id	sid	tid	token	lemma	pos
ap-928	1	1	ap07_2-3.vp	ap07_2-3.vp	VERB
ap-928	1	2	1	1	NUM
ap-928	1	3	qes	qes	NOUN
ap-928	1	4	sextic	sextic	PROPN
ap-928	1	5	ahos	ahos	NOUN
ap-928	1	6	our	our	PRON
ap-928	1	7	model	model	NOUN
ap-928	1	8	is	be	AUX
ap-928	1	9	a	a	DET
ap-928	1	10	1d	1d	NUM
ap-928	1	11	sextic	sextic	ADJ
ap-928	1	12	anharmonic	anharmonic	ADJ
ap-928	1	13	oscillator	oscillator	NOUN
ap-928	1	14	,	,	PUNCT
ap-928	1	15	which	which	PRON
ap-928	1	16	is	be	AUX
ap-928	1	17	frequently	frequently	ADV
ap-928	1	18	used	use	VERB
ap-928	1	19	to	to	PART
ap-928	1	20	approximate	approximate	VERB
ap-928	1	21	various	various	ADJ
ap-928	1	22	situations	situation	NOUN
ap-928	1	23	in	in	ADP
ap-928	1	24	quantum	quantum	ADJ
ap-928	1	25	mechanics	mechanic	NOUN
ap-928	1	26	.	.	PUNCT
ap-928	2	1	due	due	ADP
ap-928	2	2	to	to	ADP
ap-928	2	3	the	the	DET
ap-928	2	4	quasi	quasi	ADJ
ap-928	2	5	-	-	ADJ
ap-928	2	6	exact	exact	ADJ
ap-928	2	7	solvability	solvability	NOUN
ap-928	2	8	a	a	DET
ap-928	2	9	part	part	NOUN
ap-928	2	10	of	of	ADP
ap-928	2	11	the	the	DET
ap-928	2	12	spectrum	spectrum	NOUN
ap-928	2	13	is	be	AUX
ap-928	2	14	easily	easily	ADV
ap-928	2	15	tractable	tractable	ADJ
ap-928	2	16	and	and	CCONJ
ap-928	2	17	two	two	NUM
ap-928	2	18	parameters	parameter	NOUN
ap-928	2	19	of	of	ADP
ap-928	2	20	the	the	DET
ap-928	2	21	potential	potential	ADJ
ap-928	2	22	leave	leave	VERB
ap-928	2	23	enough	enough	ADJ
ap-928	2	24	space	space	NOUN
ap-928	2	25	for	for	ADP
ap-928	2	26	the	the	DET
ap-928	2	27	choice	choice	NOUN
ap-928	2	28	of	of	ADP
ap-928	2	29	application	application	NOUN
ap-928	2	30	.	.	PUNCT
ap-928	3	1	to	to	PART
ap-928	3	2	be	be	AUX
ap-928	3	3	more	more	ADV
ap-928	3	4	precise	precise	ADJ
ap-928	3	5	,	,	PUNCT
ap-928	3	6	we	we	PRON
ap-928	3	7	have	have	AUX
ap-928	3	8	been	be	AUX
ap-928	3	9	studying	study	VERB
ap-928	3	10	the	the	DET
ap-928	3	11	solutions	solution	NOUN
ap-928	3	12	of	of	ADP
ap-928	3	13	the	the	DET
ap-928	3	14	schrödinger	schrödinger	ADJ
ap-928	3	15	equation	equation	NOUN
ap-928	3	16	h	h	NOUN
ap-928	3	17	e	e	PROPN
ap-928	3	18	�	�	PROPN
ap-928	3	19	�	�	PROPN
ap-928	3	20	�	�	PROPN
ap-928	3	21	,	,	PUNCT
ap-928	3	22	where	where	SCONJ
ap-928	3	23	�	�	PROPN
ap-928	3	24	�	�	NOUN
ap-928	3	25	l2	l2	PROPN
ap-928	3	26	(	(	PUNCT
ap-928	3	27	)	)	PUNCT
ap-928	3	28	�	�	PROPN
ap-928	3	29	and	and	CCONJ
ap-928	3	30	h	h	NOUN
ap-928	3	31	x	x	NOUN
ap-928	4	1	x	x	PUNCT
ap-928	4	2	bx	bx	PROPN
ap-928	4	3	b	b	PROPN
ap-928	4	4	j	j	PROPN
ap-928	4	5	x	x	SYM
ap-928	4	6	�	�	PROPN
ap-928	4	7	�	�	PROPN
ap-928	4	8	�	�	PROPN
ap-928	4	9	�	�	PROPN
ap-928	4	10	�	�	PROPN
ap-928	4	11	�	�	PROPN
ap-928	4	12	�	�	PROPN
ap-928	4	13	�	�	PROPN
ap-928	4	14	�	�	PROPN
ap-928	4	15	�	�	PROPN
ap-928	4	16	�	�	PROPN
ap-928	4	17	�	�	PROPN
ap-928	4	18	�	�	PROPN
ap-928	4	19	d	d	PROPN
ap-928	4	20	d	d	PROPN
ap-928	4	21	2	2	NUM
ap-928	4	22	2	2	NUM
ap-928	4	23	6	6	NUM
ap-928	4	24	4	4	NUM
ap-928	4	25	2	2	NUM
ap-928	4	26	2	2	NUM
ap-928	4	27	4	4	NUM
ap-928	4	28	4	4	NUM
ap-928	4	29	3	3	NUM
ap-928	4	30	(	(	PUNCT
ap-928	4	31	)	)	PUNCT
ap-928	4	32	where	where	SCONJ
ap-928	4	33	j	j	PROPN
ap-928	4	34	is	be	AUX
ap-928	4	35	a	a	DET
ap-928	4	36	non	non	ADJ
ap-928	4	37	-	-	ADJ
ap-928	4	38	negative	negative	ADJ
ap-928	4	39	integer	integer	NOUN
ap-928	4	40	.	.	PUNCT
ap-928	5	1	during	during	ADP
ap-928	5	2	the	the	DET
ap-928	5	3	last	last	ADJ
ap-928	5	4	decade	decade	NOUN
ap-928	5	5	there	there	PRON
ap-928	5	6	has	have	AUX
ap-928	5	7	been	be	AUX
ap-928	5	8	considerable	considerable	ADJ
ap-928	5	9	interest	interest	NOUN
ap-928	5	10	in	in	ADP
ap-928	5	11	non	non	ADJ
ap-928	5	12	-	-	ADJ
ap-928	5	13	selfadjoint	selfadjoint	ADJ
ap-928	5	14	problems	problem	NOUN
ap-928	5	15	,	,	PUNCT
ap-928	5	16	e.g.	e.g.	ADV
ap-928	5	17	[	[	X
ap-928	5	18	1	1	NUM
ap-928	5	19	]	]	PUNCT
ap-928	5	20	,	,	PUNCT
ap-928	5	21	[	[	X
ap-928	5	22	2	2	NUM
ap-928	5	23	]	]	PUNCT
ap-928	5	24	.	.	PUNCT
ap-928	6	1	we	we	PRON
ap-928	6	2	recognize	recognize	VERB
ap-928	6	3	that	that	SCONJ
ap-928	6	4	b	b	PROPN
ap-928	6	5	�	�	PROPN
ap-928	6	6	�	�	PROPN
ap-928	6	7	is	be	AUX
ap-928	6	8	a	a	DET
ap-928	6	9	challenge	challenge	NOUN
ap-928	6	10	,	,	PUNCT
ap-928	6	11	but	but	CCONJ
ap-928	6	12	it	it	PRON
ap-928	6	13	goes	go	VERB
ap-928	6	14	beyond	beyond	ADP
ap-928	6	15	the	the	DET
ap-928	6	16	scope	scope	NOUN
ap-928	6	17	of	of	ADP
ap-928	6	18	this	this	DET
ap-928	6	19	paper	paper	NOUN
ap-928	6	20	,	,	PUNCT
ap-928	6	21	and	and	CCONJ
ap-928	6	22	we	we	PRON
ap-928	6	23	confine	confine	VERB
ap-928	6	24	ourselves	ourselves	PRON
ap-928	6	25	to	to	ADP
ap-928	6	26	b	b	PROPN
ap-928	6	27	�	�	PROPN
ap-928	6	28	�	�	PROPN
ap-928	6	29	.	.	PUNCT
ap-928	7	1	adopting	adopt	VERB
ap-928	7	2	the	the	DET
ap-928	7	3	idea	idea	NOUN
ap-928	7	4	of	of	ADP
ap-928	7	5	bender	bender	NOUN
ap-928	7	6	and	and	CCONJ
ap-928	7	7	dunne	dunne	PROPN
ap-928	7	8	[	[	X
ap-928	7	9	3	3	NUM
ap-928	7	10	]	]	PUNCT
ap-928	7	11	,	,	PUNCT
ap-928	7	12	we	we	PRON
ap-928	7	13	seek	seek	VERB
ap-928	7	14	the	the	DET
ap-928	7	15	solution	solution	NOUN
ap-928	7	16	�	�	PROPN
ap-928	7	17	of	of	ADP
ap-928	7	18	the	the	DET
ap-928	7	19	schrödinger	schrödinger	ADJ
ap-928	7	20	equation	equation	NOUN
ap-928	7	21	h	h	NOUN
ap-928	7	22	e	e	PROPN
ap-928	7	23	�	�	PROPN
ap-928	7	24	�	�	PROPN
ap-928	7	25	�	�	PROPN
ap-928	7	26	in	in	ADP
ap-928	7	27	the	the	DET
ap-928	7	28	form	form	NOUN
ap-928	7	29	�	�	PROPN
ap-928	7	30	(	(	PUNCT
ap-928	7	31	)	)	PUNCT
ap-928	7	32	(	(	PUNCT
ap-928	7	33	)	)	PUNCT
ap-928	7	34	!	!	PUNCT
ap-928	8	1	x	x	PUNCT
ap-928	8	2	e	e	X
ap-928	8	3	p	p	PROPN
ap-928	8	4	e	e	PROPN
ap-928	8	5	n	n	CCONJ
ap-928	8	6	n	n	NOUN
ap-928	8	7	x	x	NOUN
ap-928	8	8	x	x	SYM
ap-928	8	9	b	b	X
ap-928	8	10	x	x	SYM
ap-928	8	11	n	n	CCONJ
ap-928	8	12	n	n	CCONJ
ap-928	8	13	n	n	CCONJ
ap-928	8	14	n	n	CCONJ
ap-928	8	15	�	�	PROPN
ap-928	8	16	�	�	PROPN
ap-928	8	17	�	�	PROPN
ap-928	8	18	�	�	PROPN
ap-928	8	19	�	�	PROPN
ap-928	8	20	�	�	PROPN
ap-928	8	21	�	�	PROPN
ap-928	8	22	�	�	PROPN
ap-928	8	23	�	�	PROPN
ap-928	8	24	�	�	PROPN
ap-928	8	25	�	�	PROPN
ap-928	8	26	�	�	PROPN
ap-928	8	27	�	�	PROPN
ap-928	8	28	�	�	PROPN
ap-928	8	29	�	�	PROPN
ap-928	8	30	4	4	NUM
ap-928	8	31	2	2	NUM
ap-928	8	32	4	4	NUM
ap-928	8	33	4	4	NUM
ap-928	8	34	2	2	NUM
ap-928	8	35	0	0	NUM
ap-928	8	36	1	1	NUM
ap-928	8	37	4	4	NUM
ap-928	8	38	1	1	NUM
ap-928	8	39	2	2	NUM
ap-928	8	40	�	�	PROPN
ap-928	8	41	.	.	PUNCT
ap-928	9	1	we	we	PRON
ap-928	9	2	are	be	AUX
ap-928	9	3	interested	interested	ADJ
ap-928	9	4	in	in	ADP
ap-928	9	5	even	even	ADV
ap-928	9	6	solutions	solution	NOUN
ap-928	9	7	only	only	ADV
ap-928	9	8	,	,	PUNCT
ap-928	9	9	and	and	CCONJ
ap-928	9	10	the	the	DET
ap-928	9	11	odd	odd	ADJ
ap-928	9	12	ones	one	NOUN
ap-928	9	13	can	can	AUX
ap-928	9	14	be	be	AUX
ap-928	9	15	treated	treat	VERB
ap-928	9	16	by	by	ADP
ap-928	9	17	analogy	analogy	NOUN
ap-928	9	18	.	.	PUNCT
ap-928	10	1	for	for	SCONJ
ap-928	10	2	�	�	PROPN
ap-928	10	3	to	to	PART
ap-928	10	4	be	be	AUX
ap-928	10	5	a	a	DET
ap-928	10	6	solution	solution	NOUN
ap-928	10	7	,	,	PUNCT
ap-928	10	8	the	the	DET
ap-928	10	9	coefficients	coefficient	NOUN
ap-928	10	10	pn	pn	PROPN
ap-928	10	11	must	must	AUX
ap-928	10	12	fulfil	fulfil	VERB
ap-928	10	13	the	the	DET
ap-928	10	14	recurrence	recurrence	NOUN
ap-928	10	15	relation	relation	NOUN
ap-928	10	16	p	p	PROPN
ap-928	10	17	e	e	PROPN
ap-928	10	18	e	e	X
ap-928	10	19	n	n	PROPN
ap-928	10	20	b	b	PROPN
ap-928	10	21	p	p	X
ap-928	10	22	e	e	PROPN
ap-928	10	23	n	n	CCONJ
ap-928	10	24	n	n	PROPN
ap-928	10	25	j	j	PROPN
ap-928	10	26	n	n	CCONJ
ap-928	10	27	n	n	CCONJ
ap-928	10	28	n	n	CCONJ
ap-928	10	29	(	(	PUNCT
ap-928	10	30	)	)	PUNCT
ap-928	10	31	(	(	PUNCT
ap-928	10	32	)	)	PUNCT
ap-928	10	33	(	(	PUNCT
ap-928	10	34	)	)	PUNCT
ap-928	10	35	(	(	PUNCT
ap-928	10	36	)	)	PUNCT
ap-928	10	37	(	(	PUNCT
ap-928	10	38	)	)	PUNCT
ap-928	10	39	�	�	PROPN
ap-928	10	40	�	�	PROPN
ap-928	10	41	�	�	PROPN
ap-928	10	42	�	�	PROPN
ap-928	10	43	�	�	PROPN
ap-928	10	44	�	�	PROPN
ap-928	10	45	�	�	PROPN
ap-928	10	46	�	�	PROPN
ap-928	10	47	�	�	PROPN
ap-928	10	48	�	�	PROPN
ap-928	10	49	�	�	PROPN
ap-928	10	50	�	�	PROPN
ap-928	10	51	�	�	PROPN
ap-928	10	52	�	�	PROPN
ap-928	10	53	�	�	PROPN
ap-928	10	54	4	4	NUM
ap-928	10	55	3	3	NUM
ap-928	10	56	2	2	NUM
ap-928	10	57	16	16	NUM
ap-928	10	58	1	1	NUM
ap-928	10	59	2	2	NUM
ap-928	10	60	3	3	NUM
ap-928	10	61	2	2	NUM
ap-928	10	62	1	1	NUM
ap-928	10	63	�	�	PROPN
ap-928	10	64	�	�	PROPN
ap-928	10	65	�	�	PROPN
ap-928	10	66	p	p	PROPN
ap-928	10	67	en	en	PROPN
ap-928	10	68	2	2	NUM
ap-928	10	69	(	(	PUNCT
ap-928	10	70	)	)	PUNCT
ap-928	10	71	with	with	ADP
ap-928	10	72	the	the	DET
ap-928	10	73	initial	initial	ADJ
ap-928	10	74	conditions	condition	NOUN
ap-928	10	75	p	p	X
ap-928	10	76	e	e	PROPN
ap-928	10	77	�	�	PROPN
ap-928	10	78	�	�	PROPN
ap-928	10	79	1	1	NUM
ap-928	10	80	0	0	NUM
ap-928	10	81	(	(	PUNCT
ap-928	10	82	)	)	PUNCT
ap-928	10	83	and	and	CCONJ
ap-928	10	84	p	p	PRON
ap-928	10	85	e0	e0	PROPN
ap-928	10	86	1	1	NUM
ap-928	10	87	(	(	PUNCT
ap-928	10	88	)	)	PUNCT
ap-928	10	89	�	�	PROPN
ap-928	10	90	.	.	PUNCT
ap-928	11	1	we	we	PRON
ap-928	11	2	see	see	VERB
ap-928	11	3	that	that	SCONJ
ap-928	11	4	the	the	DET
ap-928	11	5	wave	wave	NOUN
ap-928	11	6	function	function	NOUN
ap-928	11	7	�	�	PROPN
ap-928	11	8	serves	serve	VERB
ap-928	11	9	as	as	ADP
ap-928	11	10	a	a	DET
ap-928	11	11	generating	generate	VERB
ap-928	11	12	function	function	NOUN
ap-928	11	13	for	for	ADP
ap-928	11	14	the	the	DET
ap-928	11	15	polynomials	polynomial	NOUN
ap-928	11	16	pn(e	pn(e	NOUN
ap-928	11	17	)	)	PUNCT
ap-928	11	18	.	.	PUNCT
ap-928	12	1	choosing	choose	VERB
ap-928	12	2	a	a	DET
ap-928	12	3	particular	particular	ADJ
ap-928	12	4	value	value	NOUN
ap-928	12	5	of	of	ADP
ap-928	12	6	j	j	PROPN
ap-928	12	7	we	we	PRON
ap-928	12	8	get	get	VERB
ap-928	12	9	the	the	DET
ap-928	12	10	particular	particular	ADJ
ap-928	12	11	solution	solution	NOUN
ap-928	12	12	of	of	ADP
ap-928	12	13	our	our	PRON
ap-928	12	14	problem	problem	NOUN
ap-928	12	15	,	,	PUNCT
ap-928	12	16	but	but	CCONJ
ap-928	12	17	for	for	ADP
ap-928	12	18	any	any	DET
ap-928	12	19	non	non	ADJ
ap-928	12	20	-	-	ADJ
ap-928	12	21	negative	negative	ADJ
ap-928	12	22	value	value	NOUN
ap-928	12	23	of	of	ADP
ap-928	12	24	j	j	PROPN
ap-928	12	25	the	the	DET
ap-928	12	26	infinite	infinite	ADJ
ap-928	12	27	system	system	NOUN
ap-928	12	28	of	of	ADP
ap-928	12	29	pn	pn	PROPN
ap-928	12	30	forms	form	VERB
ap-928	12	31	an	an	DET
ap-928	12	32	orthogonal	orthogonal	ADJ
ap-928	12	33	system	system	NOUN
ap-928	12	34	of	of	ADP
ap-928	12	35	monic	monic	ADJ
ap-928	12	36	polynomials	polynomial	NOUN
ap-928	12	37	with	with	ADP
ap-928	12	38	respect	respect	NOUN
ap-928	12	39	to	to	ADP
ap-928	12	40	a	a	DET
ap-928	12	41	probability	probability	NOUN
ap-928	12	42	measure	measure	NOUN
ap-928	12	43	(	(	PUNCT
ap-928	12	44	favard	favard	PROPN
ap-928	12	45	’s	’s	PART
ap-928	12	46	theorem	theorem	NOUN
ap-928	12	47	[	[	X
ap-928	12	48	4	4	NUM
ap-928	12	49	]	]	PUNCT
ap-928	12	50	,	,	PUNCT
ap-928	12	51	[	[	X
ap-928	12	52	5	5	NUM
ap-928	12	53	]	]	NUM
ap-928	12	54	)	)	PUNCT
ap-928	12	55	.	.	PUNCT
ap-928	13	1	the	the	DET
ap-928	13	2	peculiarity	peculiarity	NOUN
ap-928	13	3	is	be	AUX
ap-928	13	4	that	that	SCONJ
ap-928	13	5	the	the	DET
ap-928	13	6	polynomials	polynomial	NOUN
ap-928	13	7	of	of	ADP
ap-928	13	8	degree	degree	NOUN
ap-928	13	9	j	j	PROPN
ap-928	13	10	or	or	CCONJ
ap-928	13	11	higher	high	ADJ
ap-928	13	12	contain	contain	VERB
ap-928	13	13	a	a	DET
ap-928	13	14	common	common	ADJ
ap-928	13	15	factor	factor	NOUN
ap-928	13	16	pj	pj	PROPN
ap-928	13	17	�	�	PROPN
ap-928	13	18	1	1	NUM
ap-928	13	19	,	,	PUNCT
ap-928	13	20	i.e.	i.e.	X
ap-928	13	21	they	they	PRON
ap-928	13	22	can	can	AUX
ap-928	13	23	be	be	AUX
ap-928	13	24	factorized	factorize	VERB
ap-928	13	25	.	.	PUNCT
ap-928	14	1	the	the	DET
ap-928	14	2	roots	root	NOUN
ap-928	14	3	of	of	ADP
ap-928	14	4	the	the	DET
ap-928	14	5	pj	pj	PROPN
ap-928	14	6	polynomial	polynomial	PROPN
ap-928	14	7	are	be	AUX
ap-928	14	8	the	the	DET
ap-928	14	9	eigenvalues	eigenvalue	NOUN
ap-928	14	10	of	of	ADP
ap-928	14	11	the	the	DET
ap-928	14	12	schrödinger	schrödinger	ADJ
ap-928	14	13	equation	equation	NOUN
ap-928	14	14	.	.	PUNCT
ap-928	15	1	these	these	DET
ap-928	15	2	polynomials	polynomial	NOUN
ap-928	15	3	have	have	VERB
ap-928	15	4	other	other	ADJ
ap-928	15	5	interesting	interesting	ADJ
ap-928	15	6	properties	property	NOUN
ap-928	15	7	[	[	X
ap-928	15	8	3	3	NUM
ap-928	15	9	]	]	PUNCT
ap-928	15	10	,	,	PUNCT
ap-928	15	11	but	but	CCONJ
ap-928	15	12	we	we	PRON
ap-928	15	13	shall	shall	AUX
ap-928	15	14	not	not	PART
ap-928	15	15	use	use	VERB
ap-928	15	16	them	they	PRON
ap-928	15	17	.	.	PUNCT
ap-928	16	1	the	the	DET
ap-928	16	2	algebraic	algebraic	ADJ
ap-928	16	3	part	part	NOUN
ap-928	16	4	of	of	ADP
ap-928	16	5	the	the	DET
ap-928	16	6	spectrum	spectrum	NOUN
ap-928	16	7	,	,	PUNCT
ap-928	16	8	i.e.	i.e.	X
ap-928	16	9	the	the	DET
ap-928	16	10	quasi	quasi	ADJ
ap-928	16	11	-	-	ADJ
ap-928	16	12	exact	exact	ADJ
ap-928	16	13	energy	energy	NOUN
ap-928	16	14	eigenvalues	eigenvalue	NOUN
ap-928	16	15	,	,	PUNCT
ap-928	16	16	are	be	AUX
ap-928	16	17	solutions	solution	NOUN
ap-928	16	18	of	of	ADP
ap-928	16	19	p	p	PRON
ap-928	16	20	ej	ej	PROPN
ap-928	16	21	(	(	PUNCT
ap-928	16	22	)	)	PUNCT
ap-928	16	23	�	�	PROPN
ap-928	16	24	0	0	NUM
ap-928	16	25	and	and	CCONJ
ap-928	16	26	the	the	DET
ap-928	16	27	corresponding	corresponding	ADJ
ap-928	16	28	eigenfunctions	eigenfunction	NOUN
ap-928	16	29	are	be	AUX
ap-928	16	30	products	product	NOUN
ap-928	16	31	�	�	NOUN
ap-928	16	32	n	n	NOUN
ap-928	16	33	x	x	NOUN
ap-928	16	34	q	q	PUNCT
ap-928	16	35	x	x	X
ap-928	16	36	t	t	NOUN
ap-928	16	37	x	x	PROPN
ap-928	16	38	(	(	PUNCT
ap-928	16	39	)	)	PUNCT
ap-928	16	40	(	(	PUNCT
ap-928	16	41	)	)	PUNCT
ap-928	16	42	exp	exp	NOUN
ap-928	16	43	(	(	PUNCT
ap-928	16	44	(	(	PUNCT
ap-928	16	45	)	)	PUNCT
ap-928	16	46	)	)	PUNCT
ap-928	16	47	�	�	PROPN
ap-928	16	48	2	2	NUM
ap-928	16	49	2	2	NUM
ap-928	16	50	.	.	PUNCT
ap-928	17	1	we	we	PRON
ap-928	17	2	change	change	VERB
ap-928	17	3	the	the	DET
ap-928	17	4	variable	variable	NOUN
ap-928	17	5	x	x	SYM
ap-928	17	6	t2	t2	PROPN
ap-928	17	7	�	�	PROPN
ap-928	17	8	and	and	CCONJ
ap-928	17	9	reduce	reduce	VERB
ap-928	17	10	the	the	DET
ap-928	17	11	schrödinger	schrödinger	ADJ
ap-928	17	12	equation	equation	NOUN
ap-928	17	13	to	to	ADP
ap-928	17	14	4	4	NUM
ap-928	17	15	4	4	NUM
ap-928	17	16	2	2	NUM
ap-928	17	17	2	2	NUM
ap-928	17	18	4	4	NUM
ap-928	17	19	2	2	NUM
ap-928	17	20	0	0	NUM
ap-928	17	21	2	2	NUM
ap-928	17	22	2	2	NUM
ap-928	17	23	2	2	NUM
ap-928	17	24	t	t	NOUN
ap-928	17	25	f	f	PROPN
ap-928	17	26	t	t	PROPN
ap-928	17	27	t	t	PROPN
ap-928	17	28	bt	bt	PROPN
ap-928	17	29	f	f	PROPN
ap-928	17	30	t	t	PROPN
ap-928	17	31	jt	jt	PROPN
ap-928	17	32	e	e	PROPN
ap-928	17	33	b	b	PROPN
ap-928	17	34	f	f	X
ap-928	17	35	d	d	PROPN
ap-928	17	36	d	d	PROPN
ap-928	17	37	d	d	X
ap-928	17	38	d	d	X
ap-928	17	39	�	�	PROPN
ap-928	17	40	�	�	PROPN
ap-928	17	41	�	�	PROPN
ap-928	17	42	�	�	PROPN
ap-928	17	43	�	�	PROPN
ap-928	17	44	�	�	PROPN
ap-928	17	45	�	�	PROPN
ap-928	17	46	(	(	PUNCT
ap-928	17	47	)	)	PUNCT
ap-928	17	48	(	(	PUNCT
ap-928	17	49	)	)	PUNCT
ap-928	17	50	(	(	PUNCT
ap-928	17	51	1	1	X
ap-928	17	52	)	)	PUNCT
ap-928	17	53	we	we	PRON
ap-928	17	54	are	be	AUX
ap-928	17	55	thus	thus	ADV
ap-928	17	56	faced	face	VERB
ap-928	17	57	by	by	ADP
ap-928	17	58	a	a	DET
ap-928	17	59	linear	linear	ADJ
ap-928	17	60	differential	differential	NOUN
ap-928	17	61	operator	operator	NOUN
ap-928	17	62	and	and	CCONJ
ap-928	17	63	its	its	PRON
ap-928	17	64	polynomial	polynomial	ADJ
ap-928	17	65	solutions	solution	NOUN
ap-928	17	66	.	.	PUNCT
ap-928	18	1	this	this	PRON
ap-928	18	2	is	be	AUX
ap-928	18	3	a	a	DET
ap-928	18	4	problem	problem	NOUN
ap-928	18	5	that	that	PRON
ap-928	18	6	has	have	AUX
ap-928	18	7	been	be	AUX
ap-928	18	8	studied	study	VERB
ap-928	18	9	by	by	ADP
ap-928	18	10	many	many	ADJ
ap-928	18	11	prominent	prominent	ADJ
ap-928	18	12	mathematicians	mathematician	NOUN
ap-928	18	13	since	since	SCONJ
ap-928	18	14	the	the	DET
ap-928	18	15	first	first	ADJ
ap-928	18	16	half	half	NOUN
ap-928	18	17	of	of	ADP
ap-928	18	18	the	the	DET
ap-928	18	19	19th	19th	ADJ
ap-928	18	20	century	century	NOUN
ap-928	18	21	,	,	PUNCT
ap-928	18	22	and	and	CCONJ
ap-928	18	23	many	many	ADJ
ap-928	18	24	nice	nice	ADJ
ap-928	18	25	results	result	NOUN
ap-928	18	26	have	have	AUX
ap-928	18	27	been	be	AUX
ap-928	18	28	achieved	achieve	VERB
ap-928	18	29	.	.	PUNCT
ap-928	19	1	2	2	NUM
ap-928	19	2	heine	heine	PROPN
ap-928	19	3	-	-	PUNCT
ap-928	19	4	stieltjes	stieltjes	PROPN
ap-928	19	5	spectral	spectral	ADJ
ap-928	19	6	problem	problem	NOUN
ap-928	19	7	generally	generally	ADV
ap-928	19	8	,	,	PUNCT
ap-928	19	9	a	a	DET
ap-928	19	10	linear	linear	ADJ
ap-928	19	11	differential	differential	NOUN
ap-928	19	12	operator	operator	NOUN
ap-928	19	13	�	�	PROPN
ap-928	19	14	(	(	PUNCT
ap-928	19	15	)	)	PUNCT
ap-928	19	16	(	(	PUNCT
ap-928	19	17	)	)	PUNCT
ap-928	19	18	z	z	NOUN
ap-928	19	19	q	q	PROPN
ap-928	20	1	z	z	NOUN
ap-928	20	2	z	z	NOUN
ap-928	21	1	i	i	PRON
ap-928	21	2	i	i	PRON
ap-928	22	1	i	i	PRON
ap-928	22	2	i	i	VERB
ap-928	22	3	k	k	PROPN
ap-928	22	4	�	�	PROPN
ap-928	22	5	�	�	PROPN
ap-928	22	6	d	d	ADP
ap-928	22	7	d1	d1	PROPN
ap-928	22	8	with	with	ADP
ap-928	22	9	poynomial	poynomial	ADJ
ap-928	22	10	coefficients	coefficient	NOUN
ap-928	22	11	is	be	AUX
ap-928	22	12	called	call	VERB
ap-928	22	13	a	a	DET
ap-928	22	14	(	(	PUNCT
ap-928	22	15	higher	high	ADJ
ap-928	22	16	)	)	PUNCT
ap-928	22	17	lamé	lamé	NOUN
ap-928	22	18	operator	operator	NOUN
ap-928	22	19	(	(	PUNCT
ap-928	22	20	e.g.	e.g.	ADV
ap-928	22	21	[	[	X
ap-928	22	22	6	6	NUM
ap-928	22	23	]	]	NUM
ap-928	22	24	)	)	PUNCT
ap-928	22	25	.	.	PUNCT
ap-928	23	1	an	an	DET
ap-928	23	2	important	important	ADJ
ap-928	23	3	number	number	NOUN
ap-928	23	4	r	r	NOUN
ap-928	23	5	q	q	NOUN
ap-928	23	6	z	z	PROPN
ap-928	23	7	ii	ii	NOUN
ap-928	23	8	k	k	PROPN
ap-928	23	9	i	i	PRON
ap-928	23	10	�	�	PROPN
ap-928	23	11	�	�	PROPN
ap-928	23	12	�	�	PROPN
ap-928	23	13	max	max	PROPN
ap-928	23	14	(	(	PUNCT
ap-928	23	15	deg	deg	PROPN
ap-928	23	16	(	(	PUNCT
ap-928	23	17	)	)	PUNCT
ap-928	23	18	)	)	PUNCT
ap-928	23	19	,	,	PUNCT
ap-928	23	20	,	,	PUNCT
ap-928	23	21	1	1	NUM
ap-928	23	22	�	�	PROPN
ap-928	23	23	is	be	AUX
ap-928	23	24	called	call	VERB
ap-928	23	25	the	the	DET
ap-928	23	26	fuchs	fuchs	ADJ
ap-928	23	27	index	index	NOUN
ap-928	23	28	of	of	ADP
ap-928	23	29	�	�	PROPN
ap-928	23	30	(	(	PUNCT
ap-928	23	31	)	)	PUNCT
ap-928	23	32	z	z	NOUN
ap-928	23	33	.	.	PUNCT
ap-928	24	1	the	the	DET
ap-928	24	2	case	case	NOUN
ap-928	24	3	r	r	NOUN
ap-928	24	4	�	�	PROPN
ap-928	24	5	0	0	NUM
ap-928	24	6	is	be	AUX
ap-928	24	7	called	call	VERB
ap-928	24	8	exactly	exactly	ADV
ap-928	24	9	solvable	solvable	ADJ
ap-928	24	10	,	,	PUNCT
ap-928	24	11	and	and	CCONJ
ap-928	24	12	it	it	PRON
ap-928	24	13	has	have	AUX
ap-928	24	14	been	be	AUX
ap-928	24	15	well	well	ADV
ap-928	24	16	studied	study	VERB
ap-928	24	17	.	.	PUNCT
ap-928	25	1	these	these	DET
ap-928	25	2	operators	operator	NOUN
ap-928	25	3	and	and	CCONJ
ap-928	25	4	their	their	PRON
ap-928	25	5	polynomial	polynomial	ADJ
ap-928	25	6	eigensolutions	eigensolution	NOUN
ap-928	25	7	have	have	VERB
ap-928	25	8	many	many	ADJ
ap-928	25	9	interesting	interesting	ADJ
ap-928	25	10	properties	property	NOUN
ap-928	25	11	.	.	PUNCT
ap-928	26	1	the	the	DET
ap-928	26	2	operator	operator	NOUN
ap-928	26	3	�	�	PROPN
ap-928	26	4	(	(	PUNCT
ap-928	26	5	)	)	PUNCT
ap-928	26	6	z	z	PROPN
ap-928	26	7	is	be	AUX
ap-928	26	8	called	call	VERB
ap-928	26	9	non	non	ADJ
ap-928	26	10	-	-	ADJ
ap-928	26	11	degenerate	degenerate	ADJ
ap-928	26	12	if	if	SCONJ
ap-928	26	13	deg	deg	PROPN
ap-928	26	14	(	(	PUNCT
ap-928	26	15	)	)	PUNCT
ap-928	26	16	q	q	PROPN
ap-928	26	17	z	z	NOUN
ap-928	26	18	k	k	X
ap-928	26	19	rk	rk	PROPN
ap-928	26	20	�	�	PROPN
ap-928	26	21	�	�	PROPN
ap-928	26	22	.	.	PUNCT
ap-928	27	1	the	the	DET
ap-928	27	2	multiparameter	multiparameter	NOUN
ap-928	27	3	spectral	spectral	PROPN
ap-928	27	4	problem	problem	PROPN
ap-928	27	5	�	�	PROPN
ap-928	27	6	(	(	PUNCT
ap-928	27	7	)	)	PUNCT
ap-928	27	8	(	(	PUNCT
ap-928	27	9	)	)	PUNCT
ap-928	27	10	(	(	PUNCT
ap-928	27	11	)	)	PUNCT
ap-928	27	12	(	(	PUNCT
ap-928	27	13	)	)	PUNCT
ap-928	27	14	z	z	NOUN
ap-928	27	15	s	s	NOUN
ap-928	27	16	z	z	NOUN
ap-928	27	17	v	v	PROPN
ap-928	27	18	z	z	PROPN
ap-928	27	19	s	s	PART
ap-928	27	20	z	z	PROPN
ap-928	27	21	�	�	PROPN
ap-928	27	22	�	�	PROPN
ap-928	27	23	0	0	NUM
ap-928	27	24	,	,	PUNCT
ap-928	27	25	where	where	SCONJ
ap-928	27	26	a	a	DET
ap-928	27	27	polynomial	polynomial	ADJ
ap-928	27	28	v(z	v(z	NOUN
ap-928	27	29	)	)	PUNCT
ap-928	27	30	of	of	ADP
ap-928	27	31	degree	degree	NOUN
ap-928	27	32	at	at	ADP
ap-928	27	33	most	most	ADJ
ap-928	27	34	r	r	NOUN
ap-928	27	35	is	be	AUX
ap-928	27	36	sought	seek	VERB
ap-928	27	37	so	so	SCONJ
ap-928	27	38	that	that	SCONJ
ap-928	27	39	the	the	DET
ap-928	27	40	above	above	ADJ
ap-928	27	41	equation	equation	NOUN
ap-928	27	42	will	will	AUX
ap-928	27	43	have	have	VERB
ap-928	27	44	a	a	DET
ap-928	27	45	polynomial	polynomial	ADJ
ap-928	27	46	solution	solution	NOUN
ap-928	27	47	s(z	s(z	PROPN
ap-928	27	48	)	)	PUNCT
ap-928	27	49	of	of	ADP
ap-928	27	50	degree	degree	NOUN
ap-928	27	51	n.	n.	NOUN
ap-928	27	52	this	this	PRON
ap-928	27	53	is	be	AUX
ap-928	27	54	called	call	VERB
ap-928	27	55	the	the	DET
ap-928	27	56	(	(	PUNCT
ap-928	27	57	higher	high	ADJ
ap-928	27	58	)	)	PUNCT
ap-928	27	59	heine	heine	PROPN
ap-928	27	60	-	-	PUNCT
ap-928	27	61	stieltjes	stieltjes	PROPN
ap-928	27	62	spectral	spectral	ADJ
ap-928	27	63	problem	problem	NOUN
ap-928	27	64	,	,	PUNCT
ap-928	27	65	v(z	v(z	NOUN
ap-928	27	66	)	)	PUNCT
ap-928	27	67	a	a	DET
ap-928	27	68	(	(	PUNCT
ap-928	27	69	higher	high	ADJ
ap-928	27	70	)	)	PUNCT
ap-928	27	71	van	van	PROPN
ap-928	27	72	vleck	vleck	NOUN
ap-928	27	73	polynomial	polynomial	ADJ
ap-928	27	74	,	,	PUNCT
ap-928	27	75	and	and	CCONJ
ap-928	27	76	s(z	s(z	PROPN
ap-928	27	77	)	)	PUNCT
ap-928	27	78	a	a	DET
ap-928	27	79	(	(	PUNCT
ap-928	27	80	higher	high	ADJ
ap-928	27	81	)	)	PUNCT
ap-928	27	82	stieltjes	stieltjes	NOUN
ap-928	27	83	polynomial	polynomial	ADJ
ap-928	27	84	.	.	PUNCT
ap-928	28	1	2.1	2.1	NUM
ap-928	28	2	non	non	ADJ
ap-928	28	3	-	-	ADJ
ap-928	28	4	degenerate	degenerate	ADJ
ap-928	28	5	cases	case	NOUN
ap-928	28	6	two	two	NUM
ap-928	28	7	important	important	ADJ
ap-928	28	8	results	result	NOUN
ap-928	28	9	are	be	AUX
ap-928	28	10	worth	worth	ADJ
ap-928	28	11	mentioning	mention	VERB
ap-928	28	12	at	at	ADP
ap-928	28	13	this	this	DET
ap-928	28	14	point	point	NOUN
ap-928	28	15	.	.	PUNCT
ap-928	29	1	first	first	ADV
ap-928	29	2	,	,	PUNCT
ap-928	29	3	a	a	DET
ap-928	29	4	generalization	generalization	NOUN
ap-928	29	5	of	of	ADP
ap-928	29	6	the	the	DET
ap-928	29	7	result	result	NOUN
ap-928	29	8	by	by	ADP
ap-928	29	9	heine	heine	PROPN
ap-928	29	10	(	(	PUNCT
ap-928	29	11	cf	cf	X
ap-928	29	12	[	[	X
ap-928	29	13	6	6	NUM
ap-928	29	14	]	]	PUNCT
ap-928	29	15	)	)	PUNCT
ap-928	29	16	.	.	PUNCT
ap-928	30	1	32	32	NUM
ap-928	31	1	©	©	PROPN
ap-928	31	2	czech	czech	PROPN
ap-928	31	3	technical	technical	PROPN
ap-928	31	4	university	university	PROPN
ap-928	31	5	publishing	publishing	NOUN
ap-928	31	6	house	house	NOUN
ap-928	31	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-928	31	8	acta	acta	PROPN
ap-928	31	9	polytechnica	polytechnica	PROPN
ap-928	31	10	vol	vol	NOUN
ap-928	31	11	.	.	PUNCT
ap-928	32	1	47	47	NUM
ap-928	32	2	no	no	NOUN
ap-928	32	3	.	.	PUNCT
ap-928	33	1	2–3/2007	2–3/2007	NUM
ap-928	33	2	root	root	NOUN
ap-928	33	3	asymptotics	asymptotic	NOUN
ap-928	33	4	of	of	ADP
ap-928	33	5	spectral	spectral	ADJ
ap-928	33	6	polynomials	polynomial	NOUN
ap-928	33	7	b.	b.	PROPN
ap-928	33	8	shapiro	shapiro	PROPN
ap-928	33	9	,	,	PUNCT
ap-928	33	10	m.	m.	NOUN
ap-928	33	11	tater	tater	NOUN
ap-928	33	12	we	we	PRON
ap-928	33	13	have	have	AUX
ap-928	33	14	been	be	AUX
ap-928	33	15	studying	study	VERB
ap-928	33	16	the	the	DET
ap-928	33	17	asymptotic	asymptotic	ADJ
ap-928	33	18	energy	energy	NOUN
ap-928	33	19	distribution	distribution	NOUN
ap-928	33	20	of	of	ADP
ap-928	33	21	the	the	DET
ap-928	33	22	algebraic	algebraic	ADJ
ap-928	33	23	part	part	NOUN
ap-928	33	24	of	of	ADP
ap-928	33	25	the	the	DET
ap-928	33	26	spectrum	spectrum	NOUN
ap-928	33	27	of	of	ADP
ap-928	33	28	the	the	DET
ap-928	33	29	one	one	NUM
ap-928	33	30	-	-	PUNCT
ap-928	33	31	dimensional	dimensional	ADJ
ap-928	33	32	sextic	sextic	ADJ
ap-928	33	33	anharmonic	anharmonic	ADJ
ap-928	33	34	oscillator	oscillator	NOUN
ap-928	33	35	.	.	PUNCT
ap-928	34	1	we	we	PRON
ap-928	34	2	review	review	VERB
ap-928	34	3	some	some	PRON
ap-928	34	4	(	(	PUNCT
ap-928	34	5	both	both	CCONJ
ap-928	34	6	old	old	ADJ
ap-928	34	7	and	and	CCONJ
ap-928	34	8	recent	recent	ADJ
ap-928	34	9	)	)	PUNCT
ap-928	34	10	results	result	NOUN
ap-928	34	11	on	on	ADP
ap-928	34	12	the	the	DET
ap-928	34	13	multiparameter	multiparameter	NOUN
ap-928	34	14	spectral	spectral	ADJ
ap-928	34	15	problem	problem	NOUN
ap-928	34	16	and	and	CCONJ
ap-928	34	17	show	show	VERB
ap-928	34	18	that	that	SCONJ
ap-928	34	19	our	our	PRON
ap-928	34	20	problem	problem	NOUN
ap-928	34	21	ranks	rank	VERB
ap-928	34	22	among	among	ADP
ap-928	34	23	the	the	DET
ap-928	34	24	degenerate	degenerate	ADJ
ap-928	34	25	cases	case	NOUN
ap-928	34	26	of	of	ADP
ap-928	34	27	heine	heine	PROPN
ap-928	34	28	-	-	PUNCT
ap-928	34	29	stieltjes	stieltjes	PROPN
ap-928	34	30	spectral	spectral	ADJ
ap-928	34	31	problem	problem	NOUN
ap-928	34	32	,	,	PUNCT
ap-928	34	33	and	and	CCONJ
ap-928	34	34	we	we	PRON
ap-928	34	35	derive	derive	VERB
ap-928	34	36	the	the	DET
ap-928	34	37	density	density	NOUN
ap-928	34	38	of	of	ADP
ap-928	34	39	the	the	DET
ap-928	34	40	corresponding	corresponding	ADJ
ap-928	34	41	probability	probability	NOUN
ap-928	34	42	measure	measure	NOUN
ap-928	34	43	.	.	PUNCT
ap-928	35	1	keywords	keyword	NOUN
ap-928	35	2	:	:	PUNCT
ap-928	35	3	lamé	lamé	NOUN
ap-928	35	4	operator	operator	NOUN
ap-928	35	5	,	,	PUNCT
ap-928	35	6	van	van	PROPN
ap-928	35	7	vleck	vleck	NOUN
ap-928	35	8	polynomials	polynomial	NOUN
ap-928	35	9	,	,	PUNCT
ap-928	35	10	asymptotic	asymptotic	ADJ
ap-928	35	11	root	root	NOUN
ap-928	35	12	-	-	PUNCT
ap-928	35	13	counting	count	VERB
ap-928	35	14	measure	measure	NOUN
ap-928	35	15	.	.	PUNCT
ap-928	36	1	©	©	PROPN
ap-928	36	2	czech	czech	PROPN
ap-928	36	3	technical	technical	PROPN
ap-928	36	4	university	university	PROPN
ap-928	36	5	publishing	publishing	NOUN
ap-928	36	6	house	house	NOUN
ap-928	36	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-928	36	8	33	33	NUM
ap-928	36	9	acta	acta	PROPN
ap-928	36	10	polytechnica	polytechnica	PROPN
ap-928	36	11	vol	vol	NOUN
ap-928	36	12	.	.	PUNCT
ap-928	37	1	47	47	NUM
ap-928	37	2	no	no	NOUN
ap-928	37	3	.	.	PUNCT
ap-928	38	1	2–3/2007	2–3/2007	NUM
ap-928	38	2	theorem	theorem	NOUN
ap-928	38	3	for	for	ADP
ap-928	38	4	any	any	DET
ap-928	38	5	non	non	ADJ
ap-928	38	6	-	-	ADJ
ap-928	38	7	degenerate	degenerate	ADJ
ap-928	38	8	higher	high	ADJ
ap-928	38	9	lamé	lamé	NOUN
ap-928	38	10	operator	operator	NOUN
ap-928	38	11	�	�	PROPN
ap-928	38	12	(	(	PUNCT
ap-928	38	13	)	)	PUNCT
ap-928	38	14	z	z	NOUN
ap-928	38	15	with	with	ADP
ap-928	38	16	algebraically	algebraically	ADV
ap-928	38	17	independent	independent	ADJ
ap-928	38	18	coefficients	coefficient	NOUN
ap-928	38	19	of	of	ADP
ap-928	38	20	qi(z	qi(z	NOUN
ap-928	38	21	)	)	PUNCT
ap-928	38	22	,	,	PUNCT
ap-928	38	23	i	i	PRON
ap-928	38	24	k	k	PROPN
ap-928	38	25	�	�	PROPN
ap-928	38	26	1	1	NUM
ap-928	38	27	,	,	PUNCT
ap-928	38	28	,	,	PUNCT
ap-928	38	29	�	�	PROPN
ap-928	38	30	and	and	CCONJ
ap-928	38	31	for	for	ADP
ap-928	38	32	any	any	DET
ap-928	38	33	n	n	PRON
ap-928	38	34	�	�	NOUN
ap-928	38	35	1	1	NUM
ap-928	38	36	there	there	ADV
ap-928	38	37	exist	exist	VERB
ap-928	39	1	exactly	exactly	ADV
ap-928	39	2	n	n	ADP
ap-928	39	3	r	r	NOUN
ap-928	39	4	n	n	DET
ap-928	39	5	�	�	PROPN
ap-928	39	6	�	�	PROPN
ap-928	39	7	�	�	PROPN
ap-928	39	8	�	�	PROPN
ap-928	39	9	�	�	PROPN
ap-928	39	10	�	�	PROPN
ap-928	39	11	�	�	PROPN
ap-928	39	12	van	van	PROPN
ap-928	39	13	vleck	vleck	NOUN
ap-928	39	14	polynomials	polynomial	VERB
ap-928	39	15	v(z	v(z	NOUN
ap-928	39	16	)	)	PUNCT
ap-928	39	17	’s	’s	PART
ap-928	39	18	and	and	CCONJ
ap-928	39	19	corresponding	correspond	VERB
ap-928	39	20	degree	degree	NOUN
ap-928	39	21	n	n	PRON
ap-928	39	22	stieltjes	stieltjes	NOUN
ap-928	39	23	polynomials	polynomial	NOUN
ap-928	39	24	s(z	s(z	PROPN
ap-928	39	25	)	)	PUNCT
ap-928	39	26	’s	’s	PART
ap-928	39	27	.	.	PUNCT
ap-928	40	1	now	now	ADV
ap-928	40	2	,	,	PUNCT
ap-928	40	3	we	we	PRON
ap-928	40	4	mention	mention	VERB
ap-928	40	5	also	also	ADV
ap-928	40	6	a	a	DET
ap-928	40	7	physically	physically	ADV
ap-928	40	8	important	important	ADJ
ap-928	40	9	case	case	NOUN
ap-928	40	10	(	(	PUNCT
ap-928	40	11	)	)	PUNCT
ap-928	40	12	(	(	PUNCT
ap-928	40	13	)	)	PUNCT
ap-928	40	14	z	z	NOUN
ap-928	40	15	s	s	NOUN
ap-928	40	16	z	z	PROPN
ap-928	40	17	z	z	PROPN
ap-928	40	18	s	s	PROPN
ap-928	40	19	z	z	NOUN
ap-928	40	20	vsi	vsi	NOUN
ap-928	41	1	i	i	PRON
ap-928	41	2	l	l	PROPN
ap-928	42	1	j	j	NOUN
ap-928	43	1	i	i	PRON
ap-928	43	2	jj	jj	PROPN
ap-928	43	3	l	l	PROPN
ap-928	43	4	�	�	PROPN
ap-928	43	5	�	�	PROPN
ap-928	43	6	�	�	PROPN
ap-928	43	7	�	�	PROPN
ap-928	43	8	�	�	PROPN
ap-928	43	9	�	�	PROPN
ap-928	43	10	�	�	PROPN
ap-928	43	11	�	�	PROPN
ap-928	43	12	�	�	PROPN
ap-928	43	13	�	�	PROPN
ap-928	43	14	�	�	PROPN
ap-928	43	15	�	�	PROPN
ap-928	43	16	�	�	PROPN
ap-928	43	17	d	d	PROPN
ap-928	43	18	d	d	PROPN
ap-928	43	19	d	d	PROPN
ap-928	43	20	d	d	SYM
ap-928	43	21	2	2	NUM
ap-928	43	22	2	2	NUM
ap-928	43	23	1	1	NUM
ap-928	43	24	11	11	NUM
ap-928	43	25	0	0	NUM
ap-928	43	26	(	(	PUNCT
ap-928	43	27	2	2	NUM
ap-928	43	28	)	)	PUNCT
ap-928	43	29	with	with	ADP
ap-928	43	30	�	�	PROPN
ap-928	43	31	1<	1<	NUM
ap-928	43	32	�	�	PROPN
ap-928	43	33	2	2	NUM
ap-928	43	34	<	<	NOUN
ap-928	43	35	…	…	SYM
ap-928	43	36	�	�	SYM
ap-928	43	37	l	l	NOUN
ap-928	43	38	real	real	ADJ
ap-928	43	39	and	and	CCONJ
ap-928	43	40	�	�	PROPN
ap-928	43	41	1	1	NUM
ap-928	43	42	,	,	PUNCT
ap-928	43	43	…	…	PUNCT
ap-928	43	44	,	,	PUNCT
ap-928	43	45	�	�	PROPN
ap-928	43	46	l	l	NOUN
ap-928	43	47	positive	positive	ADJ
ap-928	43	48	.	.	PUNCT
ap-928	44	1	then	then	ADV
ap-928	44	2	the	the	DET
ap-928	44	3	following	follow	VERB
ap-928	44	4	theorem	theorem	ADJ
ap-928	44	5	holds	hold	NOUN
ap-928	44	6	.	.	PUNCT
ap-928	45	1	theorem	theorem	NOUN
ap-928	45	2	(	(	PUNCT
ap-928	45	3	stieltjes	stieltjes	NOUN
ap-928	45	4	,	,	PUNCT
ap-928	45	5	van	van	PROPN
ap-928	45	6	vleck	vleck	NOUN
ap-928	45	7	,	,	PUNCT
ap-928	45	8	bôcher	bôcher	NOUN
ap-928	45	9	,	,	PUNCT
ap-928	45	10	[	[	X
ap-928	45	11	6	6	NUM
ap-928	45	12	]	]	PUNCT
ap-928	45	13	)	)	PUNCT
ap-928	45	14	for	for	ADP
ap-928	45	15	any	any	DET
ap-928	45	16	integer	integer	NOUN
ap-928	45	17	n	n	PRON
ap-928	45	18	�	�	PROPN
ap-928	45	19	1	1	NUM
ap-928	45	20	1	1	NUM
ap-928	45	21	)	)	PUNCT
ap-928	45	22	there	there	PRON
ap-928	45	23	exist	exist	VERB
ap-928	45	24	exactly	exactly	ADV
ap-928	45	25	n	n	ADP
ap-928	45	26	l	l	NOUN
ap-928	45	27	n	n	X
ap-928	45	28	�	�	PROPN
ap-928	45	29	�	�	PROPN
ap-928	45	30	�	�	PROPN
ap-928	45	31	�	�	PROPN
ap-928	45	32	�	�	PROPN
ap-928	45	33	�	�	PROPN
ap-928	45	34	�	�	PROPN
ap-928	45	35	�	�	PROPN
ap-928	45	36	2	2	NUM
ap-928	45	37	polynomials	polynomial	NOUN
ap-928	45	38	v	v	ADP
ap-928	45	39	of	of	ADP
ap-928	45	40	degree	degree	NOUN
ap-928	45	41	l	l	X
ap-928	45	42	�	�	PROPN
ap-928	45	43	2	2	NUM
ap-928	45	44	such	such	ADJ
ap-928	45	45	that	that	DET
ap-928	45	46	equation	equation	NOUN
ap-928	45	47	(	(	PUNCT
ap-928	45	48	2	2	X
ap-928	45	49	)	)	PUNCT
ap-928	45	50	has	have	VERB
ap-928	45	51	a	a	DET
ap-928	45	52	polynomial	polynomial	ADJ
ap-928	45	53	solution	solution	NOUN
ap-928	45	54	s	s	NOUN
ap-928	45	55	of	of	ADP
ap-928	45	56	degree	degree	NOUN
ap-928	45	57	exactly	exactly	ADV
ap-928	45	58	n.	n.	NOUN
ap-928	45	59	2	2	NUM
ap-928	45	60	)	)	PUNCT
ap-928	45	61	each	each	DET
ap-928	45	62	root	root	NOUN
ap-928	45	63	of	of	ADP
ap-928	45	64	each	each	DET
ap-928	45	65	v	v	NOUN
ap-928	45	66	and	and	CCONJ
ap-928	45	67	s	s	NOUN
ap-928	45	68	is	be	AUX
ap-928	45	69	real	real	ADJ
ap-928	45	70	,	,	PUNCT
ap-928	45	71	simple	simple	ADJ
ap-928	45	72	,	,	PUNCT
ap-928	45	73	and	and	CCONJ
ap-928	45	74	belongs	belong	VERB
ap-928	45	75	to	to	ADP
ap-928	45	76	the	the	DET
ap-928	45	77	interval	interval	NOUN
ap-928	45	78	(	(	PUNCT
ap-928	45	79	�	�	PROPN
ap-928	45	80	1	1	NUM
ap-928	45	81	,	,	PUNCT
ap-928	45	82	�	�	NOUN
ap-928	45	83	l	l	NOUN
ap-928	45	84	)	)	PUNCT
ap-928	45	85	.	.	PUNCT
ap-928	46	1	3	3	X
ap-928	46	2	)	)	PUNCT
ap-928	46	3	none	none	NOUN
ap-928	46	4	of	of	ADP
ap-928	46	5	the	the	DET
ap-928	46	6	roots	root	NOUN
ap-928	46	7	of	of	ADP
ap-928	46	8	s	s	PRON
ap-928	46	9	can	can	AUX
ap-928	46	10	coincide	coincide	VERB
ap-928	46	11	with	with	ADP
ap-928	46	12	some	some	PRON
ap-928	46	13	of	of	ADP
ap-928	46	14	�	�	PROPN
ap-928	46	15	i	i	PRON
ap-928	46	16	’s	’s	NOUN
ap-928	46	17	.	.	PUNCT
ap-928	47	1	moreover	moreover	ADV
ap-928	47	2	,	,	PUNCT
ap-928	47	3	n	n	CCONJ
ap-928	47	4	l	l	NOUN
ap-928	47	5	n	n	CCONJ
ap-928	47	6	�	�	PROPN
ap-928	47	7	�	�	PROPN
ap-928	47	8	�	�	PROPN
ap-928	47	9	�	�	PROPN
ap-928	47	10	�	�	PROPN
ap-928	47	11	�	�	PROPN
ap-928	47	12	�	�	PROPN
ap-928	47	13	�	�	PROPN
ap-928	47	14	2	2	NUM
ap-928	47	15	polynomials	polynomial	NOUN
ap-928	47	16	are	be	AUX
ap-928	47	17	in	in	ADP
ap-928	47	18	one	one	NUM
ap-928	47	19	-	-	PUNCT
ap-928	47	20	to	to	ADP
ap-928	47	21	-	-	PUNCT
ap-928	47	22	one	one	NUM
ap-928	47	23	correspondence	correspondence	NOUN
ap-928	47	24	with	with	ADP
ap-928	47	25	n	n	ADP
ap-928	47	26	l	l	NOUN
ap-928	47	27	n	n	CCONJ
ap-928	47	28	�	�	PROPN
ap-928	47	29	�	�	PROPN
ap-928	47	30	�	�	PROPN
ap-928	47	31	�	�	PROPN
ap-928	47	32	�	�	PROPN
ap-928	47	33	�	�	PROPN
ap-928	47	34	�	�	PROPN
ap-928	47	35	�	�	PROPN
ap-928	47	36	2	2	NUM
ap-928	47	37	possible	possible	ADJ
ap-928	47	38	ways	way	NOUN
ap-928	47	39	to	to	PART
ap-928	47	40	distribute	distribute	VERB
ap-928	47	41	n	n	PRON
ap-928	47	42	points	point	NOUN
ap-928	47	43	into	into	ADP
ap-928	47	44	l	l	PROPN
ap-928	47	45	�	�	PROPN
ap-928	47	46	1	1	NUM
ap-928	47	47	open	open	ADJ
ap-928	47	48	intervals	interval	NOUN
ap-928	47	49	(	(	PUNCT
ap-928	47	50	,	,	PUNCT
ap-928	47	51	)	)	PUNCT
ap-928	47	52	�	�	PROPN
ap-928	47	53	�	�	PROPN
ap-928	47	54	1	1	NUM
ap-928	47	55	2	2	NUM
ap-928	47	56	,	,	PUNCT
ap-928	47	57	(	(	PUNCT
ap-928	47	58	,	,	PUNCT
ap-928	47	59	)	)	PUNCT
ap-928	47	60	�	�	PROPN
ap-928	47	61	�	�	PROPN
ap-928	47	62	2	2	NUM
ap-928	47	63	3	3	NUM
ap-928	47	64	,	,	PUNCT
ap-928	47	65	…	…	PUNCT
ap-928	47	66	,	,	PUNCT
ap-928	47	67	(	(	PUNCT
ap-928	47	68	,	,	PUNCT
ap-928	47	69	)	)	PUNCT
ap-928	47	70	�	�	PROPN
ap-928	47	71	�	�	PROPN
ap-928	47	72	l	l	PROPN
ap-928	47	73	l	l	X
ap-928	47	74	�	�	PROPN
ap-928	47	75	1	1	NUM
ap-928	47	76	.	.	PUNCT
ap-928	48	1	recently	recently	ADV
ap-928	48	2	,	,	PUNCT
ap-928	48	3	borcea	borcea	NOUN
ap-928	48	4	and	and	CCONJ
ap-928	48	5	shapiro	shapiro	PROPN
ap-928	49	1	[	[	X
ap-928	49	2	7	7	X
ap-928	49	3	]	]	PUNCT
ap-928	49	4	found	find	VERB
ap-928	49	5	the	the	DET
ap-928	49	6	density	density	NOUN
ap-928	49	7	of	of	ADP
ap-928	49	8	the	the	DET
ap-928	49	9	asymptotic	asymptotic	ADJ
ap-928	49	10	root	root	NOUN
ap-928	49	11	distribution	distribution	NOUN
ap-928	49	12	for	for	ADP
ap-928	49	13	the	the	DET
ap-928	49	14	stieltjes	stieltjes	NOUN
ap-928	49	15	polynomials	polynomial	NOUN
ap-928	49	16	.	.	PUNCT
ap-928	50	1	2.2	2.2	NUM
ap-928	50	2	the	the	DET
ap-928	50	3	degenerate	degenerate	ADJ
ap-928	50	4	case	case	NOUN
ap-928	50	5	inspecting	inspect	VERB
ap-928	50	6	the	the	DET
ap-928	50	7	structure	structure	NOUN
ap-928	50	8	of	of	ADP
ap-928	50	9	(	(	PUNCT
ap-928	50	10	1	1	X
ap-928	50	11	)	)	PUNCT
ap-928	50	12	we	we	PRON
ap-928	50	13	see	see	VERB
ap-928	50	14	that	that	SCONJ
ap-928	50	15	it	it	PRON
ap-928	50	16	is	be	AUX
ap-928	50	17	a	a	DET
ap-928	50	18	degenerate	degenerate	ADJ
ap-928	50	19	case	case	NOUN
ap-928	50	20	of	of	ADP
ap-928	50	21	the	the	DET
ap-928	50	22	r	r	NOUN
ap-928	50	23	�	�	PROPN
ap-928	50	24	1operator	1operator	NUM
ap-928	50	25	.	.	PUNCT
ap-928	51	1	the	the	DET
ap-928	51	2	roots	root	NOUN
ap-928	51	3	of	of	ADP
ap-928	51	4	van	van	PROPN
ap-928	51	5	vleck	vleck	PROPN
ap-928	51	6	polynomials	polynomial	NOUN
ap-928	51	7	are	be	AUX
ap-928	51	8	not	not	PART
ap-928	51	9	confined	confine	VERB
ap-928	51	10	to	to	ADP
ap-928	51	11	a	a	DET
ap-928	51	12	finite	finite	ADJ
ap-928	51	13	interval	interval	NOUN
ap-928	51	14	as	as	ADP
ap-928	51	15	n	n	PROPN
ap-928	51	16	�	�	PROPN
ap-928	51	17	�	�	PROPN
ap-928	51	18	.	.	PUNCT
ap-928	52	1	in	in	ADP
ap-928	52	2	order	order	NOUN
ap-928	52	3	to	to	PART
ap-928	52	4	find	find	VERB
ap-928	52	5	their	their	PRON
ap-928	52	6	limitng	limitng	ADJ
ap-928	52	7	distribution	distribution	NOUN
ap-928	52	8	we	we	PRON
ap-928	52	9	have	have	VERB
ap-928	52	10	to	to	PART
ap-928	52	11	scale	scale	VERB
ap-928	52	12	them	they	PRON
ap-928	52	13	.	.	PUNCT
ap-928	53	1	to	to	ADP
ap-928	53	2	this	this	DET
ap-928	53	3	end	end	NOUN
ap-928	53	4	we	we	PRON
ap-928	53	5	must	must	AUX
ap-928	53	6	know	know	VERB
ap-928	53	7	their	their	PRON
ap-928	53	8	rate	rate	NOUN
ap-928	53	9	of	of	ADP
ap-928	53	10	growth	growth	NOUN
ap-928	53	11	.	.	PUNCT
ap-928	54	1	thus	thus	ADV
ap-928	54	2	,	,	PUNCT
ap-928	54	3	we	we	PRON
ap-928	54	4	are	be	AUX
ap-928	54	5	interested	interested	ADJ
ap-928	54	6	in	in	ADP
ap-928	54	7	the	the	DET
ap-928	54	8	roots	root	NOUN
ap-928	54	9	of	of	ADP
ap-928	54	10	the	the	DET
ap-928	54	11	maximal	maximal	ADJ
ap-928	54	12	modulus	modulus	NOUN
ap-928	54	13	and	and	CCONJ
ap-928	54	14	their	their	PRON
ap-928	54	15	dependence	dependence	NOUN
ap-928	54	16	on	on	ADP
ap-928	54	17	parameter	parameter	PROPN
ap-928	54	18	b.	b.	PROPN
ap-928	54	19	to	to	PART
ap-928	54	20	find	find	VERB
ap-928	54	21	this	this	DET
ap-928	54	22	dependence	dependence	NOUN
ap-928	54	23	we	we	PRON
ap-928	54	24	follow	follow	VERB
ap-928	54	25	the	the	DET
ap-928	54	26	main	main	ADJ
ap-928	54	27	idea	idea	NOUN
ap-928	54	28	of	of	ADP
ap-928	54	29	the	the	DET
ap-928	54	30	gräffe	gräffe	NOUN
ap-928	54	31	-	-	PUNCT
ap-928	54	32	lobachevskii	lobachevskii	VERB
ap-928	54	33	method	method	NOUN
ap-928	54	34	.	.	PUNCT
ap-928	55	1	let	let	VERB
ap-928	55	2	p	p	NOUN
ap-928	55	3	e	e	X
ap-928	55	4	e	e	X
ap-928	55	5	p	p	PROPN
ap-928	55	6	en	en	X
ap-928	55	7	n	n	X
ap-928	55	8	l	l	NOUN
ap-928	55	9	l	l	NOUN
ap-928	55	10	l	l	NOUN
ap-928	55	11	n	n	X
ap-928	55	12	(	(	PUNCT
ap-928	55	13	)	)	PUNCT
ap-928	55	14	�	�	PROPN
ap-928	55	15	�	�	PROPN
ap-928	55	16	�	�	PROPN
ap-928	55	17	�	�	PROPN
ap-928	55	18	0	0	NUM
ap-928	55	19	1	1	NUM
ap-928	55	20	and	and	CCONJ
ap-928	55	21	we	we	PRON
ap-928	55	22	find	find	VERB
ap-928	55	23	expressions	expression	NOUN
ap-928	55	24	for	for	ADP
ap-928	55	25	the	the	DET
ap-928	55	26	sums	sum	NOUN
ap-928	55	27	of	of	ADP
ap-928	55	28	the	the	DET
ap-928	55	29	powers	power	NOUN
ap-928	55	30	of	of	ADP
ap-928	55	31	the	the	DET
ap-928	55	32	roots	root	NOUN
ap-928	55	33	s	s	PART
ap-928	55	34	e	e	NOUN
ap-928	55	35	ek	ek	PROPN
ap-928	55	36	k	k	PROPN
ap-928	55	37	n	n	CCONJ
ap-928	55	38	k	k	PROPN
ap-928	55	39	�	�	PROPN
ap-928	55	40	�	�	PROPN
ap-928	55	41	�	�	PROPN
ap-928	55	42	1	1	NUM
ap-928	55	43	�	�	PROPN
ap-928	55	44	.	.	PUNCT
ap-928	56	1	then	then	ADV
ap-928	56	2	for	for	ADP
ap-928	56	3	the	the	DET
ap-928	56	4	root	root	NOUN
ap-928	56	5	of	of	ADP
ap-928	56	6	the	the	DET
ap-928	56	7	maximal	maximal	ADJ
ap-928	56	8	modulus	modulus	NOUN
ap-928	56	9	emax	emax	NOUN
ap-928	56	10	holds	hold	VERB
ap-928	56	11	lim	lim	PROPN
ap-928	56	12	maxk	maxk	PROPN
ap-928	56	13	k	k	PROPN
ap-928	56	14	k	k	PROPN
ap-928	56	15	s	s	PROPN
ap-928	56	16	e	e	PROPN
ap-928	56	17	�	�	PROPN
ap-928	56	18	�	�	PROPN
ap-928	56	19	�	�	PROPN
ap-928	56	20	1	1	NUM
ap-928	56	21	.	.	PUNCT
ap-928	57	1	because	because	SCONJ
ap-928	57	2	sk	sk	NOUN
ap-928	57	3	are	be	AUX
ap-928	57	4	related	relate	VERB
ap-928	57	5	to	to	ADP
ap-928	57	6	pl	pl	VERB
ap-928	57	7	by	by	ADP
ap-928	57	8	s	s	PRON
ap-928	57	9	p	p	X
ap-928	57	10	s	s	PROPN
ap-928	57	11	k	k	X
ap-928	57	12	pk	pk	PROPN
ap-928	57	13	n	n	ADP
ap-928	57	14	l	l	NOUN
ap-928	57	15	k	k	X
ap-928	57	16	l	l	PROPN
ap-928	58	1	n	n	CCONJ
ap-928	58	2	k	k	NOUN
ap-928	58	3	l	l	PUNCT
ap-928	58	4	k	k	PROPN
ap-928	58	5	�	�	PROPN
ap-928	58	6	�	�	PROPN
ap-928	58	7	�	�	PROPN
ap-928	58	8	�	�	PROPN
ap-928	58	9	�	�	PROPN
ap-928	58	10	�	�	PROPN
ap-928	58	11	�	�	PROPN
ap-928	58	12	�	�	PROPN
ap-928	58	13	0	0	NUM
ap-928	58	14	1	1	NUM
ap-928	58	15	1	1	NUM
ap-928	58	16	we	we	PRON
ap-928	58	17	need	need	VERB
ap-928	58	18	explicit	explicit	ADJ
ap-928	58	19	expressions	expression	NOUN
ap-928	58	20	for	for	ADP
ap-928	58	21	pl	pl	NOUN
ap-928	58	22	up	up	ADP
ap-928	58	23	to	to	ADP
ap-928	58	24	l	l	PROPN
ap-928	58	25	n	n	CCONJ
ap-928	58	26	k	k	PROPN
ap-928	58	27	�	�	PROPN
ap-928	58	28	�	�	PROPN
ap-928	58	29	.	.	PUNCT
ap-928	59	1	these	these	DET
ap-928	59	2	formulae	formulae	NOUN
ap-928	59	3	can	can	AUX
ap-928	59	4	be	be	AUX
ap-928	59	5	derived	derive	VERB
ap-928	59	6	from	from	ADP
ap-928	59	7	the	the	DET
ap-928	59	8	recurrence	recurrence	NOUN
ap-928	59	9	relation	relation	NOUN
ap-928	59	10	.	.	PUNCT
ap-928	60	1	we	we	PRON
ap-928	60	2	arrive	arrive	VERB
ap-928	60	3	at	at	ADP
ap-928	60	4	s	s	PROPN
ap-928	60	5	c	c	NOUN
ap-928	60	6	k	k	PROPN
ap-928	60	7	b	b	PROPN
ap-928	60	8	n	n	CCONJ
ap-928	60	9	nk	nk	PROPN
ap-928	60	10	�	�	PROPN
ap-928	60	11	�	�	PROPN
ap-928	60	12	�	�	PROPN
ap-928	60	13	(	(	PUNCT
ap-928	60	14	)	)	PUNCT
ap-928	60	15	(	(	PUNCT
ap-928	60	16	)	)	PUNCT
ap-928	60	17	�	�	PROPN
ap-928	60	18	�	�	PROPN
ap-928	60	19	�	�	PROPN
ap-928	60	20	�	�	PROPN
ap-928	60	21	1	1	NUM
ap-928	60	22	where	where	SCONJ
ap-928	60	23	�	�	PROPN
ap-928	60	24	�	�	PROPN
ap-928	60	25	�	�	PROPN
ap-928	60	26	�	�	PROPN
ap-928	60	27	�	�	PROPN
ap-928	60	28	�	�	PROPN
ap-928	60	29	�	�	PROPN
ap-928	60	30	�	�	PROPN
ap-928	60	31	�	�	PROPN
ap-928	60	32	�	�	PROPN
ap-928	60	33	�	�	PROPN
ap-928	60	34	�	�	PROPN
ap-928	60	35	�	�	PROPN
ap-928	60	36	�	�	PROPN
ap-928	60	37	�	�	PROPN
ap-928	60	38	�	�	PROPN
ap-928	60	39	�	�	PROPN
ap-928	60	40	3	3	NUM
ap-928	60	41	2	2	NUM
ap-928	60	42	1	1	NUM
ap-928	60	43	2	2	NUM
ap-928	60	44	1	1	NUM
ap-928	60	45	3	3	NUM
ap-928	60	46	4	4	NUM
ap-928	60	47	0	0	NUM
ap-928	60	48	2	2	NUM
ap-928	60	49	2	2	NUM
ap-928	60	50	l	l	NOUN
ap-928	60	51	k	k	X
ap-928	60	52	l	l	PUNCT
ap-928	60	53	l	l	PUNCT
ap-928	60	54	k	k	PROPN
ap-928	60	55	l	l	PROPN
ap-928	60	56	&	&	CCONJ
ap-928	60	57	&	&	CCONJ
ap-928	60	58	if	if	SCONJ
ap-928	60	59	if	if	SCONJ
ap-928	60	60	and	and	CCONJ
ap-928	60	61	l	l	PROPN
ap-928	60	62	�	�	PROPN
ap-928	60	63	0	0	NUM
ap-928	60	64	1	1	NUM
ap-928	60	65	2	2	NUM
ap-928	60	66	,	,	PUNCT
ap-928	60	67	,	,	PUNCT
ap-928	60	68	,	,	PUNCT
ap-928	60	69	�	�	PROPN
ap-928	60	70	.	.	PUNCT
ap-928	61	1	thus	thus	ADV
ap-928	61	2	,	,	PUNCT
ap-928	61	3	lim	lim	PROPN
ap-928	61	4	lim	lim	PROPN
ap-928	61	5	(	(	PUNCT
ap-928	61	6	)	)	PUNCT
ap-928	61	7	lim	lim	PROPN
ap-928	61	8	(	(	PUNCT
ap-928	61	9	)	)	PUNCT
ap-928	62	1	k	k	PROPN
ap-928	62	2	kk	kk	X
ap-928	62	3	k	k	PROPN
ap-928	62	4	k	k	PROPN
ap-928	62	5	k	k	PROPN
ap-928	62	6	ks	ks	PROPN
ap-928	62	7	c	c	PROPN
ap-928	62	8	k	k	PROPN
ap-928	62	9	b	b	PROPN
ap-928	62	10	n	n	CCONJ
ap-928	62	11	n	n	PROPN
ap-928	62	12	c	c	NOUN
ap-928	62	13	kk	kk	PROPN
ap-928	62	14	k	k	PROPN
ap-928	62	15	�	�	PROPN
ap-928	62	16	�	�	PROPN
ap-928	62	17	�	�	PROPN
ap-928	62	18	�	�	PROPN
ap-928	62	19	�	�	PROPN
ap-928	62	20	�	�	PROPN
ap-928	62	21	�	�	PROPN
ap-928	62	22	�	�	PROPN
ap-928	62	23	�	�	PROPN
ap-928	62	24	�	�	PROPN
ap-928	62	25	3	3	NUM
ap-928	62	26	2	2	NUM
ap-928	62	27	i.e.	i.e.	X
ap-928	62	28	the	the	DET
ap-928	62	29	limit	limit	NOUN
ap-928	62	30	is	be	AUX
ap-928	62	31	independent	independent	ADJ
ap-928	62	32	of	of	ADP
ap-928	62	33	b.	b.	PROPN
ap-928	62	34	our	our	PRON
ap-928	62	35	conjecture	conjecture	NOUN
ap-928	62	36	is	be	AUX
ap-928	62	37	that	that	SCONJ
ap-928	62	38	lim	lim	PROPN
ap-928	62	39	(	(	PUNCT
ap-928	62	40	)	)	PUNCT
ap-928	63	1	k	k	PROPN
ap-928	63	2	k	k	PROPN
ap-928	63	3	c	c	X
ap-928	63	4	k	k	PROPN
ap-928	63	5	�	�	PROPN
ap-928	63	6	�	�	PROPN
ap-928	63	7	�	�	PROPN
ap-928	63	8	�	�	PROPN
ap-928	63	9	.	.	PUNCT
ap-928	64	1	polynomials	polynomial	VERB
ap-928	64	2	spn	spn	PROPN
ap-928	64	3	that	that	PRON
ap-928	64	4	have	have	VERB
ap-928	64	5	the	the	DET
ap-928	64	6	same	same	ADJ
ap-928	64	7	roots	root	NOUN
ap-928	64	8	as	as	ADP
ap-928	64	9	pn	pn	NOUN
ap-928	64	10	but	but	CCONJ
ap-928	64	11	scaled	scale	VERB
ap-928	64	12	by	by	ADP
ap-928	64	13	c	c	PROPN
ap-928	64	14	cnn	cnn	PROPN
ap-928	64	15	�	�	PROPN
ap-928	64	16	3	3	NUM
ap-928	64	17	2	2	NUM
ap-928	64	18	do	do	AUX
ap-928	64	19	not	not	PART
ap-928	64	20	fulfil	fulfil	VERB
ap-928	64	21	any	any	DET
ap-928	64	22	finite	finite	NOUN
ap-928	64	23	recurrence	recurrence	NOUN
ap-928	64	24	relation	relation	NOUN
ap-928	64	25	.	.	PUNCT
ap-928	65	1	however	however	ADV
ap-928	65	2	,	,	PUNCT
ap-928	65	3	we	we	PRON
ap-928	65	4	can	can	AUX
ap-928	65	5	rewrite	rewrite	VERB
ap-928	65	6	them	they	PRON
ap-928	65	7	as	as	ADP
ap-928	65	8	a	a	DET
ap-928	65	9	determinant	determinant	NOUN
ap-928	65	10	of	of	ADP
ap-928	65	11	an	an	DET
ap-928	65	12	n×n	n×n	PROPN
ap-928	65	13	tridiagonal	tridiagonal	ADJ
ap-928	65	14	matrix	matrix	NOUN
ap-928	65	15	sp	sp	ADP
ap-928	65	16	mn	mn	PROPN
ap-928	65	17	n	n	CCONJ
ap-928	65	18	�	�	PROPN
ap-928	65	19	det	det	PROPN
ap-928	65	20	(	(	PUNCT
ap-928	65	21	)	)	PUNCT
ap-928	65	22	,	,	PUNCT
ap-928	65	23	where	where	SCONJ
ap-928	65	24	m	m	VERB
ap-928	65	25	e	e	X
ap-928	65	26	e	e	X
ap-928	65	27	e	e	X
ap-928	65	28	n	n	CCONJ
ap-928	65	29	n	n	CCONJ
ap-928	65	30	n	n	CCONJ
ap-928	65	31	n	n	CCONJ
ap-928	65	32	n	n	CCONJ
ap-928	65	33	n	n	CCONJ
ap-928	65	34	n	n	CCONJ
ap-928	65	35	n	n	NOUN
ap-928	65	36	n	n	PROPN
ap-928	65	37	:	:	PUNCT
ap-928	65	38	,	,	PUNCT
ap-928	65	39	,	,	PUNCT
ap-928	65	40	,	,	PUNCT
ap-928	65	41	,	,	PUNCT
ap-928	65	42	,	,	PUNCT
ap-928	65	43	,	,	PUNCT
ap-928	65	44	,	,	PUNCT
ap-928	65	45	�	�	PROPN
ap-928	65	46	�	�	PROPN
ap-928	65	47	�	�	PROPN
ap-928	65	48	�	�	PROPN
ap-928	65	49	�	�	PROPN
ap-928	65	50	�	�	PROPN
ap-928	65	51	�	�	PROPN
ap-928	65	52	1	1	NUM
ap-928	65	53	2	2	NUM
ap-928	65	54	2	2	NUM
ap-928	65	55	2	2	NUM
ap-928	65	56	3	3	NUM
ap-928	65	57	3	3	NUM
ap-928	65	58	3	3	NUM
ap-928	65	59	0	0	NUM
ap-928	65	60	0	0	NUM
ap-928	65	61	0	0	NUM
ap-928	65	62	0	0	NUM
ap-928	65	63	0	0	NUM
ap-928	65	64	0	0	NUM
ap-928	65	65	0	0	SYM
ap-928	65	66	0	0	NUM
ap-928	65	67	�	�	PROPN
ap-928	65	68	�	�	PROPN
ap-928	65	69	,	,	PUNCT
ap-928	65	70	,	,	PUNCT
ap-928	65	71	,	,	PUNCT
ap-928	65	72	,	,	PUNCT
ap-928	65	73	,	,	PUNCT
ap-928	65	74	4	4	NUM
ap-928	65	75	1	1	NUM
ap-928	65	76	1	1	NUM
ap-928	65	77	1	1	NUM
ap-928	65	78	1	1	NUM
ap-928	65	79	0	0	NUM
ap-928	65	80	0	0	NUM
ap-928	65	81	0	0	NUM
ap-928	65	82	0	0	NUM
ap-928	65	83	0	0	NUM
ap-928	65	84	0	0	NUM
ap-928	65	85	0	0	NUM
ap-928	65	86	0	0	NUM
ap-928	65	87	0	0	NUM
ap-928	65	88	0	0	SYM
ap-928	65	89	0	0	NUM
ap-928	65	90	�	�	PROPN
ap-928	65	91	�	�	PROPN
ap-928	65	92	�	�	PROPN
ap-928	65	93	�	�	PROPN
ap-928	65	94	�	�	PROPN
ap-928	65	95	�	�	PROPN
ap-928	65	96	�	�	PROPN
ap-928	65	97	�	�	PROPN
ap-928	65	98	�	�	PROPN
ap-928	65	99	�	�	PROPN
ap-928	65	100	�	�	PROPN
ap-928	65	101	�	�	PROPN
ap-928	65	102	�	�	PROPN
ap-928	65	103	n	n	CCONJ
ap-928	65	104	n	n	CCONJ
ap-928	65	105	n	n	CCONJ
ap-928	65	106	n	n	CCONJ
ap-928	65	107	n	n	CCONJ
ap-928	65	108	n	n	CCONJ
ap-928	65	109	n	n	CCONJ
ap-928	65	110	ne	ne	PROPN
ap-928	65	111	�	�	PROPN
ap-928	65	112	�	�	PROPN
ap-928	65	113	�	�	PROPN
ap-928	65	114	�	�	PROPN
ap-928	65	115	�	�	PROPN
ap-928	65	116	0	0	NUM
ap-928	65	117	0	0	NUM
ap-928	65	118	�	�	PROPN
ap-928	65	119	n	n	CCONJ
ap-928	65	120	n	n	CCONJ
ap-928	65	121	n	n	PRON
ap-928	65	122	ne	ne	PROPN
ap-928	65	123	,	,	PUNCT
ap-928	65	124	,	,	PUNCT
ap-928	65	125	�	�	PROPN
ap-928	65	126	�	�	PROPN
ap-928	65	127	�	�	PROPN
ap-928	65	128	�	�	PROPN
ap-928	65	129	�	�	PROPN
ap-928	65	130	�	�	PROPN
ap-928	65	131	�	�	PROPN
ap-928	65	132	�	�	PROPN
ap-928	65	133	�	�	PROPN
ap-928	65	134	�	�	PROPN
ap-928	65	135	�	�	PROPN
ap-928	65	136	�	�	PROPN
ap-928	65	137	�	�	PROPN
ap-928	65	138	�	�	PROPN
ap-928	65	139	�	�	PROPN
ap-928	65	140	�	�	PROPN
ap-928	65	141	�	�	PROPN
ap-928	65	142	�	�	PROPN
ap-928	65	143	�	�	PROPN
ap-928	65	144	�	�	PROPN
ap-928	65	145	�	�	PROPN
ap-928	65	146	and	and	CCONJ
ap-928	65	147	n	n	PRON
ap-928	65	148	i	i	PRON
ap-928	65	149	n	n	VERB
ap-928	65	150	n	n	NOUN
ap-928	65	151	i	i	NOUN
ap-928	65	152	c	c	X
ap-928	65	153	,	,	PUNCT
ap-928	65	154	�	�	PROPN
ap-928	65	155	�	�	PROPN
ap-928	65	156	�	�	PROPN
ap-928	65	157	4	4	NUM
ap-928	65	158	4	4	NUM
ap-928	65	159	1	1	NUM
ap-928	65	160	2	2	NUM
ap-928	65	161	,	,	PUNCT
ap-928	65	162	�	�	PROPN
ap-928	65	163	n	n	CCONJ
ap-928	65	164	i	i	PRON
ap-928	66	1	n	n	VERB
ap-928	67	1	i	i	NOUN
ap-928	67	2	c	c	VERB
ap-928	67	3	,	,	PUNCT
ap-928	67	4	(	(	PUNCT
ap-928	67	5	)	)	PUNCT
ap-928	67	6	�	�	PROPN
ap-928	67	7	�	�	PROPN
ap-928	67	8	4	4	NUM
ap-928	67	9	1	1	NUM
ap-928	67	10	,	,	PUNCT
ap-928	67	11	n	n	CCONJ
ap-928	67	12	i	i	PRON
ap-928	67	13	n	n	VERB
ap-928	67	14	n	n	NOUN
ap-928	68	1	i	i	PRON
ap-928	68	2	n	n	VERB
ap-928	68	3	i	i	NOUN
ap-928	68	4	c	c	VERB
ap-928	68	5	,	,	PUNCT
ap-928	68	6	(	(	PUNCT
ap-928	68	7	)	)	PUNCT
ap-928	68	8	(	(	PUNCT
ap-928	68	9	)	)	PUNCT
ap-928	68	10	�	�	PROPN
ap-928	68	11	�	�	PROPN
ap-928	68	12	�	�	PROPN
ap-928	68	13	�	�	PROPN
ap-928	68	14	�	�	PROPN
ap-928	68	15	2	2	NUM
ap-928	68	16	2	2	NUM
ap-928	68	17	1	1	NUM
ap-928	68	18	2	2	NUM
ap-928	68	19	2	2	NUM
ap-928	68	20	2	2	NUM
ap-928	68	21	this	this	PRON
ap-928	68	22	enables	enable	VERB
ap-928	68	23	us	we	PRON
ap-928	68	24	to	to	PART
ap-928	68	25	extend	extend	VERB
ap-928	68	26	the	the	DET
ap-928	68	27	polynomial	polynomial	ADJ
ap-928	68	28	sequence	sequence	NOUN
ap-928	68	29	by	by	ADP
ap-928	68	30	introducing	introduce	VERB
ap-928	68	31	a	a	DET
ap-928	68	32	subsequence	subsequence	NOUN
ap-928	68	33	sp	sp	ADP
ap-928	68	34	mn	mn	PROPN
ap-928	68	35	i	i	PRON
ap-928	68	36	n	n	VERB
ap-928	68	37	i	i	PRON
ap-928	68	38	,	,	PUNCT
ap-928	68	39	,	,	PUNCT
ap-928	68	40	det	det	PROPN
ap-928	68	41	(	(	PUNCT
ap-928	68	42	)	)	PUNCT
ap-928	68	43	�	�	PROPN
ap-928	68	44	,	,	PUNCT
ap-928	68	45	where	where	SCONJ
ap-928	68	46	mn	mn	PROPN
ap-928	68	47	,	,	PUNCT
ap-928	68	48	i	i	PRON
ap-928	68	49	is	be	AUX
ap-928	68	50	the	the	DET
ap-928	68	51	upper	upper	ADJ
ap-928	68	52	i×	i×	INTJ
ap-928	69	1	i	i	PRON
ap-928	69	2	principal	principal	VERB
ap-928	69	3	submatrix	submatrix	NOUN
ap-928	69	4	of	of	ADP
ap-928	69	5	mn	mn	PROPN
ap-928	69	6	and	and	CCONJ
ap-928	69	7	this	this	PRON
ap-928	69	8	enables	enable	VERB
ap-928	69	9	us	we	PRON
ap-928	69	10	to	to	PART
ap-928	69	11	use	use	VERB
ap-928	69	12	the	the	DET
ap-928	69	13	result	result	NOUN
ap-928	69	14	of	of	ADP
ap-928	69	15	kuijlaars	kuijlaar	NOUN
ap-928	69	16	and	and	CCONJ
ap-928	69	17	van	van	PROPN
ap-928	69	18	assche	assche	NOUN
ap-928	69	19	concerning	concern	VERB
ap-928	69	20	the	the	DET
ap-928	69	21	three	three	NUM
ap-928	69	22	-	-	PUNCT
ap-928	69	23	term	term	NOUN
ap-928	69	24	recurrence	recurrence	NOUN
ap-928	69	25	relations	relation	NOUN
ap-928	69	26	with	with	ADP
ap-928	69	27	variable	variable	ADJ
ap-928	69	28	coefficients	coefficient	NOUN
ap-928	70	1	[	[	X
ap-928	70	2	8	8	NUM
ap-928	70	3	]	]	PUNCT
ap-928	70	4	.	.	PUNCT
ap-928	71	1	this	this	DET
ap-928	71	2	relation	relation	NOUN
ap-928	71	3	reads	read	VERB
ap-928	71	4	sp	sp	ADP
ap-928	71	5	e	e	X
ap-928	71	6	e	e	NOUN
ap-928	71	7	sp	sp	ADP
ap-928	71	8	spn	spn	PROPN
ap-928	71	9	i	i	PROPN
ap-928	71	10	n	n	VERB
ap-928	72	1	i	i	PRON
ap-928	73	1	n	n	VERB
ap-928	74	1	i	i	PRON
ap-928	75	1	n	n	VERB
ap-928	76	1	i	i	PRON
ap-928	77	1	n	n	VERB
ap-928	78	1	i	i	PRON
ap-928	79	1	n	n	VERB
ap-928	79	2	i	i	PRON
ap-928	79	3	,	,	PUNCT
ap-928	79	4	,	,	PUNCT
ap-928	79	5	,	,	PUNCT
ap-928	79	6	,	,	PUNCT
ap-928	79	7	,	,	PUNCT
ap-928	79	8	,	,	PUNCT
ap-928	79	9	(	(	PUNCT
ap-928	79	10	)	)	PUNCT
ap-928	79	11	(	(	PUNCT
ap-928	79	12	)	)	PUNCT
ap-928	79	13	�	�	PROPN
ap-928	79	14	�	�	PROPN
ap-928	79	15	�	�	PROPN
ap-928	79	16	�	�	PROPN
ap-928	79	17	�	�	PROPN
ap-928	79	18	�	�	PROPN
ap-928	79	19	1	1	NUM
ap-928	79	20	2	2	NUM
ap-928	79	21	with	with	ADP
ap-928	79	22	initial	initial	ADJ
ap-928	79	23	conditionsspn,0	conditionsspn,0	NOUN
ap-928	79	24	1	1	NUM
ap-928	79	25	�	�	NOUN
ap-928	79	26	andspn	andspn	ADJ
ap-928	79	27	,	,	PUNCT
ap-928	79	28	�	�	PROPN
ap-928	79	29	�	�	PROPN
ap-928	79	30	1	1	NUM
ap-928	79	31	0	0	NUM
ap-928	79	32	.	.	PUNCT
ap-928	80	1	now	now	ADV
ap-928	80	2	,	,	PUNCT
ap-928	80	3	it	it	PRON
ap-928	80	4	remains	remain	VERB
ap-928	80	5	to	to	PART
ap-928	80	6	go	go	VERB
ap-928	80	7	to	to	ADP
ap-928	80	8	the	the	DET
ap-928	80	9	polynomials	polynomial	NOUN
ap-928	80	10	tpn	tpn	VERB
ap-928	80	11	,	,	PUNCT
ap-928	80	12	i	i	PRON
ap-928	80	13	that	that	PRON
ap-928	80	14	have	have	VERB
ap-928	80	15	the	the	DET
ap-928	80	16	same	same	ADJ
ap-928	80	17	roots	root	NOUN
ap-928	80	18	as	as	ADP
ap-928	80	19	spn	spn	PROPN
ap-928	80	20	,	,	PUNCT
ap-928	80	21	i	i	PRON
ap-928	80	22	and	and	CCONJ
ap-928	80	23	fulfil	fulfil	VERB
ap-928	80	24	the	the	DET
ap-928	80	25	relation	relation	NOUN
ap-928	80	26	etp	etp	PROPN
ap-928	80	27	a	a	DET
ap-928	80	28	tp	tp	NOUN
ap-928	80	29	tp	tp	ADP
ap-928	80	30	a	a	DET
ap-928	80	31	tpn	tpn	NOUN
ap-928	81	1	i	i	NOUN
ap-928	81	2	n	n	NOUN
ap-928	81	3	i	i	PRON
ap-928	81	4	n	n	VERB
ap-928	81	5	i	i	PRON
ap-928	81	6	n	n	VERB
ap-928	81	7	i	i	PRON
ap-928	81	8	n	n	VERB
ap-928	81	9	i	i	PRON
ap-928	81	10	n	n	VERB
ap-928	81	11	i	i	PRON
ap-928	81	12	n	n	VERB
ap-928	81	13	i	i	PRON
ap-928	81	14	,	,	PUNCT
ap-928	81	15	,	,	PUNCT
ap-928	81	16	,	,	PUNCT
ap-928	81	17	,	,	PUNCT
ap-928	81	18	,	,	PUNCT
ap-928	81	19	,	,	PUNCT
ap-928	81	20	,	,	PUNCT
ap-928	81	21	�	�	PROPN
ap-928	81	22	�	�	PROPN
ap-928	81	23	�	�	PROPN
ap-928	81	24	�	�	PROPN
ap-928	81	25	�	�	PROPN
ap-928	81	26	�	�	PROPN
ap-928	81	27	�	�	PROPN
ap-928	81	28	1	1	NUM
ap-928	81	29	1	1	NUM
ap-928	81	30	1	1	NUM
ap-928	81	31	2	2	NUM
ap-928	81	32	,	,	PUNCT
ap-928	81	33	with	with	ADP
ap-928	81	34	a	a	DET
ap-928	81	35	i	i	NOUN
ap-928	81	36	n	n	NOUN
ap-928	82	1	i	i	PRON
ap-928	82	2	cn	cn	INTJ
ap-928	82	3	i	i	PRON
ap-928	82	4	n	n	PRON
ap-928	82	5	,	,	PUNCT
ap-928	82	6	(	(	PUNCT
ap-928	82	7	)	)	PUNCT
ap-928	82	8	(	(	PUNCT
ap-928	82	9	)	)	PUNCT
ap-928	82	10	�	�	PROPN
ap-928	82	11	�	�	PROPN
ap-928	82	12	�	�	PROPN
ap-928	82	13	�	�	PROPN
ap-928	82	14	4	4	NUM
ap-928	82	15	1	1	NUM
ap-928	82	16	2	2	NUM
ap-928	82	17	2	2	NUM
ap-928	82	18	1	1	NUM
ap-928	82	19	the	the	DET
ap-928	82	20	limits	limit	NOUN
ap-928	82	21	�	�	PROPN
ap-928	82	22	�	�	PROPN
ap-928	82	23	(	(	PUNCT
ap-928	82	24	)	)	PUNCT
ap-928	82	25	lim	lim	PROPN
ap-928	82	26	,	,	PUNCT
ap-928	82	27	�	�	PROPN
ap-928	82	28	�	�	PROPN
ap-928	82	29	�	�	PROPN
ap-928	82	30	i	i	PROPN
ap-928	82	31	n	n	VERB
ap-928	82	32	n	n	NOUN
ap-928	82	33	i	i	NOUN
ap-928	82	34	0	0	NUM
ap-928	82	35	,	,	PUNCT
ap-928	82	36	a	a	DET
ap-928	82	37	a	a	DET
ap-928	82	38	ci	ci	NOUN
ap-928	82	39	n	n	CCONJ
ap-928	82	40	n	n	NOUN
ap-928	82	41	i	i	PRON
ap-928	82	42	n	n	PROPN
ap-928	82	43	(	(	PUNCT
ap-928	82	44	)	)	PUNCT
ap-928	82	45	lim	lim	PROPN
ap-928	82	46	,	,	PUNCT
ap-928	82	47	�	�	PROPN
ap-928	82	48	�	�	PROPN
ap-928	82	49	�	�	PROPN
ap-928	82	50	�	�	PROPN
ap-928	82	51	�	�	PROPN
ap-928	82	52	�	�	PROPN
ap-928	82	53	�	�	PROPN
ap-928	82	54	�	�	PROPN
ap-928	82	55	�	�	PROPN
ap-928	82	56	4	4	NUM
ap-928	82	57	1	1	NUM
ap-928	82	58	2	2	NUM
ap-928	82	59	determine	determine	VERB
ap-928	82	60	the	the	DET
ap-928	82	61	density	density	NOUN
ap-928	82	62	of	of	ADP
ap-928	82	63	the	the	DET
ap-928	82	64	asymptotic	asymptotic	ADJ
ap-928	82	65	root	root	NOUN
ap-928	82	66	-	-	PUNCT
ap-928	82	67	counting	count	VERB
ap-928	82	68	measure	measure	NOUN
ap-928	82	69	:	:	PUNCT
ap-928	82	70	�	�	PROPN
ap-928	82	71	�	�	PROPN
ap-928	82	72	�	�	PROPN
ap-928	82	73	�	�	PROPN
ap-928	82	74	�	�	PROPN
ap-928	82	75	�	�	PROPN
ap-928	82	76	�	�	PROPN
ap-928	82	77	�	�	PROPN
ap-928	82	78	2	2	NUM
ap-928	82	79	2	2	NUM
ap-928	82	80	0	0	NUM
ap-928	82	81	1	1	NUM
ap-928	82	82	a	a	DET
ap-928	82	83	a	a	DET
ap-928	82	84	(	(	PUNCT
ap-928	82	85	)	)	PUNCT
ap-928	82	86	,	,	PUNCT
ap-928	82	87	(	(	PUNCT
ap-928	82	88	)	)	PUNCT
ap-928	82	89	d	d	NOUN
ap-928	82	90	,	,	PUNCT
ap-928	82	91	where	where	SCONJ
ap-928	82	92	�	�	PROPN
ap-928	82	93	�	�	PROPN
ap-928	82	94	�	�	PROPN
ap-928	82	95	�	�	PROPN
ap-928	82	96	�	�	PROPN
ap-928	82	97	�	�	PROPN
ap-928	82	98	x	x	PROPN
ap-928	82	99	y	y	PROPN
ap-928	82	100	y	y	PROPN
ap-928	82	101	s	s	PROPN
ap-928	82	102	s	s	X
ap-928	82	103	x	x	X
ap-928	82	104	s	s	X
ap-928	82	105	x	x	SYM
ap-928	82	106	y	y	PROPN
ap-928	82	107	,	,	PUNCT
ap-928	82	108	(	(	PUNCT
ap-928	82	109	)	)	PUNCT
ap-928	82	110	(	(	PUNCT
ap-928	82	111	)	)	PUNCT
ap-928	82	112	,	,	PUNCT
ap-928	82	113	�	�	PROPN
ap-928	82	114	�	�	PROPN
ap-928	82	115	�	�	PROPN
ap-928	82	116	�	�	PROPN
ap-928	82	117	�	�	PROPN
ap-928	82	118	�	�	PROPN
ap-928	82	119	�	�	PROPN
ap-928	82	120	�	�	PROPN
ap-928	82	121	�	�	PROPN
ap-928	82	122	1	1	NUM
ap-928	82	123	0	0	NUM
ap-928	82	124	if	if	SCONJ
ap-928	82	125	otherwise	otherwise	ADV
ap-928	82	126	the	the	DET
ap-928	82	127	sought	seek	VERB
ap-928	82	128	density	density	NOUN
ap-928	82	129	�	�	PROPN
ap-928	82	130	is	be	AUX
ap-928	82	131	then	then	ADV
ap-928	82	132	expressed	express	VERB
ap-928	82	133	as	as	ADP
ap-928	82	134	c	c	PROPN
ap-928	82	135	c	c	PROPN
ap-928	82	136	s	s	PROPN
ap-928	82	137	�	�	PROPN
ap-928	82	138	�	�	PROPN
ap-928	82	139	�	�	PROPN
ap-928	82	140	�	�	PROPN
ap-928	82	141	d	d	ADP
ap-928	82	142	64	64	NUM
ap-928	82	143	1	1	NUM
ap-928	82	144	2	2	NUM
ap-928	82	145	2	2	NUM
ap-928	82	146	2	2	NUM
ap-928	82	147	0	0	NUM
ap-928	82	148	1	1	NUM
ap-928	82	149	(	(	PUNCT
ap-928	82	150	)	)	PUNCT
ap-928	82	151	�	�	PROPN
ap-928	82	152	�	�	PROPN
ap-928	82	153	�	�	PROPN
ap-928	82	154	�	�	PROPN
ap-928	82	155	.	.	PUNCT
ap-928	83	1	we	we	PRON
ap-928	83	2	immediately	immediately	ADV
ap-928	83	3	see	see	VERB
ap-928	83	4	that	that	SCONJ
ap-928	83	5	the	the	DET
ap-928	83	6	integral	integral	NOUN
ap-928	83	7	does	do	AUX
ap-928	83	8	not	not	PART
ap-928	83	9	converge	converge	VERB
ap-928	83	10	for	for	ADP
ap-928	83	11	s	s	PROPN
ap-928	83	12	�	�	PROPN
ap-928	83	13	0	0	NUM
ap-928	83	14	.	.	PUNCT
ap-928	84	1	the	the	DET
ap-928	84	2	polynomial	polynomial	NOUN
ap-928	84	3	under	under	ADP
ap-928	84	4	the	the	DET
ap-928	84	5	square	square	ADJ
ap-928	84	6	root	root	NOUN
ap-928	84	7	has	have	VERB
ap-928	84	8	three	three	NUM
ap-928	84	9	real	real	ADJ
ap-928	84	10	roots	root	NOUN
ap-928	84	11	�	�	PROPN
ap-928	84	12	�	�	PROPN
ap-928	84	13	�	�	PROPN
ap-928	84	14	1	1	NUM
ap-928	84	15	2	2	NUM
ap-928	84	16	3	3	NUM
ap-928	84	17	(	(	PUNCT
ap-928	84	18	)	)	PUNCT
ap-928	84	19	(	(	PUNCT
ap-928	84	20	)	)	PUNCT
ap-928	84	21	(	(	PUNCT
ap-928	84	22	)	)	PUNCT
ap-928	84	23	s	s	PART
ap-928	84	24	s	s	X
ap-928	84	25	s	s	PROPN
ap-928	84	26	�	�	X
ap-928	84	27	�	�	PROPN
ap-928	84	28	if	if	SCONJ
ap-928	84	29	s	s	VERB
ap-928	84	30	c	c	PROPN
ap-928	84	31	c	c	PROPN
ap-928	84	32	�	�	PROPN
ap-928	84	33	�	�	PROPN
ap-928	84	34	�	�	PROPN
ap-928	84	35	�	�	PROPN
ap-928	84	36	�	�	PROPN
ap-928	84	37	�	�	PROPN
ap-928	84	38	�	�	PROPN
ap-928	84	39	�	�	PROPN
ap-928	85	1	16	16	NUM
ap-928	85	2	3	3	NUM
ap-928	85	3	3	3	NUM
ap-928	85	4	16	16	NUM
ap-928	85	5	3	3	NUM
ap-928	85	6	3	3	NUM
ap-928	85	7	,	,	PUNCT
ap-928	85	8	and	and	CCONJ
ap-928	85	9	�	�	PROPN
ap-928	85	10	3	3	NUM
ap-928	85	11	1	1	NUM
ap-928	85	12	�	�	PROPN
ap-928	85	13	for	for	ADP
ap-928	85	14	all	all	PRON
ap-928	85	15	s	s	PROPN
ap-928	85	16	�	�	PROPN
ap-928	85	17	�	�	PROPN
ap-928	85	18	.	.	PUNCT
ap-928	86	1	thus	thus	ADV
ap-928	86	2	�	�	PROPN
ap-928	86	3	can	can	AUX
ap-928	86	4	be	be	AUX
ap-928	86	5	written	write	VERB
ap-928	86	6	as	as	ADP
ap-928	86	7	�	�	PROPN
ap-928	86	8	�	�	PROPN
ap-928	86	9	�	�	PROPN
ap-928	86	10	�	�	PROPN
ap-928	86	11	�	�	PROPN
ap-928	86	12	�	�	PROPN
ap-928	86	13	�	�	PROPN
ap-928	86	14	�	�	PROPN
ap-928	86	15	�	�	PROPN
ap-928	86	16	�	�	PROPN
ap-928	86	17	�	�	PROPN
ap-928	86	18	�	�	PROPN
ap-928	86	19	�	�	PROPN
ap-928	86	20	�	�	PROPN
ap-928	86	21	�	�	PROPN
ap-928	86	22	�	�	PROPN
ap-928	86	23	c	c	PROPN
ap-928	86	24	d	d	NOUN
ap-928	86	25	64	64	NUM
ap-928	86	26	1	1	NUM
ap-928	86	27	2	2	NUM
ap-928	86	28	3	3	NUM
ap-928	86	29	1	1	NUM
ap-928	86	30	2	2	NUM
ap-928	86	31	(	(	PUNCT
ap-928	86	32	)	)	PUNCT
ap-928	86	33	(	(	PUNCT
ap-928	86	34	)	)	PUNCT
ap-928	86	35	(	(	PUNCT
ap-928	86	36	)	)	PUNCT
ap-928	86	37	,	,	PUNCT
ap-928	86	38	which	which	PRON
ap-928	86	39	can	can	AUX
ap-928	86	40	be	be	AUX
ap-928	86	41	evaluated	evaluate	VERB
ap-928	86	42	as	as	ADP
ap-928	86	43	[	[	X
ap-928	86	44	9	9	NUM
ap-928	86	45	]	]	SYM
ap-928	86	46	�	�	PROPN
ap-928	86	47	�	�	PROPN
ap-928	86	48	�	�	PROPN
ap-928	86	49	�	�	PROPN
ap-928	86	50	�	�	PROPN
ap-928	86	51	�	�	PROPN
ap-928	86	52	�	�	PROPN
ap-928	86	53	(	(	PUNCT
ap-928	86	54	)	)	PUNCT
ap-928	86	55	,	,	PUNCT
ap-928	86	56	,	,	PUNCT
ap-928	86	57	,	,	PUNCT
ap-928	86	58	s	s	PROPN
ap-928	86	59	c	c	NOUN
ap-928	86	60	f	f	PROPN
ap-928	86	61	�	�	PROPN
ap-928	86	62	�	�	PROPN
ap-928	86	63	�	�	PROPN
ap-928	86	64	�	�	PROPN
ap-928	86	65	�	�	PROPN
ap-928	86	66	�	�	PROPN
ap-928	86	67	�	�	PROPN
ap-928	86	68	�	�	PROPN
ap-928	86	69	�	�	PROPN
ap-928	86	70	�	�	PROPN
ap-928	86	71	8	8	NUM
ap-928	86	72	1	1	NUM
ap-928	86	73	1	1	NUM
ap-928	86	74	2	2	NUM
ap-928	86	75	1	1	NUM
ap-928	86	76	2	2	NUM
ap-928	86	77	1	1	NUM
ap-928	86	78	3	3	NUM
ap-928	86	79	1	1	NUM
ap-928	86	80	2	2	NUM
ap-928	86	81	1	1	NUM
ap-928	86	82	2	2	NUM
ap-928	86	83	1	1	NUM
ap-928	86	84	3	3	NUM
ap-928	86	85	1	1	NUM
ap-928	86	86	s	s	NOUN
ap-928	86	87	c	c	NOUN
ap-928	86	88	c	c	PROPN
ap-928	86	89	�	�	PROPN
ap-928	86	90	�	�	PROPN
ap-928	86	91	�	�	PROPN
ap-928	86	92	�	�	PROPN
ap-928	86	93	�	�	PROPN
ap-928	86	94	�	�	PROPN
ap-928	86	95	�	�	PROPN
ap-928	86	96	�	�	PROPN
ap-928	86	97	16	16	NUM
ap-928	86	98	3	3	NUM
ap-928	86	99	3	3	NUM
ap-928	86	100	16	16	NUM
ap-928	86	101	3	3	NUM
ap-928	86	102	3	3	NUM
ap-928	86	103	,	,	PUNCT
ap-928	86	104	.	.	PUNCT
ap-928	87	1	acknowledgments	acknowledgment	NOUN
ap-928	87	2	this	this	DET
ap-928	87	3	research	research	NOUN
ap-928	87	4	was	be	AUX
ap-928	87	5	partially	partially	ADV
ap-928	87	6	supported	support	VERB
ap-928	87	7	by	by	ADP
ap-928	87	8	project	project	NOUN
ap-928	87	9	lc06002	lc06002	NOUN
ap-928	87	10	.	.	PUNCT
ap-928	88	1	references	reference	NOUN
ap-928	88	2	[	[	X
ap-928	88	3	1	1	NUM
ap-928	88	4	]	]	PUNCT
ap-928	88	5	shin	shin	NOUN
ap-928	88	6	,	,	PUNCT
ap-928	88	7	k.	k.	PROPN
ap-928	88	8	c.	c.	PROPN
ap-928	88	9	:	:	PUNCT
ap-928	88	10	schrödinger	schrödinger	ADJ
ap-928	88	11	type	type	NOUN
ap-928	88	12	eigenvalue	eigenvalue	NOUN
ap-928	88	13	problems	problem	NOUN
ap-928	88	14	with	with	ADP
ap-928	88	15	polynomial	polynomial	ADJ
ap-928	88	16	potentials	potential	NOUN
ap-928	88	17	:	:	PUNCT
ap-928	88	18	asymptotics	asymptotic	NOUN
ap-928	88	19	of	of	ADP
ap-928	88	20	eigenvalues	eigenvalue	NOUN
ap-928	88	21	,	,	PUNCT
ap-928	88	22	math	math	NOUN
ap-928	88	23	.	.	PUNCT
ap-928	89	1	sp/0411143	sp/0411143	PROPN
ap-928	89	2	.	.	PUNCT
ap-928	90	1	[	[	X
ap-928	90	2	2	2	NUM
ap-928	90	3	]	]	X
ap-928	90	4	trinh	trinh	PROPN
ap-928	90	5	,	,	PUNCT
ap-928	90	6	d.	d.	PROPN
ap-928	90	7	t.	t.	PROPN
ap-928	90	8	:	:	PUNCT
ap-928	90	9	asymptotique	asymptotique	NOUN
ap-928	90	10	et	et	PROPN
ap-928	90	11	analyse	analyse	PROPN
ap-928	90	12	spectral	spectral	PROPN
ap-928	90	13	de	de	PROPN
ap-928	90	14	l’oscillateur	l’oscillateur	PROPN
ap-928	90	15	cubique	cubique	NOUN
ap-928	90	16	,	,	PUNCT
ap-928	90	17	th	th	X
ap-928	90	18	se	se	X
ap-928	90	19	,	,	PUNCT
ap-928	90	20	université	université	PROPN
ap-928	90	21	de	de	X
ap-928	90	22	nice	nice	PROPN
ap-928	90	23	,	,	PUNCT
ap-928	90	24	2002	2002	NUM
ap-928	90	25	.	.	PUNCT
ap-928	91	1	[	[	X
ap-928	91	2	3	3	NUM
ap-928	91	3	]	]	X
ap-928	91	4	bender	bender	NOUN
ap-928	91	5	,	,	PUNCT
ap-928	91	6	c.	c.	PROPN
ap-928	91	7	m.	m.	PROPN
ap-928	91	8	,	,	PUNCT
ap-928	91	9	dunne	dunne	PROPN
ap-928	91	10	,	,	PUNCT
ap-928	91	11	g.	g.	PROPN
ap-928	91	12	v.	v.	NOUN
ap-928	91	13	:	:	PUNCT
ap-928	91	14	quasi	quasi	ADJ
ap-928	91	15	-	-	ADJ
ap-928	91	16	exactly	exactly	ADV
ap-928	91	17	solvable	solvable	ADJ
ap-928	91	18	systems	system	NOUN
ap-928	91	19	and	and	CCONJ
ap-928	91	20	orthogonal	orthogonal	ADJ
ap-928	91	21	polynomials	polynomial	NOUN
ap-928	91	22	,	,	PUNCT
ap-928	91	23	j.	j.	PROPN
ap-928	91	24	math	math	PROPN
ap-928	91	25	.	.	PUNCT
ap-928	92	1	phys	phy	NOUN
ap-928	92	2	.	.	PUNCT
ap-928	92	3	,	,	PUNCT
ap-928	92	4	vol	vol	NOUN
ap-928	92	5	.	.	PROPN
ap-928	92	6	37	37	NUM
ap-928	92	7	(	(	PUNCT
ap-928	92	8	1996	1996	NUM
ap-928	92	9	)	)	PUNCT
ap-928	92	10	,	,	PUNCT
ap-928	92	11	p.	p.	PROPN
ap-928	92	12	6–11	6–11	PROPN
ap-928	92	13	.	.	PUNCT
ap-928	93	1	[	[	X
ap-928	93	2	4	4	NUM
ap-928	93	3	]	]	PUNCT
ap-928	93	4	chihara	chihara	NOUN
ap-928	93	5	,	,	PUNCT
ap-928	93	6	t.	t.	PROPN
ap-928	93	7	s.	s.	PROPN
ap-928	93	8	:	:	PUNCT
ap-928	93	9	an	an	DET
ap-928	93	10	introduction	introduction	NOUN
ap-928	93	11	to	to	ADP
ap-928	93	12	orthogonal	orthogonal	ADJ
ap-928	93	13	polynomials	polynomial	NOUN
ap-928	93	14	.	.	PUNCT
ap-928	94	1	gordon	gordon	PROPN
ap-928	94	2	and	and	CCONJ
ap-928	94	3	breach	breach	PROPN
ap-928	94	4	,	,	PUNCT
ap-928	94	5	new	new	PROPN
ap-928	94	6	york	york	PROPN
ap-928	94	7	,	,	PUNCT
ap-928	94	8	1978	1978	NUM
ap-928	94	9	.	.	PUNCT
ap-928	95	1	[	[	X
ap-928	95	2	5	5	NUM
ap-928	95	3	]	]	PUNCT
ap-928	95	4	marcellán	marcellán	NOUN
ap-928	95	5	,	,	PUNCT
ap-928	95	6	f.	f.	PROPN
ap-928	95	7	,	,	PUNCT
ap-928	95	8	álvarez	álvarez	NOUN
ap-928	95	9	-	-	PUNCT
ap-928	95	10	nodarse	nodarse	NOUN
ap-928	95	11	,	,	PUNCT
ap-928	95	12	r.	r.	PROPN
ap-928	95	13	:	:	PUNCT
ap-928	95	14	on	on	ADP
ap-928	95	15	the	the	DET
ap-928	95	16	“	"	PUNCT
ap-928	95	17	favard	favard	PROPN
ap-928	95	18	’s	’s	PART
ap-928	95	19	theorem	theorem	NOUN
ap-928	95	20	“	"	PUNCT
ap-928	95	21	and	and	CCONJ
ap-928	95	22	its	its	PRON
ap-928	95	23	extensions	extension	NOUN
ap-928	95	24	.	.	PUNCT
ap-928	96	1	j.	j.	PROPN
ap-928	96	2	comp	comp	PROPN
ap-928	96	3	.	.	PUNCT
ap-928	97	1	appl	appl	PROPN
ap-928	97	2	.	.	PROPN
ap-928	97	3	math	math	PROPN
ap-928	97	4	.	.	PUNCT
ap-928	98	1	,	,	PUNCT
ap-928	98	2	vol	vol	NOUN
ap-928	98	3	.	.	PUNCT
ap-928	99	1	127	127	NUM
ap-928	99	2	(	(	PUNCT
ap-928	99	3	2001	2001	NUM
ap-928	99	4	)	)	PUNCT
ap-928	99	5	,	,	PUNCT
ap-928	99	6	p.	p.	NOUN
ap-928	99	7	231–254	231–254	NUM
ap-928	99	8	.	.	PUNCT
ap-928	100	1	[	[	X
ap-928	100	2	6	6	NUM
ap-928	100	3	]	]	PUNCT
ap-928	100	4	borcea	borcea	PROPN
ap-928	100	5	,	,	PUNCT
ap-928	100	6	j.	j.	PROPN
ap-928	100	7	,	,	PUNCT
ap-928	100	8	brändén	brändén	NOUN
ap-928	100	9	,	,	PUNCT
ap-928	100	10	p.	p.	PROPN
ap-928	100	11	,	,	PUNCT
ap-928	100	12	shapiro	shapiro	PROPN
ap-928	100	13	,	,	PUNCT
ap-928	100	14	b.	b.	PROPN
ap-928	100	15	:	:	PUNCT
ap-928	100	16	higher	high	ADJ
ap-928	100	17	lamé	lamé	NOUN
ap-928	100	18	equations	equation	NOUN
ap-928	100	19	,	,	PUNCT
ap-928	100	20	heine	heine	PROPN
ap-928	100	21	-	-	PUNCT
ap-928	100	22	stieltjes	stieltjes	PROPN
ap-928	100	23	and	and	CCONJ
ap-928	100	24	van	van	PROPN
ap-928	100	25	vleck	vleck	NOUN
ap-928	100	26	polynomials	polynomial	NOUN
ap-928	100	27	,	,	PUNCT
ap-928	100	28	in	in	ADP
ap-928	100	29	preparation	preparation	NOUN
ap-928	100	30	.	.	PUNCT
ap-928	101	1	34	34	NUM
ap-928	102	1	©	©	PROPN
ap-928	102	2	czech	czech	PROPN
ap-928	102	3	technical	technical	PROPN
ap-928	102	4	university	university	PROPN
ap-928	102	5	publishing	publishing	NOUN
ap-928	102	6	house	house	NOUN
ap-928	102	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-928	102	8	acta	acta	PROPN
ap-928	102	9	polytechnica	polytechnica	PROPN
ap-928	102	10	vol	vol	NOUN
ap-928	102	11	.	.	PUNCT
ap-928	103	1	47	47	NUM
ap-928	103	2	no	no	NOUN
ap-928	103	3	.	.	PUNCT
ap-928	104	1	2–3/2007	2–3/2007	NUM
ap-928	104	2	fig	fig	NOUN
ap-928	104	3	.	.	PUNCT
ap-928	105	1	1	1	NUM
ap-928	105	2	:	:	PUNCT
ap-928	105	3	a	a	X
ap-928	105	4	)	)	PUNCT
ap-928	105	5	dependence	dependence	NOUN
ap-928	105	6	of	of	ADP
ap-928	105	7	the	the	DET
ap-928	105	8	three	three	NUM
ap-928	105	9	real	real	ADJ
ap-928	105	10	roots	root	NOUN
ap-928	105	11	of	of	ADP
ap-928	105	12	64	64	NUM
ap-928	105	13	1	1	NUM
ap-928	105	14	02	02	NUM
ap-928	105	15	2	2	NUM
ap-928	105	16	2	2	NUM
ap-928	105	17	�	�	PROPN
ap-928	105	18	�	�	PROPN
ap-928	105	19	(	(	PUNCT
ap-928	105	20	)	)	PUNCT
ap-928	105	21	�	�	PROPN
ap-928	105	22	�	�	PROPN
ap-928	105	23	�	�	PROPN
ap-928	105	24	c	c	NOUN
ap-928	105	25	s	s	PROPN
ap-928	105	26	on	on	ADP
ap-928	105	27	s	s	PRON
ap-928	105	28	(	(	PUNCT
ap-928	105	29	for	for	ADP
ap-928	105	30	c	c	PROPN
ap-928	105	31	�	�	PROPN
ap-928	105	32	�	�	PROPN
ap-928	105	33	)	)	PUNCT
ap-928	105	34	.	.	PUNCT
ap-928	106	1	if	if	SCONJ
ap-928	106	2	s	s	VERB
ap-928	106	3	c	c	PROPN
ap-928	106	4	c	c	PROPN
ap-928	106	5	�	�	PROPN
ap-928	106	6	�	�	PROPN
ap-928	106	7	�	�	PROPN
ap-928	106	8	�	�	PROPN
ap-928	106	9	�	�	PROPN
ap-928	106	10	�	�	PROPN
ap-928	106	11	�	�	PROPN
ap-928	106	12	16	16	NUM
ap-928	106	13	3	3	NUM
ap-928	106	14	3	3	NUM
ap-928	106	15	16	16	NUM
ap-928	106	16	3	3	NUM
ap-928	106	17	3	3	NUM
ap-928	106	18	,	,	PUNCT
ap-928	106	19	,	,	PUNCT
ap-928	106	20	there	there	PRON
ap-928	106	21	is	be	VERB
ap-928	106	22	only	only	ADV
ap-928	106	23	one	one	NUM
ap-928	106	24	real	real	ADJ
ap-928	106	25	root	root	NOUN
ap-928	106	26	�	�	PROPN
ap-928	106	27	3	3	NUM
ap-928	106	28	1	1	NUM
ap-928	106	29	(	(	PUNCT
ap-928	106	30	)	)	PUNCT
ap-928	106	31	s	s	PART
ap-928	106	32	!	!	PUNCT
ap-928	107	1	;	;	PUNCT
ap-928	107	2	b	b	X
ap-928	107	3	)	)	PUNCT
ap-928	107	4	comparison	comparison	NOUN
ap-928	107	5	of	of	ADP
ap-928	107	6	density	density	NOUN
ap-928	107	7	�	�	PROPN
ap-928	107	8	with	with	ADP
ap-928	107	9	a	a	DET
ap-928	107	10	numerical	numerical	ADJ
ap-928	107	11	example	example	NOUN
ap-928	107	12	for	for	ADP
ap-928	107	13	n	n	DET
ap-928	107	14	�	�	PROPN
ap-928	107	15	100	100	NUM
ap-928	107	16	and	and	CCONJ
ap-928	107	17	b	b	PROPN
ap-928	107	18	�	�	PROPN
ap-928	107	19	266	266	NUM
ap-928	107	20	.	.	PUNCT
ap-928	107	21	.	.	PUNCT
ap-928	108	1	©	©	PROPN
ap-928	108	2	czech	czech	PROPN
ap-928	108	3	technical	technical	PROPN
ap-928	108	4	university	university	PROPN
ap-928	108	5	publishing	publishing	NOUN
ap-928	108	6	house	house	NOUN
ap-928	108	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-928	108	8	35	35	NUM
ap-928	108	9	acta	acta	PROPN
ap-928	108	10	polytechnica	polytechnica	PROPN
ap-928	108	11	vol	vol	NOUN
ap-928	108	12	.	.	PUNCT
ap-928	109	1	47	47	NUM
ap-928	109	2	no	no	INTJ
ap-928	109	3	.	.	PUNCT
ap-928	110	1	2–3/2007	2–3/2007	NUM
ap-928	111	1	[	[	X
ap-928	111	2	7	7	NUM
ap-928	111	3	]	]	X
ap-928	111	4	borcea	borcea	NOUN
ap-928	111	5	,	,	PUNCT
ap-928	111	6	j.	j.	PROPN
ap-928	111	7	,	,	PUNCT
ap-928	111	8	shapiro	shapiro	PROPN
ap-928	111	9	,	,	PUNCT
ap-928	111	10	b.	b.	PROPN
ap-928	111	11	:	:	PUNCT
ap-928	111	12	root	root	NOUN
ap-928	111	13	asymptotics	asymptotic	NOUN
ap-928	111	14	of	of	ADP
ap-928	111	15	spectral	spectral	ADJ
ap-928	111	16	polynomials	polynomial	NOUN
ap-928	111	17	for	for	ADP
ap-928	111	18	the	the	DET
ap-928	111	19	lamé	lamé	NOUN
ap-928	111	20	polynomials	polynomial	NOUN
ap-928	111	21	,	,	PUNCT
ap-928	111	22	math	math	NOUN
ap-928	111	23	.	.	PUNCT
ap-928	112	1	ca/0701883	ca/0701883	NOUN
ap-928	112	2	.	.	PUNCT
ap-928	113	1	[	[	X
ap-928	113	2	8	8	NUM
ap-928	113	3	]	]	SYM
ap-928	113	4	kuijlaars	kuijlaar	NOUN
ap-928	113	5	,	,	PUNCT
ap-928	113	6	a.	a.	PROPN
ap-928	113	7	b.	b.	PROPN
ap-928	113	8	j.	j.	PROPN
ap-928	113	9	,	,	PUNCT
ap-928	113	10	van	van	PROPN
ap-928	113	11	assche	assche	PROPN
ap-928	113	12	,	,	PUNCT
ap-928	113	13	w.	w.	PROPN
ap-928	113	14	:	:	PUNCT
ap-928	113	15	the	the	DET
ap-928	113	16	asymptotic	asymptotic	ADJ
ap-928	113	17	zero	zero	NUM
ap-928	113	18	distribution	distribution	NOUN
ap-928	113	19	of	of	ADP
ap-928	113	20	orthogonal	orthogonal	ADJ
ap-928	113	21	polynomials	polynomial	NOUN
ap-928	113	22	with	with	ADP
ap-928	113	23	varying	vary	VERB
ap-928	113	24	recurrence	recurrence	NOUN
ap-928	113	25	coefficients	coefficient	NOUN
ap-928	113	26	,	,	PUNCT
ap-928	113	27	j.	j.	PROPN
ap-928	113	28	approx	approx	PROPN
ap-928	113	29	.	.	PUNCT
ap-928	114	1	theory	theory	NOUN
ap-928	114	2	,	,	PUNCT
ap-928	114	3	vol	vol	NOUN
ap-928	114	4	.	.	PROPN
ap-928	115	1	99	99	NUM
ap-928	115	2	(	(	PUNCT
ap-928	115	3	1999	1999	NUM
ap-928	115	4	)	)	PUNCT
ap-928	115	5	,	,	PUNCT
ap-928	116	1	p.	p.	NOUN
ap-928	116	2	167–197	167–197	NUM
ap-928	116	3	.	.	PUNCT
ap-928	117	1	[	[	X
ap-928	117	2	9	9	NUM
ap-928	117	3	]	]	X
ap-928	117	4	prudnikov	prudnikov	NOUN
ap-928	117	5	,	,	PUNCT
ap-928	117	6	a.	a.	NOUN
ap-928	117	7	p.	p.	PROPN
ap-928	117	8	,	,	PUNCT
ap-928	117	9	brychkov	brychkov	PROPN
ap-928	117	10	,	,	PUNCT
ap-928	117	11	yu	yu	PROPN
ap-928	117	12	.	.	PUNCT
ap-928	117	13	a.	a.	PROPN
ap-928	117	14	,	,	PUNCT
ap-928	117	15	marichev	marichev	ADV
ap-928	117	16	,	,	PUNCT
ap-928	117	17	o.	o.	PROPN
ap-928	117	18	i.	i.	PROPN
ap-928	117	19	:	:	PUNCT
ap-928	117	20	integrals	integral	NOUN
ap-928	117	21	and	and	CCONJ
ap-928	117	22	series	series	NOUN
ap-928	117	23	.	.	PUNCT
ap-928	117	24	elementary	elementary	ADJ
ap-928	117	25	functions	function	NOUN
ap-928	117	26	.	.	PUNCT
ap-928	118	1	nauka	nauka	PROPN
ap-928	118	2	,	,	PUNCT
ap-928	118	3	moscow	moscow	PROPN
ap-928	118	4	,	,	PUNCT
ap-928	118	5	1981	1981	NUM
ap-928	118	6	.	.	PUNCT
ap-928	119	1	prof	prof	PROPN
ap-928	119	2	.	.	PUNCT
ap-928	120	1	boris	boris	PROPN
ap-928	120	2	shapiro	shapiro	PROPN
ap-928	120	3	e	e	PROPN
ap-928	120	4	-	-	NOUN
ap-928	120	5	mail	mail	NOUN
ap-928	120	6	:	:	PUNCT
ap-928	120	7	shapiro@mat.su.se	shapiro@mat.su.se	PROPN
ap-928	120	8	department	department	PROPN
ap-928	120	9	of	of	ADP
ap-928	120	10	mathematics	mathematics	PROPN
ap-928	120	11	university	university	PROPN
ap-928	120	12	of	of	ADP
ap-928	120	13	stockholm	stockholm	PROPN
ap-928	120	14	s-10691	s-10691	PROPN
ap-928	120	15	stockholm	stockholm	PROPN
ap-928	120	16	,	,	PUNCT
ap-928	120	17	sweden	sweden	PROPN
ap-928	120	18	rndr	rndr	PROPN
ap-928	120	19	.	.	PUNCT
ap-928	121	1	miloš	miloš	PROPN
ap-928	121	2	tater	tater	NOUN
ap-928	121	3	,	,	PUNCT
ap-928	121	4	csc	csc	PROPN
ap-928	121	5	.	.	PUNCT
ap-928	122	1	e	e	X
ap-928	122	2	-	-	NOUN
ap-928	122	3	mail	mail	NOUN
ap-928	122	4	:	:	PUNCT
ap-928	122	5	tater@ujf.cas.cz	tater@ujf.cas.cz	NOUN
ap-928	122	6	nuclear	nuclear	PROPN
ap-928	122	7	physics	physics	PROPN
ap-928	122	8	institute	institute	PROPN
ap-928	122	9	,	,	PUNCT
ap-928	122	10	academy	academy	PROPN
ap-928	122	11	of	of	ADP
ap-928	122	12	sciences	sciences	PROPN
ap-928	122	13	cz-25068	cz-25068	PROPN
ap-928	122	14	řež	řež	PROPN
ap-928	122	15	near	near	ADP
ap-928	122	16	prague	prague	PROPN