id	sid	tid	token	lemma	pos
ejpam-2434	1	1	compile	compile	NOUN
ejpam-2434	1	2	/	/	SYM
ejpam-2434	1	3	output.dvi	output.dvi	NOUN
ejpam-2434	1	4	european	european	ADJ
ejpam-2434	1	5	journal	journal	NOUN
ejpam-2434	1	6	of	of	ADP
ejpam-2434	1	7	pure	pure	ADJ
ejpam-2434	1	8	and	and	CCONJ
ejpam-2434	1	9	applied	apply	VERB
ejpam-2434	1	10	mathematics	mathematic	NOUN
ejpam-2434	1	11	vol	vol	NOUN
ejpam-2434	1	12	.	.	PROPN
ejpam-2434	1	13	8	8	NUM
ejpam-2434	1	14	,	,	PUNCT
ejpam-2434	1	15	no	no	INTJ
ejpam-2434	1	16	.	.	NOUN
ejpam-2434	1	17	3	3	NUM
ejpam-2434	1	18	,	,	PUNCT
ejpam-2434	1	19	2015	2015	NUM
ejpam-2434	1	20	,	,	PUNCT
ejpam-2434	1	21	324	324	NUM
ejpam-2434	1	22	-	-	SYM
ejpam-2434	1	23	331	331	NUM
ejpam-2434	1	24	issn	issn	PROPN
ejpam-2434	1	25	1307	1307	NUM
ejpam-2434	1	26	-	-	SYM
ejpam-2434	1	27	5543	5543	NUM
ejpam-2434	1	28	–	–	PUNCT
ejpam-2434	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-2434	1	30	generalized	generalize	VERB
ejpam-2434	1	31	tschebyscheff	tschebyscheff	NOUN
ejpam-2434	1	32	of	of	ADP
ejpam-2434	1	33	the	the	DET
ejpam-2434	1	34	second	second	ADJ
ejpam-2434	1	35	kind	kind	NOUN
ejpam-2434	1	36	and	and	CCONJ
ejpam-2434	1	37	bernstein	bernstein	PROPN
ejpam-2434	1	38	polynomials	polynomials	PROPN
ejpam-2434	1	39	change	change	NOUN
ejpam-2434	1	40	of	of	ADP
ejpam-2434	1	41	bases	basis	NOUN
ejpam-2434	1	42	mohammad	mohammad	PROPN
ejpam-2434	1	43	a.	a.	PROPN
ejpam-2434	1	44	alqudah	alqudah	PROPN
ejpam-2434	1	45	department	department	PROPN
ejpam-2434	1	46	of	of	ADP
ejpam-2434	1	47	mathematics	mathematics	PROPN
ejpam-2434	1	48	,	,	PUNCT
ejpam-2434	1	49	northwood	northwood	PROPN
ejpam-2434	1	50	university	university	PROPN
ejpam-2434	1	51	,	,	PUNCT
ejpam-2434	1	52	midland	midland	PROPN
ejpam-2434	1	53	,	,	PUNCT
ejpam-2434	1	54	mi	mi	PROPN
ejpam-2434	1	55	48640	48640	NUM
ejpam-2434	1	56	usa	usa	PROPN
ejpam-2434	1	57	abstract	abstract	PROPN
ejpam-2434	1	58	.	.	PUNCT
ejpam-2434	2	1	we	we	PRON
ejpam-2434	2	2	construct	construct	VERB
ejpam-2434	2	3	multiple	multiple	ADJ
ejpam-2434	2	4	representations	representation	NOUN
ejpam-2434	2	5	relative	relative	ADJ
ejpam-2434	2	6	to	to	ADP
ejpam-2434	2	7	different	different	ADJ
ejpam-2434	2	8	bases	basis	NOUN
ejpam-2434	2	9	of	of	ADP
ejpam-2434	2	10	the	the	DET
ejpam-2434	2	11	generalized	generalize	VERB
ejpam-2434	2	12	tschebyscheff	tschebyscheff	NOUN
ejpam-2434	2	13	polynomials	polynomial	NOUN
ejpam-2434	2	14	of	of	ADP
ejpam-2434	2	15	second	second	ADJ
ejpam-2434	2	16	kind	kind	NOUN
ejpam-2434	2	17	.	.	PUNCT
ejpam-2434	3	1	also	also	ADV
ejpam-2434	3	2	,	,	PUNCT
ejpam-2434	3	3	we	we	PRON
ejpam-2434	3	4	provide	provide	VERB
ejpam-2434	3	5	an	an	DET
ejpam-2434	3	6	explicit	explicit	ADJ
ejpam-2434	3	7	closed	close	VERB
ejpam-2434	3	8	from	from	ADP
ejpam-2434	3	9	of	of	ADP
ejpam-2434	3	10	the	the	DET
ejpam-2434	3	11	generalized	generalize	VERB
ejpam-2434	3	12	polynomials	polynomial	NOUN
ejpam-2434	3	13	of	of	ADP
ejpam-2434	3	14	degree	degree	NOUN
ejpam-2434	3	15	r	r	NOUN
ejpam-2434	3	16	less	less	ADJ
ejpam-2434	3	17	than	than	ADP
ejpam-2434	3	18	or	or	CCONJ
ejpam-2434	3	19	equal	equal	ADJ
ejpam-2434	3	20	n	n	NOUN
ejpam-2434	3	21	in	in	ADP
ejpam-2434	3	22	terms	term	NOUN
ejpam-2434	3	23	of	of	ADP
ejpam-2434	3	24	the	the	DET
ejpam-2434	3	25	bernstein	bernstein	PROPN
ejpam-2434	3	26	basis	basis	NOUN
ejpam-2434	3	27	of	of	ADP
ejpam-2434	3	28	fixed	fix	VERB
ejpam-2434	3	29	degree	degree	NOUN
ejpam-2434	3	30	n.	n.	NOUN
ejpam-2434	3	31	in	in	ADP
ejpam-2434	3	32	addition	addition	NOUN
ejpam-2434	3	33	,	,	PUNCT
ejpam-2434	3	34	we	we	PRON
ejpam-2434	3	35	create	create	VERB
ejpam-2434	3	36	the	the	DET
ejpam-2434	3	37	change	change	NOUN
ejpam-2434	3	38	-	-	PUNCT
ejpam-2434	3	39	of	of	ADP
ejpam-2434	3	40	-	-	PUNCT
ejpam-2434	3	41	basis	basis	NOUN
ejpam-2434	3	42	matrices	matrix	NOUN
ejpam-2434	3	43	between	between	ADP
ejpam-2434	3	44	the	the	DET
ejpam-2434	3	45	generalized	generalized	ADJ
ejpam-2434	3	46	tschebyscheff	tschebyscheff	NOUN
ejpam-2434	3	47	of	of	ADP
ejpam-2434	3	48	the	the	DET
ejpam-2434	3	49	second	second	ADJ
ejpam-2434	3	50	kind	kind	ADJ
ejpam-2434	3	51	polynomial	polynomial	ADJ
ejpam-2434	3	52	basis	basis	NOUN
ejpam-2434	3	53	and	and	CCONJ
ejpam-2434	3	54	bernstein	bernstein	PROPN
ejpam-2434	3	55	polynomial	polynomial	PROPN
ejpam-2434	3	56	basis	basis	NOUN
ejpam-2434	3	57	.	.	PUNCT
ejpam-2434	4	1	2010	2010	NUM
ejpam-2434	4	2	mathematics	mathematic	NOUN
ejpam-2434	4	3	subject	subject	NOUN
ejpam-2434	4	4	classifications	classification	NOUN
ejpam-2434	4	5	:	:	PUNCT
ejpam-2434	4	6	42c05	42c05	NUM
ejpam-2434	4	7	,	,	PUNCT
ejpam-2434	4	8	33c50	33c50	NUM
ejpam-2434	4	9	,	,	PUNCT
ejpam-2434	4	10	33c45	33c45	NUM
ejpam-2434	4	11	,	,	PUNCT
ejpam-2434	4	12	33c70	33c70	NUM
ejpam-2434	4	13	,	,	PUNCT
ejpam-2434	4	14	05a10	05a10	NOUN
ejpam-2434	4	15	,	,	PUNCT
ejpam-2434	4	16	33b15	33b15	NUM
ejpam-2434	4	17	key	key	ADJ
ejpam-2434	4	18	words	word	NOUN
ejpam-2434	4	19	and	and	CCONJ
ejpam-2434	4	20	phrases	phrase	NOUN
ejpam-2434	4	21	:	:	PUNCT
ejpam-2434	4	22	generalized	generalized	ADJ
ejpam-2434	4	23	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	4	24	,	,	PUNCT
ejpam-2434	4	25	bernstein	bernstein	PROPN
ejpam-2434	4	26	basis	basis	NOUN
ejpam-2434	4	27	,	,	PUNCT
ejpam-2434	4	28	basis	basis	NOUN
ejpam-2434	4	29	transformation	transformation	NOUN
ejpam-2434	4	30	,	,	PUNCT
ejpam-2434	4	31	bézier	bézier	NOUN
ejpam-2434	4	32	coefficient	coefficient	NOUN
ejpam-2434	4	33	,	,	PUNCT
ejpam-2434	4	34	gamma	gamma	PROPN
ejpam-2434	4	35	function	function	PROPN
ejpam-2434	4	36	1	1	NUM
ejpam-2434	4	37	.	.	PUNCT
ejpam-2434	5	1	introduction	introduction	NOUN
ejpam-2434	5	2	,	,	PUNCT
ejpam-2434	5	3	background	background	NOUN
ejpam-2434	5	4	and	and	CCONJ
ejpam-2434	5	5	motivation	motivation	NOUN
ejpam-2434	5	6	it	it	PRON
ejpam-2434	5	7	is	be	AUX
ejpam-2434	5	8	possible	possible	ADJ
ejpam-2434	5	9	to	to	PART
ejpam-2434	5	10	approximate	approximate	VERB
ejpam-2434	5	11	a	a	DET
ejpam-2434	5	12	complicated	complicated	ADJ
ejpam-2434	5	13	continuous	continuous	ADJ
ejpam-2434	5	14	functions	function	NOUN
ejpam-2434	5	15	defined	define	VERB
ejpam-2434	5	16	over	over	ADP
ejpam-2434	5	17	finite	finite	ADJ
ejpam-2434	5	18	domains	domain	NOUN
ejpam-2434	5	19	by	by	ADP
ejpam-2434	5	20	a	a	DET
ejpam-2434	5	21	polynomial	polynomial	ADJ
ejpam-2434	5	22	and	and	CCONJ
ejpam-2434	5	23	make	make	VERB
ejpam-2434	5	24	the	the	DET
ejpam-2434	5	25	error	error	NOUN
ejpam-2434	5	26	less	less	ADJ
ejpam-2434	5	27	than	than	ADP
ejpam-2434	5	28	a	a	DET
ejpam-2434	5	29	given	give	VERB
ejpam-2434	5	30	accuracy	accuracy	NOUN
ejpam-2434	5	31	.	.	PUNCT
ejpam-2434	6	1	on	on	ADP
ejpam-2434	6	2	the	the	DET
ejpam-2434	6	3	other	other	ADJ
ejpam-2434	6	4	side	side	NOUN
ejpam-2434	6	5	,	,	PUNCT
ejpam-2434	6	6	polynomials	polynomial	NOUN
ejpam-2434	6	7	can	can	AUX
ejpam-2434	6	8	be	be	AUX
ejpam-2434	6	9	characterized	characterize	VERB
ejpam-2434	6	10	in	in	ADP
ejpam-2434	6	11	many	many	ADJ
ejpam-2434	6	12	different	different	ADJ
ejpam-2434	6	13	bases	basis	NOUN
ejpam-2434	6	14	such	such	ADJ
ejpam-2434	6	15	as	as	ADP
ejpam-2434	6	16	the	the	DET
ejpam-2434	6	17	power	power	NOUN
ejpam-2434	6	18	product	product	NOUN
ejpam-2434	6	19	,	,	PUNCT
ejpam-2434	6	20	bernstein	bernstein	PROPN
ejpam-2434	6	21	basis	basis	NOUN
ejpam-2434	6	22	,	,	PUNCT
ejpam-2434	6	23	and	and	CCONJ
ejpam-2434	6	24	tschebyscheff	tschebyscheff	NOUN
ejpam-2434	6	25	basis	basis	NOUN
ejpam-2434	6	26	form	form	NOUN
ejpam-2434	6	27	,	,	PUNCT
ejpam-2434	6	28	where	where	SCONJ
ejpam-2434	6	29	every	every	DET
ejpam-2434	6	30	type	type	NOUN
ejpam-2434	6	31	of	of	ADP
ejpam-2434	6	32	polynomial	polynomial	ADJ
ejpam-2434	6	33	basis	basis	NOUN
ejpam-2434	6	34	has	have	VERB
ejpam-2434	6	35	its	its	PRON
ejpam-2434	6	36	strength	strength	NOUN
ejpam-2434	6	37	,	,	PUNCT
ejpam-2434	6	38	advantages	advantage	NOUN
ejpam-2434	6	39	,	,	PUNCT
ejpam-2434	6	40	and	and	CCONJ
ejpam-2434	6	41	sometimes	sometimes	ADV
ejpam-2434	6	42	disadvantages	disadvantage	VERB
ejpam-2434	6	43	.	.	PUNCT
ejpam-2434	7	1	it	it	PRON
ejpam-2434	7	2	is	be	AUX
ejpam-2434	7	3	useful	useful	ADJ
ejpam-2434	7	4	to	to	PART
ejpam-2434	7	5	switch	switch	VERB
ejpam-2434	7	6	bases	basis	NOUN
ejpam-2434	7	7	and	and	CCONJ
ejpam-2434	7	8	work	work	VERB
ejpam-2434	7	9	with	with	ADP
ejpam-2434	7	10	more	more	ADJ
ejpam-2434	7	11	than	than	ADP
ejpam-2434	7	12	one	one	NUM
ejpam-2434	7	13	basis	basis	NOUN
ejpam-2434	7	14	for	for	ADP
ejpam-2434	7	15	a	a	DET
ejpam-2434	7	16	given	give	VERB
ejpam-2434	7	17	polynomial	polynomial	NOUN
ejpam-2434	7	18	;	;	PUNCT
ejpam-2434	7	19	it	it	PRON
ejpam-2434	7	20	is	be	AUX
ejpam-2434	7	21	of	of	ADP
ejpam-2434	7	22	vital	vital	ADJ
ejpam-2434	7	23	importance	importance	NOUN
ejpam-2434	7	24	in	in	ADP
ejpam-2434	7	25	the	the	DET
ejpam-2434	7	26	efficiency	efficiency	NOUN
ejpam-2434	7	27	of	of	ADP
ejpam-2434	7	28	mathematical	mathematical	ADJ
ejpam-2434	7	29	calculations	calculation	NOUN
ejpam-2434	7	30	,	,	PUNCT
ejpam-2434	7	31	since	since	SCONJ
ejpam-2434	7	32	many	many	ADJ
ejpam-2434	7	33	difficulties	difficulty	NOUN
ejpam-2434	7	34	can	can	AUX
ejpam-2434	7	35	be	be	AUX
ejpam-2434	7	36	solved	solve	VERB
ejpam-2434	7	37	and	and	CCONJ
ejpam-2434	7	38	many	many	ADJ
ejpam-2434	7	39	problems	problem	NOUN
ejpam-2434	7	40	can	can	AUX
ejpam-2434	7	41	be	be	AUX
ejpam-2434	7	42	removed	remove	VERB
ejpam-2434	7	43	.	.	PUNCT
ejpam-2434	8	1	1.1	1.1	NUM
ejpam-2434	8	2	.	.	PUNCT
ejpam-2434	9	1	bernstein	bernstein	PROPN
ejpam-2434	9	2	polynomials	polynomial	VERB
ejpam-2434	9	3	the	the	DET
ejpam-2434	9	4	n+	n+	SYM
ejpam-2434	9	5	1	1	NUM
ejpam-2434	9	6	polynomials	polynomial	NOUN
ejpam-2434	9	7	bn	bn	INTJ
ejpam-2434	9	8	k	k	PROPN
ejpam-2434	9	9	(	(	PUNCT
ejpam-2434	9	10	x	x	NOUN
ejpam-2434	9	11	)	)	PUNCT
ejpam-2434	9	12	of	of	ADP
ejpam-2434	9	13	degree	degree	NOUN
ejpam-2434	9	14	n	n	CCONJ
ejpam-2434	9	15	,	,	PUNCT
ejpam-2434	9	16	x	x	SYM
ejpam-2434	9	17	∈	∈	PROPN
ejpam-2434	10	1	[	[	X
ejpam-2434	10	2	0,1	0,1	NUM
ejpam-2434	10	3	]	]	PUNCT
ejpam-2434	10	4	,	,	PUNCT
ejpam-2434	10	5	k	k	X
ejpam-2434	10	6	=	=	SYM
ejpam-2434	10	7	0,1	0,1	NUM
ejpam-2434	10	8	,	,	PUNCT
ejpam-2434	10	9	.	.	PUNCT
ejpam-2434	10	10	.	.	PUNCT
ejpam-2434	11	1	.	.	PUNCT
ejpam-2434	12	1	,	,	PUNCT
ejpam-2434	12	2	n	n	CCONJ
ejpam-2434	12	3	,	,	PUNCT
ejpam-2434	12	4	defined	define	VERB
ejpam-2434	12	5	as	as	ADP
ejpam-2434	12	6	bn	bn	PROPN
ejpam-2434	12	7	k	k	PROPN
ejpam-2434	12	8	(	(	PUNCT
ejpam-2434	12	9	x	x	X
ejpam-2434	12	10	)	)	PUNCT
ejpam-2434	12	11	=	=	SYM
ejpam-2434	12	12	n	n	X
ejpam-2434	12	13	!	!	PUNCT
ejpam-2434	12	14	k!(n−	k!(n−	PROPN
ejpam-2434	13	1	k	k	X
ejpam-2434	13	2	)	)	PUNCT
ejpam-2434	13	3	!	!	PUNCT
ejpam-2434	14	1	xk(1−	xk(1−	PROPN
ejpam-2434	15	1	x)n−k	x)n−k	PROPN
ejpam-2434	15	2	,	,	PUNCT
ejpam-2434	15	3	k	k	PROPN
ejpam-2434	15	4	=	=	SYM
ejpam-2434	15	5	0,1	0,1	NUM
ejpam-2434	15	6	,	,	PUNCT
ejpam-2434	15	7	.	.	PUNCT
ejpam-2434	15	8	.	.	PUNCT
ejpam-2434	15	9	.	.	PUNCT
ejpam-2434	15	10	,	,	PUNCT
ejpam-2434	15	11	n	n	CCONJ
ejpam-2434	15	12	,	,	PUNCT
ejpam-2434	15	13	(	(	PUNCT
ejpam-2434	15	14	1	1	X
ejpam-2434	15	15	)	)	PUNCT
ejpam-2434	15	16	are	be	AUX
ejpam-2434	15	17	called	call	VERB
ejpam-2434	15	18	bernstein	bernstein	PROPN
ejpam-2434	15	19	polynomials	polynomial	NOUN
ejpam-2434	15	20	.	.	PUNCT
ejpam-2434	16	1	email	email	NOUN
ejpam-2434	16	2	address	address	NOUN
ejpam-2434	16	3	:	:	PUNCT
ejpam-2434	16	4	alqudahm@northwood.edu	alqudahm@northwood.edu	X
ejpam-2434	16	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2434	17	1	324	324	NUM
ejpam-2434	17	2	c	c	X
ejpam-2434	17	3	©	©	PROPN
ejpam-2434	17	4	2015	2015	NUM
ejpam-2434	17	5	ejpam	ejpam	NOUN
ejpam-2434	17	6	all	all	DET
ejpam-2434	17	7	rights	right	NOUN
ejpam-2434	17	8	reserved	reserve	VERB
ejpam-2434	17	9	.	.	PUNCT
ejpam-2434	18	1	m.	m.	NOUN
ejpam-2434	18	2	alqudah	alqudah	PROPN
ejpam-2434	18	3	/	/	SYM
ejpam-2434	18	4	eur	eur	PROPN
ejpam-2434	18	5	.	.	PUNCT
ejpam-2434	19	1	j.	j.	PROPN
ejpam-2434	19	2	pure	pure	PROPN
ejpam-2434	19	3	appl	appl	PROPN
ejpam-2434	19	4	.	.	PROPN
ejpam-2434	19	5	math	math	PROPN
ejpam-2434	19	6	,	,	PUNCT
ejpam-2434	19	7	8	8	NUM
ejpam-2434	19	8	(	(	PUNCT
ejpam-2434	19	9	2015	2015	NUM
ejpam-2434	19	10	)	)	PUNCT
ejpam-2434	19	11	,	,	PUNCT
ejpam-2434	19	12	324	324	NUM
ejpam-2434	19	13	-	-	SYM
ejpam-2434	19	14	331	331	NUM
ejpam-2434	19	15	325	325	NUM
ejpam-2434	19	16	there	there	PRON
ejpam-2434	19	17	are	be	VERB
ejpam-2434	19	18	a	a	DET
ejpam-2434	19	19	fair	fair	ADJ
ejpam-2434	19	20	amount	amount	NOUN
ejpam-2434	19	21	of	of	ADP
ejpam-2434	19	22	literature	literature	NOUN
ejpam-2434	19	23	on	on	ADP
ejpam-2434	19	24	bernstein	bernstein	PROPN
ejpam-2434	19	25	polynomials	polynomials	PROPN
ejpam-2434	19	26	,	,	PUNCT
ejpam-2434	19	27	they	they	PRON
ejpam-2434	19	28	are	be	AUX
ejpam-2434	19	29	known	know	VERB
ejpam-2434	19	30	for	for	ADP
ejpam-2434	19	31	their	their	PRON
ejpam-2434	19	32	geometric	geometric	ADJ
ejpam-2434	19	33	and	and	CCONJ
ejpam-2434	19	34	analytical	analytical	ADJ
ejpam-2434	19	35	properties	property	NOUN
ejpam-2434	19	36	,	,	PUNCT
ejpam-2434	19	37	see	see	VERB
ejpam-2434	19	38	[	[	X
ejpam-2434	19	39	2	2	X
ejpam-2434	19	40	]	]	PUNCT
ejpam-2434	19	41	for	for	ADP
ejpam-2434	19	42	more	more	ADJ
ejpam-2434	19	43	details	detail	NOUN
ejpam-2434	19	44	.	.	PUNCT
ejpam-2434	20	1	analytic	analytic	ADJ
ejpam-2434	20	2	and	and	CCONJ
ejpam-2434	20	3	geometric	geometric	ADJ
ejpam-2434	20	4	properties	property	NOUN
ejpam-2434	20	5	of	of	ADP
ejpam-2434	20	6	bernstein	bernstein	PROPN
ejpam-2434	20	7	polynomials	polynomial	NOUN
ejpam-2434	20	8	make	make	VERB
ejpam-2434	20	9	them	they	PRON
ejpam-2434	20	10	important	important	ADJ
ejpam-2434	20	11	for	for	ADP
ejpam-2434	20	12	the	the	DET
ejpam-2434	20	13	development	development	NOUN
ejpam-2434	20	14	of	of	ADP
ejpam-2434	20	15	bézier	bézier	ADJ
ejpam-2434	20	16	curves	curve	NOUN
ejpam-2434	20	17	and	and	CCONJ
ejpam-2434	20	18	surfaces	surface	NOUN
ejpam-2434	20	19	.	.	PUNCT
ejpam-2434	21	1	the	the	DET
ejpam-2434	21	2	bernstein	bernstein	PROPN
ejpam-2434	21	3	polynomials	polynomial	NOUN
ejpam-2434	21	4	are	be	AUX
ejpam-2434	21	5	the	the	DET
ejpam-2434	21	6	standard	standard	ADJ
ejpam-2434	21	7	basis	basis	NOUN
ejpam-2434	21	8	for	for	ADP
ejpam-2434	21	9	the	the	DET
ejpam-2434	21	10	bézier	bézier	ADJ
ejpam-2434	21	11	representations	representation	NOUN
ejpam-2434	21	12	of	of	ADP
ejpam-2434	21	13	curves	curve	NOUN
ejpam-2434	21	14	and	and	CCONJ
ejpam-2434	21	15	surfaces	surface	NOUN
ejpam-2434	21	16	in	in	ADP
ejpam-2434	21	17	computer	computer	NOUN
ejpam-2434	21	18	aided	aid	VERB
ejpam-2434	21	19	geometric	geometric	ADJ
ejpam-2434	21	20	design	design	NOUN
ejpam-2434	21	21	.	.	PUNCT
ejpam-2434	22	1	however	however	ADV
ejpam-2434	22	2	,	,	PUNCT
ejpam-2434	22	3	the	the	DET
ejpam-2434	22	4	bernstein	bernstein	PROPN
ejpam-2434	22	5	polynomials	polynomial	NOUN
ejpam-2434	22	6	are	be	AUX
ejpam-2434	22	7	not	not	PART
ejpam-2434	22	8	orthogonal	orthogonal	ADJ
ejpam-2434	22	9	and	and	CCONJ
ejpam-2434	22	10	could	could	AUX
ejpam-2434	22	11	not	not	PART
ejpam-2434	22	12	be	be	AUX
ejpam-2434	22	13	used	use	VERB
ejpam-2434	22	14	effectively	effectively	ADV
ejpam-2434	22	15	in	in	ADP
ejpam-2434	22	16	the	the	DET
ejpam-2434	22	17	least	least	ADJ
ejpam-2434	22	18	-	-	PUNCT
ejpam-2434	22	19	squares	square	NOUN
ejpam-2434	22	20	approximation	approximation	NOUN
ejpam-2434	22	21	[	[	X
ejpam-2434	22	22	7	7	NUM
ejpam-2434	22	23	]	]	PUNCT
ejpam-2434	22	24	.	.	PUNCT
ejpam-2434	23	1	since	since	SCONJ
ejpam-2434	23	2	then	then	ADV
ejpam-2434	23	3	the	the	DET
ejpam-2434	23	4	method	method	NOUN
ejpam-2434	23	5	of	of	ADP
ejpam-2434	23	6	least	least	ADJ
ejpam-2434	23	7	squares	square	NOUN
ejpam-2434	23	8	approximation	approximation	NOUN
ejpam-2434	23	9	accompanied	accompany	VERB
ejpam-2434	23	10	by	by	ADP
ejpam-2434	23	11	orthogonal	orthogonal	ADJ
ejpam-2434	23	12	polynomials	polynomial	NOUN
ejpam-2434	23	13	has	have	AUX
ejpam-2434	23	14	been	be	AUX
ejpam-2434	23	15	introduced	introduce	VERB
ejpam-2434	23	16	and	and	CCONJ
ejpam-2434	23	17	developed	develop	VERB
ejpam-2434	23	18	.	.	PUNCT
ejpam-2434	24	1	1.2	1.2	NUM
ejpam-2434	24	2	.	.	PUNCT
ejpam-2434	24	3	least	least	ADJ
ejpam-2434	24	4	-	-	PUNCT
ejpam-2434	24	5	square	square	NOUN
ejpam-2434	24	6	approximation	approximation	NOUN
ejpam-2434	24	7	in	in	ADP
ejpam-2434	24	8	the	the	DET
ejpam-2434	24	9	following	follow	VERB
ejpam-2434	24	10	definition	definition	NOUN
ejpam-2434	24	11	,	,	PUNCT
ejpam-2434	24	12	we	we	PRON
ejpam-2434	24	13	define	define	VERB
ejpam-2434	24	14	the	the	DET
ejpam-2434	24	15	continuous	continuous	ADJ
ejpam-2434	24	16	least	least	ADJ
ejpam-2434	24	17	-	-	PUNCT
ejpam-2434	24	18	square	square	NOUN
ejpam-2434	24	19	approximations	approximation	NOUN
ejpam-2434	24	20	of	of	ADP
ejpam-2434	24	21	a	a	DET
ejpam-2434	24	22	function	function	NOUN
ejpam-2434	24	23	f	f	X
ejpam-2434	24	24	(	(	PUNCT
ejpam-2434	24	25	x	x	X
ejpam-2434	24	26	)	)	PUNCT
ejpam-2434	24	27	by	by	ADP
ejpam-2434	24	28	using	use	VERB
ejpam-2434	24	29	polynomials	polynomial	NOUN
ejpam-2434	24	30	with	with	ADP
ejpam-2434	24	31	standard	standard	ADJ
ejpam-2434	24	32	power	power	NOUN
ejpam-2434	24	33	basis	basis	NOUN
ejpam-2434	24	34	,	,	PUNCT
ejpam-2434	24	35	{	{	PUNCT
ejpam-2434	24	36	1	1	NUM
ejpam-2434	24	37	,	,	PUNCT
ejpam-2434	24	38	x	x	INTJ
ejpam-2434	24	39	,	,	PUNCT
ejpam-2434	24	40	x2	x2	PROPN
ejpam-2434	24	41	,	,	PUNCT
ejpam-2434	24	42	.	.	PUNCT
ejpam-2434	24	43	.	.	PUNCT
ejpam-2434	25	1	.	.	PUNCT
ejpam-2434	26	1	,	,	PUNCT
ejpam-2434	26	2	xn	xn	PROPN
ejpam-2434	26	3	}	}	PUNCT
ejpam-2434	26	4	.	.	PUNCT
ejpam-2434	27	1	definition	definition	NOUN
ejpam-2434	27	2	1	1	NUM
ejpam-2434	27	3	.	.	PUNCT
ejpam-2434	28	1	for	for	ADP
ejpam-2434	28	2	a	a	DET
ejpam-2434	28	3	function	function	NOUN
ejpam-2434	28	4	f	f	NOUN
ejpam-2434	28	5	(	(	PUNCT
ejpam-2434	28	6	x	x	NOUN
ejpam-2434	28	7	)	)	PUNCT
ejpam-2434	28	8	,	,	PUNCT
ejpam-2434	28	9	continuous	continuous	ADJ
ejpam-2434	28	10	on	on	ADP
ejpam-2434	28	11	[	[	X
ejpam-2434	28	12	0,1	0,1	NUM
ejpam-2434	28	13	]	]	PUNCT
ejpam-2434	28	14	the	the	DET
ejpam-2434	28	15	least	least	ADJ
ejpam-2434	28	16	square	square	ADJ
ejpam-2434	28	17	approximation	approximation	NOUN
ejpam-2434	28	18	requires	require	VERB
ejpam-2434	28	19	finding	find	VERB
ejpam-2434	28	20	a	a	DET
ejpam-2434	28	21	least	least	ADJ
ejpam-2434	28	22	-	-	PUNCT
ejpam-2434	28	23	squares	square	NOUN
ejpam-2434	28	24	polynomial	polynomial	ADJ
ejpam-2434	28	25	p∗n(x	p∗n(x	PROPN
ejpam-2434	28	26	)	)	PUNCT
ejpam-2434	29	1	=	=	SYM
ejpam-2434	29	2	∑n	∑n	PROPN
ejpam-2434	29	3	k=0	k=0	PROPN
ejpam-2434	29	4	akφk(x	akφk(x	PROPN
ejpam-2434	29	5	)	)	PUNCT
ejpam-2434	29	6	that	that	PRON
ejpam-2434	29	7	minimizes	minimize	VERB
ejpam-2434	29	8	the	the	DET
ejpam-2434	29	9	error	error	NOUN
ejpam-2434	29	10	e(a0	e(a0	NOUN
ejpam-2434	29	11	,	,	PUNCT
ejpam-2434	29	12	a1	a1	NOUN
ejpam-2434	29	13	,	,	PUNCT
ejpam-2434	29	14	.	.	PUNCT
ejpam-2434	29	15	.	.	PUNCT
ejpam-2434	29	16	.	.	PUNCT
ejpam-2434	30	1	,	,	PUNCT
ejpam-2434	30	2	an	an	X
ejpam-2434	30	3	)	)	PUNCT
ejpam-2434	30	4	=	=	SYM
ejpam-2434	31	1	∫	∫	PROPN
ejpam-2434	31	2	1	1	NUM
ejpam-2434	31	3	0	0	NUM
ejpam-2434	32	1	[	[	PUNCT
ejpam-2434	32	2	f	f	X
ejpam-2434	32	3	(	(	PUNCT
ejpam-2434	32	4	x)−	x)−	PROPN
ejpam-2434	32	5	p∗n(x	p∗n(x	PROPN
ejpam-2434	32	6	)	)	PUNCT
ejpam-2434	32	7	]	]	PUNCT
ejpam-2434	32	8	2d	2d	NUM
ejpam-2434	32	9	x	x	X
ejpam-2434	32	10	,	,	PUNCT
ejpam-2434	32	11	are	be	AUX
ejpam-2434	32	12	called	call	VERB
ejpam-2434	32	13	least	least	ADJ
ejpam-2434	32	14	squares	square	NOUN
ejpam-2434	32	15	approximations	approximation	NOUN
ejpam-2434	32	16	.	.	PUNCT
ejpam-2434	33	1	a	a	DET
ejpam-2434	33	2	necessary	necessary	ADJ
ejpam-2434	33	3	condition	condition	NOUN
ejpam-2434	33	4	for	for	ADP
ejpam-2434	33	5	e(a0	e(a0	NOUN
ejpam-2434	33	6	,	,	PUNCT
ejpam-2434	33	7	a1	a1	NOUN
ejpam-2434	33	8	,	,	PUNCT
ejpam-2434	33	9	.	.	PUNCT
ejpam-2434	33	10	.	.	PUNCT
ejpam-2434	34	1	.	.	PUNCT
ejpam-2434	35	1	,	,	PUNCT
ejpam-2434	35	2	an	an	X
ejpam-2434	35	3	)	)	PUNCT
ejpam-2434	35	4	to	to	PART
ejpam-2434	35	5	have	have	VERB
ejpam-2434	35	6	a	a	DET
ejpam-2434	35	7	minimum	minimum	NOUN
ejpam-2434	35	8	over	over	ADP
ejpam-2434	35	9	all	all	DET
ejpam-2434	35	10	values	value	NOUN
ejpam-2434	35	11	a0	a0	PROPN
ejpam-2434	35	12	,	,	PUNCT
ejpam-2434	35	13	a1	a1	NOUN
ejpam-2434	35	14	,	,	PUNCT
ejpam-2434	35	15	.	.	PUNCT
ejpam-2434	35	16	.	.	PUNCT
ejpam-2434	36	1	.	.	PUNCT
ejpam-2434	37	1	,	,	PUNCT
ejpam-2434	37	2	an	an	PRON
ejpam-2434	37	3	,	,	PUNCT
ejpam-2434	37	4	is	be	AUX
ejpam-2434	37	5	∂	∂	NUM
ejpam-2434	37	6	e	e	NOUN
ejpam-2434	37	7	∂	∂	NOUN
ejpam-2434	37	8	ak	ak	PROPN
ejpam-2434	37	9	=	=	PROPN
ejpam-2434	37	10	0	0	PROPN
ejpam-2434	37	11	.	.	PUNCT
ejpam-2434	38	1	but	but	CCONJ
ejpam-2434	38	2	,	,	PUNCT
ejpam-2434	38	3	∂	∂	NUM
ejpam-2434	38	4	e	e	NOUN
ejpam-2434	38	5	∂	∂	PROPN
ejpam-2434	38	6	ak	ak	PROPN
ejpam-2434	38	7	=	=	PROPN
ejpam-2434	38	8	−2	−2	PROPN
ejpam-2434	38	9	∫	∫	PROPN
ejpam-2434	38	10	1	1	NUM
ejpam-2434	38	11	0	0	NUM
ejpam-2434	38	12	[	[	PUNCT
ejpam-2434	38	13	f	f	X
ejpam-2434	38	14	(	(	PUNCT
ejpam-2434	38	15	x)−	x)−	PROPN
ejpam-2434	38	16	p∗n(x)]φk(x)d	p∗n(x)]φk(x)d	VERB
ejpam-2434	38	17	x	x	PUNCT
ejpam-2434	38	18	,	,	PUNCT
ejpam-2434	38	19	k	k	X
ejpam-2434	38	20	=	=	SYM
ejpam-2434	38	21	0	0	PROPN
ejpam-2434	38	22	,	,	PUNCT
ejpam-2434	38	23	.	.	PUNCT
ejpam-2434	38	24	.	.	PUNCT
ejpam-2434	38	25	.	.	PUNCT
ejpam-2434	39	1	,	,	PUNCT
ejpam-2434	39	2	n.	n.	PROPN
ejpam-2434	39	3	thus	thus	ADV
ejpam-2434	39	4	,	,	PUNCT
ejpam-2434	39	5	for	for	ADP
ejpam-2434	39	6	i	i	PROPN
ejpam-2434	39	7	=	=	NOUN
ejpam-2434	39	8	0,1	0,1	NUM
ejpam-2434	39	9	,	,	PUNCT
ejpam-2434	39	10	.	.	PUNCT
ejpam-2434	39	11	.	.	PUNCT
ejpam-2434	40	1	.	.	PUNCT
ejpam-2434	41	1	,	,	PUNCT
ejpam-2434	41	2	n	n	CCONJ
ejpam-2434	41	3	,	,	PUNCT
ejpam-2434	41	4	ai	ai	AUX
ejpam-2434	41	5	that	that	DET
ejpam-2434	41	6	minimize	minimize	NOUN
ejpam-2434	41	7	f	f	X
ejpam-2434	41	8	(	(	PUNCT
ejpam-2434	41	9	x)−∑n	x)−∑n	PROPN
ejpam-2434	41	10	k=0	k=0	PROPN
ejpam-2434	41	11	akφk(x	akφk(x	PROPN
ejpam-2434	41	12	)	)	PUNCT
ejpam-2434	41	13	2	2	NUM
ejpam-2434	41	14	satisfy	satisfy	NOUN
ejpam-2434	41	15	the	the	DET
ejpam-2434	41	16	system	system	NOUN
ejpam-2434	41	17	∫	∫	PROPN
ejpam-2434	41	18	1	1	NUM
ejpam-2434	41	19	0	0	NUM
ejpam-2434	41	20	f	f	PROPN
ejpam-2434	41	21	(	(	PUNCT
ejpam-2434	41	22	x)φi(x)d	x)φi(x)d	X
ejpam-2434	41	23	x	x	SYM
ejpam-2434	41	24	=	=	PUNCT
ejpam-2434	41	25	n	n	PROPN
ejpam-2434	41	26	∑	∑	ADP
ejpam-2434	41	27	k=0	k=0	PROPN
ejpam-2434	41	28	ak	ak	PROPN
ejpam-2434	41	29	∫	∫	PROPN
ejpam-2434	41	30	1	1	NUM
ejpam-2434	41	31	0	0	NUM
ejpam-2434	41	32	φk(x)φi(x)d	φk(x)φi(x)d	NUM
ejpam-2434	41	33	x	x	PROPN
ejpam-2434	41	34	.	.	PUNCT
ejpam-2434	41	35	which	which	PRON
ejpam-2434	41	36	gives	give	VERB
ejpam-2434	41	37	a	a	DET
ejpam-2434	41	38	system	system	NOUN
ejpam-2434	41	39	of	of	ADP
ejpam-2434	41	40	(	(	PUNCT
ejpam-2434	41	41	n+	n+	NOUN
ejpam-2434	41	42	1	1	NUM
ejpam-2434	41	43	)	)	PUNCT
ejpam-2434	41	44	equations	equation	NOUN
ejpam-2434	41	45	,	,	PUNCT
ejpam-2434	41	46	called	call	VERB
ejpam-2434	41	47	normal	normal	ADJ
ejpam-2434	41	48	equations	equation	NOUN
ejpam-2434	41	49	,	,	PUNCT
ejpam-2434	41	50	in	in	ADP
ejpam-2434	41	51	(	(	PUNCT
ejpam-2434	41	52	n+	n+	NOUN
ejpam-2434	41	53	1	1	NUM
ejpam-2434	41	54	)	)	PUNCT
ejpam-2434	41	55	unknowns	unknown	NOUN
ejpam-2434	41	56	:	:	PUNCT
ejpam-2434	41	57	ai	ai	VERB
ejpam-2434	41	58	,	,	PUNCT
ejpam-2434	41	59	i	i	PRON
ejpam-2434	41	60	=	=	NOUN
ejpam-2434	41	61	0	0	NUM
ejpam-2434	41	62	,	,	PUNCT
ejpam-2434	41	63	.	.	PUNCT
ejpam-2434	41	64	.	.	PUNCT
ejpam-2434	41	65	.	.	PUNCT
ejpam-2434	42	1	,	,	PUNCT
ejpam-2434	42	2	n.	n.	VERB
ejpam-2434	42	3	those	those	PRON
ejpam-2434	42	4	(	(	PUNCT
ejpam-2434	42	5	n+	n+	NUM
ejpam-2434	42	6	1	1	NUM
ejpam-2434	42	7	)	)	PUNCT
ejpam-2434	42	8	unknowns	unknown	NOUN
ejpam-2434	42	9	of	of	ADP
ejpam-2434	42	10	the	the	DET
ejpam-2434	42	11	least	least	ADJ
ejpam-2434	42	12	-	-	PUNCT
ejpam-2434	42	13	squares	square	NOUN
ejpam-2434	42	14	polynomial	polynomial	ADJ
ejpam-2434	42	15	p∗n(x	p∗n(x	PROPN
ejpam-2434	42	16	)	)	PUNCT
ejpam-2434	42	17	,	,	PUNCT
ejpam-2434	42	18	can	can	AUX
ejpam-2434	42	19	be	be	AUX
ejpam-2434	42	20	found	find	VERB
ejpam-2434	42	21	by	by	ADP
ejpam-2434	42	22	solving	solve	VERB
ejpam-2434	42	23	the	the	DET
ejpam-2434	42	24	normal	normal	ADJ
ejpam-2434	42	25	equations	equation	NOUN
ejpam-2434	42	26	.	.	PUNCT
ejpam-2434	43	1	by	by	ADP
ejpam-2434	43	2	choosing	choose	VERB
ejpam-2434	43	3	φi(x	φi(x	NUM
ejpam-2434	43	4	)	)	PUNCT
ejpam-2434	43	5	=	=	PUNCT
ejpam-2434	44	1	x	x	PUNCT
ejpam-2434	44	2	i	i	PRON
ejpam-2434	44	3	,	,	PUNCT
ejpam-2434	44	4	as	as	ADP
ejpam-2434	44	5	a	a	DET
ejpam-2434	44	6	basis	basis	NOUN
ejpam-2434	44	7	,	,	PUNCT
ejpam-2434	44	8	then	then	ADV
ejpam-2434	44	9	∫	∫	PROPN
ejpam-2434	44	10	1	1	NUM
ejpam-2434	44	11	0	0	NUM
ejpam-2434	44	12	f	f	PROPN
ejpam-2434	44	13	(	(	PUNCT
ejpam-2434	44	14	x)x	x)x	X
ejpam-2434	44	15	i	i	PROPN
ejpam-2434	44	16	d	d	NOUN
ejpam-2434	44	17	x	x	PUNCT
ejpam-2434	44	18	=	=	PUNCT
ejpam-2434	44	19	n	n	PROPN
ejpam-2434	44	20	∑	∑	ADP
ejpam-2434	44	21	k=0	k=0	PROPN
ejpam-2434	44	22	ak	ak	PROPN
ejpam-2434	44	23	∫	∫	PROPN
ejpam-2434	44	24	1	1	NUM
ejpam-2434	44	25	0	0	NUM
ejpam-2434	44	26	x	x	SYM
ejpam-2434	44	27	i+kd	i+kd	NOUN
ejpam-2434	44	28	x	x	X
ejpam-2434	44	29	=	=	PUNCT
ejpam-2434	44	30	n	n	PROPN
ejpam-2434	44	31	∑	∑	ADP
ejpam-2434	44	32	k=0	k=0	PROPN
ejpam-2434	44	33	ak	ak	PROPN
ejpam-2434	44	34	i	i	PROPN
ejpam-2434	44	35	+	+	CCONJ
ejpam-2434	44	36	k+	k+	NOUN
ejpam-2434	44	37	1	1	X
ejpam-2434	44	38	.	.	PUNCT
ejpam-2434	45	1	the	the	DET
ejpam-2434	45	2	coefficients	coefficient	NOUN
ejpam-2434	45	3	matrix	matrix	NOUN
ejpam-2434	45	4	of	of	ADP
ejpam-2434	45	5	the	the	DET
ejpam-2434	45	6	normal	normal	ADJ
ejpam-2434	45	7	equations	equation	NOUN
ejpam-2434	45	8	is	be	AUX
ejpam-2434	45	9	hilbert	hilbert	NOUN
ejpam-2434	45	10	matrix	matrix	NOUN
ejpam-2434	45	11	which	which	PRON
ejpam-2434	45	12	has	have	VERB
ejpam-2434	45	13	round	round	VERB
ejpam-2434	45	14	-	-	PUNCT
ejpam-2434	45	15	off	off	ADP
ejpam-2434	45	16	error	error	NOUN
ejpam-2434	45	17	difficulties	difficulty	NOUN
ejpam-2434	45	18	and	and	CCONJ
ejpam-2434	45	19	notoriously	notoriously	ADV
ejpam-2434	45	20	ill	ill	ADV
ejpam-2434	45	21	-	-	PUNCT
ejpam-2434	45	22	conditioned	condition	VERB
ejpam-2434	45	23	for	for	ADP
ejpam-2434	45	24	even	even	ADV
ejpam-2434	45	25	modest	modest	ADJ
ejpam-2434	45	26	values	value	NOUN
ejpam-2434	45	27	of	of	ADP
ejpam-2434	45	28	n.	n.	NOUN
ejpam-2434	45	29	however	however	ADV
ejpam-2434	45	30	,	,	PUNCT
ejpam-2434	45	31	such	such	ADJ
ejpam-2434	45	32	computations	computation	NOUN
ejpam-2434	45	33	can	can	AUX
ejpam-2434	45	34	be	be	AUX
ejpam-2434	45	35	made	make	VERB
ejpam-2434	45	36	effective	effective	ADJ
ejpam-2434	45	37	by	by	ADP
ejpam-2434	45	38	using	use	VERB
ejpam-2434	45	39	orthogonal	orthogonal	ADJ
ejpam-2434	45	40	polynomials	polynomial	NOUN
ejpam-2434	45	41	.	.	PUNCT
ejpam-2434	46	1	thus	thus	ADV
ejpam-2434	46	2	,	,	PUNCT
ejpam-2434	46	3	choosing	choose	VERB
ejpam-2434	46	4	{	{	PUNCT
ejpam-2434	46	5	φ0(x),φ1(x	φ0(x),φ1(x	NOUN
ejpam-2434	46	6	)	)	PUNCT
ejpam-2434	46	7	,	,	PUNCT
ejpam-2434	46	8	.	.	PUNCT
ejpam-2434	46	9	.	.	PUNCT
ejpam-2434	47	1	.	.	PUNCT
ejpam-2434	48	1	,	,	PUNCT
ejpam-2434	48	2	φn(x	φn(x	NOUN
ejpam-2434	48	3	)	)	PUNCT
ejpam-2434	48	4	}	}	PUNCT
ejpam-2434	48	5	to	to	PART
ejpam-2434	48	6	be	be	AUX
ejpam-2434	48	7	orthogonal	orthogonal	ADJ
ejpam-2434	48	8	simplifies	simplifie	NOUN
ejpam-2434	48	9	the	the	DET
ejpam-2434	48	10	least	least	ADJ
ejpam-2434	48	11	-	-	PUNCT
ejpam-2434	48	12	squares	square	NOUN
ejpam-2434	48	13	approximation	approximation	NOUN
ejpam-2434	48	14	problem	problem	NOUN
ejpam-2434	48	15	.	.	PUNCT
ejpam-2434	49	1	the	the	DET
ejpam-2434	49	2	coefficients	coefficient	NOUN
ejpam-2434	49	3	matrix	matrix	NOUN
ejpam-2434	49	4	of	of	ADP
ejpam-2434	49	5	the	the	DET
ejpam-2434	49	6	normal	normal	ADJ
ejpam-2434	49	7	equations	equation	NOUN
ejpam-2434	49	8	will	will	AUX
ejpam-2434	49	9	be	be	AUX
ejpam-2434	49	10	diagonal	diagonal	ADJ
ejpam-2434	49	11	,	,	PUNCT
ejpam-2434	49	12	which	which	PRON
ejpam-2434	49	13	gives	give	VERB
ejpam-2434	49	14	a	a	DET
ejpam-2434	49	15	compact	compact	ADJ
ejpam-2434	49	16	form	form	NOUN
ejpam-2434	49	17	for	for	ADP
ejpam-2434	49	18	ai	ai	NOUN
ejpam-2434	49	19	,	,	PUNCT
ejpam-2434	49	20	i	i	PRON
ejpam-2434	49	21	=	=	NOUN
ejpam-2434	49	22	0,1	0,1	NUM
ejpam-2434	49	23	,	,	PUNCT
ejpam-2434	49	24	.	.	PUNCT
ejpam-2434	49	25	.	.	PUNCT
ejpam-2434	50	1	.	.	PUNCT
ejpam-2434	51	1	,	,	PUNCT
ejpam-2434	51	2	n.	n.	PROPN
ejpam-2434	51	3	see	see	VERB
ejpam-2434	51	4	[	[	X
ejpam-2434	51	5	7	7	X
ejpam-2434	51	6	]	]	PUNCT
ejpam-2434	51	7	for	for	ADP
ejpam-2434	51	8	more	more	ADJ
ejpam-2434	51	9	details	detail	NOUN
ejpam-2434	51	10	on	on	ADP
ejpam-2434	51	11	the	the	DET
ejpam-2434	51	12	least	least	ADJ
ejpam-2434	51	13	squares	square	NOUN
ejpam-2434	51	14	approximations	approximation	NOUN
ejpam-2434	51	15	.	.	PUNCT
ejpam-2434	52	1	m.	m.	NOUN
ejpam-2434	52	2	alqudah	alqudah	PROPN
ejpam-2434	52	3	/	/	SYM
ejpam-2434	52	4	eur	eur	PROPN
ejpam-2434	52	5	.	.	PUNCT
ejpam-2434	53	1	j.	j.	PROPN
ejpam-2434	53	2	pure	pure	PROPN
ejpam-2434	53	3	appl	appl	PROPN
ejpam-2434	53	4	.	.	PROPN
ejpam-2434	53	5	math	math	PROPN
ejpam-2434	53	6	,	,	PUNCT
ejpam-2434	53	7	8	8	NUM
ejpam-2434	53	8	(	(	PUNCT
ejpam-2434	53	9	2015	2015	NUM
ejpam-2434	53	10	)	)	PUNCT
ejpam-2434	53	11	,	,	PUNCT
ejpam-2434	53	12	324	324	NUM
ejpam-2434	53	13	-	-	SYM
ejpam-2434	53	14	331	331	NUM
ejpam-2434	53	15	326	326	NUM
ejpam-2434	53	16	1.3	1.3	NUM
ejpam-2434	53	17	.	.	PUNCT
ejpam-2434	54	1	gamma	gamma	NOUN
ejpam-2434	54	2	functions	function	NOUN
ejpam-2434	54	3	the	the	DET
ejpam-2434	54	4	gamma	gamma	PROPN
ejpam-2434	54	5	function	function	NOUN
ejpam-2434	54	6	γ(n	γ(n	PROPN
ejpam-2434	54	7	)	)	PUNCT
ejpam-2434	54	8	is	be	AUX
ejpam-2434	54	9	an	an	DET
ejpam-2434	54	10	extension	extension	NOUN
ejpam-2434	54	11	of	of	ADP
ejpam-2434	54	12	the	the	DET
ejpam-2434	54	13	factorial	factorial	ADJ
ejpam-2434	54	14	function	function	NOUN
ejpam-2434	54	15	,	,	PUNCT
ejpam-2434	54	16	with	with	ADP
ejpam-2434	54	17	its	its	PRON
ejpam-2434	54	18	argument	argument	NOUN
ejpam-2434	54	19	shifted	shift	VERB
ejpam-2434	54	20	down	down	ADP
ejpam-2434	54	21	by	by	ADP
ejpam-2434	54	22	1	1	NUM
ejpam-2434	54	23	.	.	PUNCT
ejpam-2434	55	1	that	that	PRON
ejpam-2434	55	2	is	be	AUX
ejpam-2434	55	3	,	,	PUNCT
ejpam-2434	55	4	if	if	SCONJ
ejpam-2434	55	5	n	n	PRON
ejpam-2434	55	6	is	be	AUX
ejpam-2434	55	7	a	a	DET
ejpam-2434	55	8	positive	positive	ADJ
ejpam-2434	55	9	integer	integer	NOUN
ejpam-2434	55	10	:	:	PUNCT
ejpam-2434	55	11	γ(n	γ(n	X
ejpam-2434	55	12	)	)	PUNCT
ejpam-2434	56	1	=	=	SYM
ejpam-2434	56	2	(	(	PUNCT
ejpam-2434	56	3	n−1	n−1	PROPN
ejpam-2434	56	4	)	)	PUNCT
ejpam-2434	56	5	!	!	PUNCT
ejpam-2434	56	6	.	.	PUNCT
ejpam-2434	57	1	the	the	DET
ejpam-2434	57	2	eulerian	eulerian	ADJ
ejpam-2434	57	3	integral	integral	NOUN
ejpam-2434	57	4	of	of	ADP
ejpam-2434	57	5	the	the	DET
ejpam-2434	57	6	first	first	ADJ
ejpam-2434	57	7	kind	kind	NOUN
ejpam-2434	57	8	is	be	AUX
ejpam-2434	57	9	useful	useful	ADJ
ejpam-2434	57	10	and	and	CCONJ
ejpam-2434	57	11	will	will	AUX
ejpam-2434	57	12	be	be	AUX
ejpam-2434	57	13	used	use	VERB
ejpam-2434	57	14	in	in	ADP
ejpam-2434	57	15	main	main	ADJ
ejpam-2434	57	16	result	result	NOUN
ejpam-2434	57	17	simplifications	simplification	NOUN
ejpam-2434	57	18	.	.	PUNCT
ejpam-2434	58	1	definition	definition	NOUN
ejpam-2434	58	2	2	2	NUM
ejpam-2434	58	3	.	.	PUNCT
ejpam-2434	59	1	the	the	DET
ejpam-2434	59	2	eulerian	eulerian	ADJ
ejpam-2434	59	3	integral	integral	NOUN
ejpam-2434	59	4	of	of	ADP
ejpam-2434	59	5	the	the	DET
ejpam-2434	59	6	first	first	ADJ
ejpam-2434	59	7	kind	kind	NOUN
ejpam-2434	59	8	is	be	AUX
ejpam-2434	59	9	a	a	DET
ejpam-2434	59	10	function	function	NOUN
ejpam-2434	59	11	of	of	ADP
ejpam-2434	59	12	two	two	NUM
ejpam-2434	59	13	complex	complex	ADJ
ejpam-2434	59	14	variables	variable	NOUN
ejpam-2434	59	15	defined	define	VERB
ejpam-2434	59	16	by	by	ADP
ejpam-2434	59	17	∫	∫	PROPN
ejpam-2434	59	18	1	1	NUM
ejpam-2434	59	19	0	0	NUM
ejpam-2434	59	20	ux−1(1−	ux−1(1−	ADJ
ejpam-2434	59	21	u)y−1du=	u)y−1du=	ADJ
ejpam-2434	59	22	γ(x)γ(y	γ(x)γ(y	NOUN
ejpam-2434	59	23	)	)	PUNCT
ejpam-2434	59	24	γ(x	γ(x	PROPN
ejpam-2434	60	1	+	+	CCONJ
ejpam-2434	60	2	y	y	NOUN
ejpam-2434	60	3	)	)	PUNCT
ejpam-2434	60	4	,	,	PUNCT
ejpam-2434	60	5	ℜ(x),ℜ(y	ℜ(x),ℜ(y	PROPN
ejpam-2434	60	6	)	)	PUNCT
ejpam-2434	60	7	>	>	X
ejpam-2434	61	1	0	0	X
ejpam-2434	61	2	.	.	PUNCT
ejpam-2434	62	1	(	(	PUNCT
ejpam-2434	62	2	2	2	X
ejpam-2434	62	3	)	)	PUNCT
ejpam-2434	62	4	the	the	DET
ejpam-2434	62	5	double	double	ADJ
ejpam-2434	62	6	factorial	factorial	NOUN
ejpam-2434	62	7	of	of	ADP
ejpam-2434	62	8	an	an	DET
ejpam-2434	62	9	integer	integer	NOUN
ejpam-2434	62	10	n	n	AUX
ejpam-2434	62	11	is	be	AUX
ejpam-2434	62	12	given	give	VERB
ejpam-2434	62	13	by	by	ADP
ejpam-2434	62	14	¨	¨	X
ejpam-2434	62	15	(	(	PUNCT
ejpam-2434	62	16	2n−	2n−	PROPN
ejpam-2434	62	17	1)!!=	1)!!=	NUM
ejpam-2434	62	18	(	(	PUNCT
ejpam-2434	62	19	2n−	2n−	PROPN
ejpam-2434	62	20	1)(2n−	1)(2n−	NUM
ejpam-2434	62	21	3)(2n−	3)(2n−	NUM
ejpam-2434	62	22	5	5	NUM
ejpam-2434	62	23	)	)	PUNCT
ejpam-2434	62	24	.	.	PUNCT
ejpam-2434	62	25	.	.	PUNCT
ejpam-2434	62	26	.	.	PUNCT
ejpam-2434	63	1	(	(	PUNCT
ejpam-2434	63	2	3)(1	3)(1	NUM
ejpam-2434	63	3	)	)	PUNCT
ejpam-2434	63	4	if	if	SCONJ
ejpam-2434	63	5	n	n	NOUN
ejpam-2434	63	6	is	be	AUX
ejpam-2434	63	7	odd	odd	ADJ
ejpam-2434	63	8	n!!=	n!!=	PROPN
ejpam-2434	63	9	(	(	PUNCT
ejpam-2434	63	10	n)(n−	n)(n−	NOUN
ejpam-2434	63	11	2)(n−	2)(n−	NUM
ejpam-2434	63	12	4	4	NUM
ejpam-2434	63	13	)	)	PUNCT
ejpam-2434	63	14	.	.	PUNCT
ejpam-2434	63	15	.	.	PUNCT
ejpam-2434	63	16	.	.	PUNCT
ejpam-2434	64	1	(	(	PUNCT
ejpam-2434	64	2	4)(2	4)(2	NOUN
ejpam-2434	64	3	)	)	PUNCT
ejpam-2434	64	4	if	if	SCONJ
ejpam-2434	64	5	n	n	PRON
ejpam-2434	64	6	is	be	AUX
ejpam-2434	64	7	even	even	ADV
ejpam-2434	64	8	,	,	PUNCT
ejpam-2434	64	9	(	(	PUNCT
ejpam-2434	64	10	3	3	X
ejpam-2434	64	11	)	)	PUNCT
ejpam-2434	64	12	where	where	SCONJ
ejpam-2434	64	13	0!!=	0!!=	X
ejpam-2434	64	14	(	(	PUNCT
ejpam-2434	64	15	−1)!!=	−1)!!=	PROPN
ejpam-2434	64	16	1	1	X
ejpam-2434	64	17	.	.	PUNCT
ejpam-2434	65	1	using	use	VERB
ejpam-2434	65	2	(	(	PUNCT
ejpam-2434	65	3	3	3	NUM
ejpam-2434	65	4	)	)	PUNCT
ejpam-2434	65	5	,	,	PUNCT
ejpam-2434	65	6	we	we	PRON
ejpam-2434	65	7	can	can	AUX
ejpam-2434	65	8	derive	derive	VERB
ejpam-2434	65	9	the	the	DET
ejpam-2434	65	10	following	follow	VERB
ejpam-2434	65	11	relation	relation	NOUN
ejpam-2434	65	12	n!!=	n!!=	PROPN
ejpam-2434	65	13			PROPN
ejpam-2434	65	14			ADP
ejpam-2434	65	15			ADJ
ejpam-2434	65	16	2	2	NUM
ejpam-2434	65	17	n	n	SYM
ejpam-2434	65	18	2	2	NUM
ejpam-2434	65	19	(	(	PUNCT
ejpam-2434	65	20	n	n	ADV
ejpam-2434	65	21	2	2	NUM
ejpam-2434	65	22	)	)	PUNCT
ejpam-2434	65	23	!	!	PUNCT
ejpam-2434	66	1	if	if	SCONJ
ejpam-2434	66	2	n	n	PRON
ejpam-2434	66	3	is	be	AUX
ejpam-2434	66	4	even	even	ADV
ejpam-2434	66	5	n	n	CCONJ
ejpam-2434	66	6	!	!	PROPN
ejpam-2434	66	7	2	2	NUM
ejpam-2434	66	8	n−1	n−1	PROPN
ejpam-2434	66	9	2	2	NUM
ejpam-2434	66	10	(	(	PUNCT
ejpam-2434	66	11	n−1	n−1	PROPN
ejpam-2434	66	12	2	2	NUM
ejpam-2434	66	13	)	)	PUNCT
ejpam-2434	66	14	!	!	PUNCT
ejpam-2434	67	1	if	if	SCONJ
ejpam-2434	67	2	n	n	NOUN
ejpam-2434	67	3	is	be	AUX
ejpam-2434	67	4	odd	odd	ADJ
ejpam-2434	67	5	(	(	PUNCT
ejpam-2434	67	6	4	4	X
ejpam-2434	67	7	)	)	PUNCT
ejpam-2434	67	8	it	it	PRON
ejpam-2434	67	9	is	be	AUX
ejpam-2434	67	10	easy	easy	ADJ
ejpam-2434	67	11	to	to	PART
ejpam-2434	67	12	derive	derive	VERB
ejpam-2434	67	13	the	the	DET
ejpam-2434	67	14	factorial	factorial	NOUN
ejpam-2434	67	15	of	of	ADP
ejpam-2434	67	16	an	an	DET
ejpam-2434	67	17	integer	integer	NOUN
ejpam-2434	67	18	plus	plus	CCONJ
ejpam-2434	67	19	half	half	NOUN
ejpam-2434	67	20	as	as	ADP
ejpam-2434	67	21	�	�	PROPN
ejpam-2434	67	22	n+	n+	NUM
ejpam-2434	67	23	1	1	NUM
ejpam-2434	67	24	2	2	NUM
ejpam-2434	67	25	�	�	NOUN
ejpam-2434	67	26	!	!	PUNCT
ejpam-2434	67	27	=	=	PUNCT
ejpam-2434	68	1	p	p	X
ejpam-2434	68	2	π	π	PROPN
ejpam-2434	68	3	2n+1	2n+1	PROPN
ejpam-2434	68	4	(	(	PUNCT
ejpam-2434	68	5	2n+	2n+	NUM
ejpam-2434	68	6	1	1	NUM
ejpam-2434	68	7	)	)	PUNCT
ejpam-2434	68	8	!	!	PUNCT
ejpam-2434	68	9	!	!	PUNCT
ejpam-2434	68	10	.	.	PUNCT
ejpam-2434	69	1	(	(	PUNCT
ejpam-2434	69	2	5	5	NUM
ejpam-2434	69	3	)	)	PUNCT
ejpam-2434	69	4	from	from	ADP
ejpam-2434	69	5	the	the	DET
ejpam-2434	69	6	relation	relation	NOUN
ejpam-2434	69	7	(	(	PUNCT
ejpam-2434	69	8	4	4	NUM
ejpam-2434	69	9	)	)	PUNCT
ejpam-2434	69	10	to	to	PART
ejpam-2434	69	11	have	have	VERB
ejpam-2434	69	12	(	(	PUNCT
ejpam-2434	69	13	2n)!!=	2n)!!=	NUM
ejpam-2434	69	14	2nn	2nn	NOUN
ejpam-2434	69	15	!	!	PUNCT
ejpam-2434	69	16	,	,	PUNCT
ejpam-2434	69	17	and	and	CCONJ
ejpam-2434	69	18	(	(	PUNCT
ejpam-2434	69	19	2n)!=	2n)!=	NUM
ejpam-2434	69	20	(	(	PUNCT
ejpam-2434	69	21	2n−	2n−	PROPN
ejpam-2434	69	22	1)!!2nn	1)!!2nn	NUM
ejpam-2434	69	23	!	!	PUNCT
ejpam-2434	69	24	.	.	PUNCT
ejpam-2434	70	1	1.4	1.4	NUM
ejpam-2434	70	2	.	.	PUNCT
ejpam-2434	71	1	univariate	univariate	ADJ
ejpam-2434	71	2	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	71	3	-	-	PUNCT
ejpam-2434	71	4	ii	ii	NOUN
ejpam-2434	71	5	and	and	CCONJ
ejpam-2434	71	6	the	the	DET
ejpam-2434	71	7	generalized	generalize	VERB
ejpam-2434	71	8	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	71	9	-	-	PUNCT
ejpam-2434	71	10	ii	ii	NOUN
ejpam-2434	71	11	polynomials	polynomial	VERB
ejpam-2434	71	12	the	the	DET
ejpam-2434	71	13	univariate	univariate	ADJ
ejpam-2434	71	14	classical	classical	ADJ
ejpam-2434	71	15	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	71	16	-	-	PUNCT
ejpam-2434	71	17	ii	ii	NOUN
ejpam-2434	71	18	orthogonal	orthogonal	ADJ
ejpam-2434	71	19	polynomials	polynomial	NOUN
ejpam-2434	71	20	un(x	un(x	PART
ejpam-2434	71	21	)	)	PUNCT
ejpam-2434	71	22	are	be	AUX
ejpam-2434	71	23	special	special	ADJ
ejpam-2434	71	24	case	case	NOUN
ejpam-2434	71	25	of	of	ADP
ejpam-2434	71	26	jacobi	jacobi	PROPN
ejpam-2434	71	27	polynomials	polynomial	VERB
ejpam-2434	71	28	p	p	PROPN
ejpam-2434	71	29	(	(	PUNCT
ejpam-2434	71	30	α	α	X
ejpam-2434	71	31	,	,	PUNCT
ejpam-2434	71	32	β	β	NOUN
ejpam-2434	71	33	)	)	PUNCT
ejpam-2434	71	34	n	n	ADP
ejpam-2434	71	35	withα=	withα=	NUM
ejpam-2434	71	36	β	β	X
ejpam-2434	71	37	=	=	SYM
ejpam-2434	71	38	1/2	1/2	NUM
ejpam-2434	71	39	,	,	PUNCT
ejpam-2434	71	40	where	where	SCONJ
ejpam-2434	71	41	the	the	DET
ejpam-2434	71	42	inter	inter	NOUN
ejpam-2434	71	43	-	-	NOUN
ejpam-2434	71	44	relationship	relationship	NOUN
ejpam-2434	71	45	between	between	ADP
ejpam-2434	71	46	tschebyscheffii	tschebyscheffii	NOUN
ejpam-2434	71	47	and	and	CCONJ
ejpam-2434	71	48	jacobi	jacobi	PROPN
ejpam-2434	71	49	polynomials	polynomial	NOUN
ejpam-2434	71	50	given	give	VERB
ejpam-2434	71	51	as	as	ADP
ejpam-2434	71	52	p	p	NOUN
ejpam-2434	71	53	(	(	PUNCT
ejpam-2434	71	54	1	1	NUM
ejpam-2434	71	55	2	2	NUM
ejpam-2434	71	56	,	,	PUNCT
ejpam-2434	71	57	1	1	NUM
ejpam-2434	71	58	2	2	NUM
ejpam-2434	71	59	)	)	PUNCT
ejpam-2434	71	60	n	n	CCONJ
ejpam-2434	71	61	(	(	PUNCT
ejpam-2434	71	62	1)un(x	1)un(x	X
ejpam-2434	71	63	)	)	PUNCT
ejpam-2434	71	64	=	=	SYM
ejpam-2434	71	65	(	(	PUNCT
ejpam-2434	71	66	n+	n+	NUM
ejpam-2434	71	67	1)p	1)p	NUM
ejpam-2434	71	68	(	(	PUNCT
ejpam-2434	71	69	1	1	NUM
ejpam-2434	71	70	2	2	NUM
ejpam-2434	71	71	,	,	PUNCT
ejpam-2434	71	72	1	1	NUM
ejpam-2434	71	73	2	2	NUM
ejpam-2434	71	74	)	)	PUNCT
ejpam-2434	71	75	n	n	CCONJ
ejpam-2434	71	76	(	(	PUNCT
ejpam-2434	71	77	x	x	NOUN
ejpam-2434	71	78	)	)	PUNCT
ejpam-2434	71	79	.	.	PUNCT
ejpam-2434	72	1	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	72	2	-	-	PUNCT
ejpam-2434	72	3	ii	ii	PROPN
ejpam-2434	72	4	polynomials	polynomial	NOUN
ejpam-2434	72	5	are	be	AUX
ejpam-2434	72	6	traditional	traditional	ADJ
ejpam-2434	72	7	defined	define	VERB
ejpam-2434	72	8	on	on	ADP
ejpam-2434	72	9	[	[	X
ejpam-2434	72	10	−1,1	−1,1	NOUN
ejpam-2434	72	11	]	]	X
ejpam-2434	72	12	,	,	PUNCT
ejpam-2434	72	13	however	however	ADV
ejpam-2434	72	14	,	,	PUNCT
ejpam-2434	72	15	it	it	PRON
ejpam-2434	72	16	is	be	AUX
ejpam-2434	72	17	more	more	ADV
ejpam-2434	72	18	convenient	convenient	ADJ
ejpam-2434	72	19	to	to	PART
ejpam-2434	72	20	use	use	VERB
ejpam-2434	72	21	[	[	X
ejpam-2434	72	22	0,1	0,1	NUM
ejpam-2434	72	23	]	]	PUNCT
ejpam-2434	72	24	.	.	PUNCT
ejpam-2434	73	1	for	for	ADP
ejpam-2434	73	2	the	the	DET
ejpam-2434	73	3	convenience	convenience	NOUN
ejpam-2434	73	4	we	we	PRON
ejpam-2434	73	5	recall	recall	VERB
ejpam-2434	73	6	the	the	DET
ejpam-2434	73	7	following	follow	VERB
ejpam-2434	73	8	explicit	explicit	ADJ
ejpam-2434	73	9	expressions	expression	NOUN
ejpam-2434	73	10	for	for	ADP
ejpam-2434	73	11	univariate	univariate	ADJ
ejpam-2434	73	12	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	73	13	-	-	PUNCT
ejpam-2434	73	14	ii	ii	NOUN
ejpam-2434	73	15	polynomials	polynomial	NOUN
ejpam-2434	73	16	of	of	ADP
ejpam-2434	73	17	degree	degree	NOUN
ejpam-2434	73	18	n	n	CCONJ
ejpam-2434	73	19	in	in	ADP
ejpam-2434	73	20	x	x	X
ejpam-2434	73	21	,	,	PUNCT
ejpam-2434	73	22	using	use	VERB
ejpam-2434	73	23	combinatorial	combinatorial	ADJ
ejpam-2434	73	24	notation	notation	NOUN
ejpam-2434	73	25	that	that	PRON
ejpam-2434	73	26	gives	give	VERB
ejpam-2434	73	27	more	more	ADV
ejpam-2434	73	28	compact	compact	ADJ
ejpam-2434	73	29	and	and	CCONJ
ejpam-2434	73	30	readable	readable	ADJ
ejpam-2434	73	31	formulas	formula	NOUN
ejpam-2434	73	32	,	,	PUNCT
ejpam-2434	73	33	see	see	VERB
ejpam-2434	73	34	szegö	szegö	NOUN
ejpam-2434	74	1	[	[	X
ejpam-2434	74	2	8	8	NUM
ejpam-2434	74	3	]	]	SYM
ejpam-2434	74	4	:	:	PUNCT
ejpam-2434	74	5	un(x	un(x	X
ejpam-2434	74	6	)	)	PUNCT
ejpam-2434	74	7	:	:	PUNCT
ejpam-2434	74	8	=	=	SYM
ejpam-2434	74	9	(	(	PUNCT
ejpam-2434	74	10	n+	n+	NOUN
ejpam-2434	74	11	1)(2n	1)(2n	NUM
ejpam-2434	74	12	)	)	PUNCT
ejpam-2434	74	13	!	!	PUNCT
ejpam-2434	74	14	!	!	PUNCT
ejpam-2434	75	1	(	(	PUNCT
ejpam-2434	75	2	2n+	2n+	NUM
ejpam-2434	75	3	1	1	NUM
ejpam-2434	75	4	)	)	PUNCT
ejpam-2434	75	5	!	!	PUNCT
ejpam-2434	75	6	!	!	PUNCT
ejpam-2434	76	1	n	n	X
ejpam-2434	76	2	∑	∑	ADP
ejpam-2434	76	3	k=0	k=0	PROPN
ejpam-2434	76	4	�	�	PROPN
ejpam-2434	76	5	n+	n+	PUNCT
ejpam-2434	76	6	1	1	NUM
ejpam-2434	76	7	2	2	NUM
ejpam-2434	76	8	n−	n−	NOUN
ejpam-2434	76	9	k	k	PROPN
ejpam-2434	76	10	�	�	PROPN
ejpam-2434	76	11	�	�	PROPN
ejpam-2434	76	12	n+	n+	NUM
ejpam-2434	76	13	1	1	NUM
ejpam-2434	76	14	2	2	NUM
ejpam-2434	76	15	k	k	X
ejpam-2434	76	16	�	�	PROPN
ejpam-2434	76	17	�	�	PROPN
ejpam-2434	76	18	x	x	PUNCT
ejpam-2434	77	1	+	+	CCONJ
ejpam-2434	77	2	1	1	NUM
ejpam-2434	77	3	2	2	NUM
ejpam-2434	77	4	�	�	PROPN
ejpam-2434	77	5	n−k	n−k	NOUN
ejpam-2434	77	6	�	�	PROPN
ejpam-2434	77	7	x	x	SYM
ejpam-2434	77	8	−	−	PROPN
ejpam-2434	77	9	1	1	NUM
ejpam-2434	77	10	2	2	NUM
ejpam-2434	77	11	�	�	PROPN
ejpam-2434	77	12	k	k	PROPN
ejpam-2434	77	13	,	,	PUNCT
ejpam-2434	77	14	(	(	PUNCT
ejpam-2434	77	15	6	6	NUM
ejpam-2434	77	16	)	)	PUNCT
ejpam-2434	77	17	which	which	PRON
ejpam-2434	77	18	it	it	PRON
ejpam-2434	77	19	can	can	AUX
ejpam-2434	77	20	be	be	AUX
ejpam-2434	77	21	transformed	transform	VERB
ejpam-2434	77	22	in	in	ADP
ejpam-2434	77	23	terms	term	NOUN
ejpam-2434	77	24	of	of	ADP
ejpam-2434	77	25	bernstein	bernstein	PROPN
ejpam-2434	77	26	basis	basis	NOUN
ejpam-2434	77	27	on	on	ADP
ejpam-2434	77	28	x	x	PROPN
ejpam-2434	77	29	∈	∈	PROPN
ejpam-2434	78	1	[	[	X
ejpam-2434	78	2	0,1	0,1	NUM
ejpam-2434	78	3	]	]	PUNCT
ejpam-2434	78	4	,	,	PUNCT
ejpam-2434	78	5	un(2x	un(2x	ADJ
ejpam-2434	78	6	−	−	PROPN
ejpam-2434	78	7	1	1	NUM
ejpam-2434	78	8	)	)	PUNCT
ejpam-2434	78	9	:	:	PUNCT
ejpam-2434	78	10	=	=	SYM
ejpam-2434	78	11	(	(	PUNCT
ejpam-2434	78	12	n+	n+	NOUN
ejpam-2434	78	13	1)(2n	1)(2n	NUM
ejpam-2434	78	14	)	)	PUNCT
ejpam-2434	78	15	!	!	PUNCT
ejpam-2434	78	16	!	!	PUNCT
ejpam-2434	79	1	(	(	PUNCT
ejpam-2434	79	2	2n+	2n+	NUM
ejpam-2434	79	3	1	1	NUM
ejpam-2434	79	4	)	)	PUNCT
ejpam-2434	79	5	!	!	PUNCT
ejpam-2434	79	6	!	!	PUNCT
ejpam-2434	80	1	n	n	X
ejpam-2434	80	2	∑	∑	ADV
ejpam-2434	80	3	k=0	k=0	X
ejpam-2434	80	4	(	(	PUNCT
ejpam-2434	80	5	−1)n+1	−1)n+1	VERB
ejpam-2434	80	6	�	�	NOUN
ejpam-2434	80	7	n+	n+	NUM
ejpam-2434	80	8	1	1	NUM
ejpam-2434	80	9	2	2	NUM
ejpam-2434	80	10	k	k	PROPN
ejpam-2434	80	11	�	�	PROPN
ejpam-2434	80	12	�	�	PROPN
ejpam-2434	80	13	n+	n+	NUM
ejpam-2434	80	14	1	1	NUM
ejpam-2434	80	15	2	2	NUM
ejpam-2434	80	16	n−k	n−k	NOUN
ejpam-2434	80	17	�	�	PROPN
ejpam-2434	80	18	�	�	PROPN
ejpam-2434	80	19	n	n	CCONJ
ejpam-2434	80	20	k	k	PROPN
ejpam-2434	80	21	�	�	PROPN
ejpam-2434	80	22	bn	bn	PROPN
ejpam-2434	80	23	k	k	PROPN
ejpam-2434	80	24	(	(	PUNCT
ejpam-2434	80	25	x	x	NOUN
ejpam-2434	80	26	)	)	PUNCT
ejpam-2434	80	27	.	.	PUNCT
ejpam-2434	81	1	(	(	PUNCT
ejpam-2434	81	2	7	7	X
ejpam-2434	81	3	)	)	PUNCT
ejpam-2434	81	4	m.	m.	NOUN
ejpam-2434	81	5	alqudah	alqudah	PROPN
ejpam-2434	81	6	/	/	SYM
ejpam-2434	81	7	eur	eur	PROPN
ejpam-2434	81	8	.	.	PUNCT
ejpam-2434	82	1	j.	j.	PROPN
ejpam-2434	82	2	pure	pure	PROPN
ejpam-2434	82	3	appl	appl	PROPN
ejpam-2434	82	4	.	.	PROPN
ejpam-2434	82	5	math	math	PROPN
ejpam-2434	82	6	,	,	PUNCT
ejpam-2434	82	7	8	8	NUM
ejpam-2434	82	8	(	(	PUNCT
ejpam-2434	82	9	2015	2015	NUM
ejpam-2434	82	10	)	)	PUNCT
ejpam-2434	82	11	,	,	PUNCT
ejpam-2434	82	12	324	324	NUM
ejpam-2434	82	13	-	-	SYM
ejpam-2434	82	14	331	331	NUM
ejpam-2434	82	15	327	327	NUM
ejpam-2434	82	16	the	the	DET
ejpam-2434	82	17	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	82	18	-	-	PUNCT
ejpam-2434	82	19	ii	ii	NOUN
ejpam-2434	82	20	polynomials	polynomial	NOUN
ejpam-2434	82	21	un(x	un(x	NOUN
ejpam-2434	82	22	)	)	PUNCT
ejpam-2434	82	23	of	of	ADP
ejpam-2434	82	24	degree	degree	NOUN
ejpam-2434	83	1	n	n	NOUN
ejpam-2434	83	2	are	be	AUX
ejpam-2434	83	3	the	the	DET
ejpam-2434	83	4	orthogonal	orthogonal	ADJ
ejpam-2434	83	5	polynomials	polynomial	NOUN
ejpam-2434	83	6	,	,	PUNCT
ejpam-2434	83	7	except	except	SCONJ
ejpam-2434	83	8	for	for	ADP
ejpam-2434	83	9	a	a	DET
ejpam-2434	83	10	constant	constant	ADJ
ejpam-2434	83	11	factor	factor	NOUN
ejpam-2434	83	12	,	,	PUNCT
ejpam-2434	83	13	with	with	ADP
ejpam-2434	83	14	respect	respect	NOUN
ejpam-2434	83	15	to	to	ADP
ejpam-2434	83	16	the	the	DET
ejpam-2434	83	17	weight	weight	NOUN
ejpam-2434	83	18	function	function	NOUN
ejpam-2434	83	19	w(x	w(x	NOUN
ejpam-2434	83	20	)	)	PUNCT
ejpam-2434	84	1	=	=	PUNCT
ejpam-2434	85	1	p	p	X
ejpam-2434	85	2	1−	1−	NUM
ejpam-2434	85	3	x2	x2	NOUN
ejpam-2434	85	4	.	.	PUNCT
ejpam-2434	86	1	also	also	ADV
ejpam-2434	86	2	,	,	PUNCT
ejpam-2434	86	3	the	the	DET
ejpam-2434	86	4	tschebyscheffii	tschebyscheffii	NOUN
ejpam-2434	86	5	polynomials	polynomial	VERB
ejpam-2434	86	6	satisfy	satisfy	VERB
ejpam-2434	86	7	the	the	DET
ejpam-2434	86	8	orthogonality	orthogonality	NOUN
ejpam-2434	86	9	relation	relation	NOUN
ejpam-2434	86	10	[	[	X
ejpam-2434	86	11	4	4	NUM
ejpam-2434	86	12	]	]	PUNCT
ejpam-2434	86	13	∫	∫	PROPN
ejpam-2434	87	1	1	1	NUM
ejpam-2434	87	2	0	0	NUM
ejpam-2434	87	3	x	x	SYM
ejpam-2434	87	4	1	1	NUM
ejpam-2434	87	5	2	2	NUM
ejpam-2434	87	6	(	(	PUNCT
ejpam-2434	87	7	1−	1−	NUM
ejpam-2434	87	8	x	x	NOUN
ejpam-2434	87	9	)	)	PUNCT
ejpam-2434	87	10	1	1	NUM
ejpam-2434	87	11	2	2	NUM
ejpam-2434	87	12	un(x)um(x)d	un(x)um(x)d	NOUN
ejpam-2434	87	13	x	x	NOUN
ejpam-2434	87	14	=	=	SYM
ejpam-2434	87	15	¨	¨	NOUN
ejpam-2434	87	16	0	0	PUNCT
ejpam-2434	87	17	if	if	SCONJ
ejpam-2434	87	18	m	m	PROPN
ejpam-2434	87	19	6=	6=	NUM
ejpam-2434	87	20	n	n	PROPN
ejpam-2434	87	21	π	π	PROPN
ejpam-2434	87	22	8	8	NUM
ejpam-2434	87	23	if	if	SCONJ
ejpam-2434	87	24	m=	m=	ADJ
ejpam-2434	87	25	n	n	PROPN
ejpam-2434	87	26	(	(	PUNCT
ejpam-2434	87	27	8)	8)	NUM
ejpam-2434	87	28	the	the	DET
ejpam-2434	87	29	generalized	generalize	VERB
ejpam-2434	87	30	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	87	31	-	-	PUNCT
ejpam-2434	87	32	ii	ii	NOUN
ejpam-2434	87	33	polynomials	polynomial	NOUN
ejpam-2434	87	34	been	be	AUX
ejpam-2434	87	35	characterization	characterization	NOUN
ejpam-2434	87	36	in	in	ADP
ejpam-2434	87	37	[	[	X
ejpam-2434	87	38	1	1	NUM
ejpam-2434	87	39	]	]	PUNCT
ejpam-2434	87	40	,	,	PUNCT
ejpam-2434	87	41	for	for	ADP
ejpam-2434	87	42	m	m	PROPN
ejpam-2434	87	43	,	,	PUNCT
ejpam-2434	87	44	n	n	PRON
ejpam-2434	87	45	≥	≥	NOUN
ejpam-2434	87	46	0	0	NUM
ejpam-2434	87	47	,	,	PUNCT
ejpam-2434	87	48	the	the	DET
ejpam-2434	87	49	generalized	generalize	VERB
ejpam-2434	87	50	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	87	51	-	-	PUNCT
ejpam-2434	87	52	ii	ii	NOUN
ejpam-2434	87	53	polynomials	polynomial	NOUN
ejpam-2434	87	54	�	�	PROPN
ejpam-2434	87	55	u	u	PROPN
ejpam-2434	87	56	(	(	PUNCT
ejpam-2434	87	57	m	m	PROPN
ejpam-2434	87	58	,	,	PUNCT
ejpam-2434	87	59	n	n	CCONJ
ejpam-2434	87	60	)	)	PUNCT
ejpam-2434	87	61	n	n	PROPN
ejpam-2434	87	62	(	(	PUNCT
ejpam-2434	87	63	x	x	X
ejpam-2434	87	64	)	)	PUNCT
ejpam-2434	87	65	∞	∞	NOUN
ejpam-2434	87	66	n=0	n=0	NUM
ejpam-2434	87	67	are	be	AUX
ejpam-2434	87	68	orthogonal	orthogonal	ADJ
ejpam-2434	87	69	on	on	ADP
ejpam-2434	87	70	[	[	X
ejpam-2434	87	71	−1,1	−1,1	X
ejpam-2434	87	72	]	]	PUNCT
ejpam-2434	87	73	with	with	ADP
ejpam-2434	87	74	respect	respect	NOUN
ejpam-2434	87	75	to	to	ADP
ejpam-2434	87	76	the	the	DET
ejpam-2434	87	77	generalized	generalize	VERB
ejpam-2434	87	78	weight	weight	NOUN
ejpam-2434	87	79	function	function	NOUN
ejpam-2434	87	80	[	[	X
ejpam-2434	87	81	5	5	NUM
ejpam-2434	87	82	]	]	PUNCT
ejpam-2434	87	83	,	,	PUNCT
ejpam-2434	87	84	2	2	NUM
ejpam-2434	87	85	π	π	X
ejpam-2434	87	86	(	(	PUNCT
ejpam-2434	87	87	1−	1−	NUM
ejpam-2434	87	88	x	x	NOUN
ejpam-2434	87	89	)	)	PUNCT
ejpam-2434	87	90	1	1	NUM
ejpam-2434	87	91	2	2	NUM
ejpam-2434	87	92	(	(	PUNCT
ejpam-2434	87	93	1	1	NUM
ejpam-2434	87	94	+	+	NUM
ejpam-2434	87	95	x	x	NOUN
ejpam-2434	87	96	)	)	PUNCT
ejpam-2434	87	97	1	1	NUM
ejpam-2434	87	98	2	2	NUM
ejpam-2434	87	99	+	+	NOUN
ejpam-2434	87	100	mδ(x	mδ(x	NOUN
ejpam-2434	87	101	+	+	NOUN
ejpam-2434	87	102	1	1	NUM
ejpam-2434	87	103	)	)	PUNCT
ejpam-2434	87	104	+	+	CCONJ
ejpam-2434	87	105	nδ(x	nδ(x	ADV
ejpam-2434	87	106	−	−	PROPN
ejpam-2434	87	107	1	1	NUM
ejpam-2434	87	108	)	)	PUNCT
ejpam-2434	87	109	.	.	PUNCT
ejpam-2434	88	1	(	(	PUNCT
ejpam-2434	88	2	9	9	NUM
ejpam-2434	88	3	)	)	PUNCT
ejpam-2434	88	4	and	and	CCONJ
ejpam-2434	88	5	defined	define	VERB
ejpam-2434	88	6	in	in	ADP
ejpam-2434	88	7	[	[	X
ejpam-2434	88	8	1	1	NUM
ejpam-2434	88	9	]	]	PUNCT
ejpam-2434	88	10	as	as	ADP
ejpam-2434	88	11	u	u	PROPN
ejpam-2434	88	12	(	(	PUNCT
ejpam-2434	88	13	m	m	PROPN
ejpam-2434	88	14	,	,	PUNCT
ejpam-2434	88	15	n	n	CCONJ
ejpam-2434	88	16	)	)	PUNCT
ejpam-2434	88	17	n	n	PROPN
ejpam-2434	88	18	(	(	PUNCT
ejpam-2434	88	19	x	x	X
ejpam-2434	88	20	)	)	PUNCT
ejpam-2434	88	21	=	=	SYM
ejpam-2434	88	22	(	(	PUNCT
ejpam-2434	88	23	2n+	2n+	NUM
ejpam-2434	88	24	1	1	NUM
ejpam-2434	88	25	)	)	PUNCT
ejpam-2434	88	26	!	!	PUNCT
ejpam-2434	88	27	!	!	PUNCT
ejpam-2434	89	1	2n(n+	2n(n+	NUM
ejpam-2434	89	2	1	1	NUM
ejpam-2434	89	3	)	)	PUNCT
ejpam-2434	89	4	!	!	PUNCT
ejpam-2434	89	5	un(x	un(x	PUNCT
ejpam-2434	89	6	)	)	PUNCT
ejpam-2434	90	1	+	+	CCONJ
ejpam-2434	90	2	n	n	CCONJ
ejpam-2434	90	3	∑	∑	PUNCT
ejpam-2434	90	4	k=0	k=0	PROPN
ejpam-2434	90	5	λk	λk	X
ejpam-2434	90	6	(	(	PUNCT
ejpam-2434	90	7	2k+	2k+	NUM
ejpam-2434	90	8	1	1	NUM
ejpam-2434	90	9	)	)	PUNCT
ejpam-2434	90	10	!	!	PUNCT
ejpam-2434	90	11	!	!	PUNCT
ejpam-2434	91	1	2k(k+	2k(k+	NUM
ejpam-2434	91	2	1	1	NUM
ejpam-2434	91	3	)	)	PUNCT
ejpam-2434	91	4	!	!	PUNCT
ejpam-2434	92	1	uk(x	uk(x	NOUN
ejpam-2434	92	2	)	)	PUNCT
ejpam-2434	93	1	,	,	PUNCT
ejpam-2434	93	2	(	(	PUNCT
ejpam-2434	93	3	10	10	NUM
ejpam-2434	93	4	)	)	PUNCT
ejpam-2434	93	5	where	where	SCONJ
ejpam-2434	93	6	λk	λk	ADP
ejpam-2434	93	7	=	=	PUNCT
ejpam-2434	93	8	k(k+	k(k+	PROPN
ejpam-2434	94	1	1)(2k+	1)(2k+	NUM
ejpam-2434	95	1	1)(m	1)(m	NUM
ejpam-2434	95	2	+	+	CCONJ
ejpam-2434	95	3	n	n	CCONJ
ejpam-2434	95	4	)	)	PUNCT
ejpam-2434	95	5	6	6	NUM
ejpam-2434	96	1	+	+	CCONJ
ejpam-2434	96	2	(	(	PUNCT
ejpam-2434	96	3	k+	k+	NOUN
ejpam-2434	96	4	2)(k+	2)(k+	NUM
ejpam-2434	96	5	1)2k2(k−	1)2k2(k−	NUM
ejpam-2434	96	6	1)mn	1)mn	NUM
ejpam-2434	96	7	9	9	NUM
ejpam-2434	96	8	.	.	PUNCT
ejpam-2434	97	1	(	(	PUNCT
ejpam-2434	97	2	11	11	NUM
ejpam-2434	97	3	)	)	SYM
ejpam-2434	97	4	2	2	NUM
ejpam-2434	97	5	.	.	X
ejpam-2434	97	6	main	main	ADJ
ejpam-2434	97	7	results	result	NOUN
ejpam-2434	97	8	in	in	ADP
ejpam-2434	97	9	this	this	DET
ejpam-2434	97	10	section	section	NOUN
ejpam-2434	97	11	we	we	PRON
ejpam-2434	97	12	provide	provide	VERB
ejpam-2434	97	13	a	a	DET
ejpam-2434	97	14	closed	closed	ADJ
ejpam-2434	97	15	form	form	NOUN
ejpam-2434	97	16	for	for	ADP
ejpam-2434	97	17	the	the	DET
ejpam-2434	97	18	matrix	matrix	NOUN
ejpam-2434	97	19	transformation	transformation	NOUN
ejpam-2434	97	20	of	of	ADP
ejpam-2434	97	21	the	the	DET
ejpam-2434	97	22	generalized	generalize	VERB
ejpam-2434	97	23	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	97	24	-	-	PUNCT
ejpam-2434	97	25	ii	ii	NOUN
ejpam-2434	97	26	polynomial	polynomial	ADJ
ejpam-2434	97	27	basis	basis	NOUN
ejpam-2434	97	28	into	into	ADP
ejpam-2434	97	29	bernstein	bernstein	PROPN
ejpam-2434	97	30	polynomial	polynomial	PROPN
ejpam-2434	97	31	basis	basis	NOUN
ejpam-2434	97	32	,	,	PUNCT
ejpam-2434	97	33	and	and	CCONJ
ejpam-2434	97	34	for	for	ADP
ejpam-2434	97	35	bernstein	bernstein	PROPN
ejpam-2434	97	36	polynomial	polynomial	PROPN
ejpam-2434	97	37	basis	basis	NOUN
ejpam-2434	97	38	into	into	ADP
ejpam-2434	97	39	generalized	generalize	VERB
ejpam-2434	97	40	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	97	41	-	-	PUNCT
ejpam-2434	97	42	ii	ii	NOUN
ejpam-2434	97	43	polynomial	polynomial	ADJ
ejpam-2434	97	44	basis	basis	NOUN
ejpam-2434	97	45	.	.	PUNCT
ejpam-2434	98	1	2.1	2.1	NUM
ejpam-2434	98	2	.	.	PUNCT
ejpam-2434	98	3	bernstein	bernstein	PROPN
ejpam-2434	98	4	to	to	PART
ejpam-2434	98	5	generalized	generalize	VERB
ejpam-2434	98	6	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	98	7	-	-	PUNCT
ejpam-2434	98	8	ii	ii	NOUN
ejpam-2434	98	9	transformation	transformation	NOUN
ejpam-2434	98	10	and	and	CCONJ
ejpam-2434	98	11	vice	vice	NOUN
ejpam-2434	98	12	versa	versa	ADV
ejpam-2434	98	13	rababah	rababah	NOUN
ejpam-2434	99	1	[	[	X
ejpam-2434	99	2	6	6	NUM
ejpam-2434	99	3	]	]	PUNCT
ejpam-2434	99	4	provided	provide	VERB
ejpam-2434	99	5	some	some	DET
ejpam-2434	99	6	results	result	NOUN
ejpam-2434	99	7	concerning	concern	VERB
ejpam-2434	99	8	the	the	DET
ejpam-2434	99	9	univariate	univariate	ADJ
ejpam-2434	99	10	tschebyscheff	tschebyscheff	NOUN
ejpam-2434	99	11	polynomials	polynomial	NOUN
ejpam-2434	99	12	of	of	ADP
ejpam-2434	99	13	first	first	ADJ
ejpam-2434	99	14	kind	kind	NOUN
ejpam-2434	99	15	with	with	ADP
ejpam-2434	99	16	respect	respect	NOUN
ejpam-2434	99	17	to	to	ADP
ejpam-2434	99	18	the	the	DET
ejpam-2434	99	19	weight	weight	NOUN
ejpam-2434	99	20	function	function	NOUN
ejpam-2434	99	21	(	(	PUNCT
ejpam-2434	99	22	1	1	NUM
ejpam-2434	99	23	−	−	NUM
ejpam-2434	99	24	x2)1/2	x2)1/2	PROPN
ejpam-2434	99	25	.	.	PUNCT
ejpam-2434	100	1	in	in	ADP
ejpam-2434	100	2	this	this	DET
ejpam-2434	100	3	paper	paper	NOUN
ejpam-2434	100	4	we	we	PRON
ejpam-2434	100	5	extend	extend	VERB
ejpam-2434	100	6	the	the	DET
ejpam-2434	100	7	procedure	procedure	NOUN
ejpam-2434	100	8	in	in	ADP
ejpam-2434	100	9	[	[	X
ejpam-2434	100	10	6	6	NUM
ejpam-2434	100	11	]	]	PUNCT
ejpam-2434	100	12	to	to	PART
ejpam-2434	100	13	generalize	generalize	VERB
ejpam-2434	100	14	the	the	DET
ejpam-2434	100	15	results	result	NOUN
ejpam-2434	100	16	for	for	ADP
ejpam-2434	100	17	the	the	DET
ejpam-2434	100	18	generalized	generalize	VERB
ejpam-2434	100	19	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	100	20	-	-	PUNCT
ejpam-2434	100	21	ii	ii	PROPN
ejpam-2434	100	22	polynomials	polynomial	NOUN
ejpam-2434	100	23	u	u	PROPN
ejpam-2434	100	24	(	(	PUNCT
ejpam-2434	100	25	m	m	PROPN
ejpam-2434	100	26	,	,	PUNCT
ejpam-2434	100	27	n	n	CCONJ
ejpam-2434	100	28	)	)	PUNCT
ejpam-2434	100	29	r	r	NOUN
ejpam-2434	100	30	(	(	PUNCT
ejpam-2434	100	31	x	x	NOUN
ejpam-2434	100	32	)	)	PUNCT
ejpam-2434	100	33	with	with	ADP
ejpam-2434	100	34	respect	respect	NOUN
ejpam-2434	100	35	to	to	ADP
ejpam-2434	100	36	the	the	DET
ejpam-2434	100	37	generalized	generalize	VERB
ejpam-2434	100	38	weight	weight	NOUN
ejpam-2434	100	39	function	function	NOUN
ejpam-2434	100	40	(	(	PUNCT
ejpam-2434	100	41	9	9	NUM
ejpam-2434	100	42	)	)	PUNCT
ejpam-2434	100	43	.	.	PUNCT
ejpam-2434	101	1	the	the	DET
ejpam-2434	101	2	next	next	PROPN
ejpam-2434	101	3	theorem	theorem	NOUN
ejpam-2434	101	4	,	,	PUNCT
ejpam-2434	101	5	see	see	VERB
ejpam-2434	101	6	[	[	X
ejpam-2434	101	7	1	1	X
ejpam-2434	101	8	]	]	PUNCT
ejpam-2434	101	9	for	for	ADP
ejpam-2434	101	10	the	the	DET
ejpam-2434	101	11	proof	proof	NOUN
ejpam-2434	101	12	,	,	PUNCT
ejpam-2434	101	13	provides	provide	VERB
ejpam-2434	101	14	a	a	DET
ejpam-2434	101	15	closed	closed	ADJ
ejpam-2434	101	16	form	form	NOUN
ejpam-2434	101	17	for	for	ADP
ejpam-2434	101	18	generalized	generalized	ADJ
ejpam-2434	101	19	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	101	20	-	-	PUNCT
ejpam-2434	101	21	ii	ii	NOUN
ejpam-2434	101	22	polynomial	polynomial	ADJ
ejpam-2434	101	23	u	u	NOUN
ejpam-2434	101	24	(	(	PUNCT
ejpam-2434	101	25	m	m	PROPN
ejpam-2434	101	26	,	,	PUNCT
ejpam-2434	101	27	n	n	CCONJ
ejpam-2434	101	28	)	)	PUNCT
ejpam-2434	101	29	r	r	NOUN
ejpam-2434	101	30	(	(	PUNCT
ejpam-2434	101	31	x	x	NOUN
ejpam-2434	101	32	)	)	PUNCT
ejpam-2434	101	33	of	of	ADP
ejpam-2434	101	34	degree	degree	NOUN
ejpam-2434	101	35	r	r	NOUN
ejpam-2434	101	36	as	as	ADP
ejpam-2434	101	37	a	a	DET
ejpam-2434	101	38	linear	linear	ADJ
ejpam-2434	101	39	combination	combination	NOUN
ejpam-2434	101	40	of	of	ADP
ejpam-2434	101	41	the	the	DET
ejpam-2434	101	42	bernstein	bernstein	PROPN
ejpam-2434	101	43	polynomials	polynomials	PROPN
ejpam-2434	101	44	br	br	INTJ
ejpam-2434	101	45	i	i	PRON
ejpam-2434	101	46	(	(	PUNCT
ejpam-2434	101	47	x	x	NOUN
ejpam-2434	101	48	)	)	PUNCT
ejpam-2434	101	49	,	,	PUNCT
ejpam-2434	102	1	i	i	NOUN
ejpam-2434	102	2	=	=	NOUN
ejpam-2434	102	3	0,1	0,1	NUM
ejpam-2434	102	4	,	,	PUNCT
ejpam-2434	102	5	.	.	PUNCT
ejpam-2434	102	6	.	.	PUNCT
ejpam-2434	103	1	.	.	PUNCT
ejpam-2434	104	1	,	,	PUNCT
ejpam-2434	104	2	r.	r.	PROPN
ejpam-2434	104	3	theorem	theorem	VERB
ejpam-2434	104	4	1	1	NUM
ejpam-2434	104	5	(	(	PUNCT
ejpam-2434	104	6	[	[	X
ejpam-2434	104	7	1	1	NUM
ejpam-2434	104	8	]	]	PUNCT
ejpam-2434	104	9	)	)	PUNCT
ejpam-2434	104	10	.	.	PUNCT
ejpam-2434	105	1	for	for	ADP
ejpam-2434	105	2	m	m	PROPN
ejpam-2434	105	3	,	,	PUNCT
ejpam-2434	105	4	n	n	PRON
ejpam-2434	105	5	≥	≥	NOUN
ejpam-2434	105	6	0	0	NUM
ejpam-2434	105	7	,	,	PUNCT
ejpam-2434	105	8	the	the	DET
ejpam-2434	105	9	generalized	generalize	VERB
ejpam-2434	105	10	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	105	11	-	-	PUNCT
ejpam-2434	105	12	ii	ii	PROPN
ejpam-2434	105	13	polynomials	polynomial	NOUN
ejpam-2434	105	14	u	u	PROPN
ejpam-2434	105	15	(	(	PUNCT
ejpam-2434	105	16	m	m	PROPN
ejpam-2434	105	17	,	,	PUNCT
ejpam-2434	105	18	n	n	CCONJ
ejpam-2434	105	19	)	)	PUNCT
ejpam-2434	105	20	r	r	NOUN
ejpam-2434	105	21	(	(	PUNCT
ejpam-2434	105	22	x	x	NOUN
ejpam-2434	105	23	)	)	PUNCT
ejpam-2434	105	24	of	of	ADP
ejpam-2434	105	25	degree	degree	NOUN
ejpam-2434	105	26	r	r	NOUN
ejpam-2434	105	27	have	have	VERB
ejpam-2434	105	28	the	the	DET
ejpam-2434	105	29	following	follow	VERB
ejpam-2434	105	30	bernstein	bernstein	PROPN
ejpam-2434	105	31	representation	representation	PROPN
ejpam-2434	105	32	:	:	PUNCT
ejpam-2434	105	33	u	u	NOUN
ejpam-2434	105	34	(	(	PUNCT
ejpam-2434	105	35	m	m	PROPN
ejpam-2434	105	36	,	,	PUNCT
ejpam-2434	105	37	n	n	CCONJ
ejpam-2434	105	38	)	)	PUNCT
ejpam-2434	105	39	r	r	NOUN
ejpam-2434	105	40	(	(	PUNCT
ejpam-2434	105	41	x	x	NOUN
ejpam-2434	105	42	)	)	PUNCT
ejpam-2434	105	43	=	=	SYM
ejpam-2434	106	1	(	(	PUNCT
ejpam-2434	106	2	2r	2r	NUM
ejpam-2434	106	3	+	+	NOUN
ejpam-2434	106	4	1	1	NUM
ejpam-2434	106	5	)	)	PUNCT
ejpam-2434	106	6	!	!	PUNCT
ejpam-2434	106	7	!	!	PUNCT
ejpam-2434	107	1	2r(r	2r(r	NOUN
ejpam-2434	108	1	+	+	CCONJ
ejpam-2434	108	2	1	1	NUM
ejpam-2434	108	3	)	)	PUNCT
ejpam-2434	108	4	!	!	PUNCT
ejpam-2434	109	1	r	r	NOUN
ejpam-2434	109	2	∑	∑	PUNCT
ejpam-2434	109	3	i=0	i=0	PROPN
ejpam-2434	109	4	(	(	PUNCT
ejpam-2434	109	5	−1)r−iϑi	−1)r−iϑi	X
ejpam-2434	109	6	,	,	PUNCT
ejpam-2434	109	7	r	r	NOUN
ejpam-2434	109	8	br	br	NOUN
ejpam-2434	109	9	i	i	PRON
ejpam-2434	109	10	(	(	PUNCT
ejpam-2434	109	11	x	x	X
ejpam-2434	109	12	)	)	PUNCT
ejpam-2434	110	1	+	+	CCONJ
ejpam-2434	110	2	r	r	NOUN
ejpam-2434	110	3	∑	∑	PUNCT
ejpam-2434	110	4	k=0	k=0	PROPN
ejpam-2434	110	5	λk	λk	X
ejpam-2434	110	6	(	(	PUNCT
ejpam-2434	110	7	2k+	2k+	NUM
ejpam-2434	110	8	1	1	NUM
ejpam-2434	110	9	)	)	PUNCT
ejpam-2434	110	10	!	!	PUNCT
ejpam-2434	110	11	!	!	PUNCT
ejpam-2434	111	1	2k(k+	2k(k+	NUM
ejpam-2434	111	2	1	1	NUM
ejpam-2434	111	3	)	)	PUNCT
ejpam-2434	111	4	!	!	PUNCT
ejpam-2434	112	1	k	k	X
ejpam-2434	112	2	∑	∑	PUNCT
ejpam-2434	112	3	i=0	i=0	PROPN
ejpam-2434	112	4	(	(	PUNCT
ejpam-2434	112	5	−1)k−iϑi	−1)k−iϑi	X
ejpam-2434	112	6	,	,	PUNCT
ejpam-2434	112	7	kbk	kbk	PROPN
ejpam-2434	112	8	i	i	PROPN
ejpam-2434	112	9	(	(	PUNCT
ejpam-2434	112	10	x	x	X
ejpam-2434	112	11	)	)	PUNCT
ejpam-2434	112	12	(	(	PUNCT
ejpam-2434	112	13	12	12	NUM
ejpam-2434	112	14	)	)	PUNCT
ejpam-2434	112	15	m.	m.	NOUN
ejpam-2434	112	16	alqudah	alqudah	PROPN
ejpam-2434	112	17	/	/	SYM
ejpam-2434	112	18	eur	eur	PROPN
ejpam-2434	112	19	.	.	PUNCT
ejpam-2434	113	1	j.	j.	PROPN
ejpam-2434	113	2	pure	pure	PROPN
ejpam-2434	113	3	appl	appl	PROPN
ejpam-2434	113	4	.	.	PROPN
ejpam-2434	113	5	math	math	PROPN
ejpam-2434	113	6	,	,	PUNCT
ejpam-2434	113	7	8	8	NUM
ejpam-2434	113	8	(	(	PUNCT
ejpam-2434	113	9	2015	2015	NUM
ejpam-2434	113	10	)	)	PUNCT
ejpam-2434	113	11	,	,	PUNCT
ejpam-2434	113	12	324	324	NUM
ejpam-2434	113	13	-	-	SYM
ejpam-2434	113	14	331	331	NUM
ejpam-2434	113	15	328	328	NUM
ejpam-2434	113	16	where	where	SCONJ
ejpam-2434	113	17	λk	λk	X
ejpam-2434	113	18	defined	define	VERB
ejpam-2434	113	19	by	by	ADP
ejpam-2434	113	20	(	(	PUNCT
ejpam-2434	113	21	11	11	NUM
ejpam-2434	113	22	)	)	PUNCT
ejpam-2434	113	23	,	,	PUNCT
ejpam-2434	114	1	ϑ0,r	ϑ0,r	PROPN
ejpam-2434	114	2	=	=	PRON
ejpam-2434	114	3	(	(	PUNCT
ejpam-2434	114	4	2r+1	2r+1	NUM
ejpam-2434	114	5	)	)	PUNCT
ejpam-2434	114	6	22r	22r	NOUN
ejpam-2434	114	7	�	�	PROPN
ejpam-2434	114	8	2r	2r	NUM
ejpam-2434	114	9	r	r	NOUN
ejpam-2434	114	10	�	�	PROPN
ejpam-2434	114	11	,	,	PUNCT
ejpam-2434	114	12	and	and	CCONJ
ejpam-2434	114	13	ϑi	ϑi	PROPN
ejpam-2434	114	14	,	,	PUNCT
ejpam-2434	114	15	r	r	NOUN
ejpam-2434	114	16	=	=	SYM
ejpam-2434	114	17	(	(	PUNCT
ejpam-2434	114	18	2r	2r	NUM
ejpam-2434	114	19	+	+	CCONJ
ejpam-2434	114	20	1)2	1)2	NUM
ejpam-2434	114	21	22r(2r	22r(2r	NUM
ejpam-2434	114	22	−	−	NOUN
ejpam-2434	114	23	2i	2i	NOUN
ejpam-2434	114	24	+	+	CCONJ
ejpam-2434	114	25	1)(2i	1)(2i	NUM
ejpam-2434	114	26	+	+	CCONJ
ejpam-2434	114	27	1	1	X
ejpam-2434	114	28	)	)	PUNCT
ejpam-2434	114	29	�	�	NOUN
ejpam-2434	114	30	2r	2r	NUM
ejpam-2434	114	31	r	r	NOUN
ejpam-2434	114	32	�	�	PROPN
ejpam-2434	114	33	�	�	PROPN
ejpam-2434	114	34	2r	2r	NUM
ejpam-2434	114	35	2i	2i	NUM
ejpam-2434	114	36	�	�	PROPN
ejpam-2434	114	37	�	�	PROPN
ejpam-2434	114	38	r	r	NOUN
ejpam-2434	114	39	i	i	PROPN
ejpam-2434	114	40	�	�	PROPN
ejpam-2434	114	41	,	,	PUNCT
ejpam-2434	114	42	i	i	NOUN
ejpam-2434	114	43	=	=	NOUN
ejpam-2434	114	44	0,1	0,1	NUM
ejpam-2434	114	45	,	,	PUNCT
ejpam-2434	114	46	.	.	PUNCT
ejpam-2434	114	47	.	.	PUNCT
ejpam-2434	114	48	.	.	PUNCT
ejpam-2434	115	1	,	,	PUNCT
ejpam-2434	115	2	r.	r.	VERB
ejpam-2434	115	3	the	the	DET
ejpam-2434	115	4	coefficients	coefficient	NOUN
ejpam-2434	115	5	ϑi	ϑi	PROPN
ejpam-2434	115	6	,	,	PUNCT
ejpam-2434	115	7	r	r	NOUN
ejpam-2434	115	8	satisfy	satisfy	VERB
ejpam-2434	115	9	the	the	DET
ejpam-2434	115	10	recurrence	recurrence	NOUN
ejpam-2434	115	11	relation	relation	NOUN
ejpam-2434	115	12	ϑi	ϑi	PROPN
ejpam-2434	115	13	,	,	PUNCT
ejpam-2434	115	14	r	r	NOUN
ejpam-2434	115	15	=	=	SYM
ejpam-2434	115	16	(	(	PUNCT
ejpam-2434	115	17	2r	2r	NUM
ejpam-2434	115	18	−	−	NOUN
ejpam-2434	115	19	2i	2i	NOUN
ejpam-2434	115	20	+	+	CCONJ
ejpam-2434	115	21	3	3	X
ejpam-2434	115	22	)	)	PUNCT
ejpam-2434	115	23	(	(	PUNCT
ejpam-2434	115	24	2i	2i	NOUN
ejpam-2434	115	25	+	+	CCONJ
ejpam-2434	115	26	1	1	NUM
ejpam-2434	115	27	)	)	PUNCT
ejpam-2434	115	28	ϑi−1,r	ϑi−1,r	NOUN
ejpam-2434	115	29	,	,	PUNCT
ejpam-2434	115	30	i	i	PRON
ejpam-2434	115	31	=	=	NOUN
ejpam-2434	115	32	1	1	NUM
ejpam-2434	115	33	,	,	PUNCT
ejpam-2434	115	34	.	.	PUNCT
ejpam-2434	115	35	.	.	PUNCT
ejpam-2434	116	1	.	.	PUNCT
ejpam-2434	117	1	,	,	PUNCT
ejpam-2434	117	2	r.	r.	PROPN
ejpam-2434	117	3	(	(	PUNCT
ejpam-2434	117	4	13	13	NUM
ejpam-2434	117	5	)	)	PUNCT
ejpam-2434	117	6	now	now	ADV
ejpam-2434	117	7	,	,	PUNCT
ejpam-2434	117	8	the	the	DET
ejpam-2434	117	9	next	next	ADJ
ejpam-2434	117	10	theorem	theorem	NOUN
ejpam-2434	117	11	used	use	VERB
ejpam-2434	117	12	to	to	PART
ejpam-2434	117	13	combine	combine	VERB
ejpam-2434	117	14	the	the	DET
ejpam-2434	117	15	superior	superior	ADJ
ejpam-2434	117	16	performance	performance	NOUN
ejpam-2434	117	17	of	of	ADP
ejpam-2434	117	18	the	the	DET
ejpam-2434	117	19	least	least	ADJ
ejpam-2434	117	20	-	-	PUNCT
ejpam-2434	117	21	squares	square	NOUN
ejpam-2434	117	22	of	of	ADP
ejpam-2434	117	23	the	the	DET
ejpam-2434	117	24	generalized	generalize	VERB
ejpam-2434	117	25	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	117	26	-	-	PUNCT
ejpam-2434	117	27	ii	ii	NOUN
ejpam-2434	117	28	polynomials	polynomial	NOUN
ejpam-2434	117	29	with	with	ADP
ejpam-2434	117	30	the	the	DET
ejpam-2434	117	31	geometric	geometric	ADJ
ejpam-2434	117	32	properties	property	NOUN
ejpam-2434	117	33	of	of	ADP
ejpam-2434	117	34	the	the	DET
ejpam-2434	117	35	bernstein	bernstein	PROPN
ejpam-2434	117	36	polynomials	polynomials	PROPN
ejpam-2434	117	37	basis	basis	NOUN
ejpam-2434	117	38	.	.	PUNCT
ejpam-2434	118	1	theorem	theorem	NOUN
ejpam-2434	118	2	2	2	NUM
ejpam-2434	118	3	.	.	PUNCT
ejpam-2434	119	1	the	the	DET
ejpam-2434	119	2	entries	entry	NOUN
ejpam-2434	119	3	m	m	VERB
ejpam-2434	119	4	n	n	PRON
ejpam-2434	119	5	i	i	PRON
ejpam-2434	119	6	,	,	PUNCT
ejpam-2434	119	7	r	r	NOUN
ejpam-2434	119	8	,	,	PUNCT
ejpam-2434	119	9	i	i	PRON
ejpam-2434	119	10	,	,	PUNCT
ejpam-2434	119	11	r	r	NOUN
ejpam-2434	119	12	=	=	SYM
ejpam-2434	119	13	0,1	0,1	NUM
ejpam-2434	119	14	,	,	PUNCT
ejpam-2434	119	15	.	.	PUNCT
ejpam-2434	119	16	.	.	PUNCT
ejpam-2434	120	1	.	.	PUNCT
ejpam-2434	121	1	,	,	PUNCT
ejpam-2434	121	2	n	n	PROPN
ejpam-2434	121	3	of	of	ADP
ejpam-2434	121	4	the	the	DET
ejpam-2434	121	5	matrix	matrix	NOUN
ejpam-2434	121	6	transformation	transformation	NOUN
ejpam-2434	121	7	of	of	ADP
ejpam-2434	121	8	the	the	DET
ejpam-2434	121	9	generalized	generalize	VERB
ejpam-2434	121	10	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	121	11	-	-	PUNCT
ejpam-2434	121	12	ii	ii	NOUN
ejpam-2434	121	13	polynomial	polynomial	ADJ
ejpam-2434	121	14	basis	basis	NOUN
ejpam-2434	121	15	into	into	ADP
ejpam-2434	121	16	bernstein	bernstein	PROPN
ejpam-2434	121	17	polynomial	polynomial	PROPN
ejpam-2434	121	18	basis	basis	NOUN
ejpam-2434	121	19	of	of	ADP
ejpam-2434	121	20	degree	degree	NOUN
ejpam-2434	121	21	n	n	NOUN
ejpam-2434	121	22	are	be	AUX
ejpam-2434	121	23	given	give	VERB
ejpam-2434	121	24	by	by	ADP
ejpam-2434	121	25	m	m	NOUN
ejpam-2434	121	26	n	n	ADV
ejpam-2434	121	27	i	i	PRON
ejpam-2434	121	28	,	,	PUNCT
ejpam-2434	121	29	r	r	NOUN
ejpam-2434	121	30	=	=	SYM
ejpam-2434	121	31	φ	φ	PROPN
ejpam-2434	121	32	r	r	NOUN
ejpam-2434	121	33	i	i	PROPN
ejpam-2434	121	34	,	,	PUNCT
ejpam-2434	121	35	n	n	PROPN
ejpam-2434	121	36	+	+	CCONJ
ejpam-2434	121	37	r	r	NOUN
ejpam-2434	121	38	∑	∑	PUNCT
ejpam-2434	121	39	k=0	k=0	X
ejpam-2434	121	40	λkφ	λkφ	NOUN
ejpam-2434	121	41	k	k	PROPN
ejpam-2434	121	42	i	i	PROPN
ejpam-2434	121	43	,	,	PUNCT
ejpam-2434	121	44	n	n	CCONJ
ejpam-2434	121	45	,	,	PUNCT
ejpam-2434	121	46	(	(	PUNCT
ejpam-2434	121	47	14	14	NUM
ejpam-2434	121	48	)	)	PUNCT
ejpam-2434	121	49	where	where	SCONJ
ejpam-2434	121	50	λk	λk	X
ejpam-2434	121	51	defined	define	VERB
ejpam-2434	121	52	in	in	ADP
ejpam-2434	121	53	(	(	PUNCT
ejpam-2434	121	54	11	11	NUM
ejpam-2434	121	55	)	)	PUNCT
ejpam-2434	121	56	and	and	CCONJ
ejpam-2434	121	57	φr	φr	ADP
ejpam-2434	121	58	i	i	PROPN
ejpam-2434	121	59	,	,	PUNCT
ejpam-2434	121	60	n	n	PROPN
ejpam-2434	121	61	=	=	SYM
ejpam-2434	121	62	(	(	PUNCT
ejpam-2434	121	63	2r	2r	NUM
ejpam-2434	121	64	+	+	NOUN
ejpam-2434	121	65	1	1	NUM
ejpam-2434	121	66	)	)	PUNCT
ejpam-2434	121	67	!	!	PUNCT
ejpam-2434	121	68	!	!	PUNCT
ejpam-2434	122	1	2r(r	2r(r	NOUN
ejpam-2434	123	1	+	+	CCONJ
ejpam-2434	123	2	1	1	NUM
ejpam-2434	123	3	)	)	PUNCT
ejpam-2434	123	4	!	!	PUNCT
ejpam-2434	124	1	min(i	min(i	PROPN
ejpam-2434	124	2	,	,	PUNCT
ejpam-2434	124	3	r	r	NOUN
ejpam-2434	124	4	)	)	PUNCT
ejpam-2434	124	5	∑	∑	NOUN
ejpam-2434	124	6	k	k	X
ejpam-2434	124	7	=	=	NOUN
ejpam-2434	124	8	max(0,i+r−n	max(0,i+r−n	PROPN
ejpam-2434	124	9	)	)	PUNCT
ejpam-2434	124	10	(	(	PUNCT
ejpam-2434	124	11	−1)r−k	−1)r−k	PROPN
ejpam-2434	124	12	�	�	PROPN
ejpam-2434	124	13	n−r	n−r	NOUN
ejpam-2434	124	14	i−k	i−k	VERB
ejpam-2434	124	15	�	�	PROPN
ejpam-2434	124	16	�	�	PROPN
ejpam-2434	124	17	r+	r+	NOUN
ejpam-2434	124	18	1	1	NUM
ejpam-2434	124	19	2	2	NUM
ejpam-2434	124	20	k	k	PROPN
ejpam-2434	124	21	�	�	PROPN
ejpam-2434	124	22	�	�	PROPN
ejpam-2434	124	23	r+	r+	PART
ejpam-2434	124	24	1	1	NUM
ejpam-2434	124	25	2	2	NUM
ejpam-2434	124	26	r−k	r−k	NUM
ejpam-2434	124	27	�	�	PROPN
ejpam-2434	124	28	�	�	PROPN
ejpam-2434	124	29	n	n	CCONJ
ejpam-2434	124	30	i	i	PROPN
ejpam-2434	124	31	�	�	PROPN
ejpam-2434	124	32	.	.	PUNCT
ejpam-2434	125	1	proof	proof	NOUN
ejpam-2434	125	2	.	.	PUNCT
ejpam-2434	126	1	a	a	DET
ejpam-2434	126	2	polynomial	polynomial	ADJ
ejpam-2434	126	3	pn(x	pn(x	X
ejpam-2434	126	4	)	)	PUNCT
ejpam-2434	126	5	,	,	PUNCT
ejpam-2434	126	6	x	x	PUNCT
ejpam-2434	126	7	∈	∈	PROPN
ejpam-2434	127	1	[	[	X
ejpam-2434	127	2	0,1	0,1	NUM
ejpam-2434	127	3	]	]	PUNCT
ejpam-2434	127	4	of	of	ADP
ejpam-2434	127	5	degree	degree	NOUN
ejpam-2434	127	6	n	n	CCONJ
ejpam-2434	127	7	,	,	PUNCT
ejpam-2434	127	8	can	can	AUX
ejpam-2434	127	9	be	be	AUX
ejpam-2434	127	10	written	write	VERB
ejpam-2434	127	11	as	as	ADP
ejpam-2434	127	12	as	as	ADP
ejpam-2434	127	13	a	a	DET
ejpam-2434	127	14	linear	linear	ADJ
ejpam-2434	127	15	combination	combination	NOUN
ejpam-2434	127	16	of	of	ADP
ejpam-2434	127	17	the	the	DET
ejpam-2434	127	18	bernstein	bernstein	PROPN
ejpam-2434	127	19	polynomial	polynomial	PROPN
ejpam-2434	127	20	basis	basis	NOUN
ejpam-2434	127	21	pn(x	pn(x	X
ejpam-2434	127	22	)	)	PUNCT
ejpam-2434	127	23	=	=	SYM
ejpam-2434	128	1	∑n	∑n	PROPN
ejpam-2434	128	2	r=0	r=0	ADJ
ejpam-2434	128	3	cr	cr	NOUN
ejpam-2434	128	4	bn	bn	INTJ
ejpam-2434	128	5	r	r	NOUN
ejpam-2434	128	6	(	(	PUNCT
ejpam-2434	128	7	x	x	NOUN
ejpam-2434	128	8	)	)	PUNCT
ejpam-2434	128	9	and	and	CCONJ
ejpam-2434	128	10	the	the	DET
ejpam-2434	128	11	generalized	generalize	VERB
ejpam-2434	128	12	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	128	13	-	-	PUNCT
ejpam-2434	128	14	ii	ii	NOUN
ejpam-2434	128	15	polynomials	polynomial	NOUN
ejpam-2434	128	16	pn(x	pn(x	X
ejpam-2434	128	17	)	)	PUNCT
ejpam-2434	128	18	=	=	SYM
ejpam-2434	129	1	∑n	∑n	PROPN
ejpam-2434	129	2	i=0	i=0	PROPN
ejpam-2434	129	3	diu	diu	PROPN
ejpam-2434	129	4	(	(	PUNCT
ejpam-2434	129	5	m	m	PROPN
ejpam-2434	129	6	,	,	PUNCT
ejpam-2434	129	7	n	n	CCONJ
ejpam-2434	129	8	)	)	PUNCT
ejpam-2434	129	9	i	i	PRON
ejpam-2434	129	10	(	(	PUNCT
ejpam-2434	129	11	x	x	NOUN
ejpam-2434	129	12	)	)	PUNCT
ejpam-2434	129	13	.	.	PUNCT
ejpam-2434	130	1	we	we	PRON
ejpam-2434	130	2	need	need	VERB
ejpam-2434	130	3	to	to	PART
ejpam-2434	130	4	find	find	VERB
ejpam-2434	130	5	the	the	DET
ejpam-2434	130	6	matrix	matrix	NOUN
ejpam-2434	130	7	m	m	NOUN
ejpam-2434	130	8	that	that	PRON
ejpam-2434	130	9	maps	map	VERB
ejpam-2434	130	10	the	the	DET
ejpam-2434	130	11	generalized	generalize	VERB
ejpam-2434	130	12	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	130	13	-	-	PUNCT
ejpam-2434	130	14	ii	ii	NOUN
ejpam-2434	130	15	coefficients	coefficient	NOUN
ejpam-2434	130	16	{	{	PUNCT
ejpam-2434	130	17	di}ni=0	di}ni=0	VERB
ejpam-2434	130	18	into	into	ADP
ejpam-2434	130	19	the	the	DET
ejpam-2434	130	20	bernstein	bernstein	PROPN
ejpam-2434	130	21	coefficients	coefficients	PROPN
ejpam-2434	130	22	{	{	PUNCT
ejpam-2434	130	23	cr}nr=0	cr}nr=0	PROPN
ejpam-2434	130	24	,	,	PUNCT
ejpam-2434	130	25	ci	ci	NOUN
ejpam-2434	130	26	=	=	SYM
ejpam-2434	130	27	n	n	CCONJ
ejpam-2434	130	28	∑	∑	ADV
ejpam-2434	130	29	r=0	r=0	PROPN
ejpam-2434	130	30	m	m	VERB
ejpam-2434	130	31	n	n	NOUN
ejpam-2434	130	32	i	i	PRON
ejpam-2434	130	33	,	,	PUNCT
ejpam-2434	130	34	r	r	PROPN
ejpam-2434	130	35	dr	dr	PROPN
ejpam-2434	130	36	,	,	PUNCT
ejpam-2434	130	37	(	(	PUNCT
ejpam-2434	130	38	15	15	NUM
ejpam-2434	130	39	)	)	PUNCT
ejpam-2434	130	40	which	which	PRON
ejpam-2434	130	41	can	can	AUX
ejpam-2434	130	42	be	be	AUX
ejpam-2434	130	43	written	write	VERB
ejpam-2434	130	44	in	in	ADP
ejpam-2434	130	45	matrix	matrix	NOUN
ejpam-2434	130	46	format	format	NOUN
ejpam-2434	130	47	as	as	ADP
ejpam-2434	130	48			NOUN
ejpam-2434	130	49			ADJ
ejpam-2434	130	50			ADJ
ejpam-2434	130	51			ADJ
ejpam-2434	130	52			NUM
ejpam-2434	130	53	c0	c0	PROPN
ejpam-2434	130	54	c1	c1	PROPN
ejpam-2434	130	55	...	...	PUNCT
ejpam-2434	131	1	cn	cn	PROPN
ejpam-2434	131	2			PROPN
ejpam-2434	131	3			PROPN
ejpam-2434	131	4			PROPN
ejpam-2434	131	5			PROPN
ejpam-2434	131	6			PROPN
ejpam-2434	131	7	=	=	PUNCT
ejpam-2434	131	8			NOUN
ejpam-2434	131	9			ADJ
ejpam-2434	131	10			ADJ
ejpam-2434	131	11			ADJ
ejpam-2434	131	12			NUM
ejpam-2434	131	13	m	m	VERB
ejpam-2434	131	14	n	n	PRON
ejpam-2434	131	15	0,0	0,0	NUM
ejpam-2434	131	16	m	m	VERB
ejpam-2434	131	17	n	n	PRON
ejpam-2434	131	18	0,1	0,1	NUM
ejpam-2434	131	19	m	m	NOUN
ejpam-2434	131	20	n	n	PRON
ejpam-2434	131	21	0,2	0,2	NUM
ejpam-2434	131	22	.	.	PUNCT
ejpam-2434	131	23	.	.	PUNCT
ejpam-2434	131	24	.	.	PUNCT
ejpam-2434	132	1	m	m	VERB
ejpam-2434	132	2	n	n	PRON
ejpam-2434	132	3	0,n	0,n	ADJ
ejpam-2434	132	4	m	m	VERB
ejpam-2434	132	5	n	n	NUM
ejpam-2434	132	6	1,0	1,0	NUM
ejpam-2434	132	7	m	m	NOUN
ejpam-2434	132	8	n	n	PRON
ejpam-2434	132	9	1,1	1,1	NUM
ejpam-2434	132	10	m	m	NOUN
ejpam-2434	132	11	n	n	PRON
ejpam-2434	132	12	1,2	1,2	NUM
ejpam-2434	132	13	.	.	PUNCT
ejpam-2434	132	14	.	.	PUNCT
ejpam-2434	132	15	.	.	PUNCT
ejpam-2434	133	1	m	m	VERB
ejpam-2434	133	2	n	n	PRON
ejpam-2434	133	3	1,n	1,n	NUM
ejpam-2434	133	4	...	...	PUNCT
ejpam-2434	133	5	...	...	PUNCT
ejpam-2434	133	6	...	...	PUNCT
ejpam-2434	133	7	.	.	PUNCT
ejpam-2434	133	8	.	.	PUNCT
ejpam-2434	133	9	.	.	PUNCT
ejpam-2434	134	1	...	...	PUNCT
ejpam-2434	135	1	m	m	VERB
ejpam-2434	135	2	n	n	PRON
ejpam-2434	135	3	n,0	n,0	NOUN
ejpam-2434	135	4	m	m	VERB
ejpam-2434	135	5	n	n	VERB
ejpam-2434	135	6	n,1	n,1	NOUN
ejpam-2434	135	7	m	m	VERB
ejpam-2434	135	8	n	n	PRON
ejpam-2434	135	9	n,2	n,2	VERB
ejpam-2434	135	10	.	.	PUNCT
ejpam-2434	135	11	.	.	PUNCT
ejpam-2434	135	12	.	.	PUNCT
ejpam-2434	136	1	m	m	VERB
ejpam-2434	136	2	n	n	VERB
ejpam-2434	136	3	n	n	CCONJ
ejpam-2434	136	4	,	,	PUNCT
ejpam-2434	136	5	n	n	PROPN
ejpam-2434	136	6			PROPN
ejpam-2434	136	7			PROPN
ejpam-2434	136	8			PROPN
ejpam-2434	136	9			PROPN
ejpam-2434	136	10			PROPN
ejpam-2434	136	11	.	.	PUNCT
ejpam-2434	137	1			PROPN
ejpam-2434	137	2			ADJ
ejpam-2434	137	3			ADJ
ejpam-2434	137	4			ADJ
ejpam-2434	137	5			NOUN
ejpam-2434	137	6	d0	d0	PROPN
ejpam-2434	137	7	d1	d1	PROPN
ejpam-2434	137	8	...	...	PUNCT
ejpam-2434	138	1	dn	dn	ADP
ejpam-2434	138	2			PROPN
ejpam-2434	139	1			PROPN
ejpam-2434	140	1			PROPN
ejpam-2434	140	2			PROPN
ejpam-2434	140	3			PROPN
ejpam-2434	140	4	.	.	PUNCT
ejpam-2434	141	1	(	(	PUNCT
ejpam-2434	141	2	16	16	NUM
ejpam-2434	141	3	)	)	PUNCT
ejpam-2434	141	4	but	but	CCONJ
ejpam-2434	141	5	,	,	PUNCT
ejpam-2434	141	6	the	the	DET
ejpam-2434	141	7	generalized	generalize	VERB
ejpam-2434	141	8	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	141	9	-	-	PUNCT
ejpam-2434	141	10	ii	ii	NOUN
ejpam-2434	141	11	polynomials	polynomial	NOUN
ejpam-2434	141	12	(	(	PUNCT
ejpam-2434	141	13	10	10	NUM
ejpam-2434	141	14	)	)	PUNCT
ejpam-2434	141	15	can	can	AUX
ejpam-2434	141	16	be	be	AUX
ejpam-2434	141	17	written	write	VERB
ejpam-2434	141	18	as	as	ADP
ejpam-2434	141	19	a	a	DET
ejpam-2434	141	20	linear	linear	ADJ
ejpam-2434	141	21	combination	combination	NOUN
ejpam-2434	141	22	of	of	ADP
ejpam-2434	141	23	the	the	DET
ejpam-2434	141	24	bernstein	bernstein	PROPN
ejpam-2434	141	25	polynomial	polynomial	PROPN
ejpam-2434	141	26	basis	basis	NOUN
ejpam-2434	141	27	as	as	ADP
ejpam-2434	141	28	u	u	PROPN
ejpam-2434	141	29	(	(	PUNCT
ejpam-2434	141	30	m	m	PROPN
ejpam-2434	141	31	,	,	PUNCT
ejpam-2434	141	32	n	n	CCONJ
ejpam-2434	141	33	)	)	PUNCT
ejpam-2434	142	1	r	r	NOUN
ejpam-2434	142	2	(	(	PUNCT
ejpam-2434	142	3	x	x	NOUN
ejpam-2434	142	4	)	)	PUNCT
ejpam-2434	142	5	=	=	SYM
ejpam-2434	142	6	n	n	CCONJ
ejpam-2434	142	7	∑	∑	PUNCT
ejpam-2434	142	8	i=0	i=0	PROPN
ejpam-2434	142	9	n	n	CCONJ
ejpam-2434	142	10	n	n	ADV
ejpam-2434	142	11	r	r	NOUN
ejpam-2434	142	12	,	,	PUNCT
ejpam-2434	142	13	ib	ib	NOUN
ejpam-2434	142	14	n	n	INTJ
ejpam-2434	142	15	i	i	PRON
ejpam-2434	142	16	(	(	PUNCT
ejpam-2434	142	17	x	x	NOUN
ejpam-2434	142	18	)	)	PUNCT
ejpam-2434	142	19	,	,	PUNCT
ejpam-2434	142	20	r	r	NOUN
ejpam-2434	142	21	=	=	SYM
ejpam-2434	142	22	0,1	0,1	NUM
ejpam-2434	142	23	,	,	PUNCT
ejpam-2434	142	24	.	.	PUNCT
ejpam-2434	142	25	.	.	PUNCT
ejpam-2434	142	26	.	.	PUNCT
ejpam-2434	142	27	,	,	PUNCT
ejpam-2434	142	28	n	n	CCONJ
ejpam-2434	142	29	,	,	PUNCT
ejpam-2434	142	30	(	(	PUNCT
ejpam-2434	142	31	17	17	NUM
ejpam-2434	142	32	)	)	PUNCT
ejpam-2434	142	33	m.	m.	NOUN
ejpam-2434	142	34	alqudah	alqudah	PROPN
ejpam-2434	142	35	/	/	SYM
ejpam-2434	142	36	eur	eur	PROPN
ejpam-2434	142	37	.	.	PUNCT
ejpam-2434	143	1	j.	j.	PROPN
ejpam-2434	143	2	pure	pure	PROPN
ejpam-2434	143	3	appl	appl	PROPN
ejpam-2434	143	4	.	.	PROPN
ejpam-2434	143	5	math	math	PROPN
ejpam-2434	143	6	,	,	PUNCT
ejpam-2434	143	7	8	8	NUM
ejpam-2434	143	8	(	(	PUNCT
ejpam-2434	143	9	2015	2015	NUM
ejpam-2434	143	10	)	)	PUNCT
ejpam-2434	143	11	,	,	PUNCT
ejpam-2434	143	12	324	324	NUM
ejpam-2434	143	13	-	-	SYM
ejpam-2434	143	14	331	331	NUM
ejpam-2434	143	15	329	329	NUM
ejpam-2434	143	16	where	where	SCONJ
ejpam-2434	143	17	the	the	DET
ejpam-2434	143	18	the	the	DET
ejpam-2434	143	19	(	(	PUNCT
ejpam-2434	143	20	n+1)×	n+1)×	PROPN
ejpam-2434	143	21	(	(	PUNCT
ejpam-2434	143	22	n+1	n+1	NOUN
ejpam-2434	143	23	)	)	PUNCT
ejpam-2434	143	24	basis	basis	NOUN
ejpam-2434	143	25	conversion	conversion	NOUN
ejpam-2434	143	26	matrix	matrix	NOUN
ejpam-2434	143	27	n	n	ADP
ejpam-2434	143	28	formed	form	VERB
ejpam-2434	143	29	by	by	ADP
ejpam-2434	143	30	the	the	DET
ejpam-2434	143	31	entries	entry	NOUN
ejpam-2434	143	32	n	n	ADP
ejpam-2434	143	33	n	n	ADV
ejpam-2434	143	34	r	r	NOUN
ejpam-2434	143	35	,	,	PUNCT
ejpam-2434	143	36	i	i	PRON
ejpam-2434	143	37	.	.	PUNCT
ejpam-2434	144	1	thus	thus	ADV
ejpam-2434	144	2	,	,	PUNCT
ejpam-2434	144	3	the	the	DET
ejpam-2434	144	4	elements	element	NOUN
ejpam-2434	144	5	of	of	ADP
ejpam-2434	144	6	c	c	NOUN
ejpam-2434	144	7	can	can	AUX
ejpam-2434	144	8	be	be	AUX
ejpam-2434	144	9	written	write	VERB
ejpam-2434	144	10	in	in	ADP
ejpam-2434	144	11	the	the	DET
ejpam-2434	144	12	form	form	NOUN
ejpam-2434	144	13	ci	ci	NOUN
ejpam-2434	144	14	=	=	SYM
ejpam-2434	144	15	n	n	CCONJ
ejpam-2434	144	16	∑	∑	ADV
ejpam-2434	144	17	r=0	r=0	PROPN
ejpam-2434	144	18	dr	dr	PROPN
ejpam-2434	144	19	n	n	PROPN
ejpam-2434	144	20	n	n	ADV
ejpam-2434	144	21	r	r	NOUN
ejpam-2434	144	22	,	,	PUNCT
ejpam-2434	144	23	i	i	PRON
ejpam-2434	144	24	.	.	PUNCT
ejpam-2434	145	1	(	(	PUNCT
ejpam-2434	145	2	18	18	NUM
ejpam-2434	145	3	)	)	PUNCT
ejpam-2434	145	4	comparing	compare	VERB
ejpam-2434	145	5	(	(	PUNCT
ejpam-2434	145	6	15	15	NUM
ejpam-2434	145	7	)	)	PUNCT
ejpam-2434	145	8	and	and	CCONJ
ejpam-2434	145	9	(	(	PUNCT
ejpam-2434	145	10	18	18	NUM
ejpam-2434	145	11	)	)	PUNCT
ejpam-2434	145	12	,	,	PUNCT
ejpam-2434	145	13	we	we	PRON
ejpam-2434	145	14	have	have	VERB
ejpam-2434	145	15	m	m	PROPN
ejpam-2434	145	16	n	n	PRON
ejpam-2434	145	17	i	i	PRON
ejpam-2434	145	18	,	,	PUNCT
ejpam-2434	145	19	r	r	NOUN
ejpam-2434	145	20	=	=	SYM
ejpam-2434	145	21	n	n	CCONJ
ejpam-2434	145	22	n	n	NOUN
ejpam-2434	145	23	r	r	NOUN
ejpam-2434	145	24	,	,	PUNCT
ejpam-2434	145	25	i	i	PRON
ejpam-2434	145	26	,	,	PUNCT
ejpam-2434	145	27	for	for	ADP
ejpam-2434	145	28	i	i	PRON
ejpam-2434	145	29	,	,	PUNCT
ejpam-2434	145	30	r	r	NOUN
ejpam-2434	145	31	=	=	SYM
ejpam-2434	145	32	0	0	NUM
ejpam-2434	145	33	,	,	PUNCT
ejpam-2434	145	34	.	.	PUNCT
ejpam-2434	145	35	.	.	PUNCT
ejpam-2434	146	1	.	.	PUNCT
ejpam-2434	147	1	,	,	PUNCT
ejpam-2434	147	2	n.	n.	NOUN
ejpam-2434	147	3	since	since	SCONJ
ejpam-2434	147	4	each	each	DET
ejpam-2434	147	5	bernstein	bernstein	PROPN
ejpam-2434	147	6	polynomial	polynomial	PROPN
ejpam-2434	147	7	of	of	ADP
ejpam-2434	147	8	degree	degree	NOUN
ejpam-2434	147	9	r	r	NOUN
ejpam-2434	147	10	≤	≤	NOUN
ejpam-2434	147	11	n	n	PRON
ejpam-2434	147	12	can	can	AUX
ejpam-2434	147	13	be	be	AUX
ejpam-2434	147	14	written	write	VERB
ejpam-2434	147	15	in	in	ADP
ejpam-2434	147	16	terms	term	NOUN
ejpam-2434	147	17	of	of	ADP
ejpam-2434	147	18	bernstein	bernstein	PROPN
ejpam-2434	147	19	polynomials	polynomial	NOUN
ejpam-2434	147	20	of	of	ADP
ejpam-2434	147	21	degree	degree	NOUN
ejpam-2434	148	1	n	n	ADP
ejpam-2434	148	2	using	use	VERB
ejpam-2434	148	3	the	the	DET
ejpam-2434	148	4	following	follow	VERB
ejpam-2434	148	5	degree	degree	NOUN
ejpam-2434	148	6	elevation	elevation	NOUN
ejpam-2434	148	7	defined	define	VERB
ejpam-2434	148	8	by	by	ADP
ejpam-2434	148	9	[	[	X
ejpam-2434	148	10	3	3	NUM
ejpam-2434	148	11	]	]	PUNCT
ejpam-2434	148	12	:	:	PUNCT
ejpam-2434	148	13	br	br	PROPN
ejpam-2434	148	14	k	k	PROPN
ejpam-2434	148	15	(	(	PUNCT
ejpam-2434	148	16	x	x	X
ejpam-2434	148	17	)	)	PUNCT
ejpam-2434	148	18	=	=	NOUN
ejpam-2434	148	19	n−r+k	n−r+k	PUNCT
ejpam-2434	148	20	∑	∑	PUNCT
ejpam-2434	148	21	i	i	PROPN
ejpam-2434	148	22	=	=	PROPN
ejpam-2434	148	23	k	k	X
ejpam-2434	148	24	�	�	PROPN
ejpam-2434	148	25	r	r	PROPN
ejpam-2434	148	26	k	k	PROPN
ejpam-2434	148	27	�	�	PROPN
ejpam-2434	148	28	�	�	PROPN
ejpam-2434	148	29	n−r	n−r	NOUN
ejpam-2434	148	30	i−k	i−k	VERB
ejpam-2434	148	31	�	�	PROPN
ejpam-2434	148	32	�	�	PROPN
ejpam-2434	148	33	n	n	CCONJ
ejpam-2434	148	34	i	i	PROPN
ejpam-2434	148	35	�	�	PROPN
ejpam-2434	149	1	bn	bn	INTJ
ejpam-2434	149	2	i	i	PROPN
ejpam-2434	149	3	(	(	PUNCT
ejpam-2434	149	4	x	x	NOUN
ejpam-2434	149	5	)	)	PUNCT
ejpam-2434	149	6	,	,	PUNCT
ejpam-2434	149	7	k	k	X
ejpam-2434	149	8	=	=	SYM
ejpam-2434	149	9	0,1	0,1	NUM
ejpam-2434	149	10	,	,	PUNCT
ejpam-2434	149	11	.	.	PUNCT
ejpam-2434	149	12	.	.	PUNCT
ejpam-2434	150	1	.	.	PUNCT
ejpam-2434	151	1	,	,	PUNCT
ejpam-2434	151	2	r.	r.	PROPN
ejpam-2434	151	3	(	(	PUNCT
ejpam-2434	151	4	19	19	NUM
ejpam-2434	151	5	)	)	PUNCT
ejpam-2434	151	6	substituting	substituting	NOUN
ejpam-2434	151	7	(	(	PUNCT
ejpam-2434	151	8	19	19	NUM
ejpam-2434	151	9	)	)	PUNCT
ejpam-2434	151	10	into	into	ADP
ejpam-2434	151	11	(	(	PUNCT
ejpam-2434	151	12	12	12	NUM
ejpam-2434	151	13	)	)	PUNCT
ejpam-2434	151	14	and	and	CCONJ
ejpam-2434	151	15	rearrange	rearrange	VERB
ejpam-2434	151	16	the	the	DET
ejpam-2434	151	17	order	order	NOUN
ejpam-2434	151	18	of	of	ADP
ejpam-2434	151	19	summations	summation	NOUN
ejpam-2434	151	20	,	,	PUNCT
ejpam-2434	151	21	we	we	PRON
ejpam-2434	151	22	find	find	VERB
ejpam-2434	151	23	the	the	DET
ejpam-2434	151	24	entries	entry	NOUN
ejpam-2434	151	25	n	n	ADP
ejpam-2434	151	26	n	n	ADV
ejpam-2434	151	27	r	r	NOUN
ejpam-2434	151	28	,	,	PUNCT
ejpam-2434	151	29	i	i	PRON
ejpam-2434	151	30	=	=	SYM
ejpam-2434	151	31	�	�	PROPN
ejpam-2434	152	1	n	n	CCONJ
ejpam-2434	152	2	i	i	PROPN
ejpam-2434	152	3	�	�	VERB
ejpam-2434	152	4	−1	−1	VERB
ejpam-2434	152	5	(	(	PUNCT
ejpam-2434	152	6	2r	2r	NUM
ejpam-2434	152	7	+	+	CCONJ
ejpam-2434	152	8	1	1	NUM
ejpam-2434	152	9	)	)	PUNCT
ejpam-2434	152	10	!	!	PUNCT
ejpam-2434	152	11	!	!	PUNCT
ejpam-2434	153	1	2r(r	2r(r	NOUN
ejpam-2434	154	1	+	+	CCONJ
ejpam-2434	154	2	1	1	NUM
ejpam-2434	154	3	)	)	PUNCT
ejpam-2434	154	4	!	!	PUNCT
ejpam-2434	155	1	min(i	min(i	PROPN
ejpam-2434	155	2	,	,	PUNCT
ejpam-2434	155	3	r	r	NOUN
ejpam-2434	155	4	)	)	PUNCT
ejpam-2434	155	5	∑	∑	NOUN
ejpam-2434	155	6	k	k	X
ejpam-2434	155	7	=	=	NOUN
ejpam-2434	155	8	max(0,i+r−n	max(0,i+r−n	PROPN
ejpam-2434	155	9	)	)	PUNCT
ejpam-2434	155	10	(	(	PUNCT
ejpam-2434	155	11	−1)r−k	−1)r−k	PROPN
ejpam-2434	155	12	�	�	PROPN
ejpam-2434	155	13	n−	n−	NOUN
ejpam-2434	155	14	r	r	NOUN
ejpam-2434	155	15	i	i	PRON
ejpam-2434	155	16	−	−	PROPN
ejpam-2434	155	17	k	k	PROPN
ejpam-2434	155	18	�	�	PROPN
ejpam-2434	155	19	�	�	PROPN
ejpam-2434	155	20	r	r	NOUN
ejpam-2434	155	21	+	+	NOUN
ejpam-2434	155	22	1	1	NUM
ejpam-2434	155	23	2	2	NUM
ejpam-2434	155	24	k	k	X
ejpam-2434	155	25	�	�	PROPN
ejpam-2434	155	26	�	�	PROPN
ejpam-2434	155	27	r	r	NOUN
ejpam-2434	155	28	+	+	NOUN
ejpam-2434	155	29	1	1	NUM
ejpam-2434	155	30	2	2	NUM
ejpam-2434	155	31	r	r	NOUN
ejpam-2434	155	32	−	−	PROPN
ejpam-2434	155	33	k	k	PROPN
ejpam-2434	155	34	�	�	PROPN
ejpam-2434	155	35	+	+	CCONJ
ejpam-2434	155	36	r	r	PROPN
ejpam-2434	155	37	∑	∑	PUNCT
ejpam-2434	155	38	k=0	k=0	PROPN
ejpam-2434	155	39	λk	λk	ADP
ejpam-2434	155	40	�	�	PROPN
ejpam-2434	155	41	n	n	CCONJ
ejpam-2434	155	42	i	i	PROPN
ejpam-2434	155	43	�	�	VERB
ejpam-2434	155	44	−1	−1	NOUN
ejpam-2434	155	45	(	(	PUNCT
ejpam-2434	155	46	2k+	2k+	NUM
ejpam-2434	155	47	1	1	NUM
ejpam-2434	155	48	)	)	PUNCT
ejpam-2434	155	49	!	!	PUNCT
ejpam-2434	155	50	!	!	PUNCT
ejpam-2434	156	1	2k(k+	2k(k+	NUM
ejpam-2434	156	2	1	1	NUM
ejpam-2434	156	3	)	)	PUNCT
ejpam-2434	156	4	!	!	PUNCT
ejpam-2434	157	1	min(i	min(i	PROPN
ejpam-2434	157	2	,	,	PUNCT
ejpam-2434	157	3	k	k	PROPN
ejpam-2434	157	4	)	)	PUNCT
ejpam-2434	157	5	∑	∑	PROPN
ejpam-2434	157	6	j	j	PROPN
ejpam-2434	157	7	=	=	SYM
ejpam-2434	157	8	max(0,i+k−n	max(0,i+k−n	PROPN
ejpam-2434	157	9	)	)	PUNCT
ejpam-2434	157	10	(	(	PUNCT
ejpam-2434	157	11	−1)k−	−1)k−	PUNCT
ejpam-2434	157	12	j	j	PROPN
ejpam-2434	157	13	�	�	PROPN
ejpam-2434	157	14	n−	n−	PROPN
ejpam-2434	157	15	k	k	NOUN
ejpam-2434	158	1	i	i	PRON
ejpam-2434	158	2	−	−	PROPN
ejpam-2434	158	3	j	j	PROPN
ejpam-2434	158	4	�	�	PROPN
ejpam-2434	158	5	�	�	PROPN
ejpam-2434	158	6	k+	k+	NOUN
ejpam-2434	158	7	1	1	NUM
ejpam-2434	158	8	2	2	NUM
ejpam-2434	158	9	j	j	PROPN
ejpam-2434	158	10	�	�	PROPN
ejpam-2434	158	11	�	�	PROPN
ejpam-2434	158	12	k+	k+	NOUN
ejpam-2434	158	13	1	1	NUM
ejpam-2434	158	14	2	2	NUM
ejpam-2434	158	15	k−	k−	PROPN
ejpam-2434	158	16	j	j	PROPN
ejpam-2434	158	17	�	�	PROPN
ejpam-2434	158	18	.	.	PUNCT
ejpam-2434	159	1	(	(	PUNCT
ejpam-2434	159	2	20	20	NUM
ejpam-2434	159	3	)	)	PUNCT
ejpam-2434	159	4	therefore	therefore	ADV
ejpam-2434	159	5	,	,	PUNCT
ejpam-2434	159	6	the	the	DET
ejpam-2434	159	7	entries	entry	NOUN
ejpam-2434	159	8	of	of	ADP
ejpam-2434	159	9	the	the	DET
ejpam-2434	159	10	matrix	matrix	NOUN
ejpam-2434	159	11	m	m	VERB
ejpam-2434	159	12	are	be	AUX
ejpam-2434	159	13	given	give	VERB
ejpam-2434	159	14	by	by	ADP
ejpam-2434	159	15	m	m	NOUN
ejpam-2434	159	16	n	n	ADV
ejpam-2434	159	17	i	i	PRON
ejpam-2434	159	18	,	,	PUNCT
ejpam-2434	159	19	r	r	NOUN
ejpam-2434	159	20	=	=	PUNCT
ejpam-2434	159	21	φr	φr	ADP
ejpam-2434	159	22	i	i	PROPN
ejpam-2434	159	23	,	,	PUNCT
ejpam-2434	159	24	n	n	PROPN
ejpam-2434	159	25	+	+	CCONJ
ejpam-2434	160	1	∑r	∑r	PROPN
ejpam-2434	160	2	k=0λkφ	k=0λkφ	NOUN
ejpam-2434	160	3	k	k	PROPN
ejpam-2434	160	4	i	i	PROPN
ejpam-2434	160	5	,	,	PUNCT
ejpam-2434	160	6	n	n	PROPN
ejpam-2434	160	7	,	,	PUNCT
ejpam-2434	160	8	where	where	SCONJ
ejpam-2434	160	9	φk	φk	ADP
ejpam-2434	160	10	i	i	PROPN
ejpam-2434	160	11	,	,	PUNCT
ejpam-2434	160	12	n	n	PROPN
ejpam-2434	160	13	=	=	SYM
ejpam-2434	160	14	(	(	PUNCT
ejpam-2434	160	15	2k+	2k+	NUM
ejpam-2434	160	16	1	1	NUM
ejpam-2434	160	17	)	)	PUNCT
ejpam-2434	160	18	!	!	PUNCT
ejpam-2434	160	19	!	!	PUNCT
ejpam-2434	161	1	2k(k+	2k(k+	NUM
ejpam-2434	161	2	1	1	NUM
ejpam-2434	161	3	)	)	PUNCT
ejpam-2434	161	4	!	!	PUNCT
ejpam-2434	162	1	min(i	min(i	PROPN
ejpam-2434	162	2	,	,	PUNCT
ejpam-2434	162	3	k	k	PROPN
ejpam-2434	162	4	)	)	PUNCT
ejpam-2434	162	5	∑	∑	PROPN
ejpam-2434	162	6	j	j	PROPN
ejpam-2434	162	7	=	=	SYM
ejpam-2434	162	8	max(0,i+k−n	max(0,i+k−n	PROPN
ejpam-2434	162	9	)	)	PUNCT
ejpam-2434	162	10	(	(	PUNCT
ejpam-2434	162	11	−1)k−	−1)k−	PUNCT
ejpam-2434	162	12	j	j	PROPN
ejpam-2434	162	13	�	�	PROPN
ejpam-2434	162	14	n−k	n−k	PROPN
ejpam-2434	162	15	i−	i−	PROPN
ejpam-2434	162	16	j	j	PROPN
ejpam-2434	162	17	�	�	PROPN
ejpam-2434	162	18	�	�	PROPN
ejpam-2434	162	19	k+	k+	NOUN
ejpam-2434	162	20	1	1	NUM
ejpam-2434	162	21	2	2	NUM
ejpam-2434	162	22	j	j	PROPN
ejpam-2434	162	23	�	�	PROPN
ejpam-2434	162	24	�	�	PROPN
ejpam-2434	162	25	k+	k+	NOUN
ejpam-2434	162	26	1	1	NUM
ejpam-2434	162	27	2	2	NUM
ejpam-2434	162	28	k−	k−	PROPN
ejpam-2434	162	29	j	j	PROPN
ejpam-2434	162	30	�	�	PROPN
ejpam-2434	162	31	�	�	PROPN
ejpam-2434	162	32	n	n	CCONJ
ejpam-2434	162	33	i	i	PROPN
ejpam-2434	162	34	�	�	PROPN
ejpam-2434	162	35	.	.	PUNCT
ejpam-2434	163	1	now	now	ADV
ejpam-2434	163	2	,	,	PUNCT
ejpam-2434	163	3	we	we	PRON
ejpam-2434	163	4	have	have	VERB
ejpam-2434	163	5	the	the	DET
ejpam-2434	163	6	following	follow	VERB
ejpam-2434	163	7	corollary	corollary	NOUN
ejpam-2434	163	8	which	which	PRON
ejpam-2434	163	9	enables	enable	VERB
ejpam-2434	163	10	us	we	PRON
ejpam-2434	163	11	to	to	PART
ejpam-2434	163	12	write	write	VERB
ejpam-2434	163	13	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	163	14	-	-	PUNCT
ejpam-2434	163	15	ii	ii	NOUN
ejpam-2434	163	16	polynomials	polynomial	NOUN
ejpam-2434	163	17	of	of	ADP
ejpam-2434	163	18	degree	degree	NOUN
ejpam-2434	163	19	r	r	NOUN
ejpam-2434	163	20	≤	≤	NOUN
ejpam-2434	163	21	n	n	CCONJ
ejpam-2434	163	22	in	in	ADP
ejpam-2434	163	23	terms	term	NOUN
ejpam-2434	163	24	of	of	ADP
ejpam-2434	163	25	bernstein	bernstein	PROPN
ejpam-2434	163	26	polynomials	polynomial	NOUN
ejpam-2434	163	27	of	of	ADP
ejpam-2434	163	28	degree	degree	NOUN
ejpam-2434	163	29	n.	n.	NOUN
ejpam-2434	163	30	corollary	corollary	NOUN
ejpam-2434	163	31	1	1	NUM
ejpam-2434	163	32	.	.	PUNCT
ejpam-2434	164	1	the	the	DET
ejpam-2434	164	2	generalized	generalize	VERB
ejpam-2434	164	3	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	164	4	-	-	PUNCT
ejpam-2434	164	5	ii	ii	PROPN
ejpam-2434	164	6	polynomials	polynomial	NOUN
ejpam-2434	164	7	u	u	PROPN
ejpam-2434	164	8	(	(	PUNCT
ejpam-2434	164	9	m	m	PROPN
ejpam-2434	164	10	,	,	PUNCT
ejpam-2434	164	11	n	n	CCONJ
ejpam-2434	164	12	)	)	PUNCT
ejpam-2434	164	13	0	0	NUM
ejpam-2434	165	1	(	(	PUNCT
ejpam-2434	165	2	x	x	NOUN
ejpam-2434	165	3	)	)	PUNCT
ejpam-2434	165	4	,	,	PUNCT
ejpam-2434	165	5	.	.	PUNCT
ejpam-2434	165	6	.	.	PUNCT
ejpam-2434	166	1	.	.	PUNCT
ejpam-2434	167	1	,	,	PUNCT
ejpam-2434	167	2	u	u	PROPN
ejpam-2434	167	3	(	(	PUNCT
ejpam-2434	167	4	m	m	PROPN
ejpam-2434	167	5	,	,	PUNCT
ejpam-2434	167	6	n	n	CCONJ
ejpam-2434	167	7	)	)	PUNCT
ejpam-2434	167	8	n	n	PROPN
ejpam-2434	167	9	(	(	PUNCT
ejpam-2434	167	10	x	x	X
ejpam-2434	167	11	)	)	PUNCT
ejpam-2434	167	12	of	of	ADP
ejpam-2434	167	13	degree	degree	NOUN
ejpam-2434	167	14	less	less	ADJ
ejpam-2434	167	15	than	than	ADP
ejpam-2434	167	16	or	or	CCONJ
ejpam-2434	167	17	equal	equal	ADJ
ejpam-2434	167	18	to	to	ADP
ejpam-2434	167	19	n	n	NUM
ejpam-2434	167	20	can	can	AUX
ejpam-2434	167	21	be	be	AUX
ejpam-2434	167	22	expressed	express	VERB
ejpam-2434	167	23	in	in	ADP
ejpam-2434	167	24	the	the	DET
ejpam-2434	167	25	bernstein	bernstein	PROPN
ejpam-2434	167	26	basis	basis	NOUN
ejpam-2434	167	27	of	of	ADP
ejpam-2434	167	28	fixed	fix	VERB
ejpam-2434	167	29	degree	degree	NOUN
ejpam-2434	167	30	n	n	NOUN
ejpam-2434	167	31	by	by	ADP
ejpam-2434	167	32	the	the	DET
ejpam-2434	167	33	following	follow	VERB
ejpam-2434	167	34	formula	formula	NOUN
ejpam-2434	167	35	u	u	PROPN
ejpam-2434	167	36	(	(	PUNCT
ejpam-2434	167	37	m	m	PROPN
ejpam-2434	167	38	,	,	PUNCT
ejpam-2434	167	39	n	n	CCONJ
ejpam-2434	167	40	)	)	PUNCT
ejpam-2434	168	1	r	r	NOUN
ejpam-2434	168	2	(	(	PUNCT
ejpam-2434	168	3	x	x	NOUN
ejpam-2434	168	4	)	)	PUNCT
ejpam-2434	168	5	=	=	SYM
ejpam-2434	168	6	n	n	CCONJ
ejpam-2434	168	7	∑	∑	PUNCT
ejpam-2434	168	8	i=0	i=0	PROPN
ejpam-2434	168	9	n	n	CCONJ
ejpam-2434	168	10	n	n	ADV
ejpam-2434	168	11	r	r	NOUN
ejpam-2434	168	12	,	,	PUNCT
ejpam-2434	168	13	ib	ib	NOUN
ejpam-2434	168	14	n	n	INTJ
ejpam-2434	168	15	i	i	PRON
ejpam-2434	168	16	(	(	PUNCT
ejpam-2434	168	17	x	x	NOUN
ejpam-2434	168	18	)	)	PUNCT
ejpam-2434	168	19	,	,	PUNCT
ejpam-2434	168	20	r	r	NOUN
ejpam-2434	168	21	=	=	SYM
ejpam-2434	168	22	0,1	0,1	NUM
ejpam-2434	168	23	,	,	PUNCT
ejpam-2434	168	24	.	.	PUNCT
ejpam-2434	168	25	.	.	PUNCT
ejpam-2434	168	26	.	.	PUNCT
ejpam-2434	168	27	,	,	PUNCT
ejpam-2434	168	28	n	n	CCONJ
ejpam-2434	168	29	where	where	SCONJ
ejpam-2434	168	30	n	n	DET
ejpam-2434	168	31	n	n	ADV
ejpam-2434	168	32	r	r	NOUN
ejpam-2434	168	33	,	,	PUNCT
ejpam-2434	168	34	i	i	PRON
ejpam-2434	168	35	=	=	PUNCT
ejpam-2434	168	36	(	(	PUNCT
ejpam-2434	168	37	2r	2r	NUM
ejpam-2434	168	38	+	+	NOUN
ejpam-2434	168	39	1	1	NUM
ejpam-2434	168	40	)	)	PUNCT
ejpam-2434	168	41	!	!	PUNCT
ejpam-2434	168	42	!	!	PUNCT
ejpam-2434	169	1	2r(r	2r(r	NOUN
ejpam-2434	170	1	+	+	CCONJ
ejpam-2434	170	2	1	1	NUM
ejpam-2434	170	3	)	)	PUNCT
ejpam-2434	170	4	!	!	PUNCT
ejpam-2434	171	1	min(i	min(i	PROPN
ejpam-2434	171	2	,	,	PUNCT
ejpam-2434	171	3	r	r	NOUN
ejpam-2434	171	4	)	)	PUNCT
ejpam-2434	171	5	∑	∑	NOUN
ejpam-2434	171	6	k	k	X
ejpam-2434	171	7	=	=	NOUN
ejpam-2434	171	8	max(0,i+r−n	max(0,i+r−n	PROPN
ejpam-2434	171	9	)	)	PUNCT
ejpam-2434	171	10	(	(	PUNCT
ejpam-2434	171	11	−1)r−k(2r	−1)r−k(2r	X
ejpam-2434	171	12	+	+	X
ejpam-2434	172	1	1)2	1)2	NUM
ejpam-2434	172	2	22r(2r	22r(2r	NUM
ejpam-2434	172	3	−	−	NOUN
ejpam-2434	172	4	2k+	2k+	NUM
ejpam-2434	172	5	1)(2k+	1)(2k+	NOUN
ejpam-2434	172	6	1	1	NUM
ejpam-2434	172	7	)	)	PUNCT
ejpam-2434	172	8	�	�	NOUN
ejpam-2434	172	9	n−r	n−r	NOUN
ejpam-2434	172	10	i−k	i−k	NOUN
ejpam-2434	172	11	�	�	NOUN
ejpam-2434	172	12	�	�	PROPN
ejpam-2434	172	13	2r	2r	NUM
ejpam-2434	172	14	r	r	NOUN
ejpam-2434	172	15	�	�	PROPN
ejpam-2434	172	16	�	�	PROPN
ejpam-2434	172	17	2r	2r	NUM
ejpam-2434	172	18	2k	2k	PROPN
ejpam-2434	172	19	�	�	PROPN
ejpam-2434	172	20	�	�	PROPN
ejpam-2434	172	21	n	n	CCONJ
ejpam-2434	172	22	i	i	PROPN
ejpam-2434	172	23	�	�	PROPN
ejpam-2434	173	1	+	+	CCONJ
ejpam-2434	173	2	r	r	NOUN
ejpam-2434	173	3	∑	∑	PUNCT
ejpam-2434	173	4	k=0	k=0	PROPN
ejpam-2434	173	5	λk	λk	X
ejpam-2434	173	6	(	(	PUNCT
ejpam-2434	173	7	2k+	2k+	NUM
ejpam-2434	173	8	1	1	NUM
ejpam-2434	173	9	)	)	PUNCT
ejpam-2434	173	10	!	!	PUNCT
ejpam-2434	173	11	!	!	PUNCT
ejpam-2434	174	1	2k(k+	2k(k+	NUM
ejpam-2434	174	2	1	1	NUM
ejpam-2434	174	3	)	)	PUNCT
ejpam-2434	174	4	!	!	PUNCT
ejpam-2434	175	1	min(i	min(i	PROPN
ejpam-2434	175	2	,	,	PUNCT
ejpam-2434	175	3	k	k	PROPN
ejpam-2434	175	4	)	)	PUNCT
ejpam-2434	175	5	∑	∑	PROPN
ejpam-2434	175	6	j	j	PROPN
ejpam-2434	175	7	=	=	SYM
ejpam-2434	175	8	max(0,i+k−n	max(0,i+k−n	PROPN
ejpam-2434	175	9	)	)	PUNCT
ejpam-2434	175	10	(	(	PUNCT
ejpam-2434	175	11	−1)k−	−1)k−	X
ejpam-2434	175	12	j(2k+	j(2k+	PROPN
ejpam-2434	175	13	1)2	1)2	NUM
ejpam-2434	175	14	22k(2k−	22k(2k−	PROPN
ejpam-2434	175	15	2	2	NUM
ejpam-2434	175	16	j	j	PROPN
ejpam-2434	175	17	+	+	CCONJ
ejpam-2434	175	18	1)(2	1)(2	NUM
ejpam-2434	175	19	j	j	NOUN
ejpam-2434	175	20	+	+	CCONJ
ejpam-2434	175	21	1	1	X
ejpam-2434	175	22	)	)	PUNCT
ejpam-2434	175	23	�	�	PROPN
ejpam-2434	175	24	n−k	n−k	PROPN
ejpam-2434	175	25	i−	i−	PROPN
ejpam-2434	175	26	j	j	PROPN
ejpam-2434	175	27	�	�	PROPN
ejpam-2434	175	28	�	�	PROPN
ejpam-2434	175	29	2k	2k	PROPN
ejpam-2434	175	30	k	k	PROPN
ejpam-2434	175	31	�	�	PROPN
ejpam-2434	175	32	�	�	PROPN
ejpam-2434	175	33	2k	2k	PROPN
ejpam-2434	175	34	2	2	NUM
ejpam-2434	175	35	j	j	PROPN
ejpam-2434	175	36	�	�	PROPN
ejpam-2434	175	37	�	�	PROPN
ejpam-2434	175	38	n	n	CCONJ
ejpam-2434	175	39	i	i	PROPN
ejpam-2434	175	40	�	�	PROPN
ejpam-2434	175	41	.	.	PUNCT
ejpam-2434	176	1	m.	m.	NOUN
ejpam-2434	176	2	alqudah	alqudah	PROPN
ejpam-2434	176	3	/	/	SYM
ejpam-2434	176	4	eur	eur	PROPN
ejpam-2434	176	5	.	.	PUNCT
ejpam-2434	177	1	j.	j.	PROPN
ejpam-2434	177	2	pure	pure	PROPN
ejpam-2434	177	3	appl	appl	PROPN
ejpam-2434	177	4	.	.	PROPN
ejpam-2434	177	5	math	math	PROPN
ejpam-2434	177	6	,	,	PUNCT
ejpam-2434	177	7	8	8	NUM
ejpam-2434	177	8	(	(	PUNCT
ejpam-2434	177	9	2015	2015	NUM
ejpam-2434	177	10	)	)	PUNCT
ejpam-2434	177	11	,	,	PUNCT
ejpam-2434	177	12	324	324	NUM
ejpam-2434	177	13	-	-	SYM
ejpam-2434	177	14	331	331	NUM
ejpam-2434	177	15	330	330	NUM
ejpam-2434	177	16	proof	proof	NOUN
ejpam-2434	177	17	.	.	PUNCT
ejpam-2434	178	1	from	from	ADP
ejpam-2434	178	2	(	(	PUNCT
ejpam-2434	178	3	17	17	NUM
ejpam-2434	178	4	)	)	PUNCT
ejpam-2434	178	5	in	in	ADP
ejpam-2434	178	6	the	the	DET
ejpam-2434	178	7	proof	proof	NOUN
ejpam-2434	178	8	of	of	ADP
ejpam-2434	178	9	the	the	DET
ejpam-2434	178	10	previous	previous	ADJ
ejpam-2434	178	11	theorem	theorem	NOUN
ejpam-2434	178	12	,	,	PUNCT
ejpam-2434	178	13	it	it	PRON
ejpam-2434	178	14	is	be	AUX
ejpam-2434	178	15	clear	clear	ADJ
ejpam-2434	178	16	that	that	SCONJ
ejpam-2434	178	17	each	each	DET
ejpam-2434	178	18	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	178	19	-	-	PUNCT
ejpam-2434	178	20	ii	ii	NOUN
ejpam-2434	178	21	polynomial	polynomial	NOUN
ejpam-2434	178	22	of	of	ADP
ejpam-2434	178	23	degree	degree	NOUN
ejpam-2434	178	24	r	r	NOUN
ejpam-2434	178	25	≤	≤	NOUN
ejpam-2434	178	26	n	n	PRON
ejpam-2434	178	27	can	can	AUX
ejpam-2434	178	28	be	be	AUX
ejpam-2434	178	29	written	write	VERB
ejpam-2434	178	30	in	in	ADP
ejpam-2434	178	31	terms	term	NOUN
ejpam-2434	178	32	of	of	ADP
ejpam-2434	178	33	bernstein	bernstein	PROPN
ejpam-2434	178	34	polynomials	polynomial	NOUN
ejpam-2434	178	35	of	of	ADP
ejpam-2434	178	36	degree	degree	NOUN
ejpam-2434	178	37	n.	n.	NOUN
ejpam-2434	178	38	applying	applying	NOUN
ejpam-2434	178	39	(	(	PUNCT
ejpam-2434	178	40	5	5	NUM
ejpam-2434	178	41	)	)	PUNCT
ejpam-2434	178	42	with	with	ADP
ejpam-2434	178	43	some	some	DET
ejpam-2434	178	44	simplifications	simplification	NOUN
ejpam-2434	178	45	,	,	PUNCT
ejpam-2434	178	46	we	we	PRON
ejpam-2434	178	47	have	have	VERB
ejpam-2434	178	48	�	�	PROPN
ejpam-2434	179	1	r	r	NOUN
ejpam-2434	179	2	+	+	NOUN
ejpam-2434	179	3	1	1	NUM
ejpam-2434	179	4	2	2	NUM
ejpam-2434	179	5	k	k	X
ejpam-2434	179	6	�	�	PROPN
ejpam-2434	179	7	�	�	PROPN
ejpam-2434	179	8	r	r	NOUN
ejpam-2434	179	9	+	+	NOUN
ejpam-2434	179	10	1	1	NUM
ejpam-2434	179	11	2	2	NUM
ejpam-2434	179	12	r	r	NOUN
ejpam-2434	179	13	−	−	NOUN
ejpam-2434	179	14	k	k	PROPN
ejpam-2434	179	15	�	�	PROPN
ejpam-2434	179	16	=	=	PUNCT
ejpam-2434	179	17	(	(	PUNCT
ejpam-2434	179	18	2r	2r	NUM
ejpam-2434	179	19	+	+	CCONJ
ejpam-2434	179	20	1	1	X
ejpam-2434	179	21	)	)	PUNCT
ejpam-2434	179	22	2r(2r	2r(2r	NUM
ejpam-2434	179	23	−	−	NOUN
ejpam-2434	179	24	2k+	2k+	NUM
ejpam-2434	179	25	1)(r	1)(r	NUM
ejpam-2434	179	26	−	−	PROPN
ejpam-2434	179	27	k)!k	k)!k	PROPN
ejpam-2434	179	28	!	!	PUNCT
ejpam-2434	180	1	(	(	PUNCT
ejpam-2434	180	2	2r	2r	NUM
ejpam-2434	180	3	−	−	NOUN
ejpam-2434	180	4	1	1	NUM
ejpam-2434	180	5	)	)	PUNCT
ejpam-2434	180	6	!	!	PUNCT
ejpam-2434	180	7	!	!	PUNCT
ejpam-2434	181	1	(	(	PUNCT
ejpam-2434	181	2	2k−	2k−	NOUN
ejpam-2434	181	3	1	1	NUM
ejpam-2434	181	4	)	)	PUNCT
ejpam-2434	181	5	!	!	PUNCT
ejpam-2434	181	6	!	!	PUNCT
ejpam-2434	182	1	(	(	PUNCT
ejpam-2434	182	2	2r	2r	NUM
ejpam-2434	182	3	+	+	NOUN
ejpam-2434	183	1	1	1	X
ejpam-2434	183	2	)	)	PUNCT
ejpam-2434	183	3	(	(	PUNCT
ejpam-2434	183	4	2k+	2k+	NUM
ejpam-2434	183	5	1	1	NUM
ejpam-2434	183	6	)	)	PUNCT
ejpam-2434	183	7	(	(	PUNCT
ejpam-2434	183	8	2r	2r	NUM
ejpam-2434	183	9	−	−	NOUN
ejpam-2434	183	10	1	1	NUM
ejpam-2434	183	11	)	)	PUNCT
ejpam-2434	183	12	!	!	PUNCT
ejpam-2434	183	13	!	!	PUNCT
ejpam-2434	184	1	(	(	PUNCT
ejpam-2434	184	2	2(r	2(r	NUM
ejpam-2434	184	3	−	−	PROPN
ejpam-2434	184	4	k)−	k)−	PROPN
ejpam-2434	184	5	1	1	NUM
ejpam-2434	184	6	)	)	PUNCT
ejpam-2434	184	7	!	!	PUNCT
ejpam-2434	184	8	!	!	PUNCT
ejpam-2434	184	9	.	.	PUNCT
ejpam-2434	185	1	using	use	VERB
ejpam-2434	185	2	the	the	DET
ejpam-2434	185	3	fact	fact	NOUN
ejpam-2434	185	4	(	(	PUNCT
ejpam-2434	185	5	2n)!=	2n)!=	NUM
ejpam-2434	185	6	(	(	PUNCT
ejpam-2434	185	7	2n−	2n−	PROPN
ejpam-2434	185	8	1)!!2nn	1)!!2nn	NUM
ejpam-2434	185	9	!	!	PUNCT
ejpam-2434	185	10	,	,	PUNCT
ejpam-2434	185	11	we	we	PRON
ejpam-2434	185	12	get	get	VERB
ejpam-2434	186	1	�	�	PROPN
ejpam-2434	186	2	r	r	NOUN
ejpam-2434	186	3	+	+	NOUN
ejpam-2434	186	4	1	1	NUM
ejpam-2434	186	5	2	2	NUM
ejpam-2434	186	6	r	r	NOUN
ejpam-2434	186	7	−	−	PROPN
ejpam-2434	186	8	k	k	PROPN
ejpam-2434	186	9	�	�	PROPN
ejpam-2434	186	10	�	�	PROPN
ejpam-2434	186	11	r	r	NOUN
ejpam-2434	186	12	+	+	NOUN
ejpam-2434	186	13	1	1	NUM
ejpam-2434	186	14	2	2	NUM
ejpam-2434	186	15	k	k	X
ejpam-2434	186	16	�	�	PROPN
ejpam-2434	186	17	=	=	SYM
ejpam-2434	186	18	(	(	PUNCT
ejpam-2434	186	19	2r	2r	NUM
ejpam-2434	186	20	+	+	CCONJ
ejpam-2434	187	1	1)2	1)2	NUM
ejpam-2434	187	2	22r(2r	22r(2r	NUM
ejpam-2434	187	3	−	−	NOUN
ejpam-2434	188	1	2k+	2k+	NUM
ejpam-2434	189	1	1)(2k+	1)(2k+	NOUN
ejpam-2434	189	2	1	1	NUM
ejpam-2434	189	3	)	)	PUNCT
ejpam-2434	189	4	�	�	NOUN
ejpam-2434	189	5	2r	2r	NUM
ejpam-2434	189	6	r	r	NOUN
ejpam-2434	189	7	�	�	PROPN
ejpam-2434	189	8	�	�	PROPN
ejpam-2434	189	9	2r	2r	NUM
ejpam-2434	189	10	2k	2k	PROPN
ejpam-2434	189	11	�	�	PROPN
ejpam-2434	189	12	.	.	PUNCT
ejpam-2434	190	1	substituting	substitute	VERB
ejpam-2434	190	2	the	the	DET
ejpam-2434	190	3	last	last	ADJ
ejpam-2434	190	4	identity	identity	NOUN
ejpam-2434	190	5	into	into	ADP
ejpam-2434	190	6	(	(	PUNCT
ejpam-2434	190	7	20	20	NUM
ejpam-2434	190	8	)	)	PUNCT
ejpam-2434	190	9	we	we	PRON
ejpam-2434	190	10	get	get	VERB
ejpam-2434	190	11	the	the	DET
ejpam-2434	190	12	desired	desire	VERB
ejpam-2434	190	13	result	result	NOUN
ejpam-2434	190	14	.	.	PUNCT
ejpam-2434	191	1	the	the	DET
ejpam-2434	191	2	following	follow	VERB
ejpam-2434	191	3	theorem	theorem	NOUN
ejpam-2434	191	4	introduced	introduce	VERB
ejpam-2434	191	5	in	in	ADP
ejpam-2434	191	6	[	[	X
ejpam-2434	191	7	1	1	NUM
ejpam-2434	191	8	]	]	PUNCT
ejpam-2434	191	9	will	will	AUX
ejpam-2434	191	10	be	be	AUX
ejpam-2434	191	11	used	use	VERB
ejpam-2434	191	12	to	to	PART
ejpam-2434	191	13	simplify	simplify	VERB
ejpam-2434	191	14	a	a	DET
ejpam-2434	191	15	main	main	ADJ
ejpam-2434	191	16	result	result	NOUN
ejpam-2434	191	17	.	.	PUNCT
ejpam-2434	192	1	theorem	theorem	ADJ
ejpam-2434	192	2	3	3	NUM
ejpam-2434	192	3	(	(	PUNCT
ejpam-2434	192	4	[	[	X
ejpam-2434	192	5	1	1	NUM
ejpam-2434	192	6	]	]	PUNCT
ejpam-2434	192	7	)	)	PUNCT
ejpam-2434	192	8	.	.	PUNCT
ejpam-2434	193	1	let	let	VERB
ejpam-2434	193	2	bn	bn	INTJ
ejpam-2434	193	3	r	r	NOUN
ejpam-2434	193	4	(	(	PUNCT
ejpam-2434	193	5	x	x	NOUN
ejpam-2434	193	6	)	)	PUNCT
ejpam-2434	193	7	be	be	VERB
ejpam-2434	193	8	the	the	DET
ejpam-2434	193	9	bernstein	bernstein	PROPN
ejpam-2434	193	10	polynomial	polynomial	PROPN
ejpam-2434	193	11	of	of	ADP
ejpam-2434	193	12	degree	degree	NOUN
ejpam-2434	193	13	n	n	NOUN
ejpam-2434	193	14	and	and	CCONJ
ejpam-2434	193	15	u	u	PROPN
ejpam-2434	193	16	(	(	PUNCT
ejpam-2434	193	17	m	m	PROPN
ejpam-2434	193	18	,	,	PUNCT
ejpam-2434	193	19	n	n	CCONJ
ejpam-2434	193	20	)	)	PUNCT
ejpam-2434	193	21	i	i	PRON
ejpam-2434	193	22	(	(	PUNCT
ejpam-2434	193	23	x	x	X
ejpam-2434	193	24	)	)	PUNCT
ejpam-2434	193	25	be	be	VERB
ejpam-2434	193	26	the	the	DET
ejpam-2434	193	27	generalized	generalize	VERB
ejpam-2434	193	28	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	193	29	-	-	PUNCT
ejpam-2434	193	30	ii	ii	NOUN
ejpam-2434	193	31	polynomial	polynomial	NOUN
ejpam-2434	193	32	of	of	ADP
ejpam-2434	193	33	degree	degree	NOUN
ejpam-2434	193	34	i	i	PRON
ejpam-2434	193	35	,	,	PUNCT
ejpam-2434	193	36	then	then	ADV
ejpam-2434	193	37	for	for	ADP
ejpam-2434	193	38	i	i	PRON
ejpam-2434	193	39	,	,	PUNCT
ejpam-2434	193	40	r	r	NOUN
ejpam-2434	193	41	=	=	SYM
ejpam-2434	193	42	0,1	0,1	NUM
ejpam-2434	193	43	,	,	PUNCT
ejpam-2434	193	44	.	.	PUNCT
ejpam-2434	193	45	.	.	PUNCT
ejpam-2434	194	1	.	.	PUNCT
ejpam-2434	195	1	,	,	PUNCT
ejpam-2434	195	2	n	n	CCONJ
ejpam-2434	195	3	we	we	PRON
ejpam-2434	195	4	have	have	VERB
ejpam-2434	195	5	∫	∫	PROPN
ejpam-2434	196	1	1	1	NUM
ejpam-2434	196	2	0	0	NUM
ejpam-2434	196	3	x	x	SYM
ejpam-2434	196	4	1	1	NUM
ejpam-2434	196	5	2	2	NUM
ejpam-2434	196	6	(	(	PUNCT
ejpam-2434	196	7	1−	1−	NUM
ejpam-2434	196	8	x	x	NOUN
ejpam-2434	196	9	)	)	PUNCT
ejpam-2434	196	10	1	1	NUM
ejpam-2434	196	11	2	2	NUM
ejpam-2434	196	12	bn	bn	NOUN
ejpam-2434	196	13	r	r	NOUN
ejpam-2434	196	14	(	(	PUNCT
ejpam-2434	196	15	x)u	x)u	X
ejpam-2434	196	16	(	(	PUNCT
ejpam-2434	196	17	m	m	PROPN
ejpam-2434	196	18	,	,	PUNCT
ejpam-2434	196	19	n	n	CCONJ
ejpam-2434	196	20	)	)	PUNCT
ejpam-2434	196	21	i	i	PRON
ejpam-2434	196	22	(	(	PUNCT
ejpam-2434	196	23	x)d	x)d	PUNCT
ejpam-2434	196	24	x	x	X
ejpam-2434	196	25	=	=	PUNCT
ejpam-2434	196	26	λi	λi	X
ejpam-2434	196	27	r	r	NOUN
ejpam-2434	196	28	,	,	PUNCT
ejpam-2434	196	29	n	n	PROPN
ejpam-2434	196	30	+	+	CCONJ
ejpam-2434	196	31	i	i	PRON
ejpam-2434	196	32	∑	∑	PUNCT
ejpam-2434	196	33	d=0	d=0	PROPN
ejpam-2434	196	34	λdλ	λdλ	VERB
ejpam-2434	196	35	d	d	X
ejpam-2434	196	36	r	r	NOUN
ejpam-2434	196	37	,	,	PUNCT
ejpam-2434	196	38	n	n	CCONJ
ejpam-2434	196	39	,	,	PUNCT
ejpam-2434	196	40	where	where	SCONJ
ejpam-2434	196	41	λd	λd	NOUN
ejpam-2434	196	42	defined	define	VERB
ejpam-2434	196	43	in	in	ADP
ejpam-2434	196	44	(	(	PUNCT
ejpam-2434	196	45	11	11	NUM
ejpam-2434	196	46	)	)	PUNCT
ejpam-2434	196	47	,	,	PUNCT
ejpam-2434	196	48	λd	λd	ADP
ejpam-2434	196	49	r	r	NOUN
ejpam-2434	196	50	,	,	PUNCT
ejpam-2434	196	51	n	n	NOUN
ejpam-2434	196	52	=	=	SYM
ejpam-2434	196	53	�	�	PROPN
ejpam-2434	196	54	n	n	CCONJ
ejpam-2434	196	55	r	r	PROPN
ejpam-2434	196	56	�	�	PROPN
ejpam-2434	196	57	(	(	PUNCT
ejpam-2434	196	58	2d	2d	NOUN
ejpam-2434	196	59	+	+	CCONJ
ejpam-2434	196	60	1	1	NUM
ejpam-2434	196	61	)	)	PUNCT
ejpam-2434	196	62	!	!	PUNCT
ejpam-2434	196	63	!	!	PUNCT
ejpam-2434	197	1	2d(d	2d(d	NUM
ejpam-2434	198	1	+	+	CCONJ
ejpam-2434	198	2	1	1	NUM
ejpam-2434	198	3	)	)	PUNCT
ejpam-2434	198	4	!	!	PUNCT
ejpam-2434	199	1	d	d	X
ejpam-2434	199	2	∑	∑	PUNCT
ejpam-2434	199	3	j=0	j=0	PROPN
ejpam-2434	199	4	(	(	PUNCT
ejpam-2434	199	5	−1)d−	−1)d−	X
ejpam-2434	200	1	j	j	PROPN
ejpam-2434	200	2	�	�	PROPN
ejpam-2434	200	3	d	d	PROPN
ejpam-2434	200	4	+	+	PROPN
ejpam-2434	200	5	1	1	NUM
ejpam-2434	200	6	2	2	NUM
ejpam-2434	200	7	j	j	PROPN
ejpam-2434	200	8	�	�	PROPN
ejpam-2434	200	9	�	�	PROPN
ejpam-2434	200	10	d	d	PROPN
ejpam-2434	200	11	+	+	PROPN
ejpam-2434	200	12	1	1	NUM
ejpam-2434	200	13	2	2	NUM
ejpam-2434	200	14	d	d	NOUN
ejpam-2434	200	15	−	−	PROPN
ejpam-2434	200	16	j	j	PROPN
ejpam-2434	200	17	�	�	PROPN
ejpam-2434	200	18	γ(r	γ(r	PROPN
ejpam-2434	200	19	+	+	CCONJ
ejpam-2434	200	20	j	j	PROPN
ejpam-2434	200	21	+	+	CCONJ
ejpam-2434	200	22	3	3	NUM
ejpam-2434	200	23	2)γ(n+	2)γ(n+	NUM
ejpam-2434	200	24	d	d	NOUN
ejpam-2434	200	25	−	−	NOUN
ejpam-2434	200	26	r	r	NOUN
ejpam-2434	200	27	−	−	PROPN
ejpam-2434	200	28	j	j	NOUN
ejpam-2434	200	29	+	+	CCONJ
ejpam-2434	200	30	3	3	NUM
ejpam-2434	200	31	2	2	NUM
ejpam-2434	200	32	)	)	PUNCT
ejpam-2434	200	33	γ(n+	γ(n+	X
ejpam-2434	201	1	d	d	NOUN
ejpam-2434	201	2	+	+	NOUN
ejpam-2434	201	3	3	3	NUM
ejpam-2434	201	4	)	)	PUNCT
ejpam-2434	201	5	,	,	PUNCT
ejpam-2434	201	6	(	(	PUNCT
ejpam-2434	201	7	21	21	NUM
ejpam-2434	201	8	)	)	PUNCT
ejpam-2434	201	9	and	and	CCONJ
ejpam-2434	201	10	γ(x	γ(x	NOUN
ejpam-2434	201	11	)	)	PUNCT
ejpam-2434	201	12	is	be	AUX
ejpam-2434	201	13	the	the	DET
ejpam-2434	201	14	gamma	gamma	PROPN
ejpam-2434	201	15	function	function	NOUN
ejpam-2434	201	16	.	.	PUNCT
ejpam-2434	202	1	finally	finally	ADV
ejpam-2434	202	2	,	,	PUNCT
ejpam-2434	202	3	to	to	PART
ejpam-2434	202	4	write	write	VERB
ejpam-2434	202	5	the	the	DET
ejpam-2434	202	6	bernstein	bernstein	PROPN
ejpam-2434	202	7	polynomial	polynomial	PROPN
ejpam-2434	202	8	basis	basis	NOUN
ejpam-2434	202	9	into	into	ADP
ejpam-2434	202	10	generalized	generalize	VERB
ejpam-2434	202	11	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	202	12	-	-	PUNCT
ejpam-2434	202	13	ii	ii	NOUN
ejpam-2434	202	14	polynomial	polynomial	ADJ
ejpam-2434	202	15	basis	basis	NOUN
ejpam-2434	202	16	of	of	ADP
ejpam-2434	202	17	degree	degree	NOUN
ejpam-2434	202	18	n	n	CCONJ
ejpam-2434	202	19	,	,	PUNCT
ejpam-2434	202	20	invert	invert	NOUN
ejpam-2434	202	21	(	(	PUNCT
ejpam-2434	202	22	16	16	NUM
ejpam-2434	202	23	)	)	PUNCT
ejpam-2434	202	24	and	and	CCONJ
ejpam-2434	202	25	let	let	VERB
ejpam-2434	202	26	m	m	PROPN
ejpam-2434	202	27	n−1	n−1	PROPN
ejpam-2434	202	28	i	i	PROPN
ejpam-2434	202	29	,	,	PUNCT
ejpam-2434	202	30	r	r	NOUN
ejpam-2434	202	31	,	,	PUNCT
ejpam-2434	202	32	n	n	PROPN
ejpam-2434	203	1	n−1	n−1	PROPN
ejpam-2434	203	2	i	i	PROPN
ejpam-2434	203	3	,	,	PUNCT
ejpam-2434	203	4	r	r	NOUN
ejpam-2434	203	5	,	,	PUNCT
ejpam-2434	203	6	i	i	PRON
ejpam-2434	203	7	,	,	PUNCT
ejpam-2434	203	8	r	r	NOUN
ejpam-2434	203	9	=	=	SYM
ejpam-2434	203	10	0	0	NUM
ejpam-2434	203	11	,	,	PUNCT
ejpam-2434	203	12	.	.	PUNCT
ejpam-2434	203	13	.	.	PUNCT
ejpam-2434	203	14	.	.	PUNCT
ejpam-2434	204	1	,	,	PUNCT
ejpam-2434	204	2	n	n	PRON
ejpam-2434	204	3	be	be	VERB
ejpam-2434	204	4	the	the	DET
ejpam-2434	204	5	entries	entry	NOUN
ejpam-2434	204	6	of	of	ADP
ejpam-2434	204	7	m−1	m−1	PROPN
ejpam-2434	204	8	and	and	CCONJ
ejpam-2434	204	9	n−1	n−1	PROPN
ejpam-2434	204	10	respectively	respectively	ADV
ejpam-2434	204	11	.	.	PUNCT
ejpam-2434	205	1	the	the	DET
ejpam-2434	205	2	transformation	transformation	NOUN
ejpam-2434	205	3	of	of	ADP
ejpam-2434	205	4	bernstein	bernstein	PROPN
ejpam-2434	205	5	polynomial	polynomial	PROPN
ejpam-2434	205	6	into	into	ADP
ejpam-2434	205	7	generalized	generalized	ADJ
ejpam-2434	205	8	tschebyscheffii	tschebyscheffii	NOUN
ejpam-2434	205	9	polynomial	polynomial	ADJ
ejpam-2434	205	10	basis	basis	NOUN
ejpam-2434	205	11	of	of	ADP
ejpam-2434	205	12	degree	degree	NOUN
ejpam-2434	205	13	n	n	NOUN
ejpam-2434	205	14	can	can	AUX
ejpam-2434	205	15	then	then	ADV
ejpam-2434	205	16	be	be	AUX
ejpam-2434	205	17	written	write	VERB
ejpam-2434	205	18	as	as	ADP
ejpam-2434	205	19	bn	bn	NOUN
ejpam-2434	205	20	r	r	NOUN
ejpam-2434	205	21	(	(	PUNCT
ejpam-2434	205	22	x	x	NOUN
ejpam-2434	205	23	)	)	PUNCT
ejpam-2434	205	24	=	=	SYM
ejpam-2434	206	1	n	n	CCONJ
ejpam-2434	206	2	∑	∑	PUNCT
ejpam-2434	206	3	i=0	i=0	PROPN
ejpam-2434	206	4	n	n	CCONJ
ejpam-2434	206	5	n−1	n−1	PROPN
ejpam-2434	206	6	r	r	NOUN
ejpam-2434	206	7	,	,	PUNCT
ejpam-2434	206	8	i	i	PRON
ejpam-2434	206	9	u	u	X
ejpam-2434	206	10	(	(	PUNCT
ejpam-2434	206	11	m	m	PROPN
ejpam-2434	206	12	,	,	PUNCT
ejpam-2434	206	13	n	n	CCONJ
ejpam-2434	206	14	)	)	PUNCT
ejpam-2434	206	15	i	i	PRON
ejpam-2434	206	16	(	(	PUNCT
ejpam-2434	206	17	x	x	NOUN
ejpam-2434	206	18	)	)	PUNCT
ejpam-2434	206	19	.	.	PUNCT
ejpam-2434	207	1	(	(	PUNCT
ejpam-2434	207	2	22	22	NUM
ejpam-2434	207	3	)	)	PUNCT
ejpam-2434	207	4	to	to	PART
ejpam-2434	207	5	find	find	VERB
ejpam-2434	207	6	the	the	DET
ejpam-2434	207	7	explicit	explicit	ADJ
ejpam-2434	207	8	closed	closed	ADJ
ejpam-2434	207	9	form	form	NOUN
ejpam-2434	207	10	of	of	ADP
ejpam-2434	207	11	n	n	PRON
ejpam-2434	207	12	n−1	n−1	PROPN
ejpam-2434	207	13	r	r	NOUN
ejpam-2434	207	14	,	,	PUNCT
ejpam-2434	207	15	i	i	PRON
ejpam-2434	207	16	,	,	PUNCT
ejpam-2434	207	17	i	i	PRON
ejpam-2434	207	18	,	,	PUNCT
ejpam-2434	207	19	r	r	NOUN
ejpam-2434	207	20	=	=	SYM
ejpam-2434	207	21	0,1	0,1	NUM
ejpam-2434	207	22	,	,	PUNCT
ejpam-2434	207	23	.	.	PUNCT
ejpam-2434	207	24	.	.	PUNCT
ejpam-2434	208	1	.	.	PUNCT
ejpam-2434	209	1	,	,	PUNCT
ejpam-2434	209	2	n	n	CCONJ
ejpam-2434	209	3	,	,	PUNCT
ejpam-2434	209	4	multiply	multiply	ADV
ejpam-2434	209	5	(	(	PUNCT
ejpam-2434	209	6	22	22	NUM
ejpam-2434	209	7	)	)	PUNCT
ejpam-2434	209	8	by	by	ADP
ejpam-2434	209	9	x	x	SYM
ejpam-2434	209	10	1	1	NUM
ejpam-2434	209	11	2	2	NUM
ejpam-2434	209	12	(	(	PUNCT
ejpam-2434	209	13	1−x	1−x	NUM
ejpam-2434	209	14	)	)	PUNCT
ejpam-2434	209	15	1	1	NUM
ejpam-2434	209	16	2	2	NUM
ejpam-2434	209	17	u	u	NOUN
ejpam-2434	209	18	(	(	PUNCT
ejpam-2434	209	19	m	m	PROPN
ejpam-2434	209	20	,	,	PUNCT
ejpam-2434	209	21	n	n	CCONJ
ejpam-2434	209	22	)	)	PUNCT
ejpam-2434	209	23	i	i	PRON
ejpam-2434	209	24	(	(	PUNCT
ejpam-2434	209	25	x	x	NOUN
ejpam-2434	209	26	)	)	PUNCT
ejpam-2434	209	27	and	and	CCONJ
ejpam-2434	209	28	integrate	integrate	VERB
ejpam-2434	209	29	over	over	ADP
ejpam-2434	209	30	[	[	X
ejpam-2434	209	31	0,1	0,1	NUM
ejpam-2434	209	32	]	]	PUNCT
ejpam-2434	209	33	to	to	PART
ejpam-2434	209	34	have	have	VERB
ejpam-2434	209	35	∫	∫	PROPN
ejpam-2434	210	1	1	1	NUM
ejpam-2434	210	2	0	0	NUM
ejpam-2434	210	3	x	x	SYM
ejpam-2434	210	4	1	1	NUM
ejpam-2434	210	5	2	2	NUM
ejpam-2434	210	6	(	(	PUNCT
ejpam-2434	210	7	1−	1−	NUM
ejpam-2434	210	8	x	x	NOUN
ejpam-2434	210	9	)	)	PUNCT
ejpam-2434	210	10	1	1	NUM
ejpam-2434	210	11	2	2	NUM
ejpam-2434	210	12	bn	bn	NOUN
ejpam-2434	210	13	r	r	NOUN
ejpam-2434	210	14	(	(	PUNCT
ejpam-2434	210	15	x)u	x)u	X
ejpam-2434	210	16	(	(	PUNCT
ejpam-2434	210	17	m	m	PROPN
ejpam-2434	210	18	,	,	PUNCT
ejpam-2434	210	19	n	n	CCONJ
ejpam-2434	210	20	)	)	PUNCT
ejpam-2434	210	21	i	i	PRON
ejpam-2434	210	22	(	(	PUNCT
ejpam-2434	210	23	x)d	x)d	PUNCT
ejpam-2434	210	24	x	x	SYM
ejpam-2434	210	25	=	=	SYM
ejpam-2434	210	26	n	n	PART
ejpam-2434	210	27	∑	∑	ADP
ejpam-2434	210	28	i=0	i=0	PROPN
ejpam-2434	210	29	n	n	CCONJ
ejpam-2434	210	30	n−1	n−1	PROPN
ejpam-2434	210	31	r	r	NOUN
ejpam-2434	210	32	,	,	PUNCT
ejpam-2434	210	33	i	i	PRON
ejpam-2434	210	34	∫	∫	VERB
ejpam-2434	210	35	1	1	NUM
ejpam-2434	210	36	0	0	NUM
ejpam-2434	210	37	x	x	SYM
ejpam-2434	210	38	1	1	NUM
ejpam-2434	210	39	2	2	NUM
ejpam-2434	210	40	(	(	PUNCT
ejpam-2434	210	41	1−	1−	NUM
ejpam-2434	210	42	x	x	NOUN
ejpam-2434	210	43	)	)	PUNCT
ejpam-2434	210	44	1	1	NUM
ejpam-2434	210	45	2	2	NUM
ejpam-2434	210	46	u	u	NOUN
ejpam-2434	210	47	(	(	PUNCT
ejpam-2434	210	48	m	m	PROPN
ejpam-2434	210	49	,	,	PUNCT
ejpam-2434	210	50	n	n	CCONJ
ejpam-2434	210	51	)	)	PUNCT
ejpam-2434	210	52	i	i	PRON
ejpam-2434	210	53	(	(	PUNCT
ejpam-2434	210	54	x)u	x)u	X
ejpam-2434	210	55	(	(	PUNCT
ejpam-2434	210	56	m	m	PROPN
ejpam-2434	210	57	,	,	PUNCT
ejpam-2434	210	58	n	n	CCONJ
ejpam-2434	210	59	)	)	PUNCT
ejpam-2434	210	60	i	i	PRON
ejpam-2434	210	61	(	(	PUNCT
ejpam-2434	210	62	x)d	x)d	PUNCT
ejpam-2434	210	63	x	x	X
ejpam-2434	210	64	.	.	PUNCT
ejpam-2434	211	1	(	(	PUNCT
ejpam-2434	211	2	23	23	X
ejpam-2434	211	3	)	)	PUNCT
ejpam-2434	211	4	use	use	VERB
ejpam-2434	211	5	the	the	DET
ejpam-2434	211	6	orthogonality	orthogonality	NOUN
ejpam-2434	211	7	relation	relation	NOUN
ejpam-2434	211	8	(	(	PUNCT
ejpam-2434	211	9	8)	8)	NUM
ejpam-2434	211	10	to	to	PART
ejpam-2434	211	11	obtain	obtain	VERB
ejpam-2434	211	12	∫	∫	PROPN
ejpam-2434	211	13	1	1	NUM
ejpam-2434	211	14	0	0	NUM
ejpam-2434	211	15	bn	bn	NOUN
ejpam-2434	211	16	r	r	NOUN
ejpam-2434	211	17	(	(	PUNCT
ejpam-2434	211	18	x)(1−	x)(1−	PROPN
ejpam-2434	211	19	x	x	SYM
ejpam-2434	211	20	)	)	PUNCT
ejpam-2434	211	21	1	1	NUM
ejpam-2434	211	22	2	2	NUM
ejpam-2434	211	23	x	x	SYM
ejpam-2434	211	24	1	1	NUM
ejpam-2434	211	25	2	2	NUM
ejpam-2434	211	26	u	u	NOUN
ejpam-2434	211	27	(	(	PUNCT
ejpam-2434	211	28	m	m	PROPN
ejpam-2434	211	29	,	,	PUNCT
ejpam-2434	211	30	n	n	CCONJ
ejpam-2434	211	31	)	)	PUNCT
ejpam-2434	211	32	i	i	PRON
ejpam-2434	211	33	(	(	PUNCT
ejpam-2434	211	34	x)d	x)d	PUNCT
ejpam-2434	211	35	x	x	X
ejpam-2434	211	36	=	=	SYM
ejpam-2434	211	37	π	π	SYM
ejpam-2434	211	38	8	8	NUM
ejpam-2434	211	39	�	�	PROPN
ejpam-2434	211	40	(	(	PUNCT
ejpam-2434	211	41	2i	2i	NOUN
ejpam-2434	211	42	+	+	CCONJ
ejpam-2434	211	43	1	1	NUM
ejpam-2434	211	44	)	)	PUNCT
ejpam-2434	211	45	!	!	PUNCT
ejpam-2434	211	46	!	!	PUNCT
ejpam-2434	212	1	2i(i	2i(i	NUM
ejpam-2434	213	1	+	+	CCONJ
ejpam-2434	214	1	1	1	NUM
ejpam-2434	214	2	)	)	PUNCT
ejpam-2434	214	3	!	!	PUNCT
ejpam-2434	215	1	�	�	PROPN
ejpam-2434	215	2	2	2	NUM
ejpam-2434	215	3	n	n	NUM
ejpam-2434	215	4	n−1	n−1	PROPN
ejpam-2434	215	5	r	r	NOUN
ejpam-2434	215	6	,	,	PUNCT
ejpam-2434	215	7	i	i	PRON
ejpam-2434	215	8	(	(	PUNCT
ejpam-2434	215	9	1+λi	1+λi	NUM
ejpam-2434	215	10	)	)	PUNCT
ejpam-2434	215	11	2	2	NUM
ejpam-2434	215	12	.	.	PUNCT
ejpam-2434	216	1	(	(	PUNCT
ejpam-2434	216	2	24	24	NUM
ejpam-2434	216	3	)	)	PUNCT
ejpam-2434	216	4	references	reference	NOUN
ejpam-2434	216	5	331	331	NUM
ejpam-2434	216	6	using	use	VERB
ejpam-2434	216	7	(	(	PUNCT
ejpam-2434	216	8	2	2	NUM
ejpam-2434	216	9	)	)	PUNCT
ejpam-2434	216	10	,	,	PUNCT
ejpam-2434	216	11	theorem	theorem	VERB
ejpam-2434	216	12	3	3	NUM
ejpam-2434	216	13	,	,	PUNCT
ejpam-2434	216	14	the	the	DET
ejpam-2434	216	15	fact	fact	NOUN
ejpam-2434	216	16	that	that	SCONJ
ejpam-2434	216	17	m	m	VERB
ejpam-2434	216	18	n	n	VERB
ejpam-2434	216	19	i	i	PRON
ejpam-2434	216	20	,	,	PUNCT
ejpam-2434	216	21	r	r	NOUN
ejpam-2434	216	22	=	=	SYM
ejpam-2434	216	23	n	n	CCONJ
ejpam-2434	216	24	n	n	NOUN
ejpam-2434	216	25	r	r	NOUN
ejpam-2434	216	26	,	,	PUNCT
ejpam-2434	216	27	i	i	PRON
ejpam-2434	216	28	,	,	PUNCT
ejpam-2434	216	29	and	and	CCONJ
ejpam-2434	216	30	λd	λd	X
ejpam-2434	216	31	r	r	NOUN
ejpam-2434	216	32	,	,	PUNCT
ejpam-2434	216	33	n	n	CCONJ
ejpam-2434	216	34	defined	define	VERB
ejpam-2434	216	35	in	in	ADP
ejpam-2434	216	36	(	(	PUNCT
ejpam-2434	216	37	21	21	NUM
ejpam-2434	216	38	)	)	PUNCT
ejpam-2434	216	39	we	we	PRON
ejpam-2434	216	40	get	get	VERB
ejpam-2434	216	41	m	m	VERB
ejpam-2434	216	42	n−1	n−1	PROPN
ejpam-2434	216	43	i	i	NOUN
ejpam-2434	216	44	,	,	PUNCT
ejpam-2434	217	1	r	r	NOUN
ejpam-2434	217	2	=	=	SYM
ejpam-2434	217	3	8	8	NUM
ejpam-2434	217	4	π(1+λi	π(1+λi	NUM
ejpam-2434	217	5	)	)	PUNCT
ejpam-2434	217	6	2	2	NUM
ejpam-2434	217	7	�	�	PROPN
ejpam-2434	217	8	2i(i	2i(i	NUM
ejpam-2434	217	9	+	+	CCONJ
ejpam-2434	217	10	1	1	NUM
ejpam-2434	217	11	)	)	PUNCT
ejpam-2434	217	12	!	!	PUNCT
ejpam-2434	218	1	(	(	PUNCT
ejpam-2434	218	2	2i	2i	NUM
ejpam-2434	218	3	+	+	CCONJ
ejpam-2434	218	4	1	1	NUM
ejpam-2434	218	5	)	)	PUNCT
ejpam-2434	218	6	!	!	PUNCT
ejpam-2434	218	7	!	!	PUNCT
ejpam-2434	219	1	�	�	PROPN
ejpam-2434	219	2	2	2	NUM
ejpam-2434	219	3	λi	λi	NOUN
ejpam-2434	219	4	r	r	NOUN
ejpam-2434	219	5	,	,	PUNCT
ejpam-2434	219	6	n	n	PROPN
ejpam-2434	219	7	+	+	CCONJ
ejpam-2434	220	1	i	i	PRON
ejpam-2434	220	2	∑	∑	PUNCT
ejpam-2434	220	3	d=0	d=0	PROPN
ejpam-2434	220	4	λdλ	λdλ	VERB
ejpam-2434	220	5	d	d	X
ejpam-2434	220	6	r	r	NOUN
ejpam-2434	220	7	,	,	PUNCT
ejpam-2434	220	8	n	n	NOUN
ejpam-2434	220	9	!	!	PUNCT
ejpam-2434	220	10	.	.	PUNCT
ejpam-2434	221	1	(	(	PUNCT
ejpam-2434	221	2	25	25	NUM
ejpam-2434	221	3	)	)	PUNCT
ejpam-2434	221	4	hence	hence	ADV
ejpam-2434	221	5	,	,	PUNCT
ejpam-2434	221	6	we	we	PRON
ejpam-2434	221	7	have	have	VERB
ejpam-2434	221	8	the	the	DET
ejpam-2434	221	9	following	follow	VERB
ejpam-2434	221	10	theorem	theorem	VERB
ejpam-2434	221	11	.	.	PUNCT
ejpam-2434	221	12	theorem	theorem	NOUN
ejpam-2434	221	13	4	4	NUM
ejpam-2434	221	14	.	.	PUNCT
ejpam-2434	222	1	the	the	DET
ejpam-2434	222	2	entries	entry	NOUN
ejpam-2434	222	3	of	of	ADP
ejpam-2434	222	4	the	the	DET
ejpam-2434	222	5	matrix	matrix	NOUN
ejpam-2434	222	6	of	of	ADP
ejpam-2434	222	7	transformation	transformation	NOUN
ejpam-2434	222	8	of	of	ADP
ejpam-2434	222	9	the	the	DET
ejpam-2434	222	10	bernstein	bernstein	PROPN
ejpam-2434	222	11	polynomial	polynomial	PROPN
ejpam-2434	222	12	basis	basis	NOUN
ejpam-2434	222	13	into	into	ADP
ejpam-2434	222	14	the	the	DET
ejpam-2434	222	15	generalized	generalize	VERB
ejpam-2434	222	16	tschebyscheff	tschebyscheff	PROPN
ejpam-2434	222	17	-	-	PUNCT
ejpam-2434	222	18	ii	ii	NOUN
ejpam-2434	222	19	polynomial	polynomial	ADJ
ejpam-2434	222	20	basis	basis	NOUN
ejpam-2434	222	21	of	of	ADP
ejpam-2434	222	22	degree	degree	NOUN
ejpam-2434	222	23	n	n	NOUN
ejpam-2434	222	24	are	be	AUX
ejpam-2434	222	25	given	give	VERB
ejpam-2434	222	26	by	by	ADP
ejpam-2434	222	27	m	m	PROPN
ejpam-2434	222	28	n−1	n−1	PROPN
ejpam-2434	222	29	i	i	PROPN
ejpam-2434	222	30	,	,	PUNCT
ejpam-2434	222	31	r	r	NOUN
ejpam-2434	222	32	=	=	SYM
ejpam-2434	222	33	8	8	NUM
ejpam-2434	222	34	π(1+λi	π(1+λi	NUM
ejpam-2434	222	35	)	)	PUNCT
ejpam-2434	222	36	2	2	NUM
ejpam-2434	222	37	�	�	PROPN
ejpam-2434	222	38	2i(i	2i(i	NUM
ejpam-2434	222	39	+	+	CCONJ
ejpam-2434	222	40	1	1	NUM
ejpam-2434	222	41	)	)	PUNCT
ejpam-2434	222	42	!	!	PUNCT
ejpam-2434	223	1	(	(	PUNCT
ejpam-2434	223	2	2i	2i	NUM
ejpam-2434	223	3	+	+	CCONJ
ejpam-2434	223	4	1	1	NUM
ejpam-2434	223	5	)	)	PUNCT
ejpam-2434	223	6	!	!	PUNCT
ejpam-2434	223	7	!	!	PUNCT
ejpam-2434	224	1	�	�	PROPN
ejpam-2434	224	2	2	2	NUM
ejpam-2434	224	3	λi	λi	NOUN
ejpam-2434	224	4	r	r	NOUN
ejpam-2434	224	5	,	,	PUNCT
ejpam-2434	224	6	n	n	PROPN
ejpam-2434	224	7	+	+	CCONJ
ejpam-2434	225	1	i	i	PRON
ejpam-2434	225	2	∑	∑	PUNCT
ejpam-2434	225	3	d=0	d=0	PROPN
ejpam-2434	225	4	λdλ	λdλ	VERB
ejpam-2434	225	5	d	d	X
ejpam-2434	225	6	r	r	NOUN
ejpam-2434	225	7	,	,	PUNCT
ejpam-2434	225	8	n	n	NOUN
ejpam-2434	225	9	!	!	PUNCT
ejpam-2434	225	10	,	,	PUNCT
ejpam-2434	226	1	i	i	PRON
ejpam-2434	226	2	,	,	PUNCT
ejpam-2434	226	3	r	r	NOUN
ejpam-2434	226	4	=	=	SYM
ejpam-2434	226	5	0,1	0,1	NUM
ejpam-2434	226	6	,	,	PUNCT
ejpam-2434	226	7	.	.	PUNCT
ejpam-2434	226	8	.	.	PUNCT
ejpam-2434	226	9	.	.	PUNCT
ejpam-2434	227	1	,	,	PUNCT
ejpam-2434	227	2	n.	n.	NOUN
ejpam-2434	227	3	acknowledgements	acknowledgement	VERB
ejpam-2434	227	4	the	the	DET
ejpam-2434	227	5	author	author	NOUN
ejpam-2434	227	6	thanks	thank	NOUN
ejpam-2434	227	7	the	the	DET
ejpam-2434	227	8	anonymous	anonymous	ADJ
ejpam-2434	227	9	referees	referee	NOUN
ejpam-2434	227	10	for	for	ADP
ejpam-2434	227	11	their	their	PRON
ejpam-2434	227	12	fruitful	fruitful	ADJ
ejpam-2434	227	13	suggestions	suggestion	NOUN
ejpam-2434	227	14	,	,	PUNCT
ejpam-2434	227	15	which	which	PRON
ejpam-2434	227	16	immensely	immensely	ADV
ejpam-2434	227	17	helped	help	VERB
ejpam-2434	227	18	to	to	PART
ejpam-2434	227	19	improve	improve	VERB
ejpam-2434	227	20	the	the	DET
ejpam-2434	227	21	presentation	presentation	NOUN
ejpam-2434	227	22	of	of	ADP
ejpam-2434	227	23	the	the	DET
ejpam-2434	227	24	paper	paper	NOUN
ejpam-2434	227	25	.	.	PUNCT
ejpam-2434	228	1	references	reference	NOUN
ejpam-2434	228	2	[	[	X
ejpam-2434	228	3	1	1	NUM
ejpam-2434	228	4	]	]	PUNCT
ejpam-2434	228	5	m.	m.	NOUN
ejpam-2434	228	6	alqudah	alqudah	PROPN
ejpam-2434	228	7	.	.	PUNCT
ejpam-2434	229	1	the	the	DET
ejpam-2434	229	2	generalized	generalize	VERB
ejpam-2434	229	3	tschebyscheff	tschebyscheff	NOUN
ejpam-2434	229	4	polynomials	polynomial	NOUN
ejpam-2434	229	5	of	of	ADP
ejpam-2434	229	6	the	the	DET
ejpam-2434	229	7	second	second	ADJ
ejpam-2434	229	8	kind	kind	NOUN
ejpam-2434	229	9	.	.	PUNCT
ejpam-2434	230	1	turkish	turkish	ADJ
ejpam-2434	230	2	journal	journal	NOUN
ejpam-2434	230	3	of	of	ADP
ejpam-2434	230	4	mathematics	mathematic	NOUN
ejpam-2434	230	5	,	,	PUNCT
ejpam-2434	230	6	39	39	NUM
ejpam-2434	230	7	.	.	PUNCT
ejpam-2434	231	1	http://dx.doi.org/10.3906/mat-1501-44	http://dx.doi.org/10.3906/mat-1501-44	PROPN
ejpam-2434	231	2	.	.	NOUN
ejpam-2434	231	3	2015	2015	NUM
ejpam-2434	231	4	.	.	PUNCT
ejpam-2434	232	1	[	[	X
ejpam-2434	232	2	2	2	NUM
ejpam-2434	232	3	]	]	PUNCT
ejpam-2434	232	4	r.	r.	PROPN
ejpam-2434	232	5	farouki	farouki	PROPN
ejpam-2434	232	6	.	.	PUNCT
ejpam-2434	233	1	the	the	DET
ejpam-2434	233	2	bernstein	bernstein	PROPN
ejpam-2434	233	3	polynomial	polynomial	PROPN
ejpam-2434	233	4	basis	basis	NOUN
ejpam-2434	233	5	:	:	PUNCT
ejpam-2434	233	6	a	a	DET
ejpam-2434	233	7	centennial	centennial	NOUN
ejpam-2434	233	8	retrospective	retrospective	NOUN
ejpam-2434	233	9	.	.	PUNCT
ejpam-2434	234	1	computer	computer	NOUN
ejpam-2434	234	2	aided	aid	VERB
ejpam-2434	234	3	geometric	geometric	ADJ
ejpam-2434	234	4	design	design	NOUN
ejpam-2434	234	5	,	,	PUNCT
ejpam-2434	234	6	29(6	29(6	NUM
ejpam-2434	234	7	)	)	PUNCT
ejpam-2434	234	8	,	,	PUNCT
ejpam-2434	234	9	379–419	379–419	NUM
ejpam-2434	234	10	.	.	PUNCT
ejpam-2434	234	11	2012	2012	NUM
ejpam-2434	234	12	.	.	PUNCT
ejpam-2434	235	1	[	[	X
ejpam-2434	235	2	3	3	NUM
ejpam-2434	235	3	]	]	X
ejpam-2434	235	4	r.	r.	PROPN
ejpam-2434	235	5	farouki	farouki	PROPN
ejpam-2434	235	6	and	and	CCONJ
ejpam-2434	235	7	v.	v.	ADP
ejpam-2434	235	8	rajan	rajan	PROPN
ejpam-2434	235	9	.	.	PROPN
ejpam-2434	235	10	algorithms	algorithm	NOUN
ejpam-2434	235	11	for	for	ADP
ejpam-2434	235	12	polynomials	polynomial	NOUN
ejpam-2434	235	13	in	in	ADP
ejpam-2434	235	14	bernstein	bernstein	PROPN
ejpam-2434	235	15	form	form	PROPN
ejpam-2434	235	16	.	.	PUNCT
ejpam-2434	236	1	computer	computer	NOUN
ejpam-2434	236	2	aided	aid	VERB
ejpam-2434	236	3	geometric	geometric	ADJ
ejpam-2434	236	4	design	design	NOUN
ejpam-2434	236	5	,	,	PUNCT
ejpam-2434	236	6	5(1	5(1	NUM
ejpam-2434	236	7	)	)	PUNCT
ejpam-2434	236	8	,	,	PUNCT
ejpam-2434	236	9	1–26	1–26	NOUN
ejpam-2434	236	10	.	.	PUNCT
ejpam-2434	237	1	1988	1988	NUM
ejpam-2434	237	2	.	.	PUNCT
ejpam-2434	238	1	[	[	X
ejpam-2434	238	2	4	4	X
ejpam-2434	238	3	]	]	X
ejpam-2434	238	4	i.	i.	NOUN
ejpam-2434	238	5	gradshtein	gradshtein	NOUN
ejpam-2434	238	6	and	and	CCONJ
ejpam-2434	238	7	i.	i.	PROPN
ejpam-2434	238	8	ryzhik	ryzhik	PROPN
ejpam-2434	238	9	.	.	PUNCT
ejpam-2434	239	1	tables	table	NOUN
ejpam-2434	239	2	of	of	ADP
ejpam-2434	239	3	integrals	integral	NOUN
ejpam-2434	239	4	,	,	PUNCT
ejpam-2434	239	5	series	series	NOUN
ejpam-2434	239	6	,	,	PUNCT
ejpam-2434	239	7	and	and	CCONJ
ejpam-2434	239	8	products	product	NOUN
ejpam-2434	239	9	.	.	PUNCT
ejpam-2434	240	1	academic	academic	ADJ
ejpam-2434	240	2	press	press	NOUN
ejpam-2434	240	3	,	,	PUNCT
ejpam-2434	240	4	new	new	PROPN
ejpam-2434	240	5	york	york	PROPN
ejpam-2434	240	6	.	.	PUNCT
ejpam-2434	241	1	1980	1980	NUM
ejpam-2434	241	2	.	.	PUNCT
ejpam-2434	242	1	[	[	X
ejpam-2434	242	2	5	5	X
ejpam-2434	242	3	]	]	PUNCT
ejpam-2434	242	4	t.	t.	NOUN
ejpam-2434	242	5	koornwinder	koornwinder	NOUN
ejpam-2434	242	6	.	.	PUNCT
ejpam-2434	243	1	orthogonal	orthogonal	ADJ
ejpam-2434	243	2	polynomials	polynomial	NOUN
ejpam-2434	243	3	with	with	ADP
ejpam-2434	243	4	weight	weight	NOUN
ejpam-2434	243	5	function	function	NOUN
ejpam-2434	243	6	(	(	PUNCT
ejpam-2434	243	7	1−	1−	NUM
ejpam-2434	243	8	x)α(1	x)α(1	PROPN
ejpam-2434	243	9	+	+	NOUN
ejpam-2434	243	10	x)β	x)β	NOUN
ejpam-2434	243	11	+	+	NOUN
ejpam-2434	243	12	mδ(x	mδ(x	NOUN
ejpam-2434	243	13	+	+	NOUN
ejpam-2434	243	14	1	1	NUM
ejpam-2434	243	15	)	)	PUNCT
ejpam-2434	243	16	+	+	CCONJ
ejpam-2434	243	17	nδ(x	nδ(x	ADV
ejpam-2434	243	18	−	−	PROPN
ejpam-2434	243	19	1	1	NUM
ejpam-2434	243	20	)	)	PUNCT
ejpam-2434	243	21	.	.	PUNCT
ejpam-2434	244	1	canadian	canadian	PROPN
ejpam-2434	244	2	mathematical	mathematical	ADJ
ejpam-2434	244	3	bulletin	bulletin	NOUN
ejpam-2434	244	4	,	,	PUNCT
ejpam-2434	244	5	27(2	27(2	NUM
ejpam-2434	244	6	)	)	PUNCT
ejpam-2434	244	7	,	,	PUNCT
ejpam-2434	244	8	205–214	205–214	NUM
ejpam-2434	244	9	.	.	PUNCT
ejpam-2434	244	10	1984	1984	NUM
ejpam-2434	244	11	.	.	PUNCT
ejpam-2434	245	1	[	[	X
ejpam-2434	245	2	6	6	NUM
ejpam-2434	245	3	]	]	PUNCT
ejpam-2434	245	4	a.	a.	NOUN
ejpam-2434	245	5	rababah	rababah	NOUN
ejpam-2434	245	6	.	.	PUNCT
ejpam-2434	246	1	transformation	transformation	NOUN
ejpam-2434	246	2	of	of	ADP
ejpam-2434	246	3	chebyshev	chebyshev	PROPN
ejpam-2434	246	4	bernstein	bernstein	PROPN
ejpam-2434	246	5	polynomial	polynomial	PROPN
ejpam-2434	246	6	basis	basis	NOUN
ejpam-2434	246	7	.	.	PUNCT
ejpam-2434	247	1	computational	computational	ADJ
ejpam-2434	247	2	methods	method	NOUN
ejpam-2434	247	3	in	in	ADP
ejpam-2434	247	4	applied	applied	ADJ
ejpam-2434	247	5	mathematics	mathematic	NOUN
ejpam-2434	247	6	,	,	PUNCT
ejpam-2434	247	7	3(4	3(4	NUM
ejpam-2434	247	8	)	)	PUNCT
ejpam-2434	247	9	,	,	PUNCT
ejpam-2434	247	10	608–622	608–622	NUM
ejpam-2434	247	11	.	.	PUNCT
ejpam-2434	247	12	2003	2003	NUM
ejpam-2434	247	13	.	.	PUNCT
ejpam-2434	248	1	[	[	X
ejpam-2434	248	2	7	7	X
ejpam-2434	248	3	]	]	PUNCT
ejpam-2434	248	4	j.	j.	PROPN
ejpam-2434	248	5	rice	rice	PROPN
ejpam-2434	248	6	.	.	PUNCT
ejpam-2434	249	1	the	the	DET
ejpam-2434	249	2	approximation	approximation	NOUN
ejpam-2434	249	3	of	of	ADP
ejpam-2434	249	4	functions	function	NOUN
ejpam-2434	249	5	,	,	PUNCT
ejpam-2434	249	6	linear	linear	PROPN
ejpam-2434	249	7	theory	theory	NOUN
ejpam-2434	249	8	.	.	PUNCT
ejpam-2434	250	1	vol	vol	NOUN
ejpam-2434	250	2	.	.	PROPN
ejpam-2434	251	1	1	1	NUM
ejpam-2434	251	2	.	.	X
ejpam-2434	251	3	addison	addison	PROPN
ejpam-2434	251	4	-	-	PUNCT
ejpam-2434	251	5	wesley	wesley	PROPN
ejpam-2434	251	6	,	,	PUNCT
ejpam-2434	251	7	reading	reading	NOUN
ejpam-2434	251	8	,	,	PUNCT
ejpam-2434	251	9	mass	mass	PROPN
ejpam-2434	251	10	.	.	PROPN
ejpam-2434	251	11	1964	1964	NUM
ejpam-2434	251	12	.	.	PUNCT
ejpam-2434	252	1	[	[	X
ejpam-2434	252	2	8	8	NUM
ejpam-2434	252	3	]	]	X
ejpam-2434	252	4	g.	g.	PROPN
ejpam-2434	252	5	szegö	szegö	PROPN
ejpam-2434	252	6	.	.	PUNCT
ejpam-2434	253	1	orthogonal	orthogonal	ADJ
ejpam-2434	253	2	polynomials	polynomial	NOUN
ejpam-2434	253	3	.	.	PUNCT
ejpam-2434	254	1	american	american	PROPN
ejpam-2434	254	2	mathematical	mathematical	PROPN
ejpam-2434	254	3	society	society	NOUN
ejpam-2434	254	4	colloquium	colloquium	NOUN
ejpam-2434	254	5	vol	vol	NOUN
ejpam-2434	254	6	.	.	PROPN
ejpam-2434	255	1	23	23	NUM
ejpam-2434	255	2	,	,	PUNCT
ejpam-2434	256	1	4th	4th	ADJ
ejpam-2434	256	2	ed	ed	NOUN
ejpam-2434	256	3	.	.	PUNCT
ejpam-2434	256	4	providence	providence	NOUN
ejpam-2434	256	5	,	,	PUNCT
ejpam-2434	256	6	ri	ri	PROPN
ejpam-2434	256	7	:	:	PUNCT
ejpam-2434	256	8	american	american	PROPN
ejpam-2434	256	9	mathematical	mathematical	PROPN
ejpam-2434	256	10	society	society	NOUN
ejpam-2434	256	11	.	.	PUNCT
ejpam-2434	257	1	1975	1975	NUM
ejpam-2434	257	2	.	.	PUNCT