547	178	4	l=0	l=0	PROPN
ejpam-3547	178	5	(	(	PUNCT
ejpam-3547	178	6	r	r	NOUN
ejpam-3547	178	7	l	l	NOUN
ejpam-3547	178	8	)	)	PUNCT
ejpam-3547	179	1	dr−1	dr−1	PROPN
ejpam-3547	179	2	dxr−1	dxr−1	PROPN
ejpam-3547	179	3	(	(	PUNCT
ejpam-3547	179	4	n	n	CCONJ
ejpam-3547	179	5	(	(	PUNCT
ejpam-3547	179	6	δ0	δ0	NOUN
ejpam-3547	179	7	+	+	X
ejpam-3547	179	8	sinh(nx	sinh(nx	NOUN
ejpam-3547	179	9	)	)	PUNCT
ejpam-3547	179	10	)	)	PUNCT
ejpam-3547	179	11	)	)	PUNCT
ejpam-3547	180	1	dl	dl	PROPN
ejpam-3547	180	2	dxl	dxl	PROPN
ejpam-3547	180	3	(	(	PUNCT
ejpam-3547	180	4	∫	∫	PROPN
ejpam-3547	180	5	x	x	SYM
ejpam-3547	180	6	0	0	NUM
ejpam-3547	180	7	cosh(nt	cosh(nt	PROPN
ejpam-3547	180	8	)	)	PUNCT
ejpam-3547	180	9	(	(	PUNCT
ejpam-3547	180	10	x−	x−	PROPN
ejpam-3547	180	11	t)r+1	t)r+1	PROPN
ejpam-3547	180	12	dt	dt	PROPN
ejpam-3547	180	13	)	)	PUNCT
ejpam-3547	181	1	=	=	SYM
ejpam-3547	181	2	f	f	PROPN
ejpam-3547	181	3	(	(	PUNCT
ejpam-3547	181	4	r+1)(ξ	r+1)(ξ	PROPN
ejpam-3547	181	5	)	)	PUNCT
ejpam-3547	181	6	(	(	PUNCT
ejpam-3547	181	7	r	r	NOUN
ejpam-3547	181	8	+	+	NOUN
ejpam-3547	181	9	1	1	NUM
ejpam-3547	181	10	)	)	PUNCT
ejpam-3547	181	11	!	!	PUNCT
ejpam-3547	182	1	(	(	PUNCT
ejpam-3547	182	2	−1)r+1	−1)r+1	INTJ
ejpam-3547	182	3	d	d	X
ejpam-3547	182	4	r	r	NOUN
ejpam-3547	182	5	dxr	dxr	NOUN
ejpam-3547	182	6	(	(	PUNCT
ejpam-3547	182	7	n	n	CCONJ
ejpam-3547	182	8	(	(	PUNCT
ejpam-3547	182	9	δ0	δ0	NOUN
ejpam-3547	182	10	+	+	X
ejpam-3547	182	11	sinh(nx	sinh(nx	NOUN
ejpam-3547	182	12	)	)	PUNCT
ejpam-3547	182	13	)	)	PUNCT
ejpam-3547	182	14	)	)	PUNCT
ejpam-3547	182	15	∫	∫	PROPN
ejpam-3547	182	16	x	x	SYM
ejpam-3547	182	17	0	0	NUM
ejpam-3547	182	18	cosh(nt	cosh(nt	PROPN
ejpam-3547	182	19	)	)	PUNCT
ejpam-3547	182	20	(	(	PUNCT
ejpam-3547	182	21	x−	x−	PROPN
ejpam-3547	182	22	t)r+1	t)r+1	PROPN
ejpam-3547	182	23	dt	dt	PROPN
ejpam-3547	183	1	+	+	CCONJ
ejpam-3547	183	2	f	f	X
ejpam-3547	183	3	(	(	PUNCT
ejpam-3547	183	4	r+1)(ξ	r+1)(ξ	PROPN
ejpam-3547	183	5	)	)	PUNCT
ejpam-3547	183	6	(	(	PUNCT
ejpam-3547	183	7	r	r	NOUN
ejpam-3547	183	8	+	+	NOUN
ejpam-3547	183	9	1	1	NUM
ejpam-3547	183	10	)	)	PUNCT
ejpam-3547	183	11	!	!	PUNCT
ejpam-3547	184	1	(	(	PUNCT
ejpam-3547	184	2	−1)r+1	−1)r+1	INTJ
ejpam-3547	184	3	r∑	r∑	NOUN
ejpam-3547	184	4	l=1	l=1	PROPN
ejpam-3547	184	5	(	(	PUNCT
ejpam-3547	184	6	r	r	NOUN
ejpam-3547	184	7	l	l	NOUN
ejpam-3547	184	8	)	)	PUNCT
ejpam-3547	185	1	dr−1	dr−1	PROPN
ejpam-3547	185	2	dxr−1	dxr−1	PROPN
ejpam-3547	185	3	(	(	PUNCT
ejpam-3547	185	4	n	n	CCONJ
ejpam-3547	185	5	(	(	PUNCT
ejpam-3547	185	6	δ0	δ0	NOUN
ejpam-3547	185	7	+	+	X
ejpam-3547	185	8	sinh(nx	sinh(nx	NOUN
ejpam-3547	185	9	)	)	PUNCT
ejpam-3547	185	10	)	)	PUNCT
ejpam-3547	185	11	)	)	PUNCT
ejpam-3547	186	1	dl	dl	PROPN
ejpam-3547	186	2	dxl	dxl	PROPN
ejpam-3547	186	3	(	(	PUNCT
ejpam-3547	186	4	∫	∫	PROPN
ejpam-3547	186	5	x	x	SYM
ejpam-3547	186	6	0	0	NUM
ejpam-3547	186	7	cosh(nt	cosh(nt	PROPN
ejpam-3547	186	8	)	)	PUNCT
ejpam-3547	186	9	(	(	PUNCT
ejpam-3547	186	10	x−	x−	PROPN
ejpam-3547	186	11	t)r+1	t)r+1	PROPN
ejpam-3547	186	12	dt	dt	NOUN
ejpam-3547	186	13	)	)	PUNCT
ejpam-3547	186	14	=	=	PROPN
ejpam-3547	186	15	i1	i1	PROPN
ejpam-3547	186	16	+	+	CCONJ
ejpam-3547	186	17	i2	i2	PROPN
ejpam-3547	186	18	.	.	PUNCT
ejpam-3547	187	1	i1	i1	PROPN
ejpam-3547	187	2	≤	≤	PROPN
ejpam-3547	187	3	∣∣∣∣∣f	∣∣∣∣∣f	NOUN
ejpam-3547	187	4	(	(	PUNCT
ejpam-3547	187	5	r+1)(ξ	r+1)(ξ	PROPN
ejpam-3547	187	6	)	)	PUNCT
ejpam-3547	187	7	(	(	PUNCT
ejpam-3547	187	8	r	r	NOUN
ejpam-3547	187	9	+	+	NOUN
ejpam-3547	187	10	1	1	NUM
ejpam-3547	187	11	)	)	PUNCT
ejpam-3547	187	12	!	!	PUNCT
ejpam-3547	188	1	∣∣∣∣∣	∣∣∣∣∣	PUNCT
ejpam-3547	189	1	r∑	r∑	NOUN
ejpam-3547	189	2	l=0	l=0	PROPN
ejpam-3547	190	1	(	(	PUNCT
ejpam-3547	190	2	r	r	NOUN
ejpam-3547	190	3	+	+	NOUN
ejpam-3547	190	4	1	1	NUM
ejpam-3547	190	5	l	l	NOUN
ejpam-3547	190	6	+	+	NUM
ejpam-3547	190	7	1	1	NUM
ejpam-3547	190	8	)	)	PUNCT
ejpam-3547	190	9	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3547	191	1	n	n	CCONJ
ejpam-3547	191	2	(	(	PUNCT
ejpam-3547	191	3	δ0	δ0	NOUN
ejpam-3547	191	4	+	+	CCONJ
ejpam-3547	191	5	sinh(nx))l+1	sinh(nx))l+1	PROPN
ejpam-3547	191	6	dr	dr	PROPN
ejpam-3547	191	7	dxr	dxr	PROPN
ejpam-3547	191	8	(	(	PUNCT
ejpam-3547	191	9	δ0	δ0	NOUN
ejpam-3547	191	10	+	+	CCONJ
ejpam-3547	191	11	sinh(nx))l	sinh(nx))l	NOUN
ejpam-3547	191	12	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3547	191	13	∫	∫	PROPN
ejpam-3547	191	14	x	x	SYM
ejpam-3547	191	15	0	0	NUM
ejpam-3547	191	16	cosh(nt	cosh(nt	PROPN
ejpam-3547	191	17	)	)	PUNCT
ejpam-3547	191	18	∣∣∣(−(x−	∣∣∣(−(x−	NOUN
ejpam-3547	191	19	t))r+1	t))r+1	ADJ
ejpam-3547	191	20	∣∣∣	∣∣∣	NOUN
ejpam-3547	191	21	dt	dt	X
ejpam-3547	191	22	.	.	PUNCT
ejpam-3547	192	1	by	by	ADP
ejpam-3547	192	2	schwartz	schwartz	PROPN
ejpam-3547	192	3	inequality	inequality	PROPN
ejpam-3547	192	4	,	,	PUNCT
ejpam-3547	192	5	we	we	PRON
ejpam-3547	192	6	have	have	AUX
ejpam-3547	192	7	:	:	PUNCT
ejpam-3547	192	8	|i1|	|i1|	VERB
ejpam-3547	192	9	≤	≤	ADJ
ejpam-3547	192	10	∣∣∣∣∣f	∣∣∣∣∣f	NOUN
ejpam-3547	192	11	(	(	PUNCT
ejpam-3547	192	12	r+1)(ξ	r+1)(ξ	PROPN
ejpam-3547	192	13	)	)	PUNCT
ejpam-3547	192	14	(	(	PUNCT
ejpam-3547	192	15	r	r	NOUN
ejpam-3547	192	16	+	+	NOUN
ejpam-3547	192	17	1	1	NUM
ejpam-3547	192	18	)	)	PUNCT
ejpam-3547	192	19	!	!	PUNCT
ejpam-3547	193	1	∣∣∣∣∣	∣∣∣∣∣	PUNCT
ejpam-3547	194	1	r∑	r∑	NOUN
ejpam-3547	194	2	l=0	l=0	PROPN
ejpam-3547	195	1	(	(	PUNCT
ejpam-3547	195	2	r	r	NOUN
ejpam-3547	195	3	+	+	NOUN
ejpam-3547	195	4	1	1	NUM
ejpam-3547	195	5	l	l	NOUN
ejpam-3547	195	6	+	+	NUM
ejpam-3547	195	7	1	1	NUM
ejpam-3547	195	8	)	)	PUNCT
ejpam-3547	195	9	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3547	195	10	1	1	NUM
ejpam-3547	195	11	(	(	PUNCT
ejpam-3547	195	12	δ0	δ0	NOUN
ejpam-3547	195	13	+	+	CCONJ
ejpam-3547	195	14	sinh(nx))l	sinh(nx))l	NOUN
ejpam-3547	195	15	dr	dr	PROPN
ejpam-3547	195	16	dxr	dxr	PROPN
ejpam-3547	195	17	(	(	PUNCT
ejpam-3547	195	18	δ0	δ0	NOUN
ejpam-3547	195	19	+	+	CCONJ
ejpam-3547	195	20	sinh(nx))l	sinh(nx))l	NOUN
ejpam-3547	195	21	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3547	195	22	×	×	NOUN
ejpam-3547	195	23	(	(	PUNCT
ejpam-3547	195	24	n	n	CCONJ
ejpam-3547	195	25	(	(	PUNCT
ejpam-3547	195	26	δ0	δ0	NOUN
ejpam-3547	195	27	+	+	X
ejpam-3547	195	28	sinh(nx	sinh(nx	NOUN
ejpam-3547	195	29	)	)	PUNCT
ejpam-3547	195	30	)	)	PUNCT
ejpam-3547	195	31	∫	∫	PROPN
ejpam-3547	196	1	x	x	SYM
ejpam-3547	196	2	0	0	NUM
ejpam-3547	196	3	cosh(nx)dt	cosh(nx)dt	PROPN
ejpam-3547	196	4	)	)	PUNCT
ejpam-3547	196	5	1/2	1/2	NUM
ejpam-3547	196	6	(	(	PUNCT
ejpam-3547	196	7	n	n	CCONJ
ejpam-3547	196	8	(	(	PUNCT
ejpam-3547	196	9	δ0	δ0	NOUN
ejpam-3547	196	10	+	+	X
ejpam-3547	196	11	sinh(nx	sinh(nx	NOUN
ejpam-3547	196	12	)	)	PUNCT
ejpam-3547	196	13	)	)	PUNCT
ejpam-3547	196	14	∫	∫	PROPN
ejpam-3547	197	1	x	x	SYM
ejpam-3547	197	2	0	0	NUM
ejpam-3547	197	3	cosh(nt	cosh(nt	NOUN
ejpam-3547	197	4	)	)	PUNCT
ejpam-3547	197	5	(	(	PUNCT
ejpam-3547	197	6	−(x−	−(x−	NOUN
ejpam-3547	197	7	t))2(r+1	t))2(r+1	NOUN
ejpam-3547	197	8	)	)	PUNCT
ejpam-3547	197	9	dt	dt	NOUN
ejpam-3547	197	10	)	)	PUNCT
ejpam-3547	197	11	1/2	1/2	NUM
ejpam-3547	197	12	=	=	SYM
ejpam-3547	197	13	m1n	m1n	PROPN
ejpam-3547	197	14	ro(1)o(n−(r+1	ro(1)o(n−(r+1	PROPN
ejpam-3547	197	15	)	)	PUNCT
ejpam-3547	197	16	)	)	PUNCT
ejpam-3547	198	1	=	=	SYM
ejpam-3547	198	2	m1o(1	m1o(1	NOUN
ejpam-3547	198	3	)	)	PUNCT
ejpam-3547	198	4	.	.	PUNCT
ejpam-3547	199	1	now	now	ADV
ejpam-3547	199	2	,	,	PUNCT
ejpam-3547	199	3	using	use	VERB
ejpam-3547	199	4	lemma	lemma	PROPN
ejpam-3547	199	5	2.5	2.5	NUM
ejpam-3547	199	6	and	and	CCONJ
ejpam-3547	199	7	lemma	lemma	PROPN
ejpam-3547	199	8	2.7	2.7	NUM
ejpam-3547	199	9	,	,	PUNCT
ejpam-3547	199	10	we	we	PRON
ejpam-3547	199	11	obtain	obtain	AUX
ejpam-3547	199	12	:	:	PUNCT
ejpam-3547	199	13	|i2|	|i2|	VERB
ejpam-3547	199	14	≤	≤	NUM
ejpam-3547	199	15	∣∣∣∣∣f	∣∣∣∣∣f	NOUN
ejpam-3547	199	16	(	(	PUNCT
ejpam-3547	199	17	r+1)(ξ	r+1)(ξ	PROPN
ejpam-3547	199	18	)	)	PUNCT
ejpam-3547	199	19	(	(	PUNCT
ejpam-3547	199	20	r	r	NOUN
ejpam-3547	199	21	+	+	NOUN
ejpam-3547	199	22	1	1	NUM
ejpam-3547	199	23	)	)	PUNCT
ejpam-3547	199	24	!	!	PUNCT
ejpam-3547	200	1	∣∣∣∣∣	∣∣∣∣∣	PUNCT
ejpam-3547	201	1	r∑	r∑	NOUN
ejpam-3547	202	1	l=1	l=1	PROPN
ejpam-3547	202	2	(	(	PUNCT
ejpam-3547	202	3	r	r	NOUN
ejpam-3547	202	4	l	l	NOUN
ejpam-3547	202	5	)	)	PUNCT
ejpam-3547	202	6	r−1∑	r−1∑	PROPN
ejpam-3547	202	7	l1=0	l1=0	PROPN
ejpam-3547	202	8	(	(	PUNCT
ejpam-3547	202	9	r	r	NOUN
ejpam-3547	202	10	−	−	PROPN
ejpam-3547	202	11	l	l	NOUN
ejpam-3547	202	12	+	+	SYM
ejpam-3547	202	13	1	1	NUM
ejpam-3547	202	14	l1	l1	NOUN
ejpam-3547	202	15	+	+	CCONJ
ejpam-3547	202	16	1	1	NUM
ejpam-3547	202	17	)	)	PUNCT
ejpam-3547	202	18	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3547	203	1	n	n	CCONJ
ejpam-3547	203	2	(	(	PUNCT
ejpam-3547	203	3	δ0	δ0	NOUN
ejpam-3547	203	4	+	+	CCONJ
ejpam-3547	203	5	sinh(nx))l1	sinh(nx))l1	ADJ
ejpam-3547	203	6	+	+	PROPN
ejpam-3547	203	7	1	1	NUM
ejpam-3547	203	8	dr−1	dr−1	PROPN
ejpam-3547	203	9	dxr−1	dxr−1	PROPN
ejpam-3547	203	10	(	(	PUNCT
ejpam-3547	203	11	δ0	δ0	NOUN
ejpam-3547	203	12	+	+	CCONJ
ejpam-3547	203	13	sinh(nx))l1	sinh(nx))l1	NOUN
ejpam-3547	203	14	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-3547	203	15	a.	a.	NOUN
ejpam-3547	203	16	j.	j.	PROPN
ejpam-3547	203	17	mohammad	mohammad	PROPN
ejpam-3547	203	18	,	,	PUNCT
ejpam-3547	203	19	h.	h.	PROPN
ejpam-3547	203	20	o.	o.	PROPN
ejpam-3547	203	21	muslim	muslim	PROPN
ejpam-3547	203	22	/	/	SYM
ejpam-3547	203	23	eur	eur	PROPN
ejpam-3547	203	24	.	.	PUNCT
ejpam-3547	204	1	j.	j.	PROPN
ejpam-3547	204	2	pure	pure	PROPN
ejpam-3547	204	3	appl	appl	PROPN
ejpam-3547	204	4	.	.	PROPN
ejpam-3547	204	5	math	math	PROPN
ejpam-3547	204	6	,	,	PUNCT
ejpam-3547	204	7	12	12	NUM
ejpam-3547	204	8	(	(	PUNCT
ejpam-3547	204	9	4	4	NUM
ejpam-3547	204	10	)	)	PUNCT
ejpam-3547	204	11	(	(	PUNCT
ejpam-3547	204	12	2019	2019	NUM
ejpam-3547	204	13	)	)	PUNCT
ejpam-3547	204	14	,	,	PUNCT
ejpam-3547	204	15	1508	1508	NUM
ejpam-3547	204	16	-	-	SYM
ejpam-3547	204	17	1523	1523	NUM
ejpam-3547	204	18	1515	1515	NUM
ejpam-3547	204	19	×	×	NOUN
ejpam-3547	204	20	∫	∫	PROPN
ejpam-3547	204	21	x	x	SYM
ejpam-3547	204	22	0	0	NUM
ejpam-3547	204	23	cosh(nt	cosh(nt	ADJ
ejpam-3547	204	24	)	)	PUNCT
ejpam-3547	204	25	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3547	204	26	dldxl	dldxl	NOUN
ejpam-3547	204	27	(	(	PUNCT
ejpam-3547	204	28	−(x−	−(x−	NOUN
ejpam-3547	204	29	t))r+1	t))r+1	ADJ
ejpam-3547	204	30	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3547	204	31	dt	dt	NOUN
ejpam-3547	204	32	=	=	SYM
ejpam-3547	204	33	m2	m2	PROPN
ejpam-3547	204	34	{	{	PUNCT
ejpam-3547	204	35	[	[	PUNCT
ejpam-3547	204	36	r2(r	r2(r	NUM
ejpam-3547	204	37	−	−	NUM
ejpam-3547	204	38	1	1	NUM
ejpam-3547	204	39	)	)	SYM
ejpam-3547	204	40	2	2	NUM
ejpam-3547	204	41	n	n	CCONJ
ejpam-3547	204	42	(	(	PUNCT
ejpam-3547	204	43	δ0	δ0	NOUN
ejpam-3547	204	44	+	+	CCONJ
ejpam-3547	204	45	sinh(nx))2	sinh(nx))2	PROPN
ejpam-3547	204	46	dr−1	dr−1	PROPN
ejpam-3547	204	47	dxr−1	dxr−1	PROPN
ejpam-3547	204	48	(	(	PUNCT
ejpam-3547	204	49	δ0	δ0	NOUN
ejpam-3547	204	50	+	+	CCONJ
ejpam-3547	204	51	sinh(nx	sinh(nx	NOUN
ejpam-3547	204	52	)	)	PUNCT
ejpam-3547	204	53	)	)	PUNCT
ejpam-3547	205	1	+	+	CCONJ
ejpam-3547	205	2	...	...	PUNCT
ejpam-3547	206	1	+	+	CCONJ
ejpam-3547	206	2	r	r	NOUN
ejpam-3547	206	3	n	n	X
ejpam-3547	206	4	(	(	PUNCT
ejpam-3547	206	5	δ0	δ0	NOUN
ejpam-3547	206	6	+	+	CCONJ
ejpam-3547	206	7	sinh(nx))r	sinh(nx))r	ADJ
ejpam-3547	206	8	dr−1	dr−1	PROPN
ejpam-3547	206	9	dxr−1	dxr−1	PROPN
ejpam-3547	206	10	(	(	PUNCT
ejpam-3547	206	11	δ0	δ0	NOUN
ejpam-3547	206	12	+	+	CCONJ
ejpam-3547	206	13	sinh(nx))r−1	sinh(nx))r−1	PROPN
ejpam-3547	206	14	]	]	X
ejpam-3547	206	15	×	×	NOUN
ejpam-3547	206	16	(	(	PUNCT
ejpam-3547	206	17	∫	∫	PROPN
ejpam-3547	206	18	x	x	SYM
ejpam-3547	206	19	0	0	NUM
ejpam-3547	206	20	cosh(nt	cosh(nt	ADJ
ejpam-3547	206	21	)	)	PUNCT
ejpam-3547	206	22	|−(r	|−(r	NOUN
ejpam-3547	206	23	+	+	NOUN
ejpam-3547	206	24	1	1	NUM
ejpam-3547	206	25	)	)	PUNCT
ejpam-3547	206	26	(	(	PUNCT
ejpam-3547	206	27	−(x−	−(x−	NOUN
ejpam-3547	206	28	t))r|	t))r|	NOUN
ejpam-3547	206	29	dt	dt	PUNCT
ejpam-3547	206	30	)	)	PUNCT
ejpam-3547	207	1	+	+	CCONJ
ejpam-3547	207	2	[	[	PUNCT
ejpam-3547	207	3	r(r	r(r	NOUN
ejpam-3547	207	4	−	−	PROPN
ejpam-3547	207	5	1)2(r	1)2(r	NUM
ejpam-3547	207	6	−	−	NOUN
ejpam-3547	207	7	2	2	NUM
ejpam-3547	207	8	)	)	SYM
ejpam-3547	207	9	4	4	NUM
ejpam-3547	207	10	n	n	NOUN
ejpam-3547	207	11	(	(	PUNCT
ejpam-3547	207	12	δ0	δ0	NOUN
ejpam-3547	207	13	+	+	CCONJ
ejpam-3547	207	14	sinh(nx))2	sinh(nx))2	PROPN
ejpam-3547	207	15	dr−2	dr−2	PROPN
ejpam-3547	207	16	dxr−2	dxr−2	PROPN
ejpam-3547	207	17	(	(	PUNCT
ejpam-3547	207	18	δ0	δ0	NOUN
ejpam-3547	207	19	+	+	X
ejpam-3547	207	20	sinh(nx	sinh(nx	NOUN
ejpam-3547	207	21	)	)	PUNCT
ejpam-3547	207	22	)	)	PUNCT
ejpam-3547	208	1	+	+	CCONJ
ejpam-3547	208	2	...	...	PUNCT
ejpam-3547	209	1	+	+	CCONJ
ejpam-3547	209	2	r(r	r(r	NOUN
ejpam-3547	209	3	−	−	PROPN
ejpam-3547	209	4	1	1	NUM
ejpam-3547	209	5	)	)	SYM
ejpam-3547	209	6	2	2	NUM
ejpam-3547	209	7	n	n	NOUN
ejpam-3547	209	8	(	(	PUNCT
ejpam-3547	209	9	δ0	δ0	NOUN
ejpam-3547	209	10	+	+	CCONJ
ejpam-3547	209	11	sinh(nx))r	sinh(nx))r	ADJ
ejpam-3547	209	12	dr−2	dr−2	PROPN
ejpam-3547	209	13	dxr−2	dxr−2	PROPN
ejpam-3547	209	14	(	(	PUNCT
ejpam-3547	209	15	δ0	δ0	NOUN
ejpam-3547	209	16	+	+	X
ejpam-3547	209	17	sinh(nx))r−1	sinh(nx))r−1	PROPN
ejpam-3547	209	18	]	]	X
ejpam-3547	209	19	×	×	NOUN
ejpam-3547	209	20	(	(	PUNCT
ejpam-3547	209	21	∫	∫	PROPN
ejpam-3547	209	22	x	x	SYM
ejpam-3547	209	23	0	0	NUM
ejpam-3547	209	24	cosh(nt	cosh(nt	PROPN
ejpam-3547	209	25	)	)	PUNCT
ejpam-3547	209	26	∣∣∣r(r	∣∣∣r(r	NOUN
ejpam-3547	209	27	+	+	NOUN
ejpam-3547	209	28	1	1	X
ejpam-3547	209	29	)	)	PUNCT
ejpam-3547	209	30	(	(	PUNCT
ejpam-3547	209	31	−(x−	−(x−	NOUN
ejpam-3547	209	32	t))r−1	t))r−1	X
ejpam-3547	209	33	∣∣∣	∣∣∣	NOUN
ejpam-3547	209	34	dt	dt	X
ejpam-3547	209	35	)	)	PUNCT
ejpam-3547	209	36	+	+	NUM
ejpam-3547	209	37	n	n	CCONJ
ejpam-3547	209	38	(	(	PUNCT
ejpam-3547	209	39	δ0	δ0	NOUN
ejpam-3547	209	40	+	+	X
ejpam-3547	209	41	sinh(nx	sinh(nx	NOUN
ejpam-3547	209	42	)	)	PUNCT
ejpam-3547	209	43	)	)	PUNCT
ejpam-3547	209	44	(	(	PUNCT
ejpam-3547	209	45	∫	∫	NOUN
ejpam-3547	209	46	x	x	SYM
ejpam-3547	209	47	0	0	NUM
ejpam-3547	209	48	cosh(nt	cosh(nt	NOUN
ejpam-3547	209	49	)	)	PUNCT
ejpam-3547	209	50	|(−1)r(r	|(−1)r(r	PUNCT
ejpam-3547	209	51	+	+	NUM
ejpam-3547	209	52	1	1	NUM
ejpam-3547	209	53	)	)	PUNCT
ejpam-3547	209	54	!	!	PUNCT
ejpam-3547	210	1	(	(	PUNCT
ejpam-3547	210	2	−(x−	−(x−	NOUN
ejpam-3547	210	3	t))|	t))|	PROPN
ejpam-3547	210	4	dt	dt	X
ejpam-3547	210	5	)	)	PUNCT
ejpam-3547	210	6	}	}	PUNCT
ejpam-3547	210	7	.	.	PUNCT
ejpam-3547	211	1	by	by	ADP
ejpam-3547	211	2	schwarz	schwarz	PROPN
ejpam-3547	211	3	inequality	inequality	PROPN
ejpam-3547	211	4	,	,	PUNCT
ejpam-3547	211	5	we	we	PRON
ejpam-3547	211	6	have	have	VERB
ejpam-3547	211	7	:	:	PUNCT
ejpam-3547	211	8	i2	i2	PROPN
ejpam-3547	211	9	=	=	SYM
ejpam-3547	211	10	m2o(n−1	m2o(n−1	PROPN
ejpam-3547	211	11	)	)	PUNCT
ejpam-3547	211	12	hence	hence	ADV
ejpam-3547	211	13	,	,	PUNCT
ejpam-3547	211	14	i2	i2	PROPN
ejpam-3547	211	15	=	=	SYM
ejpam-3547	211	16	o(1	o(1	PROPN
ejpam-3547	211	17	)	)	PUNCT
ejpam-3547	211	18	.	.	PUNCT
ejpam-3547	212	1	now	now	ADV
ejpam-3547	212	2	,	,	PUNCT
ejpam-3547	212	3	it	it	PRON
ejpam-3547	212	4	follows	follow	VERB
ejpam-3547	212	5	i1	i1	PROPN
ejpam-3547	212	6	→	→	SYM
ejpam-3547	212	7	0	0	PUNCT
ejpam-3547	212	8	as	as	ADP
ejpam-3547	212	9	n	n	PROPN
ejpam-3547	212	10	→	→	SYM
ejpam-3547	212	11	∞.	∞.	PROPN
ejpam-3547	212	12	also	also	ADV
ejpam-3547	212	13	i2	i2	PROPN
ejpam-3547	212	14	→	→	SYM
ejpam-3547	212	15	0	0	PUNCT
ejpam-3547	212	16	as	as	ADP
ejpam-3547	212	17	n	n	NOUN
ejpam-3547	212	18	→	→	SYM
ejpam-3547	212	19	∞.	∞.	PROPN
ejpam-3547	212	20	hence	hence	ADV
ejpam-3547	212	21	σ2	σ2	PROPN
ejpam-3547	212	22	=	=	SYM
ejpam-3547	212	23	o(1	o(1	PROPN
ejpam-3547	212	24	)	)	PUNCT
ejpam-3547	212	25	.	.	PUNCT
ejpam-3547	213	1	the	the	DET
ejpam-3547	213	2	uniformity	uniformity	NOUN
ejpam-3547	213	3	assertion	assertion	NOUN
ejpam-3547	213	4	follows	follow	VERB
ejpam-3547	213	5	easily	easily	ADV
ejpam-3547	213	6	from	from	ADP
ejpam-3547	213	7	the	the	DET
ejpam-3547	213	8	fact	fact	NOUN
ejpam-3547	213	9	that	that	SCONJ
ejpam-3547	213	10	δ(ε	δ(ε	NOUN
ejpam-3547	213	11	)	)	PUNCT
ejpam-3547	213	12	in	in	ADP
ejpam-3547	213	13	the	the	DET
ejpam-3547	213	14	above	above	ADJ
ejpam-3547	213	15	proof	proof	NOUN
ejpam-3547	213	16	can	can	AUX
ejpam-3547	213	17	be	be	AUX
ejpam-3547	213	18	chosen	choose	VERB
ejpam-3547	213	19	to	to	PART
ejpam-3547	213	20	be	be	AUX
ejpam-3547	213	21	independent	independent	ADJ
ejpam-3547	213	22	of	of	ADP
ejpam-3547	213	23	x	x	SYM
ejpam-3547	213	24	∈	∈	PROPN
ejpam-3547	213	25	[	[	X
ejpam-3547	213	26	a	a	X
ejpam-3547	213	27	,	,	PUNCT
ejpam-3547	213	28	b	b	NOUN
ejpam-3547	213	29	]	]	X
ejpam-3547	213	30	and	and	CCONJ
ejpam-3547	213	31	all	all	DET
ejpam-3547	213	32	the	the	DET
ejpam-3547	213	33	other	other	ADJ
ejpam-3547	213	34	estimates	estimate	NOUN
ejpam-3547	213	35	hold	hold	VERB
ejpam-3547	213	36	uniformly	uniformly	ADV
ejpam-3547	213	37	on	on	ADP
ejpam-3547	213	38	[	[	X
ejpam-3547	213	39	a	a	X
ejpam-3547	213	40	,	,	PUNCT
ejpam-3547	213	41	b	b	NOUN
ejpam-3547	213	42	]	]	X
ejpam-3547	213	43	.	.	PUNCT
ejpam-3547	214	1	our	our	PRON
ejpam-3547	214	2	next	next	ADJ
ejpam-3547	214	3	results	result	NOUN
ejpam-3547	214	4	is	be	AUX
ejpam-3547	214	5	a	a	DET
ejpam-3547	214	6	voronovskaja	voronovskaja	NOUN
ejpam-3547	214	7	-	-	PUNCT
ejpam-3547	214	8	type	type	NOUN
ejpam-3547	214	9	asymptotic	asymptotic	ADJ
ejpam-3547	214	10	formula	formula	NOUN
ejpam-3547	214	11	for	for	ADP
ejpam-3547	214	12	the	the	DET
ejpam-3547	214	13	operatorswn	operatorswn	NOUN
ejpam-3547	214	14	(	(	PUNCT
ejpam-3547	214	15	r)(f(t);x	r)(f(t);x	ADJ
ejpam-3547	214	16	)	)	PUNCT
ejpam-3547	214	17	,	,	PUNCT
ejpam-3547	214	18	r	r	NOUN
ejpam-3547	214	19	∈	∈	PROPN
ejpam-3547	214	20	n.	n.	NOUN
ejpam-3547	214	21	theorem	theorem	VERB
ejpam-3547	214	22	3.2	3.2	NUM
ejpam-3547	214	23	.	.	PUNCT
ejpam-3547	215	1	suppose	suppose	VERB
ejpam-3547	215	2	that	that	SCONJ
ejpam-3547	215	3	r	r	PROPN
ejpam-3547	215	4	∈	∈	PROPN
ejpam-3547	215	5	n	n	CCONJ
ejpam-3547	215	6	,	,	PUNCT
ejpam-3547	215	7	f	f	PROPN
ejpam-3547	215	8	∈	∈	PROPN
ejpam-3547	215	9	cα[0,∞	cα[0,∞	PROPN
ejpam-3547	215	10	)	)	PUNCT
ejpam-3547	215	11	and	and	CCONJ
ejpam-3547	215	12	f	f	PROPN
ejpam-3547	215	13	(	(	PUNCT
ejpam-3547	215	14	r+3)(x	r+3)(x	PROPN
ejpam-3547	215	15	)	)	PUNCT
ejpam-3547	215	16	exists	exist	VERB
ejpam-3547	215	17	at	at	ADP
ejpam-3547	215	18	a	a	DET
ejpam-3547	215	19	point	point	NOUN
ejpam-3547	215	20	x	x	X
ejpam-3547	215	21	∈	∈	NOUN
ejpam-3547	215	22	(	(	PUNCT
ejpam-3547	215	23	0,∞	0,∞	NOUN
ejpam-3547	215	24	)	)	PUNCT
ejpam-3547	215	25	,	,	PUNCT
ejpam-3547	215	26	then	then	ADV
ejpam-3547	215	27	:	:	PUNCT
ejpam-3547	215	28	lim	lim	PROPN
ejpam-3547	215	29	n→∞	n→∞	NUM
ejpam-3547	215	30	n	n	PROPN
ejpam-3547	215	31	(	(	PUNCT
ejpam-3547	215	32	wn	wn	PROPN
ejpam-3547	215	33	(	(	PUNCT
ejpam-3547	215	34	r)(f(t);x)−	r)(f(t);x)−	PROPN
ejpam-3547	215	35	f	f	PROPN
ejpam-3547	215	36	(	(	PUNCT
ejpam-3547	215	37	r)(x	r)(x	PROPN
ejpam-3547	215	38	)	)	PUNCT
ejpam-3547	215	39	)	)	PUNCT
ejpam-3547	216	1	=	=	SYM
ejpam-3547	216	2	−f	−f	NOUN
ejpam-3547	216	3	(	(	PUNCT
ejpam-3547	216	4	r+1)(x	r+1)(x	PROPN
ejpam-3547	216	5	)	)	PUNCT
ejpam-3547	216	6	(	(	PUNCT
ejpam-3547	216	7	3.2	3.2	NUM
ejpam-3547	216	8	)	)	PUNCT
ejpam-3547	216	9	further	far	ADV
ejpam-3547	216	10	,	,	PUNCT
ejpam-3547	216	11	if	if	SCONJ
ejpam-3547	216	12	f	f	PROPN
ejpam-3547	216	13	(	(	PUNCT
ejpam-3547	216	14	r+3)(x	r+3)(x	PROPN
ejpam-3547	216	15	)	)	PUNCT
ejpam-3547	216	16	exists	exist	VERB
ejpam-3547	216	17	and	and	CCONJ
ejpam-3547	216	18	is	be	AUX
ejpam-3547	216	19	continuous	continuous	ADJ
ejpam-3547	216	20	on	on	ADP
ejpam-3547	216	21	(	(	PUNCT
ejpam-3547	216	22	a	a	DET
ejpam-3547	216	23	−	−	PROPN
ejpam-3547	216	24	η	η	PROPN
ejpam-3547	216	25	,	,	PUNCT
ejpam-3547	216	26	b	b	PROPN
ejpam-3547	216	27	+	+	CCONJ
ejpam-3547	216	28	η	η	PROPN
ejpam-3547	216	29	)	)	PUNCT
ejpam-3547	216	30	⊂	⊂	PROPN
ejpam-3547	216	31	(	(	PUNCT
ejpam-3547	216	32	0,∞	0,∞	NOUN
ejpam-3547	216	33	)	)	PUNCT
ejpam-3547	216	34	,	,	PUNCT
ejpam-3547	216	35	η	η	PROPN
ejpam-3547	216	36	>	>	X
ejpam-3547	216	37	0	0	PROPN
ejpam-3547	216	38	,	,	PUNCT
ejpam-3547	216	39	the	the	DET
ejpam-3547	216	40	limit	limit	NOUN
ejpam-3547	216	41	(	(	PUNCT
ejpam-3547	216	42	3.2	3.2	NUM
ejpam-3547	216	43	)	)	PUNCT
ejpam-3547	216	44	holds	hold	VERB
ejpam-3547	216	45	uniformly	uniformly	ADV
ejpam-3547	216	46	on	on	ADP
ejpam-3547	216	47	[	[	X
ejpam-3547	216	48	a	a	X
ejpam-3547	216	49	,	,	PUNCT
ejpam-3547	216	50	b	b	NOUN
ejpam-3547	216	51	]	]	PUNCT
ejpam-3547	216	52	.	.	PUNCT
ejpam-3547	217	1	proof	proof	NOUN
ejpam-3547	217	2	.	.	PUNCT
ejpam-3547	218	1	by	by	ADP
ejpam-3547	218	2	using	use	VERB
ejpam-3547	218	3	taylor	taylor	PROPN
ejpam-3547	218	4	’s	’s	PART
ejpam-3547	218	5	expansion	expansion	NOUN
ejpam-3547	218	6	of	of	ADP
ejpam-3547	218	7	f	f	PROPN
ejpam-3547	218	8	,	,	PUNCT
ejpam-3547	218	9	when	when	SCONJ
ejpam-3547	218	10	ξ	ξ	PROPN
ejpam-3547	218	11	lies	lie	VERB
ejpam-3547	218	12	between	between	ADP
ejpam-3547	218	13	t	t	PROPN
ejpam-3547	218	14	and	and	CCONJ
ejpam-3547	218	15	x	x	X
ejpam-3547	218	16	,	,	PUNCT
ejpam-3547	218	17	we	we	PRON
ejpam-3547	218	18	get	get	VERB
ejpam-3547	218	19	:	:	PUNCT
ejpam-3547	218	20	f(t	f(t	NOUN
ejpam-3547	218	21	)	)	PUNCT
ejpam-3547	219	1	=	=	SYM
ejpam-3547	219	2	r+2∑	r+2∑	PROPN
ejpam-3547	219	3	i=0	i=0	PROPN
ejpam-3547	219	4	f	f	X
ejpam-3547	219	5	(	(	PUNCT
ejpam-3547	219	6	i)(x	i)(x	PROPN
ejpam-3547	219	7	)	)	PUNCT
ejpam-3547	219	8	i	i	PRON
ejpam-3547	219	9	!	!	PUNCT
ejpam-3547	220	1	(	(	PUNCT
ejpam-3547	220	2	t−	t−	PROPN
ejpam-3547	220	3	x)i	x)i	PUNCT
ejpam-3547	221	1	+	+	CCONJ
ejpam-3547	221	2	f	f	X
ejpam-3547	221	3	(	(	PUNCT
ejpam-3547	221	4	r+)(ξ	r+)(ξ	X
ejpam-3547	221	5	)	)	PUNCT
ejpam-3547	221	6	(	(	PUNCT
ejpam-3547	221	7	r	r	NOUN
ejpam-3547	221	8	+	+	NOUN
ejpam-3547	221	9	3	3	NUM
ejpam-3547	221	10	)	)	PUNCT
ejpam-3547	221	11	!	!	PUNCT
ejpam-3547	222	1	(	(	PUNCT
ejpam-3547	222	2	t−	t−	PROPN
ejpam-3547	222	3	x)r+3	x)r+3	PROPN
ejpam-3547	222	4	operating	operate	VERB
ejpam-3547	222	5	by	by	ADP
ejpam-3547	222	6	the	the	DET
ejpam-3547	222	7	sequence	sequence	NOUN
ejpam-3547	222	8	w	w	PROPN
ejpam-3547	222	9	(	(	PUNCT
ejpam-3547	222	10	r	r	NOUN
ejpam-3547	222	11	)	)	PUNCT
ejpam-3547	222	12	n	n	NOUN
ejpam-3547	222	13	,	,	PUNCT
ejpam-3547	222	14	we	we	PRON
ejpam-3547	222	15	get	get	VERB
ejpam-3547	222	16	:	:	PUNCT
ejpam-3547	222	17	a.	a.	PROPN
ejpam-3547	222	18	j.	j.	PROPN
ejpam-3547	222	19	mohammad	mohammad	PROPN
ejpam-3547	222	20	,	,	PUNCT
ejpam-3547	222	21	h.	h.	PROPN
ejpam-3547	222	22	o.	o.	PROPN
ejpam-3547	222	23	muslim	muslim	PROPN
ejpam-3547	222	24	/	/	SYM
ejpam-3547	222	25	eur	eur	PROPN
ejpam-3547	222	26	.	.	PUNCT
ejpam-3547	223	1	j.	j.	PROPN
ejpam-3547	223	2	pure	pure	PROPN
ejpam-3547	223	3	appl	appl	PROPN
ejpam-3547	223	4	.	.	PROPN
ejpam-3547	223	5	math	math	PROPN
ejpam-3547	223	6	,	,	PUNCT
ejpam-3547	223	7	12	12	NUM
ejpam-3547	223	8	(	(	PUNCT
ejpam-3547	223	9	4	4	NUM
ejpam-3547	223	10	)	)	PUNCT
ejpam-3547	223	11	(	(	PUNCT
ejpam-3547	223	12	2019	2019	NUM
ejpam-3547	223	13	)	)	PUNCT
ejpam-3547	223	14	,	,	PUNCT
ejpam-3547	223	15	1508	1508	NUM
ejpam-3547	223	16	-	-	SYM
ejpam-3547	223	17	1523	1523	NUM
ejpam-3547	223	18	1516	1516	NUM
ejpam-3547	223	19	wn	wn	PROPN
ejpam-3547	223	20	(	(	PUNCT
ejpam-3547	223	21	r)(f(t);x	r)(f(t);x	PROPN
ejpam-3547	223	22	)	)	PUNCT
ejpam-3547	223	23	=	=	SYM
ejpam-3547	224	1	r+2∑	r+2∑	PROPN
ejpam-3547	224	2	i=0	i=0	PROPN
ejpam-3547	224	3	f	f	X
ejpam-3547	224	4	(	(	PUNCT
ejpam-3547	224	5	i)(x	i)(x	PROPN
ejpam-3547	224	6	)	)	PUNCT
ejpam-3547	224	7	i	i	PRON
ejpam-3547	224	8	!	!	PUNCT
ejpam-3547	225	1	(	(	PUNCT
ejpam-3547	225	2	−1)iwn	−1)iwn	PROPN
ejpam-3547	225	3	(	(	PUNCT
ejpam-3547	225	4	r)((x−	r)((x−	PROPN
ejpam-3547	225	5	t)i;x	t)i;x	PROPN
ejpam-3547	225	6	)	)	PUNCT
ejpam-3547	226	1	+	+	NUM
ejpam-3547	226	2	f	f	X
ejpam-3547	226	3	(	(	PUNCT
ejpam-3547	226	4	r+3)(ξ	r+3)(ξ	PROPN
ejpam-3547	226	5	)	)	PUNCT
ejpam-3547	226	6	(	(	PUNCT
ejpam-3547	226	7	r	r	NOUN
ejpam-3547	226	8	+	+	NOUN
ejpam-3547	226	9	3	3	NUM
ejpam-3547	226	10	)	)	PUNCT
ejpam-3547	226	11	!	!	PUNCT
ejpam-3547	227	1	(	(	PUNCT
ejpam-3547	227	2	−1)r+3wn	−1)r+3wn	PROPN
ejpam-3547	227	3	(	(	PUNCT
ejpam-3547	227	4	r)((x−	r)((x−	PROPN
ejpam-3547	227	5	t)r+3;x	t)r+3;x	PROPN
ejpam-3547	227	6	)	)	PUNCT
ejpam-3547	227	7	:	:	PUNCT
ejpam-3547	227	8	=	=	X
ejpam-3547	227	9	σ1	σ1	PROPN
ejpam-3547	227	10	+	+	CCONJ
ejpam-3547	227	11	σ2	σ2	NOUN
ejpam-3547	227	12	using	use	VERB
ejpam-3547	227	13	the	the	DET
ejpam-3547	227	14	same	same	ADJ
ejpam-3547	227	15	technique	technique	NOUN
ejpam-3547	227	16	of	of	ADP
ejpam-3547	227	17	theorem	theorem	NOUN
ejpam-3547	227	18	3.1	3.1	NUM
ejpam-3547	227	19	,	,	PUNCT
ejpam-3547	227	20	we	we	PRON
ejpam-3547	227	21	get	get	VERB
ejpam-3547	227	22	:	:	PUNCT
ejpam-3547	227	23	σ2	σ2	NOUN
ejpam-3547	227	24	→	→	SYM
ejpam-3547	227	25	0	0	NUM
ejpam-3547	227	26	as	as	ADP
ejpam-3547	227	27	n→	n→	PUNCT
ejpam-3547	227	28	∞.	∞.	PROPN
ejpam-3547	227	29	when	when	SCONJ
ejpam-3547	227	30	i	i	PRON
ejpam-3547	227	31	<	<	X
ejpam-3547	227	32	r	r	X
ejpam-3547	227	33	then	then	ADV
ejpam-3547	227	34	from	from	ADP
ejpam-3547	227	35	lemma	lemma	PROPN
ejpam-3547	227	36	2.3	2.3	NUM
ejpam-3547	227	37	,	,	PUNCT
ejpam-3547	227	38	we	we	PRON
ejpam-3547	227	39	have	have	VERB
ejpam-3547	227	40	wn	wn	PROPN
ejpam-3547	227	41	(	(	PUNCT
ejpam-3547	227	42	r)((t−	r)((t−	PROPN
ejpam-3547	227	43	x)i;x	x)i;x	PROPN
ejpam-3547	227	44	)	)	PUNCT
ejpam-3547	228	1	−→	−→	ADV
ejpam-3547	228	2	0	0	NUM
ejpam-3547	228	3	as	as	ADP
ejpam-3547	228	4	n	n	NUM
ejpam-3547	228	5	−→∞.	−→∞.	PUNCT
ejpam-3547	228	6	using	use	VERB
ejpam-3547	228	7	lemma	lemma	PROPN
ejpam-3547	228	8	2.3	2.3	NUM
ejpam-3547	228	9	,	,	PUNCT
ejpam-3547	228	10	lemma	lemma	PROPN
ejpam-3547	228	11	2.5	2.5	NUM
ejpam-3547	228	12	,	,	PUNCT
ejpam-3547	228	13	and	and	CCONJ
ejpam-3547	228	14	lemma	lemma	PROPN
ejpam-3547	228	15	2.6	2.6	NUM
ejpam-3547	228	16	,	,	PUNCT
ejpam-3547	228	17	we	we	PRON
ejpam-3547	228	18	get	get	VERB
ejpam-3547	228	19	:	:	PUNCT
ejpam-3547	228	20	σ1	σ1	NOUN
ejpam-3547	228	21	=	=	SYM
ejpam-3547	228	22	f	f	PROPN
ejpam-3547	228	23	(	(	PUNCT
ejpam-3547	228	24	r)(x	r)(x	PROPN
ejpam-3547	228	25	)	)	PUNCT
ejpam-3547	229	1	r	r	NOUN
ejpam-3547	229	2	!	!	PUNCT
ejpam-3547	229	3	{	{	PUNCT
ejpam-3547	229	4	r	r	X
ejpam-3547	229	5	!	!	PUNCT
ejpam-3547	229	6	(	(	PUNCT
ejpam-3547	229	7	sinh(nx	sinh(nx	NOUN
ejpam-3547	229	8	)	)	PUNCT
ejpam-3547	229	9	(	(	PUNCT
ejpam-3547	229	10	δ0	δ0	NOUN
ejpam-3547	229	11	+	+	CCONJ
ejpam-3547	229	12	sinh(nx	sinh(nx	NOUN
ejpam-3547	229	13	)	)	PUNCT
ejpam-3547	229	14	)	)	PUNCT
ejpam-3547	229	15	)	)	PUNCT
ejpam-3547	230	1	+	+	CCONJ
ejpam-3547	230	2	rr!x	rr!x	PROPN
ejpam-3547	230	3	ncosh(nx	ncosh(nx	NOUN
ejpam-3547	230	4	)	)	PUNCT
ejpam-3547	230	5	(	(	PUNCT
ejpam-3547	230	6	δ0	δ0	NOUN
ejpam-3547	230	7	+	+	CCONJ
ejpam-3547	230	8	sinh(nx	sinh(nx	NOUN
ejpam-3547	230	9	)	)	PUNCT
ejpam-3547	230	10	)	)	PUNCT
ejpam-3547	231	1	(	(	PUNCT
ejpam-3547	231	2	1−	1−	NUM
ejpam-3547	231	3	sinh(nx	sinh(nx	NOUN
ejpam-3547	231	4	)	)	PUNCT
ejpam-3547	231	5	(	(	PUNCT
ejpam-3547	231	6	δ0	δ0	NOUN
ejpam-3547	231	7	+	+	CCONJ
ejpam-3547	231	8	sinh(nx	sinh(nx	NOUN
ejpam-3547	231	9	)	)	PUNCT
ejpam-3547	231	10	)	)	PUNCT
ejpam-3547	231	11	)	)	PUNCT
ejpam-3547	232	1	+	+	CCONJ
ejpam-3547	232	2	...	...	PUNCT
ejpam-3547	233	1	+	+	CCONJ
ejpam-3547	233	2	xr	xr	PROPN
ejpam-3547	233	3	dr	dr	PROPN
ejpam-3547	233	4	dxr	dxr	PROPN
ejpam-3547	233	5	(	(	PUNCT
ejpam-3547	233	6	sinh(nx	sinh(nx	NOUN
ejpam-3547	233	7	)	)	PUNCT
ejpam-3547	233	8	(	(	PUNCT
ejpam-3547	233	9	δ0	δ0	NOUN
ejpam-3547	233	10	+	+	CCONJ
ejpam-3547	233	11	sinh(nx	sinh(nx	NOUN
ejpam-3547	233	12	)	)	PUNCT
ejpam-3547	233	13	)	)	PUNCT
ejpam-3547	233	14	)	)	PUNCT
ejpam-3547	234	1	−	−	PROPN
ejpam-3547	234	2	rr	rr	NOUN
ejpam-3547	234	3	!	!	PUNCT
ejpam-3547	235	1	(	(	PUNCT
ejpam-3547	235	2	sinh(nx	sinh(nx	NOUN
ejpam-3547	235	3	)	)	PUNCT
ejpam-3547	235	4	(	(	PUNCT
ejpam-3547	235	5	δ0	δ0	NOUN
ejpam-3547	235	6	+	+	CCONJ
ejpam-3547	235	7	sinh(nx	sinh(nx	NOUN
ejpam-3547	235	8	)	)	PUNCT
ejpam-3547	235	9	)	)	PUNCT
ejpam-3547	235	10	−	−	PROPN
ejpam-3547	236	1	cosh2(nx	cosh2(nx	NOUN
ejpam-3547	236	2	)	)	PUNCT
ejpam-3547	236	3	(	(	PUNCT
ejpam-3547	236	4	δ0	δ0	NOUN
ejpam-3547	236	5	+	+	CCONJ
ejpam-3547	236	6	sinh(nx))2	sinh(nx))2	NOUN
ejpam-3547	236	7	)	)	PUNCT
ejpam-3547	236	8	−	−	PROPN
ejpam-3547	236	9	...	...	PUNCT
ejpam-3547	237	1	−	−	PUNCT
ejpam-3547	237	2	r	r	NOUN
ejpam-3547	238	1	n	n	PROPN
ejpam-3547	238	2	xr−1	xr−1	PROPN
ejpam-3547	238	3	dr	dr	PROPN
ejpam-3547	238	4	dxr	dxr	PROPN
ejpam-3547	238	5	(	(	PUNCT
ejpam-3547	238	6	cosh(nx	cosh(nx	NOUN
ejpam-3547	238	7	)	)	PUNCT
ejpam-3547	238	8	(	(	PUNCT
ejpam-3547	238	9	δ0	δ0	NOUN
ejpam-3547	238	10	+	+	CCONJ
ejpam-3547	238	11	sinh(nx	sinh(nx	NOUN
ejpam-3547	238	12	)	)	PUNCT
ejpam-3547	238	13	)	)	PUNCT
ejpam-3547	238	14	)	)	PUNCT
ejpam-3547	239	1	}	}	PUNCT
ejpam-3547	240	1	−	−	X
ejpam-3547	240	2	f	f	PROPN
ejpam-3547	240	3	r(x	r(x	PROPN
ejpam-3547	240	4	)	)	PUNCT
ejpam-3547	241	1	+	+	NUM
ejpam-3547	241	2	f	f	X
ejpam-3547	241	3	(	(	PUNCT
ejpam-3547	241	4	r+1)(x	r+1)(x	PROPN
ejpam-3547	241	5	)	)	PUNCT
ejpam-3547	241	6	(	(	PUNCT
ejpam-3547	241	7	r	r	NOUN
ejpam-3547	241	8	+	+	NOUN
ejpam-3547	241	9	1	1	NUM
ejpam-3547	241	10	)	)	PUNCT
ejpam-3547	241	11	!	!	PUNCT
ejpam-3547	242	1	{	{	PUNCT
ejpam-3547	242	2	−r(r	−r(r	NOUN
ejpam-3547	242	3	+	+	NOUN
ejpam-3547	242	4	1	1	NUM
ejpam-3547	242	5	)	)	PUNCT
ejpam-3547	242	6	!	!	PUNCT
ejpam-3547	243	1	2	2	NUM
ejpam-3547	243	2	x2	x2	PROPN
ejpam-3547	243	3	ncosh(nx	ncosh(nx	NOUN
ejpam-3547	243	4	)	)	PUNCT
ejpam-3547	243	5	(	(	PUNCT
ejpam-3547	243	6	δ0	δ0	NOUN
ejpam-3547	243	7	+	+	CCONJ
ejpam-3547	243	8	sinh(nx	sinh(nx	NOUN
ejpam-3547	243	9	)	)	PUNCT
ejpam-3547	243	10	)	)	PUNCT
ejpam-3547	244	1	(	(	PUNCT
ejpam-3547	244	2	1−	1−	NUM
ejpam-3547	244	3	sinh(nx	sinh(nx	NOUN
ejpam-3547	244	4	)	)	PUNCT
ejpam-3547	244	5	(	(	PUNCT
ejpam-3547	244	6	δ0	δ0	NOUN
ejpam-3547	244	7	+	+	CCONJ
ejpam-3547	244	8	sinh(nx	sinh(nx	NOUN
ejpam-3547	244	9	)	)	PUNCT
ejpam-3547	244	10	)	)	PUNCT
ejpam-3547	244	11	)	)	PUNCT
ejpam-3547	245	1	−	−	PROPN
ejpam-3547	245	2	...	...	PUNCT
ejpam-3547	246	1	−	−	PROPN
ejpam-3547	247	1	rxr+1	rxr+1	NOUN
ejpam-3547	247	2	d	d	X
ejpam-3547	247	3	r	r	NOUN
ejpam-3547	247	4	dxr	dxr	ADJ
ejpam-3547	247	5	(	(	PUNCT
ejpam-3547	247	6	sinh(nx	sinh(nx	NOUN
ejpam-3547	247	7	)	)	PUNCT
ejpam-3547	247	8	(	(	PUNCT
ejpam-3547	247	9	δ0	δ0	NOUN
ejpam-3547	247	10	+	+	CCONJ
ejpam-3547	247	11	sinh(nx	sinh(nx	NOUN
ejpam-3547	247	12	)	)	PUNCT
ejpam-3547	247	13	)	)	PUNCT
ejpam-3547	247	14	)	)	PUNCT
ejpam-3547	248	1	−	−	PROPN
ejpam-3547	249	1	(	(	PUNCT
ejpam-3547	249	2	r	r	NOUN
ejpam-3547	249	3	+	+	NOUN
ejpam-3547	249	4	1	1	NUM
ejpam-3547	249	5	)	)	PUNCT
ejpam-3547	249	6	!	!	PUNCT
ejpam-3547	250	1	n	n	PRON
ejpam-3547	250	2	cosh(nx	cosh(nx	NOUN
ejpam-3547	250	3	)	)	PUNCT
ejpam-3547	250	4	(	(	PUNCT
ejpam-3547	250	5	δ0	δ0	NOUN
ejpam-3547	250	6	+	+	CCONJ
ejpam-3547	250	7	sinh(nx	sinh(nx	NOUN
ejpam-3547	250	8	)	)	PUNCT
ejpam-3547	250	9	)	)	PUNCT
ejpam-3547	251	1	+	+	CCONJ
ejpam-3547	251	2	..	..	PUNCT
ejpam-3547	251	3	+	+	PUNCT
ejpam-3547	251	4	(	(	PUNCT
ejpam-3547	251	5	r	r	NOUN
ejpam-3547	251	6	+	+	NUM
ejpam-3547	251	7	1)(r	1)(r	NUM
ejpam-3547	251	8	−	−	NOUN
ejpam-3547	251	9	1	1	NUM
ejpam-3547	251	10	)	)	PUNCT
ejpam-3547	251	11	n	n	PROPN
ejpam-3547	251	12	xr	xr	PROPN
ejpam-3547	251	13	dr	dr	PROPN
ejpam-3547	251	14	dxr	dxr	PROPN
ejpam-3547	251	15	(	(	PUNCT
ejpam-3547	251	16	cosh(nx	cosh(nx	NOUN
ejpam-3547	251	17	)	)	PUNCT
ejpam-3547	251	18	(	(	PUNCT
ejpam-3547	251	19	δ0	δ0	NOUN
ejpam-3547	251	20	+	+	CCONJ
ejpam-3547	251	21	sinh(nx	sinh(nx	NOUN
ejpam-3547	251	22	)	)	PUNCT
ejpam-3547	251	23	)	)	PUNCT
ejpam-3547	251	24	)	)	PUNCT
ejpam-3547	251	25	}	}	PUNCT
ejpam-3547	252	1	+	+	NUM
ejpam-3547	252	2	f	f	X
ejpam-3547	252	3	(	(	PUNCT
ejpam-3547	252	4	r+2)(x	r+2)(x	PROPN
ejpam-3547	252	5	)	)	PUNCT
ejpam-3547	252	6	(	(	PUNCT
ejpam-3547	252	7	r	r	NOUN
ejpam-3547	252	8	+	+	NOUN
ejpam-3547	252	9	2	2	NUM
ejpam-3547	252	10	)	)	PUNCT
ejpam-3547	252	11	!	!	PUNCT
ejpam-3547	252	12	{	{	PUNCT
ejpam-3547	253	1	r(r	r(r	NOUN
ejpam-3547	253	2	+	+	CCONJ
ejpam-3547	253	3	2	2	NUM
ejpam-3547	253	4	)	)	PUNCT
ejpam-3547	253	5	!	!	PUNCT
ejpam-3547	254	1	6	6	NUM
ejpam-3547	254	2	x3	x3	ADJ
ejpam-3547	254	3	ncosh(nx	ncosh(nx	NOUN
ejpam-3547	254	4	)	)	PUNCT
ejpam-3547	254	5	(	(	PUNCT
ejpam-3547	254	6	δ0	δ0	NOUN
ejpam-3547	254	7	+	+	CCONJ
ejpam-3547	254	8	sinh(nx	sinh(nx	NOUN
ejpam-3547	254	9	)	)	PUNCT
ejpam-3547	254	10	)	)	PUNCT
ejpam-3547	254	11	(	(	PUNCT
ejpam-3547	254	12	1−	1−	NUM
ejpam-3547	254	13	sinh(nx	sinh(nx	NOUN
ejpam-3547	254	14	)	)	PUNCT
ejpam-3547	254	15	(	(	PUNCT
ejpam-3547	254	16	δ0	δ0	NOUN
ejpam-3547	254	17	+	+	CCONJ
ejpam-3547	254	18	sinh(nx	sinh(nx	NOUN
ejpam-3547	254	19	)	)	PUNCT
ejpam-3547	254	20	)	)	PUNCT
ejpam-3547	254	21	)	)	PUNCT
ejpam-3547	255	1	+	+	CCONJ
ejpam-3547	255	2	...	...	PUNCT
ejpam-3547	256	1	+	+	CCONJ
ejpam-3547	256	2	r(r	r(r	NOUN
ejpam-3547	256	3	+	+	CCONJ
ejpam-3547	256	4	1	1	X
ejpam-3547	256	5	)	)	PUNCT
ejpam-3547	256	6	2	2	NUM
ejpam-3547	256	7	xr+2	xr+2	NOUN
ejpam-3547	256	8	d	d	NOUN
ejpam-3547	256	9	r	r	NOUN
ejpam-3547	256	10	dxr	dxr	ADJ
ejpam-3547	256	11	(	(	PUNCT
ejpam-3547	256	12	sinh(nx	sinh(nx	NOUN
ejpam-3547	256	13	)	)	PUNCT
ejpam-3547	256	14	(	(	PUNCT
ejpam-3547	256	15	δ0	δ0	NOUN
ejpam-3547	256	16	+	+	CCONJ
ejpam-3547	256	17	sinh(nx	sinh(nx	NOUN
ejpam-3547	256	18	)	)	PUNCT
ejpam-3547	256	19	)	)	PUNCT
ejpam-3547	256	20	)	)	PUNCT
ejpam-3547	257	1	−	−	PROPN
ejpam-3547	257	2	...	...	PUNCT
ejpam-3547	258	1	−	−	PROPN
ejpam-3547	258	2	r(r	r(r	NOUN
ejpam-3547	258	3	−	−	PROPN
ejpam-3547	259	1	1)(r	1)(r	NUM
ejpam-3547	259	2	+	+	CCONJ
ejpam-3547	259	3	2	2	NUM
ejpam-3547	259	4	)	)	PUNCT
ejpam-3547	259	5	2n	2n	NUM
ejpam-3547	260	1	xr+1	xr+1	PROPN
ejpam-3547	260	2	×	×	PROPN
ejpam-3547	260	3	dr	dr	PROPN
ejpam-3547	260	4	dxr	dxr	PROPN
ejpam-3547	260	5	(	(	PUNCT
ejpam-3547	260	6	cosh(nx	cosh(nx	NOUN
ejpam-3547	260	7	)	)	PUNCT
ejpam-3547	260	8	(	(	PUNCT
ejpam-3547	260	9	δ0	δ0	NOUN
ejpam-3547	260	10	+	+	CCONJ
ejpam-3547	260	11	sinh(nx	sinh(nx	NOUN
ejpam-3547	260	12	)	)	PUNCT
ejpam-3547	260	13	)	)	PUNCT
ejpam-3547	260	14	)	)	PUNCT
ejpam-3547	260	15	}	}	PUNCT
ejpam-3547	260	16	.	.	PUNCT
ejpam-3547	261	1	therefore	therefore	ADV
ejpam-3547	261	2	,	,	PUNCT
ejpam-3547	261	3	limn→∞	limn→∞	PROPN
ejpam-3547	261	4	n	n	CCONJ
ejpam-3547	261	5	(	(	PUNCT
ejpam-3547	261	6	wn	wn	PROPN
ejpam-3547	261	7	(	(	PUNCT
ejpam-3547	261	8	r)(f(t);x)−	r)(f(t);x)−	PROPN
ejpam-3547	261	9	f	f	PROPN
ejpam-3547	261	10	(	(	PUNCT
ejpam-3547	261	11	r)(x	r)(x	PROPN
ejpam-3547	261	12	)	)	PUNCT
ejpam-3547	261	13	)	)	PUNCT
ejpam-3547	262	1	=	=	SYM
ejpam-3547	262	2	−f	−f	NOUN
ejpam-3547	262	3	(	(	PUNCT
ejpam-3547	262	4	r+1)(x	r+1)(x	PROPN
ejpam-3547	262	5	)	)	PUNCT
ejpam-3547	262	6	the	the	DET
ejpam-3547	262	7	uniformity	uniformity	NOUN
ejpam-3547	262	8	assertion	assertion	NOUN
ejpam-3547	262	9	follows	follow	VERB
ejpam-3547	262	10	easily	easily	ADV
ejpam-3547	262	11	from	from	ADP
ejpam-3547	262	12	the	the	DET
ejpam-3547	262	13	fact	fact	NOUN
ejpam-3547	262	14	that	that	SCONJ
ejpam-3547	262	15	δ(ε	δ(ε	NOUN
ejpam-3547	262	16	)	)	PUNCT
ejpam-3547	262	17	in	in	ADP
ejpam-3547	262	18	the	the	DET
ejpam-3547	262	19	above	above	ADJ
ejpam-3547	262	20	proof	proof	NOUN
ejpam-3547	262	21	can	can	AUX
ejpam-3547	262	22	be	be	AUX
ejpam-3547	262	23	chosen	choose	VERB
ejpam-3547	262	24	to	to	PART
ejpam-3547	262	25	be	be	AUX
ejpam-3547	262	26	independent	independent	ADJ
ejpam-3547	262	27	of	of	ADP
ejpam-3547	262	28	x	x	SYM
ejpam-3547	262	29	∈	∈	PROPN
ejpam-3547	262	30	[	[	X
ejpam-3547	262	31	a	a	X
ejpam-3547	262	32	,	,	PUNCT
ejpam-3547	262	33	b	b	NOUN
ejpam-3547	262	34	]	]	X
ejpam-3547	262	35	and	and	CCONJ
ejpam-3547	262	36	all	all	DET
ejpam-3547	262	37	the	the	DET
ejpam-3547	262	38	other	other	ADJ
ejpam-3547	262	39	estimates	estimate	NOUN
ejpam-3547	262	40	hold	hold	VERB
ejpam-3547	262	41	uniformly	uniformly	ADV
ejpam-3547	262	42	on	on	ADP
ejpam-3547	262	43	[	[	X
ejpam-3547	262	44	a	a	X
ejpam-3547	262	45	,	,	PUNCT
ejpam-3547	262	46	b	b	NOUN
ejpam-3547	262	47	]	]	X
ejpam-3547	262	48	.	.	PUNCT
ejpam-3547	263	1	finally	finally	ADV
ejpam-3547	263	2	,	,	PUNCT
ejpam-3547	263	3	we	we	PRON
ejpam-3547	263	4	give	give	VERB
ejpam-3547	263	5	an	an	DET
ejpam-3547	263	6	estimate	estimate	NOUN
ejpam-3547	263	7	of	of	ADP
ejpam-3547	263	8	the	the	DET
ejpam-3547	263	9	degree	degree	NOUN
ejpam-3547	263	10	of	of	ADP
ejpam-3547	263	11	approximation	approximation	NOUN
ejpam-3547	263	12	by	by	ADP
ejpam-3547	263	13	wn	wn	PROPN
ejpam-3547	263	14	(	(	PUNCT
ejpam-3547	263	15	r)(f	r)(f	PROPN
ejpam-3547	263	16	;	;	PUNCT
ejpam-3547	263	17	x	x	X
ejpam-3547	263	18	)	)	PUNCT
ejpam-3547	263	19	.	.	PUNCT
ejpam-3547	264	1	theorem	theorem	VERB
ejpam-3547	264	2	3.3	3.3	NUM
ejpam-3547	264	3	.	.	PUNCT
ejpam-3547	265	1	let	let	VERB
ejpam-3547	265	2	f	f	PROPN
ejpam-3547	265	3	∈	∈	PROPN
ejpam-3547	265	4	cα[0,∞	cα[0,∞	PROPN
ejpam-3547	265	5	)	)	PUNCT
ejpam-3547	265	6	,	,	PUNCT
ejpam-3547	265	7	α	α	X
ejpam-3547	265	8	>	>	X
ejpam-3547	265	9	0	0	PUNCT
ejpam-3547	266	1	for	for	ADP
ejpam-3547	266	2	some	some	DET
ejpam-3547	266	3	h	h	NOUN
ejpam-3547	266	4	>	>	X
ejpam-3547	266	5	0	0	PUNCT
ejpam-3547	267	1	and	and	CCONJ
ejpam-3547	267	2	r	r	PROPN
ejpam-3547	267	3	6	6	NUM
ejpam-3547	267	4	q	q	NOUN
ejpam-3547	267	5	6	6	NUM
ejpam-3547	267	6	r+	r+	NOUN
ejpam-3547	267	7	2	2	NUM
ejpam-3547	267	8	.	.	PUNCT
ejpam-3547	268	1	if	if	SCONJ
ejpam-3547	268	2	f	f	PROPN
ejpam-3547	268	3	(	(	PUNCT
ejpam-3547	268	4	q+1	q+1	NOUN
ejpam-3547	268	5	)	)	PUNCT
ejpam-3547	268	6	exists	exist	VERB
ejpam-3547	268	7	and	and	CCONJ
ejpam-3547	268	8	is	be	AUX
ejpam-3547	268	9	continuous	continuous	ADJ
ejpam-3547	268	10	on	on	ADP
ejpam-3547	268	11	(	(	PUNCT
ejpam-3547	268	12	a−	a−	PROPN
ejpam-3547	268	13	η	η	PROPN
ejpam-3547	268	14	,	,	PUNCT
ejpam-3547	268	15	b+	b+	NOUN
ejpam-3547	268	16	η	η	PROPN
ejpam-3547	268	17	)	)	PUNCT
ejpam-3547	268	18	⊂	⊂	PROPN
ejpam-3547	268	19	(	(	PUNCT
ejpam-3547	268	20	0,∞	0,∞	NOUN
ejpam-3547	268	21	)	)	PUNCT
ejpam-3547	268	22	,	,	PUNCT
ejpam-3547	268	23	η	η	PROPN
ejpam-3547	268	24	>	>	X
ejpam-3547	268	25	0	0	PROPN
ejpam-3547	268	26	,	,	PUNCT
ejpam-3547	268	27	then	then	ADV
ejpam-3547	268	28	for	for	ADP
ejpam-3547	268	29	sufficiently	sufficiently	ADV
ejpam-3547	268	30	large	large	ADJ
ejpam-3547	268	31	n	n	NOUN
ejpam-3547	268	32	,	,	PUNCT
ejpam-3547	268	33	a.	a.	PROPN
ejpam-3547	268	34	j.	j.	PROPN
ejpam-3547	268	35	mohammad	mohammad	PROPN
ejpam-3547	268	36	,	,	PUNCT
ejpam-3547	268	37	h.	h.	PROPN
ejpam-3547	268	38	o.	o.	PROPN
ejpam-3547	268	39	muslim	muslim	PROPN
ejpam-3547	268	40	/	/	SYM
ejpam-3547	268	41	eur	eur	PROPN
ejpam-3547	268	42	.	.	PUNCT
ejpam-3547	269	1	j.	j.	PROPN
ejpam-3547	269	2	pure	pure	PROPN
ejpam-3547	269	3	appl	appl	PROPN
ejpam-3547	269	4	.	.	PROPN
ejpam-3547	269	5	math	math	PROPN
ejpam-3547	269	6	,	,	PUNCT
ejpam-3547	269	7	12	12	NUM
ejpam-3547	269	8	(	(	PUNCT
ejpam-3547	269	9	4	4	NUM
ejpam-3547	269	10	)	)	PUNCT
ejpam-3547	269	11	(	(	PUNCT
ejpam-3547	269	12	2019	2019	NUM
ejpam-3547	269	13	)	)	PUNCT
ejpam-3547	269	14	,	,	PUNCT
ejpam-3547	269	15	1508	1508	NUM
ejpam-3547	269	16	-	-	SYM
ejpam-3547	269	17	1523	1523	NUM
ejpam-3547	269	18	1517	1517	NUM
ejpam-3547	269	19	∥∥∥wn	∥∥∥wn	PROPN
ejpam-3547	269	20	(	(	PUNCT
ejpam-3547	269	21	r)(f(t);x)−	r)(f(t);x)−	PROPN
ejpam-3547	269	22	f	f	PROPN
ejpam-3547	269	23	(	(	PUNCT
ejpam-3547	269	24	r)(x	r)(x	PROPN
ejpam-3547	269	25	)	)	PUNCT
ejpam-3547	269	26	∥∥∥	∥∥∥	PROPN
ejpam-3547	269	27	c[a	c[a	NUM
ejpam-3547	269	28	,	,	PUNCT
ejpam-3547	269	29	b	b	NOUN
ejpam-3547	269	30	]	]	PUNCT
ejpam-3547	269	31	6	6	NUM
ejpam-3547	269	32	c1n	c1n	NOUN
ejpam-3547	269	33	−1	−1	NOUN
ejpam-3547	269	34	q∑	q∑	PROPN
ejpam-3547	270	1	i	i	PRON
ejpam-3547	270	2	=	=	NOUN
ejpam-3547	270	3	r	r	NOUN
ejpam-3547	270	4	∥∥∥f	∥∥∥f	NOUN
ejpam-3547	270	5	(	(	PUNCT
ejpam-3547	270	6	i)∥∥∥	i)∥∥∥	PROPN
ejpam-3547	270	7	c[a	c[a	NUM
ejpam-3547	270	8	,	,	PUNCT
ejpam-3547	270	9	b	b	X
ejpam-3547	270	10	]	]	X
ejpam-3547	271	1	+	+	NUM
ejpam-3547	271	2	c2n	c2n	NOUN
ejpam-3547	271	3	−1/2ωf	−1/2ωf	X
ejpam-3547	271	4	(	(	PUNCT
ejpam-3547	271	5	q+1	q+1	NOUN
ejpam-3547	271	6	)	)	PUNCT
ejpam-3547	271	7	×	×	NOUN
ejpam-3547	271	8	(	(	PUNCT
ejpam-3547	271	9	n−1/2	n−1/2	PROPN
ejpam-3547	271	10	;	;	PUNCT
ejpam-3547	271	11	(	(	PUNCT
ejpam-3547	271	12	a−	a−	PROPN
ejpam-3547	271	13	η	η	PROPN
ejpam-3547	271	14	,	,	PUNCT
ejpam-3547	271	15	b+	b+	X
ejpam-3547	271	16	η	η	NOUN
ejpam-3547	271	17	)	)	PUNCT
ejpam-3547	271	18	)	)	PUNCT
ejpam-3547	272	1	+	+	VERB
ejpam-3547	272	2	o(n−2	o(n−2	NOUN
ejpam-3547	272	3	)	)	PUNCT
ejpam-3547	272	4	,	,	PUNCT
ejpam-3547	272	5	where	where	SCONJ
ejpam-3547	272	6	,	,	PUNCT
ejpam-3547	272	7	c1	c1	PROPN
ejpam-3547	272	8	,	,	PUNCT
ejpam-3547	272	9	c2	c2	PROPN
ejpam-3547	272	10	are	be	AUX
ejpam-3547	272	11	constants	constant	NOUN
ejpam-3547	272	12	independent	independent	ADJ
ejpam-3547	272	13	of	of	ADP
ejpam-3547	272	14	f	f	PROPN
ejpam-3547	272	15	and	and	CCONJ
ejpam-3547	272	16	n.	n.	PROPN
ejpam-3547	272	17	proof	proof	NOUN
ejpam-3547	272	18	.	.	PUNCT
ejpam-3547	273	1	by	by	ADP
ejpam-3547	273	2	our	our	PRON
ejpam-3547	273	3	hypothesis	hypothesis	NOUN
ejpam-3547	273	4	f(t	f(t	NOUN
ejpam-3547	273	5	)	)	PUNCT
ejpam-3547	274	1	=	=	PUNCT
ejpam-3547	274	2	q∑	q∑	PROPN
ejpam-3547	274	3	i=0	i=0	PROPN
ejpam-3547	274	4	f	f	X
ejpam-3547	274	5	(	(	PUNCT
ejpam-3547	274	6	i)(x	i)(x	PROPN
ejpam-3547	274	7	)	)	PUNCT
ejpam-3547	274	8	i	i	PRON
ejpam-3547	274	9	!	!	PUNCT
ejpam-3547	275	1	(	(	PUNCT
ejpam-3547	275	2	t−	t−	PROPN
ejpam-3547	275	3	x)i	x)i	PUNCT
ejpam-3547	276	1	+	+	CCONJ
ejpam-3547	276	2	f	f	X
ejpam-3547	276	3	(	(	PUNCT
ejpam-3547	276	4	q+1)(ξ)−	q+1)(ξ)−	NOUN
ejpam-3547	276	5	f	f	PROPN
ejpam-3547	277	1	(	(	PUNCT
ejpam-3547	277	2	q+1)(x	q+1)(x	PROPN
ejpam-3547	277	3	)	)	PUNCT
ejpam-3547	277	4	(	(	PUNCT
ejpam-3547	277	5	q	q	NOUN
ejpam-3547	278	1	+	+	NOUN
ejpam-3547	278	2	1	1	NUM
ejpam-3547	278	3	)	)	PUNCT
ejpam-3547	278	4	!	!	PUNCT
ejpam-3547	279	1	(	(	PUNCT
ejpam-3547	279	2	t−	t−	PROPN
ejpam-3547	279	3	x)q+1χ(t	x)q+1χ(t	PROPN
ejpam-3547	279	4	)	)	PUNCT
ejpam-3547	280	1	+	+	CCONJ
ejpam-3547	280	2	h(t	h(t	PROPN
ejpam-3547	280	3	,	,	PUNCT
ejpam-3547	280	4	x)(1−	x)(1−	PROPN
ejpam-3547	280	5	χ(t	χ(t	PROPN
ejpam-3547	280	6	)	)	PUNCT
ejpam-3547	280	7	)	)	PUNCT
ejpam-3547	280	8	,	,	PUNCT
ejpam-3547	280	9	where	where	SCONJ
ejpam-3547	280	10	,	,	PUNCT
ejpam-3547	280	11	ξ	ξ	PROPN
ejpam-3547	280	12	lies	lie	NOUN
ejpam-3547	280	13	between	between	ADP
ejpam-3547	280	14	t	t	PROPN
ejpam-3547	280	15	,	,	PUNCT
ejpam-3547	280	16	x	x	X
ejpam-3547	280	17	and	and	CCONJ
ejpam-3547	280	18	χ(t	χ(t	NOUN
ejpam-3547	280	19	)	)	PUNCT
ejpam-3547	280	20	is	be	AUX
ejpam-3547	280	21	the	the	DET
ejpam-3547	280	22	characteristic	characteristic	ADJ
ejpam-3547	280	23	function	function	NOUN
ejpam-3547	280	24	of	of	ADP
ejpam-3547	280	25	the	the	DET
ejpam-3547	280	26	interval	interval	NOUN
ejpam-3547	280	27	(	(	PUNCT
ejpam-3547	280	28	a−η	a−η	PROPN
ejpam-3547	280	29	,	,	PUNCT
ejpam-3547	280	30	b+η	b+η	NOUN
ejpam-3547	280	31	)	)	PUNCT
ejpam-3547	280	32	.	.	PUNCT
ejpam-3547	281	1	for	for	ADP
ejpam-3547	281	2	t	t	PROPN
ejpam-3547	281	3	∈	∈	PROPN
ejpam-3547	281	4	(	(	PUNCT
ejpam-3547	281	5	a−	a−	PROPN
ejpam-3547	281	6	η	η	PROPN
ejpam-3547	281	7	,	,	PUNCT
ejpam-3547	281	8	b+	b+	NOUN
ejpam-3547	281	9	η	η	X
ejpam-3547	281	10	)	)	PUNCT
ejpam-3547	281	11	and	and	CCONJ
ejpam-3547	281	12	x	x	PUNCT
ejpam-3547	281	13	∈	∈	PROPN
ejpam-3547	281	14	(	(	PUNCT
ejpam-3547	281	15	0,∞	0,∞	NUM
ejpam-3547	281	16	)	)	PUNCT
ejpam-3547	281	17	we	we	PRON
ejpam-3547	281	18	get	get	VERB
ejpam-3547	281	19	:	:	PUNCT
ejpam-3547	281	20	f(t	f(t	NOUN
ejpam-3547	281	21	)	)	PUNCT
ejpam-3547	282	1	=	=	PUNCT
ejpam-3547	282	2	q∑	q∑	PROPN
ejpam-3547	282	3	i=0	i=0	PROPN
ejpam-3547	282	4	f	f	X
ejpam-3547	282	5	(	(	PUNCT
ejpam-3547	282	6	i)(x	i)(x	PROPN
ejpam-3547	282	7	)	)	PUNCT
ejpam-3547	282	8	i	i	PRON
ejpam-3547	282	9	!	!	PUNCT
ejpam-3547	283	1	(	(	PUNCT
ejpam-3547	283	2	t−	t−	PROPN
ejpam-3547	283	3	x)i	x)i	PUNCT
ejpam-3547	284	1	+	+	CCONJ
ejpam-3547	284	2	f	f	X
ejpam-3547	284	3	(	(	PUNCT
ejpam-3547	284	4	q+1)(ξ)−	q+1)(ξ)−	NOUN
ejpam-3547	284	5	f	f	PROPN
ejpam-3547	285	1	(	(	PUNCT
ejpam-3547	285	2	q+1)(x	q+1)(x	PROPN
ejpam-3547	285	3	)	)	PUNCT
ejpam-3547	285	4	(	(	PUNCT
ejpam-3547	285	5	q	q	NOUN
ejpam-3547	286	1	+	+	NOUN
ejpam-3547	286	2	1	1	NUM
ejpam-3547	286	3	)	)	PUNCT
ejpam-3547	286	4	!	!	PUNCT
ejpam-3547	287	1	(	(	PUNCT
ejpam-3547	287	2	t−	t−	PROPN
ejpam-3547	287	3	x)q+1	x)q+1	PROPN
ejpam-3547	287	4	.	.	PUNCT
ejpam-3547	288	1	for	for	ADP
ejpam-3547	288	2	t	t	PROPN
ejpam-3547	288	3	∈	∈	PROPN
ejpam-3547	288	4	[	[	X
ejpam-3547	288	5	0,∞)\(a−	0,∞)\(a−	NUM
ejpam-3547	288	6	η	η	NOUN
ejpam-3547	288	7	,	,	PUNCT
ejpam-3547	288	8	b+	b+	X
ejpam-3547	288	9	η	η	X
ejpam-3547	288	10	)	)	PUNCT
ejpam-3547	288	11	and	and	CCONJ
ejpam-3547	288	12	x	x	PUNCT
ejpam-3547	288	13	∈	∈	PROPN
ejpam-3547	289	1	[	[	X
ejpam-3547	289	2	a	a	X
ejpam-3547	289	3	,	,	PUNCT
ejpam-3547	289	4	b	b	NOUN
ejpam-3547	289	5	]	]	X
ejpam-3547	289	6	,	,	PUNCT
ejpam-3547	289	7	we	we	PRON
ejpam-3547	289	8	define	define	VERB
ejpam-3547	289	9	h(t	h(t	PROPN
ejpam-3547	289	10	,	,	PUNCT
ejpam-3547	289	11	x	x	X
ejpam-3547	289	12	)	)	PUNCT
ejpam-3547	289	13	=	=	SYM
ejpam-3547	289	14	f(t)−	f(t)−	PROPN
ejpam-3547	289	15	q∑	q∑	PROPN
ejpam-3547	289	16	i=0	i=0	PROPN
ejpam-3547	289	17	f	f	X
ejpam-3547	289	18	(	(	PUNCT
ejpam-3547	289	19	i)(x	i)(x	PROPN
ejpam-3547	289	20	)	)	PUNCT
ejpam-3547	289	21	i	i	PRON
ejpam-3547	289	22	!	!	PUNCT
ejpam-3547	290	1	(	(	PUNCT
ejpam-3547	290	2	t−	t−	PROPN
ejpam-3547	290	3	x)i	x)i	NOUN
ejpam-3547	290	4	.	.	PUNCT
ejpam-3547	291	1	∂r	∂r	PROPN
ejpam-3547	291	2	∂xr	∂xr	PROPN
ejpam-3547	291	3	h(t	h(t	PROPN
ejpam-3547	291	4	,	,	PUNCT
ejpam-3547	291	5	x	x	X
ejpam-3547	291	6	)	)	PUNCT
ejpam-3547	292	1	=	=	SYM
ejpam-3547	292	2	q∑	q∑	PROPN
ejpam-3547	292	3	i=0	i=0	PROPN
ejpam-3547	292	4	f	f	X
ejpam-3547	292	5	(	(	PUNCT
ejpam-3547	292	6	i)(x	i)(x	PROPN
ejpam-3547	292	7	)	)	PUNCT
ejpam-3547	292	8	i	i	PRON
ejpam-3547	292	9	!	!	PUNCT
ejpam-3547	293	1	(	(	PUNCT
ejpam-3547	293	2	t−	t−	PROPN
ejpam-3547	293	3	x)i	x)i	ADJ
ejpam-3547	293	4	now	now	ADV
ejpam-3547	293	5	,	,	PUNCT
ejpam-3547	293	6	wn	wn	INTJ
ejpam-3547	293	7	(	(	PUNCT
ejpam-3547	293	8	r)(f(t);x)−	r)(f(t);x)−	PROPN
ejpam-3547	293	9	f	f	PROPN
ejpam-3547	293	10	(	(	PUNCT
ejpam-3547	293	11	r)(x	r)(x	PROPN
ejpam-3547	293	12	)	)	PUNCT
ejpam-3547	293	13	=	=	PRON
ejpam-3547	294	1	[	[	PUNCT
ejpam-3547	294	2	q∑	q∑	X
ejpam-3547	294	3	i=0	i=0	PROPN
ejpam-3547	294	4	f	f	X
ejpam-3547	294	5	(	(	PUNCT
ejpam-3547	294	6	i)(x	i)(x	PROPN
ejpam-3547	294	7	)	)	PUNCT
ejpam-3547	294	8	i	i	PRON
ejpam-3547	294	9	!	!	PUNCT
ejpam-3547	295	1	(	(	PUNCT
ejpam-3547	295	2	−1)iwn	−1)iwn	PROPN
ejpam-3547	295	3	(	(	PUNCT
ejpam-3547	295	4	r)((x−	r)((x−	PROPN
ejpam-3547	295	5	t)i;x)−	t)i;x)−	PROPN
ejpam-3547	295	6	f	f	PROPN
ejpam-3547	295	7	(	(	PUNCT
ejpam-3547	295	8	r)(x	r)(x	PROPN
ejpam-3547	295	9	)	)	PUNCT
ejpam-3547	295	10	]	]	PUNCT
ejpam-3547	296	1	+	+	CCONJ
ejpam-3547	296	2	(	(	PUNCT
ejpam-3547	296	3	−1)q+1wn	−1)q+1wn	X
ejpam-3547	296	4	(	(	PUNCT
ejpam-3547	296	5	r	r	NOUN
ejpam-3547	296	6	)	)	PUNCT
ejpam-3547	296	7	(	(	PUNCT
ejpam-3547	296	8	f	f	X
ejpam-3547	296	9	(	(	PUNCT
ejpam-3547	296	10	q+1)(ξ)−	q+1)(ξ)−	NOUN
ejpam-3547	296	11	f	f	PROPN
ejpam-3547	296	12	(	(	PUNCT
ejpam-3547	296	13	q+1)(x	q+1)(x	PROPN
ejpam-3547	296	14	)	)	PUNCT
ejpam-3547	296	15	(	(	PUNCT
ejpam-3547	296	16	q	q	NOUN
ejpam-3547	296	17	+	+	NOUN
ejpam-3547	296	18	1	1	NUM
ejpam-3547	296	19	)	)	PUNCT
ejpam-3547	296	20	!	!	PUNCT
ejpam-3547	297	1	(	(	PUNCT
ejpam-3547	297	2	x−	x−	PROPN
ejpam-3547	297	3	t)q+1χ(t);x	t)q+1χ(t);x	PROPN
ejpam-3547	297	4	)	)	PUNCT
ejpam-3547	297	5	)	)	PUNCT
ejpam-3547	298	1	+	+	X
ejpam-3547	298	2	wn	wn	X
ejpam-3547	298	3	(	(	PUNCT
ejpam-3547	298	4	r	r	NOUN
ejpam-3547	298	5	)	)	PUNCT
ejpam-3547	298	6	(	(	PUNCT
ejpam-3547	298	7	h(t	h(t	PROPN
ejpam-3547	298	8	,	,	PUNCT
ejpam-3547	298	9	x)(1−	x)(1−	PROPN
ejpam-3547	298	10	χ(t));x	χ(t));x	PROPN
ejpam-3547	298	11	)	)	PUNCT
ejpam-3547	298	12	)	)	PUNCT
ejpam-3547	299	1	=	=	SYM
ejpam-3547	299	2	σ1	σ1	PROPN
ejpam-3547	299	3	+	+	CCONJ
ejpam-3547	299	4	σ2	σ2	PROPN
ejpam-3547	299	5	+	+	CCONJ
ejpam-3547	299	6	σ3	σ3	PROPN
ejpam-3547	299	7	.	.	PUNCT
ejpam-3547	300	1	using	use	VERB
ejpam-3547	300	2	lemma	lemma	PROPN
ejpam-3547	300	3	2.3	2.3	NUM
ejpam-3547	300	4	,	,	PUNCT
ejpam-3547	300	5	we	we	PRON
ejpam-3547	300	6	get	get	VERB
ejpam-3547	300	7	:	:	PUNCT
ejpam-3547	300	8	σ1	σ1	PROPN
ejpam-3547	300	9	=	=	PUNCT
ejpam-3547	301	1	q∑	q∑	PROPN
ejpam-3547	301	2	i=0	i=0	PROPN
ejpam-3547	301	3	f	f	X
ejpam-3547	301	4	(	(	PUNCT
ejpam-3547	301	5	i)(x	i)(x	PROPN
ejpam-3547	301	6	)	)	PUNCT
ejpam-3547	301	7	i	i	PRON
ejpam-3547	301	8	!	!	PUNCT
ejpam-3547	302	1	(	(	PUNCT
ejpam-3547	302	2	−1)i	−1)i	X
ejpam-3547	302	3	i∑	i∑	ADJ
ejpam-3547	302	4	j=0	j=0	PROPN
ejpam-3547	302	5	(	(	PUNCT
ejpam-3547	302	6	i	i	NOUN
ejpam-3547	302	7	j	j	PROPN
ejpam-3547	302	8	)	)	PUNCT
ejpam-3547	302	9	xi−j(−1)jwn	xi−j(−1)jwn	PROPN
ejpam-3547	303	1	(	(	PUNCT
ejpam-3547	303	2	r)(tj	r)(tj	X
ejpam-3547	303	3	;	;	PUNCT
ejpam-3547	303	4	x)−	x)−	PROPN
ejpam-3547	303	5	f	f	PROPN
ejpam-3547	303	6	(	(	PUNCT
ejpam-3547	303	7	r)(x	r)(x	PROPN
ejpam-3547	303	8	)	)	PUNCT
ejpam-3547	304	1	=	=	PUNCT
ejpam-3547	305	1	q∑	q∑	PROPN
ejpam-3547	305	2	i	i	PRON
ejpam-3547	306	1	=	=	VERB
ejpam-3547	306	2	r	r	NOUN
ejpam-3547	306	3	f	f	X
ejpam-3547	306	4	(	(	PUNCT
ejpam-3547	306	5	i)(x	i)(x	NOUN
ejpam-3547	306	6	)	)	PUNCT
ejpam-3547	306	7	i	i	PRON
ejpam-3547	306	8	!	!	PUNCT
ejpam-3547	307	1	(	(	PUNCT
ejpam-3547	307	2	−1)i	−1)i	X
ejpam-3547	307	3	i∑	i∑	ADJ
ejpam-3547	307	4	j=0	j=0	PROPN
ejpam-3547	307	5	(	(	PUNCT
ejpam-3547	307	6	i	i	NOUN
ejpam-3547	307	7	j	j	PROPN
ejpam-3547	307	8	)	)	PUNCT
ejpam-3547	307	9	xi−j(−1)j	xi−j(−1)j	PROPN
ejpam-3547	308	1	dr	dr	PROPN
ejpam-3547	308	2	dxr	dxr	PROPN
ejpam-3547	308	3	[	[	PUNCT
ejpam-3547	308	4	(	(	PUNCT
ejpam-3547	308	5	sinh(nx	sinh(nx	NOUN
ejpam-3547	308	6	)	)	PUNCT
ejpam-3547	308	7	(	(	PUNCT
ejpam-3547	308	8	δ0	δ0	NOUN
ejpam-3547	308	9	+	+	CCONJ
ejpam-3547	308	10	sinh(nx	sinh(nx	NOUN
ejpam-3547	308	11	)	)	PUNCT
ejpam-3547	308	12	)	)	PUNCT
ejpam-3547	308	13	)	)	PUNCT
ejpam-3547	308	14	xj	xj	PROPN
ejpam-3547	308	15	a.	a.	PROPN
ejpam-3547	308	16	j.	j.	PROPN
ejpam-3547	308	17	mohammad	mohammad	PROPN
ejpam-3547	308	18	,	,	PUNCT
ejpam-3547	308	19	h.	h.	PROPN
ejpam-3547	308	20	o.	o.	PROPN
ejpam-3547	308	21	muslim	muslim	PROPN
ejpam-3547	308	22	/	/	SYM
ejpam-3547	308	23	eur	eur	PROPN
ejpam-3547	308	24	.	.	PUNCT
ejpam-3547	309	1	j.	j.	PROPN
ejpam-3547	309	2	pure	pure	PROPN
ejpam-3547	309	3	appl	appl	PROPN
ejpam-3547	309	4	.	.	PROPN
ejpam-3547	309	5	math	math	PROPN
ejpam-3547	309	6	,	,	PUNCT
ejpam-3547	309	7	12	12	NUM
ejpam-3547	309	8	(	(	PUNCT
ejpam-3547	309	9	4	4	NUM
ejpam-3547	309	10	)	)	PUNCT
ejpam-3547	309	11	(	(	PUNCT
ejpam-3547	309	12	2019	2019	NUM
ejpam-3547	309	13	)	)	PUNCT
ejpam-3547	309	14	,	,	PUNCT
ejpam-3547	309	15	1508	1508	NUM
ejpam-3547	309	16	-	-	SYM
ejpam-3547	309	17	1523	1523	NUM
ejpam-3547	309	18	1518	1518	NUM
ejpam-3547	309	19	−	−	PROPN
ejpam-3547	309	20	j	j	PROPN
ejpam-3547	309	21	n	n	CCONJ
ejpam-3547	309	22	(	(	PUNCT
ejpam-3547	309	23	cosh(nx	cosh(nx	NOUN
ejpam-3547	309	24	)	)	PUNCT
ejpam-3547	309	25	(	(	PUNCT
ejpam-3547	309	26	δ0	δ0	NOUN
ejpam-3547	309	27	+	+	CCONJ
ejpam-3547	309	28	sinh(nx	sinh(nx	NOUN
ejpam-3547	309	29	)	)	PUNCT
ejpam-3547	309	30	)	)	PUNCT
ejpam-3547	309	31	)	)	PUNCT
ejpam-3547	310	1	xj−1	xj−1	VERB
ejpam-3547	311	1	+	+	PUNCT
ejpam-3547	311	2	o(n−2	o(n−2	X
ejpam-3547	311	3	)	)	PUNCT
ejpam-3547	311	4	]	]	PUNCT
ejpam-3547	312	1	−	−	PROPN
ejpam-3547	312	2	f	f	PROPN
ejpam-3547	312	3	r(x	r(x	PROPN
ejpam-3547	312	4	)	)	PUNCT
ejpam-3547	312	5	consequently	consequently	ADV
ejpam-3547	312	6	,	,	PUNCT
ejpam-3547	312	7	‖σ1‖c[a	‖σ1‖c[a	NOUN
ejpam-3547	312	8	,	,	PUNCT
ejpam-3547	312	9	b	b	NOUN
ejpam-3547	312	10	]	]	SYM
ejpam-3547	312	11	6	6	NUM
ejpam-3547	312	12	c1n	c1n	NOUN
ejpam-3547	312	13	−1	−1	NOUN
ejpam-3547	313	1	[	[	X
ejpam-3547	313	2	∑q	∑q	PROPN
ejpam-3547	313	3	i	i	NOUN
ejpam-3547	313	4	=	=	NOUN
ejpam-3547	313	5	r	r	NOUN
ejpam-3547	313	6	∥∥f	∥∥f	NOUN
ejpam-3547	313	7	(	(	PUNCT
ejpam-3547	313	8	i)∥∥	i)∥∥	PROPN
ejpam-3547	313	9	c[a	c[a	PROPN
ejpam-3547	313	10	,	,	PUNCT
ejpam-3547	313	11	b	b	X
ejpam-3547	313	12	]	]	X
ejpam-3547	313	13	]	]	PUNCT
ejpam-3547	314	1	+	+	PUNCT
ejpam-3547	314	2	o(n−2	o(n−2	X
ejpam-3547	314	3	)	)	PUNCT
ejpam-3547	314	4	,	,	PUNCT
ejpam-3547	314	5	uniformly	uniformly	ADV
ejpam-3547	314	6	on	on	ADP
ejpam-3547	314	7	[	[	X
ejpam-3547	314	8	a	a	X
ejpam-3547	314	9	,	,	PUNCT
ejpam-3547	314	10	b	b	NOUN
ejpam-3547	314	11	]	]	PUNCT
ejpam-3547	314	12	.	.	PUNCT
ejpam-3547	315	1	to	to	PART
ejpam-3547	315	2	estimate	estimate	VERB
ejpam-3547	315	3	σ2	σ2	NOUN
ejpam-3547	315	4	we	we	PRON
ejpam-3547	315	5	proceed	proceed	VERB
ejpam-3547	315	6	as	as	SCONJ
ejpam-3547	315	7	follows	follow	VERB
ejpam-3547	315	8	:	:	PUNCT
ejpam-3547	315	9	|σ2|	|σ2|	NOUN
ejpam-3547	315	10	6wn	6wn	ADJ
ejpam-3547	315	11	(	(	PUNCT
ejpam-3547	315	12	r	r	NOUN
ejpam-3547	315	13	)	)	PUNCT
ejpam-3547	315	14	(	(	PUNCT
ejpam-3547	315	15	|f	|f	PROPN
ejpam-3547	315	16	(	(	PUNCT
ejpam-3547	315	17	q+1)(ξ)−	q+1)(ξ)−	NOUN
ejpam-3547	315	18	f	f	PROPN
ejpam-3547	315	19	(	(	PUNCT
ejpam-3547	315	20	q+1)(x)|	q+1)(x)|	PROPN
ejpam-3547	315	21	(	(	PUNCT
ejpam-3547	315	22	q	q	NOUN
ejpam-3547	315	23	+	+	NUM
ejpam-3547	315	24	1	1	NUM
ejpam-3547	315	25	)	)	PUNCT
ejpam-3547	315	26	!	!	PUNCT
ejpam-3547	316	1	|	|	ADV
ejpam-3547	316	2	−	−	PROPN
ejpam-3547	316	3	(	(	PUNCT
ejpam-3547	316	4	x−	x−	PROPN
ejpam-3547	316	5	t)|q+1χ(t);x	t)|q+1χ(t);x	PROPN
ejpam-3547	316	6	)	)	PUNCT
ejpam-3547	316	7	6	6	NUM
ejpam-3547	316	8	ωf	ωf	PROPN
ejpam-3547	316	9	(	(	PUNCT
ejpam-3547	316	10	q+1	q+1	NOUN
ejpam-3547	316	11	)	)	PUNCT
ejpam-3547	316	12	(	(	PUNCT
ejpam-3547	316	13	δ	δ	PROPN
ejpam-3547	316	14	;	;	PUNCT
ejpam-3547	316	15	(	(	PUNCT
ejpam-3547	316	16	a−	a−	PROPN
ejpam-3547	316	17	η	η	PROPN
ejpam-3547	316	18	,	,	PUNCT
ejpam-3547	316	19	b+	b+	X
ejpam-3547	316	20	η	η	NOUN
ejpam-3547	316	21	)	)	PUNCT
ejpam-3547	316	22	)	)	PUNCT
ejpam-3547	317	1	(	(	PUNCT
ejpam-3547	317	2	q	q	NOUN
ejpam-3547	317	3	+	+	NOUN
ejpam-3547	317	4	1	1	NUM
ejpam-3547	317	5	)	)	PUNCT
ejpam-3547	317	6	!	!	PUNCT
ejpam-3547	318	1	wn	wn	INTJ
ejpam-3547	318	2	(	(	PUNCT
ejpam-3547	318	3	r	r	NOUN
ejpam-3547	318	4	)	)	PUNCT
ejpam-3547	318	5	(	(	PUNCT
ejpam-3547	318	6	δ	δ	PROPN
ejpam-3547	319	1	+	+	CCONJ
ejpam-3547	319	2	|	|	ADV
ejpam-3547	319	3	−	−	PROPN
ejpam-3547	319	4	(	(	PUNCT
ejpam-3547	319	5	x−	x−	PROPN
ejpam-3547	319	6	t)|	t)|	PROPN
ejpam-3547	319	7	δ	δ	PROPN
ejpam-3547	320	1	|	|	ADV
ejpam-3547	320	2	−	−	PROPN
ejpam-3547	320	3	(	(	PUNCT
ejpam-3547	320	4	x−	x−	PROPN
ejpam-3547	320	5	t)|q+1χ(t);x	t)|q+1χ(t);x	PROPN
ejpam-3547	320	6	)	)	PUNCT
ejpam-3547	320	7	6	6	NUM
ejpam-3547	320	8	ωf	ωf	PROPN
ejpam-3547	320	9	(	(	PUNCT
ejpam-3547	320	10	q+1	q+1	NOUN
ejpam-3547	320	11	)	)	PUNCT
ejpam-3547	320	12	(	(	PUNCT
ejpam-3547	320	13	δ	δ	PROPN
ejpam-3547	320	14	;	;	PUNCT
ejpam-3547	320	15	(	(	PUNCT
ejpam-3547	320	16	a−	a−	PROPN
ejpam-3547	320	17	η	η	PROPN
ejpam-3547	320	18	,	,	PUNCT
ejpam-3547	320	19	b+	b+	X
ejpam-3547	320	20	η	η	NOUN
ejpam-3547	320	21	)	)	PUNCT
ejpam-3547	320	22	)	)	PUNCT
ejpam-3547	321	1	(	(	PUNCT
ejpam-3547	321	2	q	q	NOUN
ejpam-3547	321	3	+	+	NOUN
ejpam-3547	321	4	1	1	NUM
ejpam-3547	321	5	)	)	PUNCT
ejpam-3547	321	6	!	!	PUNCT
ejpam-3547	322	1	dr	dr	PROPN
ejpam-3547	322	2	dxr	dxr	PROPN
ejpam-3547	322	3	[	[	PUNCT
ejpam-3547	322	4	n	n	CCONJ
ejpam-3547	322	5	(	(	PUNCT
ejpam-3547	322	6	δ0	δ0	NOUN
ejpam-3547	322	7	+	+	X
ejpam-3547	322	8	sinh(nx	sinh(nx	NOUN
ejpam-3547	322	9	)	)	PUNCT
ejpam-3547	322	10	)	)	PUNCT
ejpam-3547	322	11	∫	∫	PROPN
ejpam-3547	322	12	x	x	SYM
ejpam-3547	322	13	0	0	NUM
ejpam-3547	322	14	cosh(nt)(|	cosh(nt)(|	NOUN
ejpam-3547	322	15	−	−	PROPN
ejpam-3547	322	16	(	(	PUNCT
ejpam-3547	322	17	x−	x−	PROPN
ejpam-3547	322	18	t)|q+1	t)|q+1	PROPN
ejpam-3547	322	19	+	+	CCONJ
ejpam-3547	322	20	δ−1|	δ−1|	ADJ
ejpam-3547	322	21	−	−	PROPN
ejpam-3547	322	22	(	(	PUNCT
ejpam-3547	322	23	x−	x−	PROPN
ejpam-3547	322	24	t)|q+2)dt	t)|q+2)dt	PROPN
ejpam-3547	322	25	]	]	PUNCT
ejpam-3547	322	26	δ	δ	PROPN
ejpam-3547	322	27	>	>	X
ejpam-3547	322	28	0	0	X
ejpam-3547	322	29	.	.	PUNCT
ejpam-3547	323	1	now	now	ADV
ejpam-3547	323	2	,	,	PUNCT
ejpam-3547	323	3	for	for	ADP
ejpam-3547	323	4	k	k	PROPN
ejpam-3547	323	5	=	=	SYM
ejpam-3547	323	6	0	0	NUM
ejpam-3547	323	7	,	,	PUNCT
ejpam-3547	323	8	1	1	NUM
ejpam-3547	323	9	,	,	PUNCT
ejpam-3547	323	10	2	2	NUM
ejpam-3547	323	11	,	,	PUNCT
ejpam-3547	323	12	....	....	PUNCT
ejpam-3547	323	13	and	and	CCONJ
ejpam-3547	323	14	using	use	VERB
ejpam-3547	323	15	lemma	lemma	PROPN
ejpam-3547	323	16	2.5	2.5	NUM
ejpam-3547	323	17	,	,	PUNCT
ejpam-3547	323	18	lemma	lemma	PROPN
ejpam-3547	323	19	2.7	2.7	NUM
ejpam-3547	323	20	,	,	PUNCT
ejpam-3547	323	21	,	,	PUNCT
ejpam-3547	323	22	we	we	PRON
ejpam-3547	323	23	have:∣∣∣∣	have:∣∣∣∣	VERB
ejpam-3547	323	24	drdxr	drdxr	PROPN
ejpam-3547	323	25	[	[	PUNCT
ejpam-3547	323	26	n	n	CCONJ
ejpam-3547	323	27	(	(	PUNCT
ejpam-3547	323	28	δ0	δ0	NOUN
ejpam-3547	323	29	+	+	X
ejpam-3547	323	30	sinh(nx	sinh(nx	NOUN
ejpam-3547	323	31	)	)	PUNCT
ejpam-3547	323	32	)	)	PUNCT
ejpam-3547	324	1	∫	∫	PROPN
ejpam-3547	324	2	x	x	SYM
ejpam-3547	324	3	0	0	NUM
ejpam-3547	324	4	cosh(nt	cosh(nt	NOUN
ejpam-3547	324	5	)	)	PUNCT
ejpam-3547	324	6	(	(	PUNCT
ejpam-3547	324	7	−(x−	−(x−	NOUN
ejpam-3547	324	8	t))k+1	t))k+1	VERB
ejpam-3547	324	9	dt	dt	NOUN
ejpam-3547	324	10	]	]	X
ejpam-3547	324	11	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3547	324	12	(	(	PUNCT
ejpam-3547	324	13	3.3	3.3	NUM
ejpam-3547	324	14	)	)	PUNCT
ejpam-3547	324	15	=	=	SYM
ejpam-3547	325	1	r∑	r∑	NOUN
ejpam-3547	325	2	l=0	l=0	PROPN
ejpam-3547	325	3	(	(	PUNCT
ejpam-3547	325	4	r	r	NOUN
ejpam-3547	325	5	l	l	NOUN
ejpam-3547	325	6	)	)	PUNCT
ejpam-3547	325	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3547	325	8	dr−ldxr−l	dr−ldxr−l	NOUN
ejpam-3547	325	9	(	(	PUNCT
ejpam-3547	325	10	n	n	CCONJ
ejpam-3547	325	11	δ0	δ0	NOUN
ejpam-3547	325	12	+	+	CCONJ
ejpam-3547	325	13	sinh(nx	sinh(nx	NOUN
ejpam-3547	325	14	)	)	PUNCT
ejpam-3547	325	15	)	)	PUNCT
ejpam-3547	325	16	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3547	325	17	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3547	325	18	dldxl	dldxl	NOUN
ejpam-3547	325	19	(	(	PUNCT
ejpam-3547	325	20	∫	∫	PROPN
ejpam-3547	325	21	x	x	SYM
ejpam-3547	325	22	0	0	NUM
ejpam-3547	325	23	cosh(nx	cosh(nx	NOUN
ejpam-3547	325	24	)	)	PUNCT
ejpam-3547	325	25	(	(	PUNCT
ejpam-3547	325	26	−(x−	−(x−	NOUN
ejpam-3547	325	27	t))k+1	t))k+1	VERB
ejpam-3547	325	28	dt	dt	NOUN
ejpam-3547	325	29	)	)	PUNCT
ejpam-3547	325	30	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3547	325	31	=	=	PUNCT
ejpam-3547	325	32	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3547	325	33	drdxr	drdxr	NOUN
ejpam-3547	325	34	(	(	PUNCT
ejpam-3547	325	35	n	n	CCONJ
ejpam-3547	325	36	δ0	δ0	NOUN
ejpam-3547	325	37	+	+	CCONJ
ejpam-3547	325	38	sinh(nx	sinh(nx	NOUN
ejpam-3547	325	39	)	)	PUNCT
ejpam-3547	325	40	)	)	PUNCT
ejpam-3547	325	41	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3547	325	42	∫	∫	PROPN
ejpam-3547	325	43	x	x	SYM
ejpam-3547	325	44	0	0	NUM
ejpam-3547	325	45	cosh(nt	cosh(nt	PROPN
ejpam-3547	325	46	)	)	PUNCT
ejpam-3547	325	47	|−(x−	|−(x−	NOUN
ejpam-3547	325	48	t)|k+1	t)|k+1	NOUN
ejpam-3547	325	49	dt	dt	NOUN
ejpam-3547	326	1	+	+	CCONJ
ejpam-3547	326	2	r∑	r∑	NOUN
ejpam-3547	326	3	l=1	l=1	PROPN
ejpam-3547	326	4	(	(	PUNCT
ejpam-3547	326	5	r	r	NOUN
ejpam-3547	326	6	l	l	NOUN
ejpam-3547	326	7	)	)	PUNCT
ejpam-3547	327	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3547	327	2	dr−ldxr−l	dr−ldxr−l	NOUN
ejpam-3547	327	3	(	(	PUNCT
ejpam-3547	327	4	n	n	CCONJ
ejpam-3547	327	5	δ0	δ0	NOUN
ejpam-3547	327	6	+	+	CCONJ
ejpam-3547	327	7	sinh(nx	sinh(nx	NOUN
ejpam-3547	327	8	)	)	PUNCT
ejpam-3547	327	9	)	)	PUNCT
ejpam-3547	327	10	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3547	327	11	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3547	327	12	dldxl	dldxl	NOUN
ejpam-3547	327	13	(	(	PUNCT
ejpam-3547	327	14	∫	∫	PROPN
ejpam-3547	327	15	x	x	SYM
ejpam-3547	327	16	0	0	NUM
ejpam-3547	327	17	cosh(nx	cosh(nx	NOUN
ejpam-3547	327	18	)	)	PUNCT
ejpam-3547	327	19	|−(x−	|−(x−	PROPN
ejpam-3547	327	20	t)|k+1	t)|k+1	NOUN
ejpam-3547	327	21	dt	dt	X
ejpam-3547	327	22	)	)	PUNCT
ejpam-3547	327	23	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3547	327	24	:	:	PUNCT
ejpam-3547	327	25	=	=	X
ejpam-3547	327	26	j1	j1	PROPN
ejpam-3547	327	27	+	+	CCONJ
ejpam-3547	327	28	j2	j2	PROPN
ejpam-3547	327	29	using	use	VERB
ejpam-3547	327	30	the	the	DET
ejpam-3547	327	31	same	same	ADJ
ejpam-3547	327	32	technique	technique	NOUN
ejpam-3547	327	33	in	in	ADP
ejpam-3547	327	34	i1	i1	PROPN
ejpam-3547	327	35	,	,	PUNCT
ejpam-3547	327	36	i2(theorem	i2(theorem	VERB
ejpam-3547	327	37	3.1	3.1	NUM
ejpam-3547	327	38	)	)	PUNCT
ejpam-3547	327	39	,	,	PUNCT
ejpam-3547	327	40	we	we	PRON
ejpam-3547	327	41	get	get	VERB
ejpam-3547	327	42	:	:	PUNCT
ejpam-3547	327	43	j1	j1	PROPN
ejpam-3547	327	44	=	=	SYM
ejpam-3547	327	45	o(nr−(k+1	o(nr−(k+1	PROPN
ejpam-3547	327	46	)	)	PUNCT
ejpam-3547	327	47	)	)	PUNCT
ejpam-3547	327	48	,	,	PUNCT
ejpam-3547	327	49	uniformly	uniformly	ADV
ejpam-3547	327	50	on	on	ADP
ejpam-3547	327	51	[	[	X
ejpam-3547	327	52	a	a	X
ejpam-3547	327	53	,	,	PUNCT
ejpam-3547	327	54	b	b	NOUN
ejpam-3547	327	55	]	]	PUNCT
ejpam-3547	327	56	and	and	CCONJ
ejpam-3547	327	57	j2	j2	PROPN
ejpam-3547	327	58	=	=	SYM
ejpam-3547	327	59	o(n−1	o(n−1	PROPN
ejpam-3547	327	60	)	)	PUNCT
ejpam-3547	327	61	.	.	PUNCT
ejpam-3547	328	1	choosing	choose	VERB
ejpam-3547	328	2	δ	δ	PROPN
ejpam-3547	328	3	=	=	SYM
ejpam-3547	328	4	n−1/2	n−1/2	PROPN
ejpam-3547	328	5	and	and	CCONJ
ejpam-3547	328	6	applying	apply	VERB
ejpam-3547	328	7	3.3	3.3	NUM
ejpam-3547	328	8	,	,	PUNCT
ejpam-3547	328	9	we	we	PRON
ejpam-3547	328	10	are	be	AUX
ejpam-3547	328	11	led	lead	VERB
ejpam-3547	328	12	to	to	ADP
ejpam-3547	328	13	:	:	PUNCT
ejpam-3547	328	14	‖σ2‖c[a	‖σ2‖c[a	VERB
ejpam-3547	328	15	,	,	PUNCT
ejpam-3547	328	16	b	b	NOUN
ejpam-3547	328	17	]	]	PUNCT
ejpam-3547	328	18	6	6	NUM
ejpam-3547	328	19	ωf	ωf	PROPN
ejpam-3547	328	20	(	(	PUNCT
ejpam-3547	328	21	q+1	q+1	NOUN
ejpam-3547	328	22	)	)	PUNCT
ejpam-3547	328	23	(	(	PUNCT
ejpam-3547	328	24	n−1/2	n−1/2	PROPN
ejpam-3547	328	25	;	;	PUNCT
ejpam-3547	328	26	(	(	PUNCT
ejpam-3547	328	27	a−	a−	PROPN
ejpam-3547	328	28	η	η	PROPN
ejpam-3547	328	29	,	,	PUNCT
ejpam-3547	328	30	b+	b+	X
ejpam-3547	328	31	η	η	NOUN
ejpam-3547	328	32	)	)	PUNCT
ejpam-3547	328	33	)	)	PUNCT
ejpam-3547	329	1	(	(	PUNCT
ejpam-3547	329	2	q	q	NOUN
ejpam-3547	329	3	+	+	NOUN
ejpam-3547	329	4	1	1	NUM
ejpam-3547	329	5	)	)	PUNCT
ejpam-3547	329	6	!	!	PUNCT
ejpam-3547	330	1	[	[	PUNCT
ejpam-3547	330	2	o	o	X
ejpam-3547	330	3	(	(	PUNCT
ejpam-3547	330	4	n(r−(q+1	n(r−(q+1	PROPN
ejpam-3547	330	5	)	)	PUNCT
ejpam-3547	330	6	)	)	PUNCT
ejpam-3547	330	7	)	)	PUNCT
ejpam-3547	331	1	+	+	CCONJ
ejpam-3547	331	2	n1/2o	n1/2o	NOUN
ejpam-3547	331	3	(	(	PUNCT
ejpam-3547	331	4	n(r−(q+2	n(r−(q+2	NOUN
ejpam-3547	331	5	)	)	PUNCT
ejpam-3547	331	6	)	)	PUNCT
ejpam-3547	331	7	)	)	PUNCT
ejpam-3547	332	1	+	+	VERB
ejpam-3547	332	2	o(n−1	o(n−1	X
ejpam-3547	332	3	)	)	PUNCT
ejpam-3547	332	4	]	]	PUNCT
ejpam-3547	332	5	6	6	NUM
ejpam-3547	332	6	c2n	c2n	NOUN
ejpam-3547	332	7	−(r−(q+1))ωf	−(r−(q+1))ωf	NOUN
ejpam-3547	332	8	(	(	PUNCT
ejpam-3547	332	9	q+1	q+1	NOUN
ejpam-3547	332	10	)	)	PUNCT
ejpam-3547	332	11	(	(	PUNCT
ejpam-3547	332	12	n−1/2	n−1/2	PROPN
ejpam-3547	332	13	;	;	PUNCT
ejpam-3547	332	14	(	(	PUNCT
ejpam-3547	332	15	a−	a−	PROPN
ejpam-3547	332	16	η	η	PROPN
ejpam-3547	332	17	,	,	PUNCT
ejpam-3547	332	18	b+	b+	X
ejpam-3547	332	19	η	η	NOUN
ejpam-3547	332	20	)	)	PUNCT
ejpam-3547	332	21	)	)	PUNCT
ejpam-3547	332	22	.	.	PUNCT
ejpam-3547	333	1	since	since	SCONJ
ejpam-3547	333	2	t	t	PROPN
ejpam-3547	333	3	∈	∈	PROPN
ejpam-3547	333	4	[	[	X
ejpam-3547	333	5	0,∞)\(a	0,∞)\(a	PROPN
ejpam-3547	333	6	−	−	PROPN
ejpam-3547	333	7	η	η	PROPN
ejpam-3547	333	8	,	,	PUNCT
ejpam-3547	333	9	b	b	PROPN
ejpam-3547	333	10	+	+	CCONJ
ejpam-3547	333	11	η	η	PROPN
ejpam-3547	333	12	)	)	PUNCT
ejpam-3547	333	13	,	,	PUNCT
ejpam-3547	333	14	we	we	PRON
ejpam-3547	333	15	can	can	AUX
ejpam-3547	333	16	choose	choose	VERB
ejpam-3547	333	17	δ	δ	PROPN
ejpam-3547	333	18	>	>	X
ejpam-3547	333	19	0	0	PUNCT
ejpam-3547	333	20	in	in	ADP
ejpam-3547	333	21	such	such	DET
ejpam-3547	333	22	a	a	DET
ejpam-3547	333	23	way	way	NOUN
ejpam-3547	333	24	that	that	PRON
ejpam-3547	334	1	x	x	PUNCT
ejpam-3547	334	2	−	−	PROPN
ejpam-3547	334	3	t	t	X
ejpam-3547	334	4	>	>	X
ejpam-3547	334	5	δ	δ	PROPN
ejpam-3547	334	6	for	for	ADP
ejpam-3547	334	7	all	all	DET
ejpam-3547	334	8	x	x	SYM
ejpam-3547	334	9	∈	∈	PROPN
ejpam-3547	334	10	[	[	X
ejpam-3547	334	11	a	a	X
ejpam-3547	334	12	,	,	PUNCT
ejpam-3547	334	13	b	b	NOUN
ejpam-3547	334	14	]	]	X
ejpam-3547	334	15	.	.	PUNCT
ejpam-3547	335	1	thus	thus	ADV
ejpam-3547	335	2	,	,	PUNCT
ejpam-3547	335	3	|σ3|	|σ3|	NOUN
ejpam-3547	335	4	6	6	NUM
ejpam-3547	335	5	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3547	335	6	drdxr	drdxr	NOUN
ejpam-3547	335	7	[	[	PUNCT
ejpam-3547	335	8	n	n	CCONJ
ejpam-3547	335	9	(	(	PUNCT
ejpam-3547	335	10	δ0	δ0	NOUN
ejpam-3547	335	11	+	+	X
ejpam-3547	335	12	sinh(nx	sinh(nx	NOUN
ejpam-3547	335	13	)	)	PUNCT
ejpam-3547	335	14	)	)	PUNCT
ejpam-3547	335	15	∫	∫	PROPN
ejpam-3547	336	1	x	x	SYM
ejpam-3547	336	2	0	0	NUM
ejpam-3547	336	3	cosh(nt	cosh(nt	NOUN
ejpam-3547	336	4	)	)	PUNCT
ejpam-3547	336	5	(	(	PUNCT
ejpam-3547	336	6	h(t	h(t	PROPN
ejpam-3547	336	7	,	,	PUNCT
ejpam-3547	336	8	x)(1−	x)(1−	PROPN
ejpam-3547	336	9	χ(t	χ(t	PROPN
ejpam-3547	336	10	)	)	PUNCT
ejpam-3547	336	11	)	)	PUNCT
ejpam-3547	336	12	)	)	PUNCT
ejpam-3547	337	1	dt	dt	X
ejpam-3547	337	2	]	]	PUNCT
ejpam-3547	337	3	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3547	337	4	a.	a.	NOUN
ejpam-3547	337	5	j.	j.	PROPN
ejpam-3547	337	6	mohammad	mohammad	PROPN
ejpam-3547	337	7	,	,	PUNCT
ejpam-3547	337	8	h.	h.	PROPN
ejpam-3547	337	9	o.	o.	PROPN
ejpam-3547	337	10	muslim	muslim	PROPN
ejpam-3547	337	11	/	/	SYM
ejpam-3547	337	12	eur	eur	PROPN
ejpam-3547	337	13	.	.	PUNCT
ejpam-3547	338	1	j.	j.	PROPN
ejpam-3547	338	2	pure	pure	PROPN
ejpam-3547	338	3	appl	appl	PROPN
ejpam-3547	338	4	.	.	PROPN
ejpam-3547	338	5	math	math	PROPN
ejpam-3547	338	6	,	,	PUNCT
ejpam-3547	338	7	12	12	NUM
ejpam-3547	338	8	(	(	PUNCT
ejpam-3547	338	9	4	4	NUM
ejpam-3547	338	10	)	)	PUNCT
ejpam-3547	338	11	(	(	PUNCT
ejpam-3547	338	12	2019	2019	NUM
ejpam-3547	338	13	)	)	PUNCT
ejpam-3547	338	14	,	,	PUNCT
ejpam-3547	338	15	1508	1508	NUM
ejpam-3547	338	16	-	-	SYM
ejpam-3547	338	17	1523	1523	NUM
ejpam-3547	338	18	1519	1519	NUM
ejpam-3547	338	19	6	6	NUM
ejpam-3547	338	20	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3547	338	21	drdxr	drdxr	NOUN
ejpam-3547	338	22	[	[	PUNCT
ejpam-3547	338	23	n	n	CCONJ
ejpam-3547	338	24	(	(	PUNCT
ejpam-3547	338	25	δ0	δ0	NOUN
ejpam-3547	338	26	+	+	X
ejpam-3547	338	27	sinh(nx	sinh(nx	NOUN
ejpam-3547	338	28	)	)	PUNCT
ejpam-3547	338	29	)	)	PUNCT
ejpam-3547	338	30	∫	∫	PROPN
ejpam-3547	338	31	x−t≥δ	x−t≥δ	PROPN
ejpam-3547	338	32	cosh(nt)h(t	cosh(nt)h(t	PROPN
ejpam-3547	338	33	,	,	PUNCT
ejpam-3547	338	34	x)dt	x)dt	PROPN
ejpam-3547	338	35	]	]	SYM
ejpam-3547	338	36	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3547	338	37	=	=	PUNCT
ejpam-3547	338	38	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3547	338	39	drdxr	drdxr	NOUN
ejpam-3547	338	40	(	(	PUNCT
ejpam-3547	338	41	n	n	CCONJ
ejpam-3547	338	42	(	(	PUNCT
ejpam-3547	338	43	δ0	δ0	NOUN
ejpam-3547	338	44	+	+	X
ejpam-3547	338	45	sinh(nx	sinh(nx	NOUN
ejpam-3547	338	46	)	)	PUNCT
ejpam-3547	338	47	)	)	PUNCT
ejpam-3547	338	48	)	)	PUNCT
ejpam-3547	339	1	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3547	339	2	∫	∫	PROPN
ejpam-3547	339	3	x−t≥δ	x−t≥δ	PROPN
ejpam-3547	339	4	cosh(nt)h(t	cosh(nt)h(t	PROPN
ejpam-3547	339	5	,	,	PUNCT
ejpam-3547	339	6	x)dt	x)dt	PROPN
ejpam-3547	340	1	+	+	PUNCT
ejpam-3547	340	2	r∑	r∑	NOUN
ejpam-3547	340	3	l=1	l=1	PROPN
ejpam-3547	340	4	(	(	PUNCT
ejpam-3547	340	5	r	r	NOUN
ejpam-3547	340	6	l	l	NOUN
ejpam-3547	340	7	)	)	PUNCT
ejpam-3547	341	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3547	341	2	dr−ldxr−l	dr−ldxr−l	NOUN
ejpam-3547	341	3	(	(	PUNCT
ejpam-3547	341	4	n	n	CCONJ
ejpam-3547	341	5	(	(	PUNCT
ejpam-3547	341	6	δ0	δ0	NOUN
ejpam-3547	341	7	+	+	X
ejpam-3547	341	8	sinh(nx	sinh(nx	NOUN
ejpam-3547	341	9	)	)	PUNCT
ejpam-3547	341	10	)	)	PUNCT
ejpam-3547	341	11	)	)	PUNCT
ejpam-3547	341	12	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3547	341	13	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3547	341	14	dldxl	dldxl	NOUN
ejpam-3547	341	15	(	(	PUNCT
ejpam-3547	341	16	∫	∫	PROPN
ejpam-3547	341	17	x−t≥δ	x−t≥δ	PROPN
ejpam-3547	341	18	cosh(nt)h(t	cosh(nt)h(t	PROPN
ejpam-3547	341	19	,	,	PUNCT
ejpam-3547	341	20	x)dt	x)dt	PROPN
ejpam-3547	341	21	)	)	PUNCT
ejpam-3547	341	22	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3547	341	23	=	=	PROPN
ejpam-3547	341	24	j3	j3	PROPN
ejpam-3547	341	25	+	+	PROPN
ejpam-3547	341	26	j4	j4	PROPN
ejpam-3547	341	27	.	.	PROPN
ejpam-3547	341	28	for	for	ADP
ejpam-3547	341	29	x−	x−	PROPN
ejpam-3547	341	30	t	t	PROPN
ejpam-3547	341	31	>	>	X
ejpam-3547	341	32	δ	δ	PROPN
ejpam-3547	341	33	,	,	PUNCT
ejpam-3547	341	34	we	we	PRON
ejpam-3547	341	35	can	can	AUX
ejpam-3547	341	36	find	find	VERB
ejpam-3547	341	37	a	a	DET
ejpam-3547	341	38	constant	constant	ADJ
ejpam-3547	341	39	c	c	NOUN
ejpam-3547	341	40	>	>	X
ejpam-3547	341	41	0	0	NUM
ejpam-3547	342	1	such	such	ADJ
ejpam-3547	342	2	that	that	DET
ejpam-3547	342	3	|h(t	|h(t	PROPN
ejpam-3547	342	4	,	,	PUNCT
ejpam-3547	342	5	x)|	x)|	PROPN
ejpam-3547	342	6	6	6	NUM
ejpam-3547	342	7	ceαt	ceαt	NOUN
ejpam-3547	342	8	and	and	CCONJ
ejpam-3547	342	9	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3547	342	10	∂r∂xr	∂r∂xr	PROPN
ejpam-3547	342	11	h(t	h(t	PROPN
ejpam-3547	342	12	,	,	PUNCT
ejpam-3547	342	13	x	x	X
ejpam-3547	342	14	)	)	PUNCT
ejpam-3547	342	15	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3547	342	16	6	6	NUM
ejpam-3547	342	17	ceαt	ceαt	NOUN
ejpam-3547	342	18	using	use	VERB
ejpam-3547	342	19	lemma	lemma	PROPN
ejpam-3547	342	20	2.4	2.4	NUM
ejpam-3547	342	21	,	,	PUNCT
ejpam-3547	342	22	we	we	PRON
ejpam-3547	342	23	get	get	VERB
ejpam-3547	342	24	|σ3|	|σ3|	NOUN
ejpam-3547	342	25	=	=	SYM
ejpam-3547	342	26	o(n−λ	o(n−λ	PROPN
ejpam-3547	342	27	)	)	PUNCT
ejpam-3547	342	28	,	,	PUNCT
ejpam-3547	342	29	λ	λ	X
ejpam-3547	342	30	>	>	X
ejpam-3547	342	31	0	0	PUNCT
ejpam-3547	342	32	uniformly	uniformly	ADV
ejpam-3547	342	33	on	on	ADP
ejpam-3547	342	34	[	[	X
ejpam-3547	342	35	a	a	X
ejpam-3547	342	36	,	,	PUNCT
ejpam-3547	342	37	b	b	NOUN
ejpam-3547	342	38	]	]	PUNCT
ejpam-3547	342	39	.	.	PUNCT
ejpam-3547	343	1	combining	combine	VERB
ejpam-3547	343	2	the	the	DET
ejpam-3547	343	3	estimates	estimate	NOUN
ejpam-3547	343	4	of	of	ADP
ejpam-3547	343	5	σ1,σ2,σ3	σ1,σ2,σ3	PRON
ejpam-3547	343	6	the	the	DET
ejpam-3547	343	7	required	require	VERB
ejpam-3547	343	8	results	result	NOUN
ejpam-3547	343	9	are	be	AUX
ejpam-3547	343	10	immediate	immediate	ADJ
ejpam-3547	343	11	.	.	PUNCT
ejpam-3547	344	1	4	4	X
ejpam-3547	344	2	.	.	X
ejpam-3547	344	3	numerical	numerical	ADJ
ejpam-3547	344	4	examples	example	NOUN
ejpam-3547	344	5	in	in	ADP
ejpam-3547	344	6	this	this	DET
ejpam-3547	344	7	section	section	NOUN
ejpam-3547	344	8	,	,	PUNCT
ejpam-3547	344	9	we	we	PRON
ejpam-3547	344	10	give	give	VERB
ejpam-3547	344	11	some	some	DET
ejpam-3547	344	12	numerical	numerical	ADJ
ejpam-3547	344	13	examples	example	NOUN
ejpam-3547	344	14	for	for	ADP
ejpam-3547	344	15	the	the	DET
ejpam-3547	344	16	sequence	sequence	NOUN
ejpam-3547	344	17	of	of	ADP
ejpam-3547	344	18	linear	linear	ADJ
ejpam-3547	344	19	positive	positive	ADJ
ejpam-3547	344	20	operators	operator	NOUN
ejpam-3547	344	21	wn(.;x	wn(.;x	PROPN
ejpam-3547	344	22	)	)	PUNCT
ejpam-3547	344	23	,	,	PUNCT
ejpam-3547	344	24	by	by	ADP
ejpam-3547	344	25	using	use	VERB
ejpam-3547	344	26	two	two	NUM
ejpam-3547	344	27	test	test	NOUN
ejpam-3547	344	28	functions	function	NOUN
ejpam-3547	344	29	g1(t	g1(t	PART
ejpam-3547	344	30	)	)	PUNCT
ejpam-3547	344	31	=	=	SYM
ejpam-3547	344	32	sin(10t)e−2	sin(10t)e−2	PROPN
ejpam-3547	344	33	t	t	NOUN
ejpam-3547	344	34	and	and	CCONJ
ejpam-3547	344	35	g2(t	g2(t	NOUN
ejpam-3547	344	36	)	)	PUNCT
ejpam-3547	345	1	=	=	NOUN
ejpam-3547	345	2	√	√	NUM
ejpam-3547	345	3	1−	1−	NUM
ejpam-3547	345	4	(	(	PUNCT
ejpam-3547	345	5	t−	t−	PROPN
ejpam-3547	345	6	1)2	1)2	NUM
ejpam-3547	345	7	,	,	PUNCT
ejpam-3547	345	8	t	t	PROPN
ejpam-3547	345	9	∈	∈	PROPN
ejpam-3547	346	1	[	[	X
ejpam-3547	346	2	0	0	NUM
ejpam-3547	346	3	,	,	PUNCT
ejpam-3547	346	4	2	2	NUM
ejpam-3547	346	5	]	]	PUNCT
ejpam-3547	346	6	.	.	PUNCT
ejpam-3547	347	1	we	we	PRON
ejpam-3547	347	2	calculate	calculate	VERB
ejpam-3547	347	3	the	the	DET
ejpam-3547	347	4	maximum	maximum	ADJ
ejpam-3547	347	5	error	error	NOUN
ejpam-3547	347	6	and	and	CCONJ
ejpam-3547	347	7	compare	compare	VERB
ejpam-3547	347	8	the	the	DET
ejpam-3547	347	9	results	result	NOUN
ejpam-3547	347	10	of	of	ADP
ejpam-3547	347	11	the	the	DET
ejpam-3547	347	12	sequence	sequence	NOUN
ejpam-3547	347	13	wn(.;x	wn(.;x	PROPN
ejpam-3547	347	14	)	)	PUNCT
ejpam-3547	347	15	,	,	PUNCT
ejpam-3547	347	16	with	with	ADP
ejpam-3547	347	17	the	the	DET
ejpam-3547	347	18	results	result	NOUN
ejpam-3547	347	19	of	of	ADP
ejpam-3547	347	20	classical	classical	ADJ
ejpam-3547	347	21	szãsz	szãsz	ADJ
ejpam-3547	347	22	sequence	sequence	NOUN
ejpam-3547	347	23	sn(.;x	sn(.;x	NOUN
ejpam-3547	347	24	)	)	PUNCT
ejpam-3547	347	25	in	in	ADP
ejpam-3547	347	26	the	the	DET
ejpam-3547	347	27	interval	interval	NOUN
ejpam-3547	347	28	[	[	X
ejpam-3547	347	29	0	0	NUM
ejpam-3547	347	30	,	,	PUNCT
ejpam-3547	347	31	2	2	NUM
ejpam-3547	347	32	]	]	PUNCT
ejpam-3547	347	33	and	and	CCONJ
ejpam-3547	347	34	we	we	PRON
ejpam-3547	347	35	describe	describe	VERB
ejpam-3547	347	36	the	the	DET
ejpam-3547	347	37	results	result	NOUN
ejpam-3547	347	38	by	by	ADP
ejpam-3547	347	39	figures	figure	NOUN
ejpam-3547	347	40	(	(	PUNCT
ejpam-3547	347	41	1	1	NUM
ejpam-3547	347	42	−	−	NOUN
ejpam-3547	347	43	24	24	NUM
ejpam-3547	347	44	)	)	PUNCT
ejpam-3547	347	45	for	for	ADP
ejpam-3547	347	46	some	some	DET
ejpam-3547	347	47	n	n	NOUN
ejpam-3547	347	48	=	=	SYM
ejpam-3547	347	49	30	30	NUM
ejpam-3547	347	50	,	,	PUNCT
ejpam-3547	347	51	60	60	NUM
ejpam-3547	347	52	,	,	PUNCT
ejpam-3547	347	53	100	100	NUM
ejpam-3547	347	54	and	and	CCONJ
ejpam-3547	347	55	the	the	DET
ejpam-3547	347	56	positive	positive	ADJ
ejpam-3547	347	57	parameter	parameter	NOUN
ejpam-3547	347	58	δ0	δ0	NOUN
ejpam-3547	347	59	=	=	NOUN
ejpam-3547	347	60	0.01	0.01	NUM
ejpam-3547	347	61	,	,	PUNCT
ejpam-3547	347	62	0.1	0.1	NUM
ejpam-3547	347	63	,	,	PUNCT
ejpam-3547	347	64	1	1	NUM
ejpam-3547	347	65	.	.	PUNCT
ejpam-3547	347	66	respectvely	respectvely	ADV
ejpam-3547	347	67	.	.	PUNCT
ejpam-3547	348	1	definition	definition	NOUN
ejpam-3547	348	2	4.1	4.1	NUM
ejpam-3547	348	3	.	.	PUNCT
ejpam-3547	349	1	given	give	VERB
ejpam-3547	349	2	a	a	DET
ejpam-3547	349	3	sequence	sequence	NOUN
ejpam-3547	349	4	mn	mn	PROPN
ejpam-3547	349	5	,	,	PUNCT
ejpam-3547	349	6	here	here	ADV
ejpam-3547	349	7	(	(	PUNCT
ejpam-3547	349	8	mn	mn	PROPN
ejpam-3547	349	9	=	=	SYM
ejpam-3547	349	10	wnorsn	wnorsn	PROPN
ejpam-3547	349	11	)	)	PUNCT
ejpam-3547	349	12	,	,	PUNCT
ejpam-3547	349	13	and	and	CCONJ
ejpam-3547	349	14	let	let	VERB
ejpam-3547	349	15	f	f	PRON
ejpam-3547	349	16	be	be	AUX
ejpam-3547	349	17	a	a	DET
ejpam-3547	349	18	function	function	NOUN
ejpam-3547	349	19	,	,	PUNCT
ejpam-3547	349	20	the	the	DET
ejpam-3547	349	21	error	error	NOUN
ejpam-3547	349	22	function	function	NOUN
ejpam-3547	349	23	e(x	e(x	NUM
ejpam-3547	349	24	)	)	PUNCT
ejpam-3547	349	25	occurring	occur	VERB
ejpam-3547	349	26	by	by	ADP
ejpam-3547	349	27	approximate	approximate	ADJ
ejpam-3547	349	28	the	the	DET
ejpam-3547	349	29	function	function	NOUN
ejpam-3547	349	30	f	f	PROPN
ejpam-3547	349	31	by	by	ADP
ejpam-3547	349	32	the	the	DET
ejpam-3547	349	33	sequence	sequence	NOUN
ejpam-3547	349	34	mn	mn	PROPN
ejpam-3547	349	35	is	be	AUX
ejpam-3547	349	36	defined	define	VERB
ejpam-3547	349	37	as	as	ADP
ejpam-3547	349	38	e(x	e(x	NUM
ejpam-3547	349	39	)	)	PUNCT
ejpam-3547	350	1	=	=	SYM
ejpam-3547	350	2	|mn(f	|mn(f	PROPN
ejpam-3547	350	3	;	;	PUNCT
ejpam-3547	350	4	x	x	X
ejpam-3547	350	5	)	)	PUNCT
ejpam-3547	350	6	−	−	PRON
ejpam-3547	350	7	f(x)|	f(x)|	NOUN
ejpam-3547	350	8	.	.	PUNCT
ejpam-3547	351	1	also	also	ADV
ejpam-3547	351	2	,	,	PUNCT
ejpam-3547	351	3	the	the	DET
ejpam-3547	351	4	maximum	maximum	ADJ
ejpam-3547	351	5	error	error	NOUN
ejpam-3547	351	6	of	of	ADP
ejpam-3547	351	7	the	the	DET
ejpam-3547	351	8	function	function	NOUN
ejpam-3547	351	9	e(x	e(x	NUM
ejpam-3547	351	10	)	)	PUNCT
ejpam-3547	351	11	is	be	AUX
ejpam-3547	351	12	denote	denote	VERB
ejpam-3547	351	13	and	and	CCONJ
ejpam-3547	351	14	define	define	VERB
ejpam-3547	351	15	as	as	ADP
ejpam-3547	351	16	maxe	maxe	NOUN
ejpam-3547	351	17	=	=	SYM
ejpam-3547	351	18	maxx∈[0,2	maxx∈[0,2	PROPN
ejpam-3547	351	19	]	]	X
ejpam-3547	351	20	|e(x)|	|e(x)|	PROPN
ejpam-3547	351	21	.	.	PROPN
ejpam-3547	351	22	example	example	NOUN
ejpam-3547	351	23	4.1	4.1	NUM
ejpam-3547	351	24	.	.	PUNCT
ejpam-3547	352	1	for	for	ADP
ejpam-3547	352	2	n	n	NOUN
ejpam-3547	352	3	=	=	SYM
ejpam-3547	352	4	30	30	NUM
ejpam-3547	352	5	,	,	PUNCT
ejpam-3547	352	6	60	60	NUM
ejpam-3547	352	7	,	,	PUNCT
ejpam-3547	352	8	100	100	NUM
ejpam-3547	352	9	and	and	CCONJ
ejpam-3547	352	10	δ0	δ0	NOUN
ejpam-3547	352	11	=	=	NOUN
ejpam-3547	352	12	0.01	0.01	NUM
ejpam-3547	352	13	,	,	PUNCT
ejpam-3547	352	14	0.1	0.1	NUM
ejpam-3547	352	15	,	,	PUNCT
ejpam-3547	352	16	1	1	NUM
ejpam-3547	352	17	.	.	NUM
ejpam-3547	352	18	respectively	respectively	ADV
ejpam-3547	352	19	the	the	DET
ejpam-3547	352	20	sequences	sequence	NOUN
ejpam-3547	352	21	wn(g1;x	wn(g1;x	PROPN
ejpam-3547	352	22	)	)	PUNCT
ejpam-3547	352	23	and	and	CCONJ
ejpam-3547	352	24	sn(g1;x	sn(g1;x	PROPN
ejpam-3547	352	25	)	)	PUNCT
ejpam-3547	352	26	converge	converge	VERB
ejpam-3547	352	27	to	to	ADP
ejpam-3547	352	28	the	the	DET
ejpam-3547	352	29	test	test	NOUN
ejpam-3547	352	30	function	function	NOUN
ejpam-3547	352	31	g1(x	g1(x	NOUN
ejpam-3547	352	32	)	)	PUNCT
ejpam-3547	352	33	=	=	SYM
ejpam-3547	352	34	sin(10x)e−2x	sin(10x)e−2x	NOUN
ejpam-3547	352	35	,	,	PUNCT
ejpam-3547	352	36	with	with	ADP
ejpam-3547	352	37	maximum	maximum	ADJ
ejpam-3547	352	38	error(maxe	error(maxe	NOUN
ejpam-3547	352	39	)	)	PUNCT
ejpam-3547	352	40	given	give	VERB
ejpam-3547	352	41	in	in	ADP
ejpam-3547	352	42	the	the	DET
ejpam-3547	352	43	following	follow	VERB
ejpam-3547	352	44	figures	figure	NOUN
ejpam-3547	352	45	(	(	PUNCT
ejpam-3547	352	46	1−	1−	NUM
ejpam-3547	352	47	12	12	NUM
ejpam-3547	352	48	)	)	PUNCT
ejpam-3547	352	49	(	(	PUNCT
ejpam-3547	352	50	a	a	X
ejpam-3547	352	51	)	)	PUNCT
ejpam-3547	352	52	maxe	maxe	NOUN
ejpam-3547	352	53	:	:	PUNCT
ejpam-3547	353	1	=	=	SYM
ejpam-3547	353	2	0.1844077862	0.1844077862	NUM
ejpam-3547	353	3	(	(	PUNCT
ejpam-3547	353	4	b	b	X
ejpam-3547	353	5	)	)	PUNCT
ejpam-3547	353	6	maxe	maxe	NOUN
ejpam-3547	353	7	:	:	PUNCT
ejpam-3547	354	1	=	=	SYM
ejpam-3547	354	2	0.1201880456	0.1201880456	NUM
ejpam-3547	354	3	(	(	PUNCT
ejpam-3547	354	4	c	c	NOUN
ejpam-3547	354	5	)	)	PUNCT
ejpam-3547	354	6	maxe	maxe	NOUN
ejpam-3547	354	7	:	:	PUNCT
ejpam-3547	354	8	=	=	SYM
ejpam-3547	354	9	0.0806800064	0.0806800064	NUM
ejpam-3547	354	10	a.	a.	NOUN
ejpam-3547	354	11	j.	j.	PROPN
ejpam-3547	354	12	mohammad	mohammad	PROPN
ejpam-3547	354	13	,	,	PUNCT
ejpam-3547	354	14	h.	h.	PROPN
ejpam-3547	354	15	o.	o.	PROPN
ejpam-3547	354	16	muslim	muslim	PROPN
ejpam-3547	354	17	/	/	SYM
ejpam-3547	354	18	eur	eur	PROPN
ejpam-3547	354	19	.	.	PUNCT
ejpam-3547	355	1	j.	j.	PROPN
ejpam-3547	355	2	pure	pure	PROPN
ejpam-3547	355	3	appl	appl	PROPN
ejpam-3547	355	4	.	.	PROPN
ejpam-3547	355	5	math	math	PROPN
ejpam-3547	355	6	,	,	PUNCT
ejpam-3547	355	7	12	12	NUM
ejpam-3547	355	8	(	(	PUNCT
ejpam-3547	355	9	4	4	NUM
ejpam-3547	355	10	)	)	PUNCT
ejpam-3547	355	11	(	(	PUNCT
ejpam-3547	355	12	2019	2019	NUM
ejpam-3547	355	13	)	)	PUNCT
ejpam-3547	355	14	,	,	PUNCT
ejpam-3547	355	15	1508	1508	NUM
ejpam-3547	355	16	-	-	SYM
ejpam-3547	355	17	1523	1523	NUM
ejpam-3547	355	18	1520	1520	NUM
ejpam-3547	355	19	(	(	PUNCT
ejpam-3547	355	20	a	a	X
ejpam-3547	355	21	)	)	PUNCT
ejpam-3547	355	22	maxe	maxe	NOUN
ejpam-3547	355	23	:	:	PUNCT
ejpam-3547	355	24	=	=	SYM
ejpam-3547	355	25	0.192609996	0.192609996	NUM
ejpam-3547	355	26	(	(	PUNCT
ejpam-3547	355	27	b	b	NOUN
ejpam-3547	355	28	)	)	PUNCT
ejpam-3547	355	29	maxe	maxe	NOUN
ejpam-3547	355	30	:	:	PUNCT
ejpam-3547	356	1	=	=	SYM
ejpam-3547	356	2	0.1229776897	0.1229776897	NUM
ejpam-3547	356	3	(	(	PUNCT
ejpam-3547	356	4	c	c	X
ejpam-3547	356	5	)	)	PUNCT
ejpam-3547	356	6	maxe	maxe	NOUN
ejpam-3547	356	7	:	:	PUNCT
ejpam-3547	356	8	=	=	SYM
ejpam-3547	356	9	0.08243795854	0.08243795854	NUM
ejpam-3547	356	10	(	(	PUNCT
ejpam-3547	356	11	a	a	X
ejpam-3547	356	12	)	)	PUNCT
ejpam-3547	356	13	maxe	maxe	NOUN
ejpam-3547	356	14	:	:	PUNCT
ejpam-3547	356	15	=	=	SYM
ejpam-3547	356	16	0.2624406460	0.2624406460	NUM
ejpam-3547	356	17	(	(	PUNCT
ejpam-3547	356	18	b	b	NOUN
ejpam-3547	356	19	)	)	PUNCT
ejpam-3547	356	20	maxe	maxe	NOUN
ejpam-3547	356	21	:	:	PUNCT
ejpam-3547	356	22	=	=	NOUN
ejpam-3547	356	23	0.1553141469	0.1553141469	NUM
ejpam-3547	356	24	(	(	PUNCT
ejpam-3547	356	25	c	c	NOUN
ejpam-3547	356	26	)	)	PUNCT
ejpam-3547	356	27	maxe	maxe	NOUN
ejpam-3547	356	28	:	:	PUNCT
ejpam-3547	356	29	=	=	SYM
ejpam-3547	356	30	0.0984378898	0.0984378898	NUM
ejpam-3547	356	31	(	(	PUNCT
ejpam-3547	356	32	a	a	X
ejpam-3547	356	33	)	)	PUNCT
ejpam-3547	356	34	maxe	maxe	NOUN
ejpam-3547	356	35	:	:	PUNCT
ejpam-3547	356	36	=	=	SYM
ejpam-3547	356	37	0.2259276806	0.2259276806	NUM
ejpam-3547	356	38	(	(	PUNCT
ejpam-3547	356	39	b	b	NOUN
ejpam-3547	356	40	)	)	PUNCT
ejpam-3547	356	41	maxe	maxe	NOUN
ejpam-3547	356	42	:	:	PUNCT
ejpam-3547	356	43	=	=	NOUN
ejpam-3547	356	44	0.1323992412	0.1323992412	NUM
ejpam-3547	356	45	(	(	PUNCT
ejpam-3547	356	46	c	c	NOUN
ejpam-3547	356	47	)	)	PUNCT
ejpam-3547	356	48	maxe	maxe	NOUN
ejpam-3547	356	49	:	:	PUNCT
ejpam-3547	357	1	=	=	SYM
ejpam-3547	357	2	0.085016286	0.085016286	NUM
ejpam-3547	357	3	example	example	NOUN
ejpam-3547	357	4	4.2	4.2	NUM
ejpam-3547	357	5	.	.	PUNCT
ejpam-3547	358	1	for	for	ADP
ejpam-3547	358	2	n	n	NOUN
ejpam-3547	358	3	=	=	SYM
ejpam-3547	358	4	30	30	NUM
ejpam-3547	358	5	,	,	PUNCT
ejpam-3547	358	6	60	60	NUM
ejpam-3547	358	7	,	,	PUNCT
ejpam-3547	358	8	100	100	NUM
ejpam-3547	358	9	and	and	CCONJ
ejpam-3547	358	10	δ0	δ0	NOUN
ejpam-3547	358	11	=	=	NOUN
ejpam-3547	358	12	0.01	0.01	NUM
ejpam-3547	358	13	,	,	PUNCT
ejpam-3547	358	14	0.1	0.1	NUM
ejpam-3547	358	15	,	,	PUNCT
ejpam-3547	358	16	1	1	NUM
ejpam-3547	358	17	.	.	NUM
ejpam-3547	358	18	respectively	respectively	ADV
ejpam-3547	358	19	the	the	DET
ejpam-3547	358	20	sequences	sequence	NOUN
ejpam-3547	358	21	wn(g2;x	wn(g2;x	PROPN
ejpam-3547	358	22	)	)	PUNCT
ejpam-3547	358	23	and	and	CCONJ
ejpam-3547	358	24	sn(g2;x	sn(g2;x	PROPN
ejpam-3547	358	25	)	)	PUNCT
ejpam-3547	358	26	converge	converge	VERB
ejpam-3547	358	27	to	to	ADP
ejpam-3547	358	28	the	the	DET
ejpam-3547	358	29	test	test	NOUN
ejpam-3547	358	30	function	function	NOUN
ejpam-3547	358	31	g2(t	g2(t	PROPN
ejpam-3547	358	32	)	)	PUNCT
ejpam-3547	358	33	=	=	SYM
ejpam-3547	359	1	√	√	NUM
ejpam-3547	359	2	1−	1−	NUM
ejpam-3547	359	3	(	(	PUNCT
ejpam-3547	359	4	t−	t−	PROPN
ejpam-3547	359	5	1)2	1)2	PROPN
ejpam-3547	359	6	,	,	PUNCT
ejpam-3547	359	7	with	with	ADP
ejpam-3547	359	8	maximum	maximum	ADJ
ejpam-3547	359	9	error	error	NOUN
ejpam-3547	359	10	(	(	PUNCT
ejpam-3547	359	11	maxe	maxe	NOUN
ejpam-3547	359	12	)	)	PUNCT
ejpam-3547	359	13	given	give	VERB
ejpam-3547	359	14	in	in	ADP
ejpam-3547	359	15	the	the	DET
ejpam-3547	359	16	following	follow	VERB
ejpam-3547	359	17	figures	figure	NOUN
ejpam-3547	359	18	(	(	PUNCT
ejpam-3547	359	19	13−	13−	NUM
ejpam-3547	359	20	24	24	NUM
ejpam-3547	359	21	)	)	PUNCT
ejpam-3547	359	22	(	(	PUNCT
ejpam-3547	359	23	a	a	X
ejpam-3547	359	24	)	)	PUNCT
ejpam-3547	359	25	maxe	maxe	NOUN
ejpam-3547	359	26	:	:	PUNCT
ejpam-3547	359	27	=	=	SYM
ejpam-3547	359	28	0.1319652402	0.1319652402	NUM
ejpam-3547	359	29	(	(	PUNCT
ejpam-3547	359	30	b	b	NOUN
ejpam-3547	359	31	)	)	PUNCT
ejpam-3547	359	32	maxe	maxe	NOUN
ejpam-3547	359	33	:	:	PUNCT
ejpam-3547	359	34	=	=	SYM
ejpam-3547	359	35	0.0791847229	0.0791847229	NUM
ejpam-3547	359	36	(	(	PUNCT
ejpam-3547	359	37	c	c	X
ejpam-3547	359	38	)	)	PUNCT
ejpam-3547	359	39	maxe	maxe	NOUN
ejpam-3547	359	40	:	:	PUNCT
ejpam-3547	359	41	=	=	NOUN
ejpam-3547	359	42	0.0528549386	0.0528549386	NUM
ejpam-3547	359	43	references	reference	NOUN
ejpam-3547	359	44	1521	1521	NUM
ejpam-3547	359	45	(	(	PUNCT
ejpam-3547	359	46	a	a	X
ejpam-3547	359	47	)	)	PUNCT
ejpam-3547	359	48	maxe	maxe	NOUN
ejpam-3547	359	49	:	:	PUNCT
ejpam-3547	359	50	=	=	SYM
ejpam-3547	359	51	0.1319652402	0.1319652402	NUM
ejpam-3547	359	52	(	(	PUNCT
ejpam-3547	359	53	b	b	NOUN
ejpam-3547	359	54	)	)	PUNCT
ejpam-3547	359	55	maxe	maxe	NOUN
ejpam-3547	359	56	:	:	PUNCT
ejpam-3547	359	57	=	=	SYM
ejpam-3547	359	58	0.0791847229	0.0791847229	NUM
ejpam-3547	359	59	(	(	PUNCT
ejpam-3547	359	60	c	c	X
ejpam-3547	359	61	)	)	PUNCT
ejpam-3547	359	62	maxe	maxe	NOUN
ejpam-3547	359	63	:	:	PUNCT
ejpam-3547	360	1	=	=	SYM
ejpam-3547	360	2	0.0528549386	0.0528549386	NUM
ejpam-3547	360	3	(	(	PUNCT
ejpam-3547	360	4	a	a	X
ejpam-3547	360	5	)	)	PUNCT
ejpam-3547	360	6	maxe	maxe	NOUN
ejpam-3547	360	7	:	:	PUNCT
ejpam-3547	360	8	=	=	SYM
ejpam-3547	360	9	0.1605861444	0.1605861444	NUM
ejpam-3547	360	10	(	(	PUNCT
ejpam-3547	360	11	b	b	NOUN
ejpam-3547	360	12	)	)	PUNCT
ejpam-3547	360	13	maxe	maxe	NOUN
ejpam-3547	360	14	:	:	PUNCT
ejpam-3547	360	15	=	=	SYM
ejpam-3547	360	16	0.1142832076	0.1142832076	NUM
ejpam-3547	360	17	(	(	PUNCT
ejpam-3547	360	18	c	c	NOUN
ejpam-3547	360	19	)	)	PUNCT
ejpam-3547	360	20	maxe	maxe	NOUN
ejpam-3547	360	21	:	:	PUNCT
ejpam-3547	360	22	=	=	SYM
ejpam-3547	360	23	0.08801539766	0.08801539766	NUM
ejpam-3547	360	24	(	(	PUNCT
ejpam-3547	360	25	a	a	X
ejpam-3547	360	26	)	)	PUNCT
ejpam-3547	360	27	maxe	maxe	NOUN
ejpam-3547	360	28	:	:	PUNCT
ejpam-3547	360	29	=	=	SYM
ejpam-3547	360	30	0.2753815754	0.2753815754	NUM
ejpam-3547	360	31	(	(	PUNCT
ejpam-3547	360	32	b	b	NOUN
ejpam-3547	360	33	)	)	PUNCT
ejpam-3547	360	34	maxe	maxe	NOUN
ejpam-3547	360	35	:	:	PUNCT
ejpam-3547	360	36	=	=	SYM
ejpam-3547	360	37	0.2368816505	0.2368816505	NUM
ejpam-3547	360	38	(	(	PUNCT
ejpam-3547	360	39	c	c	NOUN
ejpam-3547	360	40	)	)	PUNCT
ejpam-3547	360	41	maxe	maxe	NOUN
ejpam-3547	360	42	:	:	PUNCT
ejpam-3547	361	1	=	=	SYM
ejpam-3547	361	2	0.2109249528	0.2109249528	NUM
ejpam-3547	361	3	5	5	NUM
ejpam-3547	361	4	.	.	PUNCT
ejpam-3547	361	5	conclusions	conclusion	NOUN
ejpam-3547	361	6	in	in	ADP
ejpam-3547	361	7	this	this	DET
ejpam-3547	361	8	section	section	NOUN
ejpam-3547	361	9	,	,	PUNCT
ejpam-3547	361	10	we	we	PRON
ejpam-3547	361	11	gave	give	VERB
ejpam-3547	361	12	some	some	DET
ejpam-3547	361	13	numerical	numerical	ADJ
ejpam-3547	361	14	examples	example	NOUN
ejpam-3547	361	15	for	for	ADP
ejpam-3547	361	16	our	our	PRON
ejpam-3547	361	17	sequences	sequence	NOUN
ejpam-3547	361	18	wn(.;x	wn(.;x	PROPN
ejpam-3547	361	19	)	)	PUNCT
ejpam-3547	361	20	,	,	PUNCT
ejpam-3547	361	21	in	in	ADP
ejpam-3547	361	22	cases	case	NOUN
ejpam-3547	361	23	n	n	PRON
ejpam-3547	361	24	=	=	SYM
ejpam-3547	361	25	30	30	NUM
ejpam-3547	361	26	,	,	PUNCT
ejpam-3547	361	27	60	60	NUM
ejpam-3547	361	28	,	,	PUNCT
ejpam-3547	361	29	100	100	NUM
ejpam-3547	361	30	and	and	CCONJ
ejpam-3547	361	31	the	the	DET
ejpam-3547	361	32	positive	positive	ADJ
ejpam-3547	361	33	parameter	parameter	NOUN
ejpam-3547	361	34	δ0	δ0	NOUN
ejpam-3547	361	35	=	=	NOUN
ejpam-3547	361	36	0.01	0.01	NUM
ejpam-3547	361	37	,	,	PUNCT
ejpam-3547	361	38	0.1	0.1	NUM
ejpam-3547	361	39	,	,	PUNCT
ejpam-3547	361	40	1	1	NUM
ejpam-3547	361	41	.	.	PUNCT
ejpam-3547	361	42	to	to	PART
ejpam-3547	361	43	approximate	approximate	VERB
ejpam-3547	361	44	two	two	NUM
ejpam-3547	361	45	test	test	NOUN
ejpam-3547	361	46	functions	function	NOUN
ejpam-3547	361	47	g1(t	g1(t	PART
ejpam-3547	361	48	)	)	PUNCT
ejpam-3547	361	49	=	=	SYM
ejpam-3547	361	50	sin(10t)e−2	sin(10t)e−2	PROPN
ejpam-3547	361	51	t	t	NOUN
ejpam-3547	361	52	and	and	CCONJ
ejpam-3547	361	53	g2(t	g2(t	NOUN
ejpam-3547	361	54	)	)	PUNCT
ejpam-3547	361	55	=	=	PUNCT
ejpam-3547	362	1	√	√	NUM
ejpam-3547	362	2	1−	1−	NUM
ejpam-3547	362	3	(	(	PUNCT
ejpam-3547	362	4	t−	t−	PROPN
ejpam-3547	362	5	1)2	1)2	NUM
ejpam-3547	362	6	,	,	PUNCT
ejpam-3547	362	7	in	in	ADP
ejpam-3547	362	8	the	the	DET
ejpam-3547	362	9	space	space	NOUN
ejpam-3547	362	10	cα[0,∞	cα[0,∞	PROPN
ejpam-3547	362	11	)	)	PUNCT
ejpam-3547	363	1	and	and	CCONJ
ejpam-3547	363	2	compared	compare	VERB
ejpam-3547	363	3	the	the	DET
ejpam-3547	363	4	results	result	NOUN
ejpam-3547	363	5	of	of	ADP
ejpam-3547	363	6	the	the	DET
ejpam-3547	363	7	sequence	sequence	NOUN
ejpam-3547	363	8	wn(.;x	wn(.;x	PROPN
ejpam-3547	363	9	)	)	PUNCT
ejpam-3547	363	10	,	,	PUNCT
ejpam-3547	363	11	with	with	ADP
ejpam-3547	363	12	the	the	DET
ejpam-3547	363	13	results	result	NOUN
ejpam-3547	363	14	of	of	ADP
ejpam-3547	363	15	classical	classical	ADJ
ejpam-3547	363	16	szãsz	szãsz	ADJ
ejpam-3547	363	17	sequence	sequence	NOUN
ejpam-3547	363	18	sn(.;x	sn(.;x	NOUN
ejpam-3547	363	19	)	)	PUNCT
ejpam-3547	363	20	in	in	ADP
ejpam-3547	363	21	the	the	DET
ejpam-3547	363	22	interval	interval	NOUN
ejpam-3547	363	23	[	[	X
ejpam-3547	363	24	0	0	NUM
ejpam-3547	363	25	,	,	PUNCT
ejpam-3547	363	26	2	2	NUM
ejpam-3547	363	27	]	]	PUNCT
ejpam-3547	363	28	.	.	PUNCT
ejpam-3547	364	1	it	it	PRON
ejpam-3547	364	2	turns	turn	VERB
ejpam-3547	364	3	out	out	ADP
ejpam-3547	364	4	that	that	SCONJ
ejpam-3547	364	5	:	:	PUNCT
ejpam-3547	364	6	if	if	SCONJ
ejpam-3547	364	7	i	i	PRON
ejpam-3547	364	8	=	=	NOUN
ejpam-3547	364	9	1	1	NUM
ejpam-3547	364	10	,	,	PUNCT
ejpam-3547	364	11	the	the	DET
ejpam-3547	364	12	sequence	sequence	NOUN
ejpam-3547	364	13	wn(gi(t);x	wn(gi(t);x	NOUN
ejpam-3547	364	14	)	)	PUNCT
ejpam-3547	364	15	gives	give	VERB
ejpam-3547	364	16	better	well	ADJ
ejpam-3547	364	17	results	result	NOUN
ejpam-3547	364	18	than	than	ADP
ejpam-3547	364	19	the	the	DET
ejpam-3547	364	20	result	result	NOUN
ejpam-3547	364	21	of	of	ADP
ejpam-3547	364	22	the	the	DET
ejpam-3547	364	23	szãsz	szãsz	ADJ
ejpam-3547	364	24	sequence	sequence	NOUN
ejpam-3547	364	25	sn(gi;x	sn(gi;x	NOUN
ejpam-3547	364	26	)	)	PUNCT
ejpam-3547	364	27	for	for	ADP
ejpam-3547	364	28	all	all	DET
ejpam-3547	364	29	value	value	NOUN
ejpam-3547	364	30	of	of	ADP
ejpam-3547	364	31	n	n	NOUN
ejpam-3547	364	32	and	and	CCONJ
ejpam-3547	364	33	δ0	δ0	NOUN
ejpam-3547	364	34	=	=	PUNCT
ejpam-3547	364	35	0.01	0.01	NUM
ejpam-3547	364	36	,	,	PUNCT
ejpam-3547	364	37	0.1	0.1	NUM
ejpam-3547	364	38	,	,	PUNCT
ejpam-3547	364	39	except	except	SCONJ
ejpam-3547	364	40	δ0	δ0	NOUN
ejpam-3547	364	41	=	=	SYM
ejpam-3547	364	42	1	1	NUM
ejpam-3547	364	43	the	the	DET
ejpam-3547	364	44	sequence	sequence	NOUN
ejpam-3547	364	45	of	of	ADP
ejpam-3547	364	46	szãsz	szãsz	ADJ
ejpam-3547	364	47	sequence	sequence	NOUN
ejpam-3547	364	48	give	give	VERB
ejpam-3547	364	49	little	little	ADJ
ejpam-3547	364	50	better	well	ADJ
ejpam-3547	364	51	results	result	NOUN
ejpam-3547	364	52	than	than	ADP
ejpam-3547	364	53	the	the	DET
ejpam-3547	364	54	sequence	sequence	NOUN
ejpam-3547	364	55	wn(.;x	wn(.;x	PROPN
ejpam-3547	364	56	)	)	PUNCT
ejpam-3547	364	57	.	.	PUNCT
ejpam-3547	365	1	when	when	SCONJ
ejpam-3547	365	2	i	i	PRON
ejpam-3547	365	3	=	=	SYM
ejpam-3547	365	4	2	2	NUM
ejpam-3547	365	5	,	,	PUNCT
ejpam-3547	365	6	the	the	DET
ejpam-3547	365	7	sequence	sequence	NOUN
ejpam-3547	365	8	wn(gi(t);x	wn(gi(t);x	NOUN
ejpam-3547	365	9	)	)	PUNCT
ejpam-3547	365	10	gives	give	VERB
ejpam-3547	365	11	better	well	ADJ
ejpam-3547	365	12	results	result	NOUN
ejpam-3547	365	13	than	than	ADP
ejpam-3547	365	14	the	the	DET
ejpam-3547	365	15	szãsz	szãsz	ADJ
ejpam-3547	365	16	sequence	sequence	NOUN
ejpam-3547	365	17	sn(gi;x	sn(gi;x	NOUN
ejpam-3547	365	18	)	)	PUNCT
ejpam-3547	365	19	for	for	ADP
ejpam-3547	365	20	all	all	DET
ejpam-3547	365	21	value	value	NOUN
ejpam-3547	365	22	of	of	ADP
ejpam-3547	365	23	n	n	NOUN
ejpam-3547	365	24	and	and	CCONJ
ejpam-3547	365	25	δ0	δ0	NOUN
ejpam-3547	365	26	.	.	PUNCT
ejpam-3547	366	1	hence	hence	ADV
ejpam-3547	366	2	,	,	PUNCT
ejpam-3547	366	3	we	we	PRON
ejpam-3547	366	4	recommend	recommend	VERB
ejpam-3547	366	5	to	to	PART
ejpam-3547	366	6	use	use	VERB
ejpam-3547	366	7	the	the	DET
ejpam-3547	366	8	sequence	sequence	NOUN
ejpam-3547	366	9	wn(.;x	wn(.;x	PROPN
ejpam-3547	366	10	)	)	PUNCT
ejpam-3547	366	11	instead	instead	ADV
ejpam-3547	366	12	of	of	ADP
ejpam-3547	366	13	the	the	DET
ejpam-3547	366	14	sequence	sequence	NOUN
ejpam-3547	366	15	sn(.;x	sn(.;x	NOUN
ejpam-3547	366	16	)	)	PUNCT
ejpam-3547	366	17	in	in	ADP
ejpam-3547	366	18	the	the	DET
ejpam-3547	366	19	application	application	NOUN
ejpam-3547	366	20	.	.	PUNCT
ejpam-3547	367	1	references	reference	NOUN
ejpam-3547	367	2	[	[	X
ejpam-3547	367	3	1	1	X
ejpam-3547	367	4	]	]	PUNCT
ejpam-3547	367	5	s.	s.	PROPN
ejpam-3547	367	6	n.	n.	PROPN
ejpam-3547	367	7	bernstein	bernstein	PROPN
ejpam-3547	367	8	,	,	PUNCT
ejpam-3547	367	9	démonstration	démonstration	PROPN
ejpam-3547	367	10	du	du	X
ejpam-3547	367	11	théoréme	théoréme	X
ejpam-3547	367	12	de	de	X
ejpam-3547	367	13	weierstrass	weierstrass	PROPN
ejpam-3547	367	14	fondée	fondée	PROPN
ejpam-3547	367	15	surle	surle	PROPN
ejpam-3547	367	16	calculde	calculde	NOUN
ejpam-3547	367	17	probabilités	probabilités	PROPN
ejpam-3547	367	18	,	,	PUNCT
ejpam-3547	367	19	comm	comm	NOUN
ejpam-3547	367	20	.	.	PUNCT
ejpam-3547	368	1	soc	soc	PROPN
ejpam-3547	368	2	.	.	PUNCT
ejpam-3547	369	1	math	math	PROPN
ejpam-3547	369	2	.	.	PUNCT
ejpam-3547	370	1	kharkow13	kharkow13	PROPN
ejpam-3547	370	2	(	(	PUNCT
ejpam-3547	370	3	1912/13	1912/13	NUM
ejpam-3547	370	4	)	)	PUNCT
ejpam-3547	370	5	,	,	PUNCT
ejpam-3547	370	6	1	1	NUM
ejpam-3547	370	7	-	-	SYM
ejpam-3547	370	8	2	2	NUM
ejpam-3547	370	9	.	.	PUNCT
ejpam-3547	371	1	references	reference	NOUN
ejpam-3547	371	2	1522	1522	NUM
ejpam-3547	372	1	[	[	X
ejpam-3547	372	2	2	2	NUM
ejpam-3547	372	3	]	]	PUNCT
ejpam-3547	372	4	r.	r.	PROPN
ejpam-3547	372	5	c.	c.	PROPN
ejpam-3547	372	6	buck	buck	PROPN
ejpam-3547	372	7	,	,	PUNCT
ejpam-3547	372	8	advanced	advanced	ADJ
ejpam-3547	372	9	calculus	calculus	NOUN
ejpam-3547	372	10	,	,	PUNCT
ejpam-3547	372	11	3rd	3rd	ADJ
ejpam-3547	372	12	ed	ed	NOUN
ejpam-3547	372	13	.	.	PUNCT
ejpam-3547	372	14	univ	univ	PROPN
ejpam-3547	372	15	.	.	PROPN
ejpam-3547	372	16	of	of	ADP
ejpam-3547	372	17	wisconsin	wisconsin	PROPN
ejpam-3547	372	18	,	,	PUNCT
ejpam-3547	372	19	mc	mc	PROPN
ejpam-3547	372	20	graw	graw	PROPN
ejpam-3547	372	21	-	-	PUNCT
ejpam-3547	372	22	hill	hill	PROPN
ejpam-3547	372	23	,	,	PUNCT
ejpam-3547	372	24	inc	inc	PROPN
ejpam-3547	372	25	.	.	PROPN
ejpam-3547	372	26	,	,	PUNCT
ejpam-3547	372	27	1978	1978	NUM
ejpam-3547	372	28	.	.	PUNCT
ejpam-3547	373	1	[	[	X
ejpam-3547	373	2	3	3	NUM
ejpam-3547	373	3	]	]	X
ejpam-3547	373	4	q.	q.	PROPN
ejpam-3547	373	5	cai1	cai1	PROPN
ejpam-3547	373	6	,	,	PUNCT
ejpam-3547	373	7	b.	b.	PROPN
ejpam-3547	373	8	lian	lian	PROPN
ejpam-3547	373	9	and	and	CCONJ
ejpam-3547	373	10	g.	g.	PROPN
ejpam-3547	373	11	zhou	zhou	PROPN
ejpam-3547	373	12	,	,	PUNCT
ejpam-3547	373	13	approximation	approximation	NOUN
ejpam-3547	373	14	properties	property	NOUN
ejpam-3547	373	15	of	of	ADP
ejpam-3547	373	16	λ	λ	PROPN
ejpam-3547	373	17	-	-	PROPN
ejpam-3547	373	18	bernstein	bernstein	PROPN
ejpam-3547	373	19	operators	operators	PROPN
ejpam-3547	373	20	,	,	PUNCT
ejpam-3547	373	21	cai	cai	PROPN
ejpam-3547	373	22	et	et	PROPN
ejpam-3547	373	23	al	al	PROPN
ejpam-3547	373	24	.	.	PROPN
ejpam-3547	373	25	journal	journal	PROPN
ejpam-3547	373	26	of	of	ADP
ejpam-3547	373	27	inequalities	inequality	NOUN
ejpam-3547	373	28	and	and	CCONJ
ejpam-3547	373	29	applications	application	NOUN
ejpam-3547	373	30	(	(	PUNCT
ejpam-3547	373	31	2018	2018	NUM
ejpam-3547	373	32	)	)	PUNCT
ejpam-3547	373	33	2018:61	2018:61	NUM
ejpam-3547	373	34	.	.	PUNCT
ejpam-3547	374	1	[	[	X
ejpam-3547	374	2	4	4	X
ejpam-3547	374	3	]	]	X
ejpam-3547	374	4	m.	m.	NOUN
ejpam-3547	374	5	dhamija	dhamija	PROPN
ejpam-3547	374	6	,	,	PUNCT
ejpam-3547	374	7	r.	r.	PROPN
ejpam-3547	374	8	pratap	pratap	PROPN
ejpam-3547	374	9	and	and	CCONJ
ejpam-3547	374	10	n.	n.	PROPN
ejpam-3547	374	11	deo	deo	PROPN
ejpam-3547	374	12	,	,	PUNCT
ejpam-3547	374	13	approximation	approximation	NOUN
ejpam-3547	374	14	by	by	ADP
ejpam-3547	374	15	kantorovich	kantorovich	PROPN
ejpam-3547	374	16	form	form	NOUN
ejpam-3547	374	17	of	of	ADP
ejpam-3547	374	18	modified	modify	VERB
ejpam-3547	374	19	szász	szász	NUM
ejpam-3547	374	20	–	–	PUNCT
ejpam-3547	374	21	mirakyan	mirakyan	ADJ
ejpam-3547	374	22	operators	operator	NOUN
ejpam-3547	374	23	,	,	PUNCT
ejpam-3547	374	24	applied	apply	VERB
ejpam-3547	374	25	mathematics	mathematic	NOUN
ejpam-3547	374	26	and	and	CCONJ
ejpam-3547	374	27	computation	computation	NOUN
ejpam-3547	374	28	317	317	NUM
ejpam-3547	374	29	(	(	PUNCT
ejpam-3547	374	30	2018	2018	NUM
ejpam-3547	374	31	)	)	PUNCT
ejpam-3547	374	32	,	,	PUNCT
ejpam-3547	374	33	pp	pp	ADP
ejpam-3547	374	34	.	.	PUNCT
ejpam-3547	375	1	109–120	109–120	NUM
ejpam-3547	375	2	.	.	PUNCT
ejpam-3547	376	1	[	[	X
ejpam-3547	376	2	5	5	NUM
ejpam-3547	376	3	]	]	X
ejpam-3547	376	4	a.r	a.r	PROPN
ejpam-3547	376	5	.	.	PROPN
ejpam-3547	376	6	gairola	gairola	PROPN
ejpam-3547	376	7	,	,	PUNCT
ejpam-3547	376	8	deepmala	deepmala	PROPN
ejpam-3547	376	9	,	,	PUNCT
ejpam-3547	376	10	l.n	l.n	PROPN
ejpam-3547	376	11	.	.	PROPN
ejpam-3547	376	12	mishra	mishra	PROPN
ejpam-3547	376	13	,	,	PUNCT
ejpam-3547	376	14	rate	rate	NOUN
ejpam-3547	376	15	of	of	ADP
ejpam-3547	376	16	approximation	approximation	NOUN
ejpam-3547	376	17	by	by	ADP
ejpam-3547	376	18	finite	finite	ADJ
ejpam-3547	376	19	iterates	iterate	NOUN
ejpam-3547	376	20	of	of	ADP
ejpam-3547	376	21	q	q	NOUN
ejpam-3547	376	22	-	-	PUNCT
ejpam-3547	376	23	durrmeyer	durrmeyer	NOUN
ejpam-3547	376	24	operators	operator	NOUN
ejpam-3547	376	25	,	,	PUNCT
ejpam-3547	376	26	proc	proc	PROPN
ejpam-3547	376	27	.	.	PUNCT
ejpam-3547	377	1	natl	natl	PROPN
ejpam-3547	377	2	.	.	PUNCT
ejpam-3547	378	1	acad	acad	PROPN
ejpam-3547	378	2	.	.	PUNCT
ejpam-3547	379	1	sci	sci	PROPN
ejpam-3547	379	2	.	.	PROPN
ejpam-3547	379	3	,	,	PUNCT
ejpam-3547	379	4	india	india	PROPN
ejpam-3547	379	5	,	,	PUNCT
ejpam-3547	379	6	sect	sect	NOUN
ejpam-3547	379	7	.	.	PUNCT
ejpam-3547	380	1	a	a	DET
ejpam-3547	380	2	phys	phy	NOUN
ejpam-3547	380	3	.	.	PUNCT
ejpam-3547	381	1	sci	sci	PROPN
ejpam-3547	381	2	.	.	PUNCT
ejpam-3547	381	3	(	(	PUNCT
ejpam-3547	381	4	april	april	PROPN
ejpam-3547	381	5	–	–	PUNCT
ejpam-3547	381	6	june	june	PROPN
ejpam-3547	381	7	2016	2016	NUM
ejpam-3547	381	8	)	)	PUNCT
ejpam-3547	381	9	86(2):229–234	86(2):229–234	NOUN
ejpam-3547	381	10	(	(	PUNCT
ejpam-3547	381	11	2016	2016	NUM
ejpam-3547	381	12	)	)	PUNCT
ejpam-3547	381	13	.	.	PUNCT
ejpam-3547	382	1	doi	doi	NOUN
ejpam-3547	382	2	:	:	PUNCT
ejpam-3547	382	3	10.1007	10.1007	NUM
ejpam-3547	382	4	/	/	SYM
ejpam-3547	382	5	s40010	s40010	NOUN
ejpam-3547	382	6	-	-	PUNCT
ejpam-3547	382	7	016	016	NUM
ejpam-3547	382	8	-	-	PUNCT
ejpam-3547	382	9	0267	0267	NUM
ejpam-3547	382	10	-	-	PUNCT
ejpam-3547	382	11	z.	z.	PROPN
ejpam-3547	383	1	[	[	X
ejpam-3547	383	2	6	6	NUM
ejpam-3547	383	3	]	]	X
ejpam-3547	383	4	a.r	a.r	PROPN
ejpam-3547	383	5	.	.	PROPN
ejpam-3547	383	6	gairola	gairola	PROPN
ejpam-3547	383	7	,	,	PUNCT
ejpam-3547	383	8	deepmala	deepmala	PROPN
ejpam-3547	383	9	,	,	PUNCT
ejpam-3547	383	10	l.n	l.n	PROPN
ejpam-3547	383	11	.	.	PROPN
ejpam-3547	383	12	mishra	mishra	PROPN
ejpam-3547	383	13	,	,	PUNCT
ejpam-3547	383	14	on	on	ADP
ejpam-3547	383	15	the	the	DET
ejpam-3547	383	16	q−derivatives	q−derivative	NOUN
ejpam-3547	383	17	of	of	ADP
ejpam-3547	383	18	a	a	DET
ejpam-3547	383	19	certain	certain	ADJ
ejpam-3547	383	20	linear	linear	ADJ
ejpam-3547	383	21	positive	positive	ADJ
ejpam-3547	383	22	operators	operator	NOUN
ejpam-3547	383	23	,	,	PUNCT
ejpam-3547	383	24	iranian	iranian	ADJ
ejpam-3547	383	25	journal	journal	PROPN
ejpam-3547	383	26	of	of	ADP
ejpam-3547	383	27	science	science	NOUN
ejpam-3547	383	28	and	and	CCONJ
ejpam-3547	383	29	technology	technology	NOUN
ejpam-3547	383	30	,	,	PUNCT
ejpam-3547	383	31	transactions	transaction	VERB
ejpam-3547	383	32	a	a	DET
ejpam-3547	383	33	:	:	PUNCT
ejpam-3547	383	34	science	science	NOUN
ejpam-3547	383	35	,	,	PUNCT
ejpam-3547	383	36	vol	vol	NOUN
ejpam-3547	383	37	.	.	PROPN
ejpam-3547	384	1	42	42	NUM
ejpam-3547	384	2	,	,	PUNCT
ejpam-3547	384	3	no	no	INTJ
ejpam-3547	384	4	.	.	NOUN
ejpam-3547	384	5	3	3	NUM
ejpam-3547	384	6	,	,	PUNCT
ejpam-3547	384	7	(	(	PUNCT
ejpam-3547	384	8	2018	2018	NUM
ejpam-3547	384	9	)	)	PUNCT
ejpam-3547	384	10	,	,	PUNCT
ejpam-3547	385	1	pp	pp	ADJ
ejpam-3547	385	2	.	.	PUNCT
ejpam-3547	386	1	1409	1409	NUM
ejpam-3547	386	2	-	-	SYM
ejpam-3547	386	3	1417	1417	NUM
ejpam-3547	386	4	.	.	PUNCT
ejpam-3547	387	1	doi	doi	NOUN
ejpam-3547	387	2	10.1007	10.1007	NUM
ejpam-3547	387	3	/	/	SYM
ejpam-3547	387	4	s40995	s40995	VERB
ejpam-3547	387	5	-	-	PUNCT
ejpam-3547	387	6	017	017	NUM
ejpam-3547	387	7	-	-	PUNCT
ejpam-3547	387	8	0227	0227	NUM
ejpam-3547	387	9	-	-	SYM
ejpam-3547	387	10	8	8	NUM
ejpam-3547	387	11	.	.	PUNCT
ejpam-3547	388	1	[	[	X
ejpam-3547	388	2	7	7	X
ejpam-3547	388	3	]	]	X
ejpam-3547	388	4	r.b	r.b	PROPN
ejpam-3547	388	5	.	.	PROPN
ejpam-3547	388	6	gandhi	gandhi	PROPN
ejpam-3547	388	7	,	,	PUNCT
ejpam-3547	388	8	deepmala	deepmala	PROPN
ejpam-3547	388	9	,	,	PUNCT
ejpam-3547	388	10	v.n	v.n	PROPN
ejpam-3547	388	11	.	.	PROPN
ejpam-3547	388	12	mishra	mishra	PROPN
ejpam-3547	388	13	,	,	PUNCT
ejpam-3547	388	14	local	local	ADJ
ejpam-3547	388	15	and	and	CCONJ
ejpam-3547	388	16	global	global	ADJ
ejpam-3547	388	17	results	result	NOUN
ejpam-3547	388	18	for	for	ADP
ejpam-3547	388	19	modified	modified	ADJ
ejpam-3547	388	20	szász	szász	NUM
ejpam-3547	388	21	mirakjan	mirakjan	NOUN
ejpam-3547	388	22	operators	operators	PROPN
ejpam-3547	388	23	,	,	PUNCT
ejpam-3547	388	24	math	math	NOUN
ejpam-3547	388	25	.	.	PUNCT
ejpam-3547	388	26	method	method	PROPN
ejpam-3547	388	27	.	.	PUNCT
ejpam-3547	389	1	appl	appl	PROPN
ejpam-3547	389	2	.	.	PUNCT
ejpam-3547	390	1	sci	sci	PROPN
ejpam-3547	390	2	.	.	PROPN
ejpam-3547	390	3	,	,	PUNCT
ejpam-3547	390	4	vol	vol	NOUN
ejpam-3547	390	5	.	.	PROPN
ejpam-3547	390	6	40	40	NUM
ejpam-3547	390	7	,	,	PUNCT
ejpam-3547	390	8	issue	issue	NOUN
ejpam-3547	390	9	7	7	NUM
ejpam-3547	390	10	,	,	PUNCT
ejpam-3547	390	11	(	(	PUNCT
ejpam-3547	390	12	2017	2017	NUM
ejpam-3547	390	13	)	)	PUNCT
ejpam-3547	390	14	,	,	PUNCT
ejpam-3547	390	15	pp	pp	ADJ
ejpam-3547	390	16	.	.	PUNCT
ejpam-3547	390	17	24912504	24912504	NUM
ejpam-3547	390	18	.	.	PUNCT
ejpam-3547	391	1	doi	doi	NOUN
ejpam-3547	391	2	:	:	PUNCT
ejpam-3547	391	3	10.1002	10.1002	NUM
ejpam-3547	391	4	/	/	SYM
ejpam-3547	391	5	mma.4171	mma.4171	NOUN
ejpam-3547	391	6	.	.	PUNCT
ejpam-3547	392	1	[	[	X
ejpam-3547	392	2	8	8	NUM
ejpam-3547	392	3	]	]	X
ejpam-3547	392	4	d.	d.	PROPN
ejpam-3547	392	5	jackson	jackson	PROPN
ejpam-3547	392	6	,	,	PUNCT
ejpam-3547	392	7	a	a	DET
ejpam-3547	392	8	proof	proof	NOUN
ejpam-3547	392	9	of	of	ADP
ejpam-3547	392	10	weierstrass	weierstrass	PROPN
ejpam-3547	392	11	’s	’s	PART
ejpam-3547	392	12	theorem	theorem	PROPN
ejpam-3547	392	13	,	,	PUNCT
ejpam-3547	392	14	the	the	DET
ejpam-3547	392	15	american	american	PROPN
ejpam-3547	392	16	,	,	PUNCT
ejpam-3547	392	17	mathematical	mathematical	ADJ
ejpam-3547	392	18	,	,	PUNCT
ejpam-3547	392	19	monthly	monthly	ADJ
ejpam-3547	392	20	,	,	PUNCT
ejpam-3547	392	21	vol	vol	NOUN
ejpam-3547	392	22	.	.	PUNCT
ejpam-3547	392	23	(	(	PUNCT
ejpam-3547	392	24	41	41	NUM
ejpam-3547	392	25	)	)	PUNCT
ejpam-3547	392	26	,	,	PUNCT
ejpam-3547	392	27	no	no	INTJ
ejpam-3547	392	28	.	.	PUNCT
ejpam-3547	393	1	(	(	PUNCT
ejpam-3547	393	2	5	5	NUM
ejpam-3547	393	3	)	)	PUNCT
ejpam-3547	393	4	,	,	PUNCT
ejpam-3547	393	5	may	may	AUX
ejpam-3547	393	6	(	(	PUNCT
ejpam-3547	393	7	1934	1934	NUM
ejpam-3547	393	8	)	)	PUNCT
ejpam-3547	393	9	,	,	PUNCT
ejpam-3547	394	1	pp	pp	PROPN
ejpam-3547	394	2	.	.	PUNCT
ejpam-3547	395	1	309	309	NUM
ejpam-3547	395	2	-	-	SYM
ejpam-3547	395	3	312	312	NUM
ejpam-3547	395	4	;	;	PUNCT
ejpam-3547	396	1	[	[	X
ejpam-3547	396	2	9	9	NUM
ejpam-3547	396	3	]	]	PUNCT
ejpam-3547	397	1	p.	p.	NOUN
ejpam-3547	397	2	p.	p.	NOUN
ejpam-3547	398	1	korovkin	korovkin	PROPN
ejpam-3547	398	2	,	,	PUNCT
ejpam-3547	398	3	linear	linear	PROPN
ejpam-3547	398	4	operators	operator	NOUN
ejpam-3547	398	5	and	and	CCONJ
ejpam-3547	398	6	approximation	approximation	NOUN
ejpam-3547	398	7	theory	theory	NOUN
ejpam-3547	398	8	,	,	PUNCT
ejpam-3547	398	9	hindustan	hindustan	PROPN
ejpam-3547	398	10	publ	publ	PROPN
ejpam-3547	398	11	.	.	PUNCT
ejpam-3547	399	1	corp	corp	PROPN
ejpam-3547	399	2	.	.	PROPN
ejpam-3547	399	3	delhi	delhi	PROPN
ejpam-3547	399	4	,	,	PUNCT
ejpam-3547	399	5	1960	1960	NUM
ejpam-3547	399	6	(	(	PUNCT
ejpam-3547	399	7	translated	translate	VERB
ejpam-3547	399	8	from	from	ADP
ejpam-3547	399	9	russian	russian	ADJ
ejpam-3547	399	10	edition	edition	NOUN
ejpam-3547	399	11	of	of	ADP
ejpam-3547	399	12	1959	1959	NUM
ejpam-3547	399	13	)	)	PUNCT
ejpam-3547	399	14	.	.	PUNCT
ejpam-3547	400	1	[	[	X
ejpam-3547	400	2	10	10	NUM
ejpam-3547	400	3	]	]	X
ejpam-3547	400	4	a.	a.	NOUN
ejpam-3547	400	5	kumar	kumar	PROPN
ejpam-3547	400	6	,	,	PUNCT
ejpam-3547	400	7	l.n	l.n	PROPN
ejpam-3547	400	8	.	.	PROPN
ejpam-3547	400	9	mishra	mishra	PROPN
ejpam-3547	400	10	,	,	PUNCT
ejpam-3547	400	11	approximation	approximation	NOUN
ejpam-3547	400	12	by	by	ADP
ejpam-3547	400	13	modified	modify	VERB
ejpam-3547	400	14	jain	jain	PROPN
ejpam-3547	400	15	-	-	PUNCT
ejpam-3547	400	16	baskakov	baskakov	PROPN
ejpam-3547	400	17	-	-	PUNCT
ejpam-3547	400	18	stancu	stancu	PROPN
ejpam-3547	400	19	operators	operator	NOUN
ejpam-3547	400	20	,	,	PUNCT
ejpam-3547	400	21	tbilisi	tbilisi	PROPN
ejpam-3547	400	22	mathematical	mathematical	PROPN
ejpam-3547	400	23	journal	journal	PROPN
ejpam-3547	400	24	,	,	PUNCT
ejpam-3547	400	25	10(2	10(2	NUM
ejpam-3547	400	26	)	)	PUNCT
ejpam-3547	400	27	(	(	PUNCT
ejpam-3547	400	28	2017	2017	NUM
ejpam-3547	400	29	)	)	PUNCT
ejpam-3547	400	30	,	,	PUNCT
ejpam-3547	400	31	pp	pp	ADP
ejpam-3547	400	32	.	.	PUNCT
ejpam-3547	401	1	185–199	185–199	NUM
ejpam-3547	401	2	.	.	PUNCT
ejpam-3547	402	1	[	[	X
ejpam-3547	402	2	11	11	NUM
ejpam-3547	402	3	]	]	X
ejpam-3547	402	4	v.n	v.n	PROPN
ejpam-3547	402	5	.	.	PROPN
ejpam-3547	402	6	mishra	mishra	PROPN
ejpam-3547	402	7	,	,	PUNCT
ejpam-3547	402	8	k.	k.	PROPN
ejpam-3547	402	9	khatri	khatri	PROPN
ejpam-3547	402	10	,	,	PUNCT
ejpam-3547	402	11	l.n	l.n	PROPN
ejpam-3547	402	12	.	.	PROPN
ejpam-3547	402	13	mishra	mishra	PROPN
ejpam-3547	402	14	;	;	PUNCT
ejpam-3547	402	15	on	on	ADP
ejpam-3547	402	16	simultaneous	simultaneous	ADJ
ejpam-3547	402	17	approximation	approximation	NOUN
ejpam-3547	402	18	for	for	ADP
ejpam-3547	402	19	baskakov	baskakov	PROPN
ejpam-3547	402	20	durrmeyer	durrmeyer	PROPN
ejpam-3547	402	21	-	-	PUNCT
ejpam-3547	402	22	stancu	stancu	PROPN
ejpam-3547	402	23	type	type	NOUN
ejpam-3547	402	24	operators	operator	NOUN
ejpam-3547	402	25	,	,	PUNCT
ejpam-3547	402	26	journal	journal	NOUN
ejpam-3547	402	27	of	of	ADP
ejpam-3547	402	28	ultra	ultra	ADJ
ejpam-3547	402	29	scientist	scientist	NOUN
ejpam-3547	402	30	of	of	ADP
ejpam-3547	402	31	physical	physical	ADJ
ejpam-3547	402	32	sciences	science	NOUN
ejpam-3547	402	33	,	,	PUNCT
ejpam-3547	402	34	vol	vol	NOUN
ejpam-3547	402	35	.	.	PROPN
ejpam-3547	402	36	24	24	NUM
ejpam-3547	402	37	,	,	PUNCT
ejpam-3547	402	38	no	no	INTJ
ejpam-3547	402	39	.	.	PUNCT
ejpam-3547	403	1	(	(	PUNCT
ejpam-3547	403	2	3	3	X
ejpam-3547	403	3	)	)	PUNCT
ejpam-3547	403	4	a	a	PRON
ejpam-3547	403	5	,	,	PUNCT
ejpam-3547	403	6	2012	2012	NUM
ejpam-3547	403	7	,	,	PUNCT
ejpam-3547	403	8	pp	pp	ADJ
ejpam-3547	403	9	.	.	PUNCT
ejpam-3547	404	1	567	567	NUM
ejpam-3547	404	2	-	-	SYM
ejpam-3547	404	3	577	577	NUM
ejpam-3547	404	4	.	.	PUNCT
ejpam-3547	405	1	[	[	X
ejpam-3547	405	2	12	12	NUM
ejpam-3547	405	3	]	]	X
ejpam-3547	405	4	v.n	v.n	PROPN
ejpam-3547	405	5	.	.	PROPN
ejpam-3547	405	6	mishra	mishra	PROPN
ejpam-3547	405	7	,	,	PUNCT
ejpam-3547	405	8	k.	k.	PROPN
ejpam-3547	405	9	khatri	khatri	PROPN
ejpam-3547	405	10	,	,	PUNCT
ejpam-3547	405	11	l.n	l.n	PROPN
ejpam-3547	405	12	.	.	PROPN
ejpam-3547	405	13	mishra	mishra	PROPN
ejpam-3547	405	14	,	,	PUNCT
ejpam-3547	405	15	deepmala	deepmala	PROPN
ejpam-3547	405	16	;	;	PUNCT
ejpam-3547	405	17	inverse	inverse	NOUN
ejpam-3547	405	18	result	result	NOUN
ejpam-3547	405	19	in	in	ADP
ejpam-3547	405	20	simultaneous	simultaneous	ADJ
ejpam-3547	405	21	approximation	approximation	NOUN
ejpam-3547	405	22	by	by	ADP
ejpam-3547	405	23	baskakov	baskakov	PROPN
ejpam-3547	405	24	-	-	PUNCT
ejpam-3547	405	25	durrmeyer	durrmeyer	NOUN
ejpam-3547	405	26	-	-	PUNCT
ejpam-3547	405	27	stancu	stancu	PROPN
ejpam-3547	405	28	operators	operator	NOUN
ejpam-3547	405	29	,	,	PUNCT
ejpam-3547	405	30	journal	journal	NOUN
ejpam-3547	405	31	of	of	ADP
ejpam-3547	405	32	inequalities	inequality	NOUN
ejpam-3547	405	33	and	and	CCONJ
ejpam-3547	405	34	applications	application	NOUN
ejpam-3547	405	35	2013	2013	NUM
ejpam-3547	405	36	,	,	PUNCT
ejpam-3547	405	37	2013:586	2013:586	NUM
ejpam-3547	405	38	.	.	PUNCT
ejpam-3547	405	39	doi:10.1186/1029	doi:10.1186/1029	VERB
ejpam-3547	405	40	-	-	PROPN
ejpam-3547	405	41	242x-2013	242x-2013	NUM
ejpam-3547	405	42	-	-	PUNCT
ejpam-3547	405	43	586	586	NUM
ejpam-3547	405	44	.	.	PUNCT
ejpam-3547	406	1	[	[	X
ejpam-3547	406	2	13	13	NUM
ejpam-3547	406	3	]	]	X
ejpam-3547	406	4	d.	d.	PROPN
ejpam-3547	406	5	c.	c.	PROPN
ejpam-3547	406	6	morales	morales	PROPN
ejpam-3547	406	7	,	,	PUNCT
ejpam-3547	406	8	p.	p.	NOUN
ejpam-3547	406	9	garrancho	garrancho	PROPN
ejpam-3547	406	10	and	and	CCONJ
ejpam-3547	406	11	i.	i.	PROPN
ejpam-3547	406	12	rasa	rasa	PROPN
ejpam-3547	406	13	,	,	PUNCT
ejpam-3547	406	14	approximation	approximation	NOUN
ejpam-3547	406	15	properties	property	NOUN
ejpam-3547	406	16	of	of	ADP
ejpam-3547	406	17	bernstein	bernstein	PROPN
ejpam-3547	406	18	–	–	PUNCT
ejpam-3547	406	19	durrmeyer	durrmeyer	NOUN
ejpam-3547	406	20	type	type	NOUN
ejpam-3547	406	21	operators	operator	NOUN
ejpam-3547	406	22	,	,	PUNCT
ejpam-3547	406	23	applied	apply	VERB
ejpam-3547	406	24	mathematics	mathematic	NOUN
ejpam-3547	406	25	and	and	CCONJ
ejpam-3547	406	26	computation	computation	NOUN
ejpam-3547	406	27	232	232	NUM
ejpam-3547	406	28	(	(	PUNCT
ejpam-3547	406	29	2014	2014	NUM
ejpam-3547	406	30	)	)	PUNCT
ejpam-3547	406	31	,	,	PUNCT
ejpam-3547	406	32	1–8	1–8	X
ejpam-3547	406	33	.	.	PUNCT
ejpam-3547	407	1	[	[	X
ejpam-3547	407	2	14	14	NUM
ejpam-3547	407	3	]	]	X
ejpam-3547	407	4	p.	p.	NOUN
ejpam-3547	407	5	patel	patel	PROPN
ejpam-3547	407	6	,	,	PUNCT
ejpam-3547	407	7	v.	v.	PROPN
ejpam-3547	407	8	mishra	mishra	PROPN
ejpam-3547	407	9	and	and	CCONJ
ejpam-3547	407	10	m.	m.	PROPN
ejpam-3547	407	11	örkcü	örkcü	PROPN
ejpam-3547	407	12	,	,	PUNCT
ejpam-3547	407	13	approximation	approximation	NOUN
ejpam-3547	407	14	properties	property	NOUN
ejpam-3547	407	15	of	of	ADP
ejpam-3547	407	16	modified	modify	VERB
ejpam-3547	407	17	szász	szász	NUM
ejpam-3547	407	18	–	–	PUNCT
ejpam-3547	407	19	mirakyan	mirakyan	ADJ
ejpam-3547	407	20	operators	operator	NOUN
ejpam-3547	407	21	in	in	ADP
ejpam-3547	407	22	polynomial	polynomial	ADJ
ejpam-3547	407	23	weighted	weight	VERB
ejpam-3547	407	24	space	space	NOUN
ejpam-3547	407	25	,	,	PUNCT
ejpam-3547	407	26	patel	patel	PROPN
ejpam-3547	407	27	et	et	PROPN
ejpam-3547	407	28	al	al	PROPN
ejpam-3547	407	29	.	.	PROPN
ejpam-3547	407	30	,	,	PUNCT
ejpam-3547	407	31	cogent	cogent	NOUN
ejpam-3547	407	32	mathematics	mathematic	NOUN
ejpam-3547	407	33	(	(	PUNCT
ejpam-3547	407	34	2015	2015	NUM
ejpam-3547	407	35	)	)	PUNCT
ejpam-3547	407	36	,	,	PUNCT
ejpam-3547	407	37	2	2	NUM
ejpam-3547	407	38	:	:	SYM
ejpam-3547	407	39	1106195	1106195	NUM
ejpam-3547	407	40	.	.	PUNCT
ejpam-3547	408	1	[	[	X
ejpam-3547	408	2	15	15	NUM
ejpam-3547	408	3	]	]	X
ejpam-3547	408	4	j.	j.	PROPN
ejpam-3547	408	5	quaintance	quaintance	PROPN
ejpam-3547	408	6	,	,	PUNCT
ejpam-3547	408	7	combinatorial	combinatorial	ADJ
ejpam-3547	408	8	identities	identity	NOUN
ejpam-3547	408	9	for	for	ADP
ejpam-3547	408	10	stirling	stirling	NOUN
ejpam-3547	408	11	numbers	number	NOUN
ejpam-3547	408	12	,	,	PUNCT
ejpam-3547	408	13	world	world	NOUN
ejpam-3547	408	14	scientific	scientific	PROPN
ejpam-3547	408	15	publishing	publishing	PROPN
ejpam-3547	408	16	co.	co.	PROPN
ejpam-3547	408	17	pte	pte	PROPN
ejpam-3547	408	18	.	.	PROPN
ejpam-3547	408	19	ltd	ltd	PROPN
ejpam-3547	408	20	.	.	PROPN
ejpam-3547	408	21	5	5	NUM
ejpam-3547	408	22	toh	toh	PROPN
ejpam-3547	408	23	tuck	tuck	NOUN
ejpam-3547	408	24	link	link	PROPN
ejpam-3547	408	25	,	,	PUNCT
ejpam-3547	408	26	singapore	singapore	PROPN
ejpam-3547	408	27	596224	596224	NUM
ejpam-3547	408	28	,	,	PUNCT
ejpam-3547	408	29	2016	2016	NUM
ejpam-3547	408	30	.	.	PUNCT
ejpam-3547	409	1	references	reference	NOUN
ejpam-3547	409	2	1523	1523	NUM
ejpam-3547	410	1	[	[	X
ejpam-3547	410	2	16	16	NUM
ejpam-3547	410	3	]	]	X
ejpam-3547	410	4	o.	o.	PROPN
ejpam-3547	410	5	szãsz	szãsz	PROPN
ejpam-3547	410	6	,	,	PUNCT
ejpam-3547	410	7	generalization	generalization	NOUN
ejpam-3547	410	8	of	of	ADP
ejpam-3547	410	9	s.	s.	PROPN
ejpam-3547	410	10	bernstein	bernstein	PROPN
ejpam-3547	410	11	’s	’s	PART
ejpam-3547	410	12	polynomials	polynomial	NOUN
ejpam-3547	410	13	to	to	ADP
ejpam-3547	410	14	the	the	DET
ejpam-3547	410	15	infinite	infinite	ADJ
ejpam-3547	410	16	interval	interval	NOUN
ejpam-3547	410	17	,	,	PUNCT
ejpam-3547	410	18	j.	j.	PROPN
ejpam-3547	410	19	res	res	PROPN
ejpam-3547	410	20	.	.	PUNCT
ejpam-3547	411	1	nat	nat	PROPN
ejpam-3547	411	2	.	.	PUNCT
ejpam-3547	412	1	bur	bur	PROPN
ejpam-3547	412	2	.	.	PROPN
ejpam-3547	412	3	standard	standard	PROPN
ejpam-3547	412	4	,	,	PUNCT
ejpam-3547	412	5	45(1950	45(1950	NUM
ejpam-3547	412	6	)	)	PUNCT
ejpam-3547	412	7	,	,	PUNCT
ejpam-3547	412	8	pp.239	pp.239	PROPN
ejpam-3547	412	9	-	-	SYM
ejpam-3547	412	10	245	245	NUM
ejpam-3547	412	11	.	.	PUNCT
ejpam-3547	413	1	[	[	X
ejpam-3547	413	2	17	17	NUM
ejpam-3547	413	3	]	]	PUNCT
ejpam-3547	413	4	t.	t.	NOUN
ejpam-3547	413	5	tunç	tunç	PROPN
ejpam-3547	413	6	,	,	PUNCT
ejpam-3547	413	7	and	and	CCONJ
ejpam-3547	413	8	e.	e.	PROPN
ejpam-3547	413	9	simsek	simsek	PROPN
ejpam-3547	413	10	,	,	PUNCT
ejpam-3547	413	11	some	some	DET
ejpam-3547	413	12	approximation	approximation	NOUN
ejpam-3547	413	13	properties	property	NOUN
ejpam-3547	413	14	of	of	ADP
ejpam-3547	413	15	szasz	szasz	NOUN
ejpam-3547	413	16	-	-	PUNCT
ejpam-3547	413	17	mirakyanbernstein	mirakyanbernstein	NOUN
ejpam-3547	413	18	operators	operator	NOUN
ejpam-3547	413	19	,	,	PUNCT
ejpam-3547	413	20	eu	eu	PROPN
ejpam-3547	413	21	.	.	PROPN
ejpam-3547	413	22	j.	j.	PROPN
ejpam-3547	413	23	of	of	ADP
ejpam-3547	413	24	pure	pure	ADJ
ejpam-3547	413	25	and	and	CCONJ
ejpam-3547	413	26	app	app	PROPN
ejpam-3547	413	27	.	.	PROPN
ejpam-3547	413	28	math	math	PROPN
ejpam-3547	413	29	.	.	PUNCT
ejpam-3547	414	1	vol	vol	NOUN
ejpam-3547	414	2	.	.	PROPN
ejpam-3547	415	1	7	7	NUM
ejpam-3547	415	2	,	,	PUNCT
ejpam-3547	415	3	no	no	INTJ
ejpam-3547	415	4	.	.	NOUN
ejpam-3547	415	5	4	4	NUM
ejpam-3547	415	6	,	,	PUNCT
ejpam-3547	415	7	2014	2014	NUM
ejpam-3547	415	8	,	,	PUNCT
ejpam-3547	415	9	419	419	NUM
ejpam-3547	415	10	-	-	SYM
ejpam-3547	415	11	428	428	NUM
ejpam-3547	415	12	.	.	PUNCT
ejpam-3547	416	1	[	[	X
ejpam-3547	416	2	18	18	NUM
ejpam-3547	416	3	]	]	X
ejpam-3547	416	4	e.	e.	PROPN
ejpam-3547	416	5	voronovskaja	voronovskaja	PROPN
ejpam-3547	416	6	,	,	PUNCT
ejpam-3547	416	7	détermination	détermination	PROPN
ejpam-3547	416	8	de	de	X
ejpam-3547	416	9	la	la	X
ejpam-3547	416	10	forme	forme	X
ejpam-3547	416	11	asymptotique	asymptotique	PROPN
ejpam-3547	416	12	d’ápproximation	d’ápproximation	PROPN
ejpam-3547	416	13	des	des	PROPN
ejpam-3547	416	14	functions	functions	PROPN
ejpam-3547	416	15	par	par	PROPN
ejpam-3547	416	16	les	les	X
ejpam-3547	416	17	polynômes	polynômes	PROPN
ejpam-3547	416	18	de	de	X
ejpam-3547	416	19	s.n	s.n	PROPN
ejpam-3547	416	20	.	.	PROPN
ejpam-3547	416	21	bernstein	bernstein	PROPN
ejpam-3547	416	22	,	,	PUNCT
ejpam-3547	416	23	c.r	c.r	PROPN
ejpam-3547	416	24	.	.	PROPN
ejpam-3547	416	25	acad	acad	PROPN
ejpam-3547	416	26	.	.	PUNCT
ejpam-3547	417	1	sci	sci	PROPN
ejpam-3547	417	2	.	.	PUNCT
ejpam-3547	417	3	ussr	ussr	PROPN
ejpam-3547	417	4	(	(	PUNCT
ejpam-3547	417	5	1932	1932	NUM
ejpam-3547	417	6	)	)	PUNCT
ejpam-3547	417	7	,	,	PUNCT
ejpam-3547	417	8	pp	pp	PROPN
ejpam-3547	417	9	.	.	PUNCT
ejpam-3547	418	1	79	79	NUM
ejpam-3547	418	2	-	-	SYM
ejpam-3547	418	3	85	85	NUM
ejpam-3547	418	4	.	.	PUNCT
ejpam-3547	419	1	[	[	X
ejpam-3547	419	2	19	19	NUM
ejpam-3547	419	3	]	]	PUNCT
ejpam-3547	419	4	k.	k.	NOUN
ejpam-3547	419	5	weierstrass	weierstrass	PROPN
ejpam-3547	419	6	,	,	PUNCT
ejpam-3547	419	7	über	über	PROPN
ejpam-3547	419	8	die	die	VERB
ejpam-3547	419	9	analytische	analytische	PROPN
ejpam-3547	419	10	darstellbarkeit	darstellbarkeit	PROPN
ejpam-3547	419	11	sogenannter	sogenannter	PROPN
ejpam-3547	419	12	willkrlicher	willkrlicher	PROPN
ejpam-3547	419	13	functionen	functionen	PROPN
ejpam-3547	419	14	einer	einer	NOUN
ejpam-3547	419	15	reellen	reellen	VERB
ejpam-3547	419	16	vernderlichen	vernderlichen	ADV
ejpam-3547	419	17	,	,	PUNCT
ejpam-3547	419	18	sitzungsber	sitzungsber	NOUN
ejpam-3547	419	19	,	,	PUNCT
ejpam-3547	419	20	akad	akad	NOUN
ejpam-3547	419	21	.	.	PUNCT
ejpam-3547	420	1	berlin	berlin	PROPN
ejpam-3547	420	2	(	(	PUNCT
ejpam-3547	420	3	1885	1885	NUM
ejpam-3547	420	4	)	)	PUNCT
ejpam-3547	420	5	,	,	PUNCT
ejpam-3547	420	6	pp	pp	ADP
ejpam-3547	420	7	.	.	PUNCT
ejpam-3547	421	1	633	633	NUM
ejpam-3547	421	2	-	-	SYM
ejpam-3547	421	3	639	639	NUM
ejpam-3547	421	4	,	,	PUNCT
ejpam-3547	421	5	789	789	NUM
ejpam-3547	421	6	-	-	SYM
ejpam-3547	421	7	805	805	NUM
ejpam-3547	421	8	.	.	NUM
ejpam-3547	421	9	appeared	appear	VERB
ejpam-3547	421	10	in	in	ADP
ejpam-3547	421	11	two	two	NUM
ejpam-3547	421	12	parts	part	NOUN
ejpam-3547	421	13	.	.	PUNCT
ejpam-3547	422	1	[	[	X
ejpam-3547	422	2	20	20	NUM
ejpam-3547	422	3	]	]	X
ejpam-3547	422	4	o.	o.	NOUN
ejpam-3547	422	5	g.	g.	PROPN
ejpam-3547	422	6	yılmaza	yılmaza	PROPN
ejpam-3547	422	7	,	,	PUNCT
ejpam-3547	422	8	m.	m.	NOUN
ejpam-3547	422	9	bodura	bodura	NOUN
ejpam-3547	422	10	and	and	CCONJ
ejpam-3547	422	11	a.	a.	NOUN
ejpam-3547	422	12	aralb	aralb	PROPN
ejpam-3547	422	13	,	,	PUNCT
ejpam-3547	422	14	on	on	ADP
ejpam-3547	422	15	approximation	approximation	NOUN
ejpam-3547	422	16	properties	property	NOUN
ejpam-3547	422	17	of	of	ADP
ejpam-3547	422	18	baskakovschurer	baskakovschurer	NOUN
ejpam-3547	422	19	-	-	PUNCT
ejpam-3547	422	20	szasz	szasz	NOUN
ejpam-3547	422	21	operators	operator	NOUN
ejpam-3547	422	22	preserving	preserve	VERB
ejpam-3547	422	23	exponential	exponential	ADJ
ejpam-3547	422	24	functions	function	NOUN
ejpam-3547	422	25	,	,	PUNCT
ejpam-3547	422	26	filomat	filomat	NOUN
ejpam-3547	422	27	32:15	32:15	NUM
ejpam-3547	422	28	(	(	PUNCT
ejpam-3547	422	29	2018	2018	NUM
ejpam-3547	422	30	)	)	PUNCT
ejpam-3547	422	31	,	,	PUNCT
ejpam-3547	422	32	pp	pp	ADP
ejpam-3547	422	33	.	.	PUNCT
ejpam-3547	423	1	5433–5440	5433–5440	X
ejpam-3547	423	2	.	.	PUNCT