id	sid	tid	token	lemma	pos
ap-1416	1	1	acta	acta	PROPN
ap-1416	1	2	polytechnica	polytechnica	PROPN
ap-1416	1	3	vol	vol	NOUN
ap-1416	1	4	.	.	PUNCT
ap-1416	2	1	51	51	NUM
ap-1416	2	2	no	no	INTJ
ap-1416	2	3	.	.	PUNCT
ap-1416	3	1	4/2011	4/2011	NUM
ap-1416	3	2	polynomial	polynomial	ADJ
ap-1416	3	3	solutions	solution	NOUN
ap-1416	3	4	of	of	ADP
ap-1416	3	5	the	the	DET
ap-1416	3	6	heun	heun	PROPN
ap-1416	3	7	equation	equation	PROPN
ap-1416	3	8	b.	b.	PROPN
ap-1416	3	9	shapiro	shapiro	PROPN
ap-1416	3	10	,	,	PUNCT
ap-1416	3	11	m.	m.	NOUN
ap-1416	3	12	tater	tater	NOUN
ap-1416	3	13	abstract	abstract	NOUN
ap-1416	3	14	we	we	PRON
ap-1416	3	15	review	review	VERB
ap-1416	3	16	properties	property	NOUN
ap-1416	3	17	of	of	ADP
ap-1416	3	18	certain	certain	ADJ
ap-1416	3	19	types	type	NOUN
ap-1416	3	20	of	of	ADP
ap-1416	3	21	polynomial	polynomial	ADJ
ap-1416	3	22	solutions	solution	NOUN
ap-1416	3	23	of	of	ADP
ap-1416	3	24	the	the	DET
ap-1416	3	25	heun	heun	PROPN
ap-1416	3	26	equation	equation	NOUN
ap-1416	3	27	.	.	PUNCT
ap-1416	4	1	two	two	NUM
ap-1416	4	2	aspects	aspect	NOUN
ap-1416	4	3	are	be	AUX
ap-1416	4	4	particularly	particularly	ADV
ap-1416	4	5	concerned	concern	VERB
ap-1416	4	6	,	,	PUNCT
ap-1416	4	7	the	the	DET
ap-1416	4	8	interlacing	interlace	VERB
ap-1416	4	9	property	property	NOUN
ap-1416	4	10	of	of	ADP
ap-1416	4	11	spectral	spectral	ADJ
ap-1416	4	12	and	and	CCONJ
ap-1416	4	13	stieltjes	stieltjes	NOUN
ap-1416	4	14	polynomials	polynomial	VERB
ap-1416	4	15	in	in	ADP
ap-1416	4	16	the	the	DET
ap-1416	4	17	case	case	NOUN
ap-1416	4	18	of	of	ADP
ap-1416	4	19	real	real	ADJ
ap-1416	4	20	roots	root	NOUN
ap-1416	4	21	of	of	ADP
ap-1416	4	22	these	these	DET
ap-1416	4	23	polynomials	polynomial	NOUN
ap-1416	4	24	and	and	CCONJ
ap-1416	4	25	asymptotic	asymptotic	ADJ
ap-1416	4	26	root	root	NOUN
ap-1416	4	27	distribution	distribution	NOUN
ap-1416	4	28	when	when	SCONJ
ap-1416	4	29	complex	complex	ADJ
ap-1416	4	30	roots	root	NOUN
ap-1416	4	31	are	be	AUX
ap-1416	4	32	present	present	ADJ
ap-1416	4	33	.	.	PUNCT
ap-1416	5	1	keywords	keyword	NOUN
ap-1416	5	2	:	:	PUNCT
ap-1416	5	3	heun	heun	PROPN
ap-1416	5	4	equation	equation	NOUN
ap-1416	5	5	,	,	PUNCT
ap-1416	5	6	van	van	PROPN
ap-1416	5	7	vleck	vleck	NOUN
ap-1416	5	8	and	and	CCONJ
ap-1416	5	9	stieltjes	stieltjes	PROPN
ap-1416	5	10	polynomials	polynomial	NOUN
ap-1416	5	11	,	,	PUNCT
ap-1416	5	12	asymptotic	asymptotic	ADJ
ap-1416	5	13	root	root	NOUN
ap-1416	5	14	distribution	distribution	NOUN
ap-1416	5	15	,	,	PUNCT
ap-1416	5	16	logarithmic	logarithmic	ADJ
ap-1416	5	17	potential	potential	NOUN
ap-1416	5	18	.	.	PUNCT
ap-1416	6	1	1	1	NUM
ap-1416	6	2	introduction	introduction	NOUN
ap-1416	6	3	we	we	PRON
ap-1416	6	4	study	study	VERB
ap-1416	6	5	polynomial	polynomial	ADJ
ap-1416	6	6	solutions	solution	NOUN
ap-1416	6	7	of	of	ADP
ap-1416	6	8	the	the	DET
ap-1416	6	9	heun	heun	NOUN
ap-1416	6	10	equation	equation	NOUN
ap-1416	6	11	{	{	PUNCT
ap-1416	6	12	q(z	q(z	PROPN
ap-1416	6	13	)	)	PUNCT
ap-1416	6	14	d2	d2	NOUN
ap-1416	6	15	dz2	dz2	NOUN
ap-1416	6	16	+	+	CCONJ
ap-1416	7	1	p	p	X
ap-1416	7	2	(	(	PUNCT
ap-1416	7	3	z	z	NOUN
ap-1416	7	4	)	)	PUNCT
ap-1416	8	1	d	d	NOUN
ap-1416	8	2	dz	dz	PROPN
ap-1416	9	1	+	+	NUM
ap-1416	9	2	v	v	ADJ
ap-1416	9	3	(	(	PUNCT
ap-1416	9	4	z	z	NOUN
ap-1416	9	5	)	)	PUNCT
ap-1416	9	6	}	}	PUNCT
ap-1416	9	7	s(z	s(z	PROPN
ap-1416	9	8	)	)	PUNCT
ap-1416	9	9	=	=	SYM
ap-1416	9	10	0	0	NUM
ap-1416	9	11	,	,	PUNCT
ap-1416	9	12	(	(	PUNCT
ap-1416	9	13	1	1	X
ap-1416	9	14	)	)	PUNCT
ap-1416	9	15	where	where	SCONJ
ap-1416	9	16	q	q	X
ap-1416	9	17	,	,	PUNCT
ap-1416	9	18	p	p	X
ap-1416	9	19	,	,	PUNCT
ap-1416	9	20	and	and	CCONJ
ap-1416	9	21	v	v	NOUN
ap-1416	9	22	are	be	AUX
ap-1416	9	23	given	give	VERB
ap-1416	9	24	polynomials	polynomial	NOUN
ap-1416	9	25	.	.	PUNCT
ap-1416	10	1	q	q	PUNCT
ap-1416	10	2	is	be	AUX
ap-1416	10	3	a	a	DET
ap-1416	10	4	polynomial	polynomial	NOUN
ap-1416	10	5	of	of	ADP
ap-1416	10	6	degree	degree	NOUN
ap-1416	10	7	k	k	PROPN
ap-1416	10	8	,	,	PUNCT
ap-1416	10	9	p	p	NOUN
ap-1416	10	10	is	be	AUX
ap-1416	10	11	at	at	ADP
ap-1416	10	12	most	most	ADJ
ap-1416	10	13	of	of	ADP
ap-1416	10	14	degree	degree	NOUN
ap-1416	10	15	k	k	NOUN
ap-1416	10	16	−	−	PROPN
ap-1416	10	17	1	1	NUM
ap-1416	10	18	,	,	PUNCT
ap-1416	10	19	and	and	CCONJ
ap-1416	10	20	v	v	NOUN
ap-1416	10	21	is	be	AUX
ap-1416	10	22	at	at	ADP
ap-1416	10	23	most	most	ADJ
ap-1416	10	24	of	of	ADP
ap-1416	10	25	degree	degree	NOUN
ap-1416	11	1	k	k	NOUN
ap-1416	11	2	−	−	PROPN
ap-1416	12	1	2	2	X
ap-1416	12	2	.	.	PUNCT
ap-1416	12	3	e.	e.	PROPN
ap-1416	12	4	heine	heine	PROPN
ap-1416	12	5	and	and	CCONJ
ap-1416	12	6	t.	t.	PROPN
ap-1416	12	7	stieltjes	stieltjes	PROPN
ap-1416	12	8	posed	pose	VERB
ap-1416	12	9	the	the	DET
ap-1416	12	10	following	follow	VERB
ap-1416	12	11	problem	problem	NOUN
ap-1416	12	12	:	:	PUNCT
ap-1416	12	13	problem	problem	NOUN
ap-1416	12	14	.	.	PUNCT
ap-1416	13	1	given	give	VERB
ap-1416	13	2	a	a	DET
ap-1416	13	3	pair	pair	NOUN
ap-1416	13	4	of	of	ADP
ap-1416	13	5	polynomials	polynomial	NOUN
ap-1416	13	6	{	{	PUNCT
ap-1416	13	7	q	q	NOUN
ap-1416	13	8	,	,	PUNCT
ap-1416	13	9	p	p	X
ap-1416	13	10	}	}	PUNCT
ap-1416	13	11	and	and	CCONJ
ap-1416	13	12	a	a	DET
ap-1416	13	13	positive	positive	ADJ
ap-1416	13	14	integer	integer	NOUN
ap-1416	13	15	n	n	PRON
ap-1416	13	16	find	find	VERB
ap-1416	13	17	all	all	DET
ap-1416	13	18	polynomials	polynomial	NOUN
ap-1416	13	19	v	v	ADP
ap-1416	13	20	such	such	ADJ
ap-1416	13	21	that	that	SCONJ
ap-1416	13	22	(	(	PUNCT
ap-1416	13	23	1	1	X
ap-1416	13	24	)	)	PUNCT
ap-1416	13	25	has	have	VERB
ap-1416	13	26	a	a	DET
ap-1416	13	27	polynomial	polynomial	ADJ
ap-1416	13	28	solution	solution	NOUN
ap-1416	13	29	s	s	NOUN
ap-1416	13	30	of	of	ADP
ap-1416	13	31	degree	degree	NOUN
ap-1416	13	32	n.	n.	NOUN
ap-1416	13	33	polynomials	polynomial	NOUN
ap-1416	13	34	v	v	NOUN
ap-1416	13	35	are	be	AUX
ap-1416	13	36	referred	refer	VERB
ap-1416	13	37	to	to	ADP
ap-1416	13	38	as	as	SCONJ
ap-1416	13	39	van	van	PROPN
ap-1416	13	40	vleck	vleck	NOUN
ap-1416	13	41	polynomials	polynomial	NOUN
ap-1416	13	42	and	and	CCONJ
ap-1416	13	43	polynomials	polynomial	NOUN
ap-1416	13	44	s	s	NOUN
ap-1416	13	45	as	as	ADP
ap-1416	13	46	stieltjes	stieltjes	PROPN
ap-1416	13	47	polynomials	polynomial	NOUN
ap-1416	13	48	.	.	PUNCT
ap-1416	14	1	for	for	ADP
ap-1416	14	2	a	a	DET
ap-1416	14	3	generic	generic	ADJ
ap-1416	14	4	pair	pair	NOUN
ap-1416	14	5	{	{	PUNCT
ap-1416	14	6	q	q	NOUN
ap-1416	14	7	,	,	PUNCT
ap-1416	14	8	p	p	NOUN
ap-1416	14	9	}	}	PUNCT
ap-1416	14	10	there	there	PRON
ap-1416	14	11	exist	exist	VERB
ap-1416	14	12	(	(	PUNCT
ap-1416	14	13	n+k−2	n+k−2	PROPN
ap-1416	14	14	n	n	ADJ
ap-1416	14	15	)	)	PUNCT
ap-1416	14	16	distinct	distinct	ADJ
ap-1416	14	17	van	van	PROPN
ap-1416	14	18	vleck	vleck	NOUN
ap-1416	14	19	polynomials	polynomial	NOUN
ap-1416	14	20	.	.	PUNCT
ap-1416	15	1	the	the	DET
ap-1416	15	2	simplest	simple	ADJ
ap-1416	15	3	case	case	NOUN
ap-1416	15	4	is	be	AUX
ap-1416	15	5	k	k	NOUN
ap-1416	15	6	=	=	SYM
ap-1416	15	7	2	2	NUM
ap-1416	15	8	,	,	PUNCT
ap-1416	15	9	when	when	SCONJ
ap-1416	15	10	equation	equation	NOUN
ap-1416	15	11	(	(	PUNCT
ap-1416	15	12	1	1	X
ap-1416	15	13	)	)	PUNCT
ap-1416	15	14	is	be	AUX
ap-1416	15	15	an	an	DET
ap-1416	15	16	equation	equation	NOUN
ap-1416	15	17	of	of	ADP
ap-1416	15	18	hypergeometric	hypergeometric	ADJ
ap-1416	15	19	type	type	NOUN
ap-1416	15	20	:	:	PUNCT
ap-1416	15	21	q	q	X
ap-1416	15	22	is	be	AUX
ap-1416	15	23	quadratic	quadratic	ADJ
ap-1416	15	24	,	,	PUNCT
ap-1416	15	25	p	p	NOUN
ap-1416	15	26	is	be	AUX
ap-1416	15	27	at	at	ADP
ap-1416	15	28	most	most	ADJ
ap-1416	15	29	linear	linear	ADJ
ap-1416	15	30	and	and	CCONJ
ap-1416	15	31	v	v	NOUN
ap-1416	15	32	reduces	reduce	VERB
ap-1416	15	33	to	to	ADP
ap-1416	15	34	a	a	DET
ap-1416	15	35	(	(	PUNCT
ap-1416	15	36	spectral	spectral	ADJ
ap-1416	15	37	)	)	PUNCT
ap-1416	15	38	parameter	parameter	NOUN
ap-1416	15	39	.	.	PUNCT
ap-1416	16	1	this	this	DET
ap-1416	16	2	situation	situation	NOUN
ap-1416	16	3	was	be	AUX
ap-1416	16	4	thoroughly	thoroughly	ADV
ap-1416	16	5	studied	study	VERB
ap-1416	16	6	in	in	ADP
ap-1416	16	7	the	the	DET
ap-1416	16	8	past	past	NOUN
ap-1416	16	9	and	and	CCONJ
ap-1416	16	10	all	all	DET
ap-1416	16	11	polynomial	polynomial	ADJ
ap-1416	16	12	solutions	solution	NOUN
ap-1416	16	13	are	be	AUX
ap-1416	16	14	brought	bring	VERB
ap-1416	16	15	to	to	ADP
ap-1416	16	16	six	six	NUM
ap-1416	16	17	types	type	NOUN
ap-1416	16	18	of	of	ADP
ap-1416	16	19	either	either	CCONJ
ap-1416	16	20	finite	finite	NOUN
ap-1416	16	21	or	or	CCONJ
ap-1416	16	22	infinite	infinite	ADJ
ap-1416	16	23	systems	system	NOUN
ap-1416	16	24	of	of	ADP
ap-1416	16	25	orthogonal	orthogonal	ADJ
ap-1416	16	26	polynomials	polynomial	NOUN
ap-1416	16	27	e.g.	e.g.	ADV
ap-1416	17	1	[	[	X
ap-1416	17	2	4	4	NUM
ap-1416	17	3	]	]	PUNCT
ap-1416	17	4	.	.	PUNCT
ap-1416	18	1	asymptotic	asymptotic	ADJ
ap-1416	18	2	distribution	distribution	NOUN
ap-1416	18	3	of	of	ADP
ap-1416	18	4	zeros	zero	NOUN
ap-1416	18	5	of	of	ADP
ap-1416	18	6	orthogonal	orthogonal	ADJ
ap-1416	18	7	polynomials	polynomial	NOUN
ap-1416	18	8	has	have	AUX
ap-1416	18	9	been	be	AUX
ap-1416	18	10	studied	study	VERB
ap-1416	18	11	for	for	ADP
ap-1416	18	12	quite	quite	DET
ap-1416	18	13	a	a	DET
ap-1416	18	14	long	long	ADJ
ap-1416	18	15	time	time	NOUN
ap-1416	18	16	and	and	CCONJ
ap-1416	18	17	many	many	ADJ
ap-1416	18	18	important	important	ADJ
ap-1416	18	19	results	result	NOUN
ap-1416	18	20	are	be	AUX
ap-1416	18	21	known	know	VERB
ap-1416	18	22	[	[	PUNCT
ap-1416	18	23	13	13	NUM
ap-1416	18	24	]	]	PUNCT
ap-1416	18	25	.	.	PUNCT
ap-1416	19	1	2	2	NUM
ap-1416	19	2	k	k	X
ap-1416	19	3	=	=	SYM
ap-1416	19	4	3	3	NUM
ap-1416	19	5	case	case	NOUN
ap-1416	19	6	next	next	ADJ
ap-1416	19	7	natural	natural	ADJ
ap-1416	19	8	step	step	NOUN
ap-1416	19	9	is	be	AUX
ap-1416	19	10	k	k	NOUN
ap-1416	19	11	=	=	SYM
ap-1416	19	12	3	3	X
ap-1416	19	13	.	.	PUNCT
ap-1416	20	1	even	even	ADV
ap-1416	20	2	this	this	DET
ap-1416	20	3	problem	problem	NOUN
ap-1416	20	4	has	have	VERB
ap-1416	20	5	a	a	DET
ap-1416	20	6	long	long	ADJ
ap-1416	20	7	history	history	NOUN
ap-1416	20	8	,	,	PUNCT
ap-1416	20	9	going	go	VERB
ap-1416	20	10	back	back	ADV
ap-1416	20	11	to	to	ADP
ap-1416	20	12	g.	g.	PROPN
ap-1416	20	13	lamé.	lamé.	PROPN
ap-1416	20	14	already	already	ADV
ap-1416	20	15	heine	heine	PROPN
ap-1416	20	16	and	and	CCONJ
ap-1416	20	17	stieltjes	stieltjes	PROPN
ap-1416	20	18	knew	know	VERB
ap-1416	20	19	that	that	SCONJ
ap-1416	20	20	for	for	ADP
ap-1416	20	21	a	a	DET
ap-1416	20	22	fixed	fix	VERB
ap-1416	20	23	n	n	NOUN
ap-1416	20	24	the	the	DET
ap-1416	20	25	above	above	ADJ
ap-1416	20	26	mentioned	mention	VERB
ap-1416	20	27	problem	problem	NOUN
ap-1416	20	28	has	have	VERB
ap-1416	20	29	n	n	PROPN
ap-1416	20	30	+	+	CCONJ
ap-1416	20	31	1	1	NUM
ap-1416	20	32	solutions	solution	NOUN
ap-1416	20	33	,	,	PUNCT
ap-1416	20	34	i.e.	i.e.	X
ap-1416	20	35	that	that	SCONJ
ap-1416	20	36	there	there	PRON
ap-1416	20	37	exist	exist	VERB
ap-1416	20	38	n	n	PROPN
ap-1416	20	39	+	+	CCONJ
ap-1416	20	40	1	1	NUM
ap-1416	20	41	distinct	distinct	ADJ
ap-1416	20	42	van	van	PROPN
ap-1416	20	43	vleck	vleck	NOUN
ap-1416	20	44	polynomials	polynomial	NOUN
ap-1416	20	45	.	.	PUNCT
ap-1416	21	1	moreover	moreover	ADV
ap-1416	21	2	,	,	PUNCT
ap-1416	21	3	in	in	ADP
ap-1416	21	4	the	the	DET
ap-1416	21	5	case	case	NOUN
ap-1416	21	6	of	of	ADP
ap-1416	21	7	the	the	DET
ap-1416	21	8	lamé	lamé	NOUN
ap-1416	21	9	equation	equation	NOUN
ap-1416	21	10	(	(	PUNCT
ap-1416	21	11	p	p	X
ap-1416	21	12	=	=	NOUN
ap-1416	21	13	q′/2	q′/2	NUM
ap-1416	21	14	)	)	PUNCT
ap-1416	21	15	and	and	CCONJ
ap-1416	21	16	if	if	SCONJ
ap-1416	21	17	we	we	PRON
ap-1416	21	18	additionally	additionally	ADV
ap-1416	21	19	assume	assume	VERB
ap-1416	21	20	that	that	SCONJ
ap-1416	21	21	q	q	PROPN
ap-1416	21	22	has	have	VERB
ap-1416	21	23	three	three	NUM
ap-1416	21	24	real	real	ADJ
ap-1416	21	25	and	and	CCONJ
ap-1416	21	26	distinct	distinct	ADJ
ap-1416	21	27	roots	root	NOUN
ap-1416	21	28	a1	a1	VERB
ap-1416	21	29	<	<	X
ap-1416	21	30	a2	a2	PROPN
ap-1416	21	31	<	<	X
ap-1416	21	32	a3	a3	NOUN
ap-1416	21	33	then	then	ADV
ap-1416	21	34	each	each	DET
ap-1416	21	35	root	root	NOUN
ap-1416	21	36	of	of	ADP
ap-1416	21	37	each	each	DET
ap-1416	21	38	v	v	NOUN
ap-1416	21	39	and	and	CCONJ
ap-1416	21	40	each	each	DET
ap-1416	21	41	s	s	VERB
ap-1416	21	42	is	be	AUX
ap-1416	21	43	real	real	ADJ
ap-1416	21	44	and	and	CCONJ
ap-1416	21	45	simple	simple	ADJ
ap-1416	21	46	,	,	PUNCT
ap-1416	21	47	the	the	DET
ap-1416	21	48	roots	root	NOUN
ap-1416	21	49	of	of	ADP
ap-1416	21	50	v	v	NOUN
ap-1416	21	51	and	and	CCONJ
ap-1416	21	52	s	s	PRON
ap-1416	21	53	lie	lie	NOUN
ap-1416	21	54	between	between	ADP
ap-1416	21	55	a1	a1	NOUN
ap-1416	21	56	and	and	CCONJ
ap-1416	21	57	a3	a3	NOUN
ap-1416	21	58	,	,	PUNCT
ap-1416	21	59	none	none	NOUN
ap-1416	21	60	of	of	ADP
ap-1416	21	61	the	the	DET
ap-1416	21	62	roots	root	NOUN
ap-1416	21	63	of	of	ADP
ap-1416	21	64	s	s	PRON
ap-1416	21	65	coincides	coincide	NOUN
ap-1416	21	66	with	with	ADP
ap-1416	21	67	any	any	DET
ap-1416	21	68	ai	ai	NOUN
ap-1416	21	69	(	(	PUNCT
ap-1416	21	70	i	i	NOUN
ap-1416	21	71	=	=	NOUN
ap-1416	21	72	1	1	NUM
ap-1416	21	73	,	,	PUNCT
ap-1416	21	74	2	2	NUM
ap-1416	21	75	,	,	PUNCT
ap-1416	21	76	3	3	NUM
ap-1416	21	77	)	)	PUNCT
ap-1416	21	78	,	,	PUNCT
ap-1416	21	79	and	and	CCONJ
ap-1416	21	80	n	n	CCONJ
ap-1416	21	81	+	+	CCONJ
ap-1416	21	82	1	1	NUM
ap-1416	21	83	polynomials	polynomial	NOUN
ap-1416	21	84	s	s	PART
ap-1416	21	85	can	can	AUX
ap-1416	21	86	be	be	AUX
ap-1416	21	87	distinguished	distinguish	VERB
ap-1416	21	88	by	by	ADP
ap-1416	21	89	the	the	DET
ap-1416	21	90	number	number	NOUN
ap-1416	21	91	of	of	ADP
ap-1416	21	92	roots	root	NOUN
ap-1416	21	93	lying	lie	VERB
ap-1416	21	94	in	in	ADP
ap-1416	21	95	the	the	DET
ap-1416	21	96	interval	interval	NOUN
ap-1416	21	97	(	(	PUNCT
ap-1416	21	98	a1	a1	NOUN
ap-1416	21	99	,	,	PUNCT
ap-1416	21	100	a2	a2	PROPN
ap-1416	21	101	)	)	PUNCT
ap-1416	21	102	(	(	PUNCT
ap-1416	21	103	the	the	DET
ap-1416	21	104	remaining	remain	VERB
ap-1416	21	105	roots	root	NOUN
ap-1416	21	106	lie	lie	VERB
ap-1416	21	107	in	in	ADP
ap-1416	21	108	(	(	PUNCT
ap-1416	21	109	a2	a2	PROPN
ap-1416	21	110	,	,	PUNCT
ap-1416	21	111	a3	a3	NOUN
ap-1416	21	112	)	)	PUNCT
ap-1416	21	113	)	)	PUNCT
ap-1416	22	1	[	[	X
ap-1416	22	2	14	14	NUM
ap-1416	22	3	]	]	PUNCT
ap-1416	22	4	.	.	PUNCT
ap-1416	23	1	besides	besides	SCONJ
ap-1416	23	2	this	this	PRON
ap-1416	23	3	,	,	PUNCT
ap-1416	23	4	there	there	PRON
ap-1416	23	5	is	be	VERB
ap-1416	23	6	no	no	DET
ap-1416	23	7	zero	zero	NUM
ap-1416	23	8	of	of	ADP
ap-1416	23	9	s	s	PRON
ap-1416	23	10	between	between	ADP
ap-1416	23	11	a2	a2	PROPN
ap-1416	23	12	and	and	CCONJ
ap-1416	23	13	the	the	DET
ap-1416	23	14	zero	zero	NUM
ap-1416	23	15	of	of	ADP
ap-1416	23	16	the	the	DET
ap-1416	23	17	corresponding	correspond	VERB
ap-1416	23	18	van	van	PROPN
ap-1416	23	19	vleck	vleck	NOUN
ap-1416	23	20	polynomial	polynomial	NOUN
ap-1416	23	21	[	[	X
ap-1416	23	22	1	1	NUM
ap-1416	23	23	]	]	PUNCT
ap-1416	23	24	,	,	PUNCT
ap-1416	23	25	cf	cf	INTJ
ap-1416	23	26	.	.	PUNCT
ap-1416	23	27	figure	figure	NOUN
ap-1416	23	28	1	1	NUM
ap-1416	23	29	.	.	PUNCT
ap-1416	24	1	some	some	DET
ap-1416	24	2	additional	additional	ADJ
ap-1416	24	3	results	result	NOUN
ap-1416	24	4	are	be	AUX
ap-1416	24	5	known	know	VERB
ap-1416	24	6	for	for	ADP
ap-1416	24	7	fixed	fix	VERB
ap-1416	24	8	n.	n.	NOUN
ap-1416	24	9	each	each	DET
ap-1416	24	10	van	van	PROPN
ap-1416	24	11	vleck	vleck	NOUN
ap-1416	24	12	(	(	PUNCT
ap-1416	24	13	linear	linear	ADJ
ap-1416	24	14	)	)	PUNCT
ap-1416	24	15	polynomial	polynomial	NOUN
ap-1416	24	16	has	have	VERB
ap-1416	24	17	a	a	DET
ap-1416	24	18	single	single	ADJ
ap-1416	24	19	zero	zero	NUM
ap-1416	24	20	νi	νi	NOUN
ap-1416	24	21	,	,	PUNCT
ap-1416	24	22	i	i	PRON
ap-1416	24	23	=	=	NOUN
ap-1416	24	24	1	1	NUM
ap-1416	24	25	,	,	PUNCT
ap-1416	24	26	.	.	PUNCT
ap-1416	24	27	.	.	PUNCT
ap-1416	25	1	.	.	PUNCT
ap-1416	26	1	,	,	PUNCT
ap-1416	26	2	n	n	PROPN
ap-1416	26	3	+	+	NOUN
ap-1416	26	4	1	1	X
ap-1416	26	5	.	.	X
ap-1416	26	6	we	we	PRON
ap-1416	26	7	can	can	AUX
ap-1416	26	8	form	form	VERB
ap-1416	26	9	a	a	DET
ap-1416	26	10	so	so	ADV
ap-1416	26	11	-	-	PUNCT
ap-1416	26	12	called	call	VERB
ap-1416	26	13	spectral	spectral	ADJ
ap-1416	26	14	polynomial	polynomial	ADJ
ap-1416	26	15	made	make	VERB
ap-1416	26	16	of	of	ADP
ap-1416	26	17	these	these	DET
ap-1416	26	18	zeros	zero	NOUN
ap-1416	26	19	spn(λ	spn(λ	PROPN
ap-1416	26	20	)	)	PUNCT
ap-1416	26	21	=	=	SYM
ap-1416	27	1	n+1∏	n+1∏	NOUN
ap-1416	27	2	i=1	i=1	PROPN
ap-1416	28	1	(	(	PUNCT
ap-1416	28	2	λ	λ	X
ap-1416	28	3	−	−	NOUN
ap-1416	28	4	νi	νi	NOUN
ap-1416	28	5	)	)	PUNCT
ap-1416	28	6	.	.	PUNCT
ap-1416	29	1	zeros	zero	NOUN
ap-1416	29	2	of	of	ADP
ap-1416	29	3	two	two	NUM
ap-1416	29	4	successive	successive	ADJ
ap-1416	29	5	spectral	spectral	ADJ
ap-1416	29	6	polynomials	polynomial	NOUN
ap-1416	29	7	,	,	PUNCT
ap-1416	29	8	i.e.	i.e.	X
ap-1416	29	9	spn	spn	PROPN
ap-1416	29	10	and	and	CCONJ
ap-1416	29	11	spn+1	spn+1	VERB
ap-1416	29	12	interlace	interlace	NOUN
ap-1416	29	13	:	:	PUNCT
ap-1416	29	14	between	between	ADP
ap-1416	29	15	any	any	DET
ap-1416	29	16	two	two	NUM
ap-1416	29	17	roots	root	NOUN
ap-1416	29	18	of	of	ADP
ap-1416	29	19	spn	spn	PROPN
ap-1416	29	20	lies	lie	VERB
ap-1416	29	21	a	a	DET
ap-1416	29	22	root	root	NOUN
ap-1416	29	23	of	of	ADP
ap-1416	29	24	spn+1	spn+1	NOUN
ap-1416	29	25	,	,	PUNCT
ap-1416	29	26	and	and	CCONJ
ap-1416	29	27	vice	vice	ADV
ap-1416	29	28	versa	versa	ADV
ap-1416	29	29	[	[	X
ap-1416	29	30	2	2	NUM
ap-1416	29	31	]	]	PUNCT
ap-1416	29	32	.	.	PUNCT
ap-1416	30	1	on	on	ADP
ap-1416	30	2	the	the	DET
ap-1416	30	3	other	other	ADJ
ap-1416	30	4	hand	hand	NOUN
ap-1416	30	5	,	,	PUNCT
ap-1416	30	6	in	in	ADP
ap-1416	30	7	spite	spite	NOUN
ap-1416	30	8	of	of	ADP
ap-1416	30	9	the	the	DET
ap-1416	30	10	fact	fact	NOUN
ap-1416	30	11	that	that	SCONJ
ap-1416	30	12	these	these	DET
ap-1416	30	13	polynomials	polynomial	NOUN
ap-1416	30	14	have	have	AUX
ap-1416	30	15	simple	simple	ADJ
ap-1416	30	16	zeros	zero	NOUN
ap-1416	30	17	that	that	PRON
ap-1416	30	18	interlace	interlace	VERB
ap-1416	30	19	,	,	PUNCT
ap-1416	30	20	the	the	DET
ap-1416	30	21	system	system	NOUN
ap-1416	30	22	{	{	PUNCT
ap-1416	30	23	spn}∞n=1	spn}∞n=1	PROPN
ap-1416	30	24	is	be	AUX
ap-1416	30	25	not	not	PART
ap-1416	30	26	orthogonal	orthogonal	ADJ
ap-1416	30	27	with	with	ADP
ap-1416	30	28	respect	respect	NOUN
ap-1416	30	29	to	to	ADP
ap-1416	30	30	any	any	DET
ap-1416	30	31	measure	measure	NOUN
ap-1416	30	32	.	.	PUNCT
ap-1416	31	1	the	the	DET
ap-1416	31	2	proof	proof	NOUN
ap-1416	31	3	in	in	ADP
ap-1416	31	4	[	[	X
ap-1416	31	5	2	2	NUM
ap-1416	31	6	]	]	PUNCT
ap-1416	31	7	is	be	AUX
ap-1416	31	8	based	base	VERB
ap-1416	31	9	on	on	ADP
ap-1416	31	10	the	the	DET
ap-1416	31	11	finding	finding	NOUN
ap-1416	31	12	that	that	SCONJ
ap-1416	31	13	the	the	DET
ap-1416	31	14	asymptotic	asymptotic	ADJ
ap-1416	31	15	zero	zero	NUM
ap-1416	31	16	distribution	distribution	NOUN
ap-1416	31	17	of	of	ADP
ap-1416	31	18	spn	spn	PROPN
ap-1416	31	19	[	[	X
ap-1416	31	20	3	3	X
ap-1416	31	21	]	]	PUNCT
ap-1416	31	22	is	be	AUX
ap-1416	31	23	different	different	ADJ
ap-1416	31	24	from	from	ADP
ap-1416	31	25	that	that	PRON
ap-1416	31	26	of	of	ADP
ap-1416	31	27	orthogonal	orthogonal	ADJ
ap-1416	31	28	polynomials	polynomial	NOUN
ap-1416	31	29	,	,	PUNCT
ap-1416	31	30	showing	show	VERB
ap-1416	31	31	also	also	ADV
ap-1416	31	32	that	that	SCONJ
ap-1416	31	33	spn	spn	PROPN
ap-1416	31	34	do	do	AUX
ap-1416	31	35	not	not	PART
ap-1416	31	36	obey	obey	VERB
ap-1416	31	37	any	any	DET
ap-1416	31	38	three	three	NUM
ap-1416	31	39	-	-	PUNCT
ap-1416	31	40	term	term	NOUN
ap-1416	31	41	recurrence	recurrence	NOUN
ap-1416	31	42	relation	relation	NOUN
ap-1416	31	43	.	.	PUNCT
ap-1416	32	1	as	as	SCONJ
ap-1416	32	2	already	already	ADV
ap-1416	32	3	mentioned	mention	VERB
ap-1416	32	4	above	above	ADV
ap-1416	32	5	,	,	PUNCT
ap-1416	32	6	the	the	DET
ap-1416	32	7	roots	root	NOUN
ap-1416	32	8	of	of	ADP
ap-1416	32	9	van	van	PROPN
ap-1416	32	10	vleck	vleck	PROPN
ap-1416	32	11	’s	’s	PART
ap-1416	32	12	νi	νi	DET
ap-1416	32	13	lie	lie	NOUN
ap-1416	32	14	between	between	ADP
ap-1416	32	15	a1	a1	NOUN
ap-1416	32	16	and	and	CCONJ
ap-1416	32	17	a3	a3	NOUN
ap-1416	32	18	,	,	PUNCT
ap-1416	32	19	and	and	CCONJ
ap-1416	32	20	are	be	AUX
ap-1416	32	21	mutually	mutually	ADV
ap-1416	32	22	different	different	ADJ
ap-1416	32	23	,	,	PUNCT
ap-1416	32	24	making	make	VERB
ap-1416	32	25	it	it	PRON
ap-1416	32	26	thus	thus	ADV
ap-1416	32	27	possible	possible	ADJ
ap-1416	32	28	to	to	PART
ap-1416	32	29	order	order	VERB
ap-1416	32	30	stieltjes	stieltjes	NOUN
ap-1416	32	31	polynomials	polynomial	NOUN
ap-1416	32	32	accordingly	accordingly	ADV
ap-1416	32	33	.	.	PUNCT
ap-1416	33	1	so	so	ADV
ap-1416	33	2	,	,	PUNCT
ap-1416	33	3	for	for	ADP
ap-1416	33	4	a	a	DET
ap-1416	33	5	fixed	fix	VERB
ap-1416	33	6	n	n	CCONJ
ap-1416	33	7	,	,	PUNCT
ap-1416	33	8	we	we	PRON
ap-1416	33	9	have	have	VERB
ap-1416	33	10	a	a	DET
ap-1416	33	11	sequence	sequence	NOUN
ap-1416	33	12	of	of	ADP
ap-1416	33	13	n+1	n+1	NUM
ap-1416	33	14	stieltjes	stieltjes	PROPN
ap-1416	33	15	polynomials	polynomial	NOUN
ap-1416	33	16	s	s	PART
ap-1416	33	17	(	(	PUNCT
ap-1416	33	18	n	n	CCONJ
ap-1416	33	19	)	)	PUNCT
ap-1416	33	20	i	i	PRON
ap-1416	33	21	of	of	ADP
ap-1416	33	22	degree	degree	NOUN
ap-1416	33	23	n	n	CCONJ
ap-1416	33	24	,	,	PUNCT
ap-1416	33	25	i	i	PRON
ap-1416	33	26	=	=	NOUN
ap-1416	33	27	1	1	NUM
ap-1416	33	28	,	,	PUNCT
ap-1416	33	29	.	.	PUNCT
ap-1416	33	30	.	.	PUNCT
ap-1416	34	1	.	.	PUNCT
ap-1416	35	1	,	,	PUNCT
ap-1416	35	2	n+1	n+1	X
ap-1416	35	3	.	.	PROPN
ap-1416	36	1	two	two	NUM
ap-1416	36	2	interesting	interesting	ADJ
ap-1416	36	3	results	result	NOUN
ap-1416	36	4	are	be	AUX
ap-1416	36	5	proved	prove	VERB
ap-1416	36	6	in	in	ADP
ap-1416	36	7	[	[	X
ap-1416	36	8	1	1	NUM
ap-1416	36	9	]	]	PUNCT
ap-1416	36	10	.	.	PUNCT
ap-1416	37	1	the	the	DET
ap-1416	37	2	n	n	PROPN
ap-1416	37	3	zeros	zero	NOUN
ap-1416	37	4	of	of	ADP
ap-1416	37	5	s	s	PROPN
ap-1416	37	6	(	(	PUNCT
ap-1416	37	7	n	n	CCONJ
ap-1416	37	8	)	)	PUNCT
ap-1416	37	9	i	i	PRON
ap-1416	37	10	and	and	CCONJ
ap-1416	37	11	the	the	DET
ap-1416	37	12	n	n	ADJ
ap-1416	37	13	zeros	zero	NOUN
ap-1416	37	14	of	of	ADP
ap-1416	37	15	s	s	PROPN
ap-1416	37	16	(	(	PUNCT
ap-1416	37	17	n	n	CCONJ
ap-1416	37	18	)	)	PUNCT
ap-1416	37	19	i+1	i+1	NUM
ap-1416	37	20	interlace	interlace	NOUN
ap-1416	37	21	.	.	PUNCT
ap-1416	38	1	in	in	ADP
ap-1416	38	2	addition	addition	NOUN
ap-1416	38	3	,	,	PUNCT
ap-1416	38	4	the	the	DET
ap-1416	38	5	smallest	small	ADJ
ap-1416	38	6	zero	zero	NUM
ap-1416	38	7	of	of	ADP
ap-1416	38	8	s	s	PROPN
ap-1416	38	9	(	(	PUNCT
ap-1416	38	10	n	n	CCONJ
ap-1416	38	11	)	)	PUNCT
ap-1416	38	12	i+1	i+1	VERB
ap-1416	38	13	is	be	AUX
ap-1416	38	14	smaller	small	ADJ
ap-1416	38	15	than	than	ADP
ap-1416	38	16	the	the	DET
ap-1416	38	17	smallest	small	ADJ
ap-1416	38	18	zero	zero	NUM
ap-1416	38	19	of	of	ADP
ap-1416	38	20	s	s	PROPN
ap-1416	38	21	(	(	PUNCT
ap-1416	38	22	n	n	CCONJ
ap-1416	38	23	)	)	PUNCT
ap-1416	39	1	i	i	PRON
ap-1416	39	2	.	.	PUNCT
ap-1416	40	1	besides	besides	SCONJ
ap-1416	40	2	this	this	PRON
ap-1416	40	3	,	,	PUNCT
ap-1416	40	4	the	the	DET
ap-1416	40	5	zeros	zero	NOUN
ap-1416	40	6	of	of	ADP
ap-1416	40	7	s	s	PROPN
ap-1416	40	8	(	(	PUNCT
ap-1416	40	9	n	n	CCONJ
ap-1416	40	10	)	)	PUNCT
ap-1416	40	11	i	i	PRON
ap-1416	40	12	and	and	CCONJ
ap-1416	40	13	s	s	PROPN
ap-1416	40	14	(	(	PUNCT
ap-1416	40	15	n+1	n+1	PROPN
ap-1416	40	16	)	)	PUNCT
ap-1416	40	17	j	j	PROPN
ap-1416	40	18	interlace	interlace	NOUN
ap-1416	40	19	if	if	SCONJ
ap-1416	40	20	and	and	CCONJ
ap-1416	40	21	only	only	ADV
ap-1416	40	22	if	if	SCONJ
ap-1416	40	23	i	i	PRON
ap-1416	40	24	=	=	SYM
ap-1416	40	25	j	j	PROPN
ap-1416	40	26	or	or	CCONJ
ap-1416	40	27	i	i	PRON
ap-1416	40	28	=	=	SYM
ap-1416	40	29	j	j	PROPN
ap-1416	41	1	+	+	CCONJ
ap-1416	41	2	1	1	NUM
ap-1416	41	3	,	,	PUNCT
ap-1416	41	4	otherwise	otherwise	ADV
ap-1416	41	5	they	they	PRON
ap-1416	41	6	do	do	AUX
ap-1416	41	7	not	not	PART
ap-1416	41	8	interlace	interlace	VERB
ap-1416	41	9	.	.	PUNCT
ap-1416	42	1	there	there	PRON
ap-1416	42	2	is	be	VERB
ap-1416	42	3	no	no	DET
ap-1416	42	4	definitive	definitive	ADJ
ap-1416	42	5	answer	answer	NOUN
ap-1416	42	6	to	to	ADP
ap-1416	42	7	the	the	DET
ap-1416	42	8	question	question	NOUN
ap-1416	42	9	of	of	ADP
ap-1416	42	10	orthogonality	orthogonality	NOUN
ap-1416	42	11	of	of	ADP
ap-1416	42	12	s	s	NOUN
ap-1416	42	13	(	(	PUNCT
ap-1416	42	14	n	n	CCONJ
ap-1416	42	15	)	)	PUNCT
ap-1416	42	16	i	i	PRON
ap-1416	42	17	.	.	PUNCT
ap-1416	43	1	if	if	SCONJ
ap-1416	43	2	complex	complex	ADJ
ap-1416	43	3	roots	root	NOUN
ap-1416	43	4	of	of	ADP
ap-1416	43	5	q	q	NOUN
ap-1416	43	6	are	be	AUX
ap-1416	43	7	admitted	admit	VERB
ap-1416	43	8	,	,	PUNCT
ap-1416	43	9	g.	g.	PROPN
ap-1416	43	10	pólya	pólya	PROPN
ap-1416	43	11	proved	prove	VERB
ap-1416	43	12	[	[	X
ap-1416	43	13	9	9	NUM
ap-1416	43	14	]	]	PUNCT
ap-1416	43	15	that	that	SCONJ
ap-1416	43	16	all	all	DET
ap-1416	43	17	roots	root	NOUN
ap-1416	43	18	of	of	ADP
ap-1416	43	19	both	both	PRON
ap-1416	43	20	v	v	NOUN
ap-1416	43	21	and	and	CCONJ
ap-1416	43	22	s	s	VERB
ap-1416	43	23	belong	belong	VERB
ap-1416	43	24	to	to	ADP
ap-1416	43	25	the	the	DET
ap-1416	43	26	convex	convex	PROPN
ap-1416	43	27	hull	hull	NOUN
ap-1416	43	28	convq	convq	PROPN
ap-1416	43	29	of	of	ADP
ap-1416	43	30	a1	a1	PROPN
ap-1416	43	31	,	,	PUNCT
ap-1416	43	32	a2	a2	PROPN
ap-1416	43	33	,	,	PUNCT
ap-1416	43	34	a3	a3	NOUN
ap-1416	43	35	provided	provide	VERB
ap-1416	43	36	that	that	SCONJ
ap-1416	43	37	all	all	DET
ap-1416	43	38	residues	residue	NOUN
ap-1416	43	39	of	of	ADP
ap-1416	43	40	p	p	X
ap-1416	43	41	/	/	SYM
ap-1416	43	42	q	q	NOUN
ap-1416	43	43	are	be	AUX
ap-1416	43	44	positive	positive	ADJ
ap-1416	43	45	.	.	PUNCT
ap-1416	44	1	investigations	investigation	NOUN
ap-1416	44	2	of	of	ADP
ap-1416	44	3	the	the	DET
ap-1416	44	4	root	root	NOUN
ap-1416	44	5	asymptotics	asymptotic	NOUN
ap-1416	44	6	of	of	ADP
ap-1416	44	7	both	both	CCONJ
ap-1416	44	8	van	van	PROPN
ap-1416	44	9	vleck	vleck	NOUN
ap-1416	44	10	and	and	CCONJ
ap-1416	44	11	stieltjes	stieltjes	PROPN
ap-1416	44	12	polynomials	polynomial	NOUN
ap-1416	44	13	have	have	VERB
ap-1416	44	14	a	a	DET
ap-1416	44	15	considerably	considerably	ADV
ap-1416	44	16	shorter	short	ADJ
ap-1416	44	17	history	history	NOUN
ap-1416	44	18	.	.	PUNCT
ap-1416	45	1	we	we	PRON
ap-1416	45	2	summarize	summarize	VERB
ap-1416	45	3	here	here	ADV
ap-1416	45	4	some	some	DET
ap-1416	45	5	salient	salient	NOUN
ap-1416	45	6	results	result	NOUN
ap-1416	46	1	[	[	X
ap-1416	46	2	10–12	10–12	NUM
ap-1416	46	3	]	]	PUNCT
ap-1416	46	4	.	.	PUNCT
ap-1416	47	1	90	90	NUM
ap-1416	47	2	acta	acta	PROPN
ap-1416	47	3	polytechnica	polytechnica	PROPN
ap-1416	47	4	vol	vol	NOUN
ap-1416	47	5	.	.	PUNCT
ap-1416	48	1	51	51	NUM
ap-1416	48	2	no	no	INTJ
ap-1416	48	3	.	.	PUNCT
ap-1416	49	1	4/2011	4/2011	NUM
ap-1416	49	2	−2	−2	NOUN
ap-1416	49	3	−1	−1	NOUN
ap-1416	49	4	0	0	NUM
ap-1416	49	5	1	1	NUM
ap-1416	49	6	2	2	NUM
ap-1416	49	7	3	3	NUM
ap-1416	49	8	4	4	NUM
ap-1416	49	9	fig	fig	NOUN
ap-1416	49	10	.	.	PUNCT
ap-1416	50	1	1	1	NUM
ap-1416	50	2	:	:	PUNCT
ap-1416	50	3	the	the	DET
ap-1416	50	4	situation	situation	NOUN
ap-1416	50	5	for	for	ADP
ap-1416	50	6	p	p	NOUN
ap-1416	50	7	=	=	SYM
ap-1416	50	8	0	0	NUM
ap-1416	50	9	and	and	CCONJ
ap-1416	50	10	n	n	CCONJ
ap-1416	50	11	=	=	NUM
ap-1416	50	12	25	25	NUM
ap-1416	50	13	.	.	PUNCT
ap-1416	51	1	the	the	DET
ap-1416	51	2	thick	thick	ADJ
ap-1416	51	3	black	black	ADJ
ap-1416	51	4	dots	dot	NOUN
ap-1416	51	5	mark	mark	VERB
ap-1416	51	6	the	the	DET
ap-1416	51	7	roots	root	NOUN
ap-1416	51	8	of	of	ADP
ap-1416	51	9	q(x	q(x	NOUN
ap-1416	51	10	)	)	PUNCT
ap-1416	51	11	=	=	PUNCT
ap-1416	52	1	(	(	PUNCT
ap-1416	52	2	x	x	SYM
ap-1416	52	3	+	+	NUM
ap-1416	52	4	2)(x	2)(x	NUM
ap-1416	52	5	−	−	NOUN
ap-1416	52	6	1)(x	1)(x	NUM
ap-1416	52	7	−	−	NOUN
ap-1416	52	8	4	4	NUM
ap-1416	52	9	)	)	PUNCT
ap-1416	52	10	,	,	PUNCT
ap-1416	52	11	the	the	DET
ap-1416	52	12	thick	thick	ADJ
ap-1416	52	13	green	green	ADJ
ap-1416	52	14	dots	dot	NOUN
ap-1416	52	15	mark	mark	VERB
ap-1416	52	16	the	the	DET
ap-1416	52	17	roots	root	NOUN
ap-1416	52	18	of	of	ADP
ap-1416	52	19	n+1	n+1	PROPN
ap-1416	52	20	van	van	PROPN
ap-1416	52	21	vleck	vleck	NOUN
ap-1416	52	22	polynomials	polynomial	NOUN
ap-1416	52	23	,	,	PUNCT
ap-1416	52	24	and	and	CCONJ
ap-1416	52	25	the	the	DET
ap-1416	52	26	small	small	ADJ
ap-1416	52	27	red	red	ADJ
ap-1416	52	28	dots	dot	NOUN
ap-1416	52	29	mark	mark	VERB
ap-1416	53	1	n	n	PRON
ap-1416	53	2	roots	root	NOUN
ap-1416	53	3	of	of	ADP
ap-1416	53	4	the	the	DET
ap-1416	53	5	corresponding	corresponding	ADJ
ap-1416	53	6	stieltjes	stieltjes	NOUN
ap-1416	53	7	polynomials	polynomial	VERB
ap-1416	53	8	−1	−1	NOUN
ap-1416	53	9	0	0	NUM
ap-1416	53	10	1	1	NUM
ap-1416	53	11	2	2	NUM
ap-1416	53	12	0	0	NUM
ap-1416	53	13	0.5	0.5	NUM
ap-1416	53	14	1	1	NUM
ap-1416	53	15	1.5	1.5	NUM
ap-1416	53	16	2	2	NUM
ap-1416	53	17	2.5	2.5	NUM
ap-1416	53	18	3	3	NUM
ap-1416	53	19	3.5	3.5	NUM
ap-1416	53	20	4	4	NUM
ap-1416	53	21	−1	−1	NOUN
ap-1416	53	22	0	0	NUM
ap-1416	53	23	1	1	NUM
ap-1416	53	24	2	2	NUM
ap-1416	53	25	0	0	NUM
ap-1416	53	26	0.5	0.5	NUM
ap-1416	53	27	1	1	NUM
ap-1416	53	28	1.5	1.5	NUM
ap-1416	53	29	2	2	NUM
ap-1416	53	30	2.5	2.5	NUM
ap-1416	53	31	3	3	NUM
ap-1416	53	32	3.5	3.5	NUM
ap-1416	53	33	4	4	NUM
ap-1416	53	34	fig	fig	NOUN
ap-1416	53	35	.	.	PUNCT
ap-1416	54	1	2	2	NUM
ap-1416	54	2	:	:	PUNCT
ap-1416	54	3	the	the	DET
ap-1416	54	4	left	left	ADJ
ap-1416	54	5	part	part	NOUN
ap-1416	54	6	:	:	PUNCT
ap-1416	54	7	the	the	DET
ap-1416	54	8	roots	root	NOUN
ap-1416	54	9	of	of	ADP
ap-1416	54	10	the	the	DET
ap-1416	54	11	spectral	spectral	ADJ
ap-1416	54	12	polynomial	polynomial	ADJ
ap-1416	54	13	sp51(λ	sp51(λ	NOUN
ap-1416	54	14	)	)	PUNCT
ap-1416	54	15	for	for	ADP
ap-1416	54	16	q(z	q(z	PROPN
ap-1416	54	17	)	)	PUNCT
ap-1416	54	18	=	=	PUNCT
ap-1416	55	1	(	(	PUNCT
ap-1416	55	2	z	z	NOUN
ap-1416	55	3	+	+	NOUN
ap-1416	55	4	1)(z	1)(z	NUM
ap-1416	55	5	−	−	NOUN
ap-1416	55	6	2)(z	2)(z	NUM
ap-1416	55	7	−	−	NUM
ap-1416	55	8	2	2	NUM
ap-1416	55	9	−	−	PROPN
ap-1416	55	10	4i	4i	NUM
ap-1416	55	11	)	)	PUNCT
ap-1416	55	12	and	and	CCONJ
ap-1416	55	13	p	p	X
ap-1416	55	14	(	(	PUNCT
ap-1416	55	15	z	z	NOUN
ap-1416	55	16	)	)	PUNCT
ap-1416	55	17	=	=	SYM
ap-1416	55	18	(	(	PUNCT
ap-1416	55	19	z+2	z+2	NUM
ap-1416	55	20	+	+	NOUN
ap-1416	55	21	2i)(z−1	2i)(z−1	ADJ
ap-1416	55	22	+	+	NOUN
ap-1416	55	23	3i	3i	NOUN
ap-1416	55	24	)	)	PUNCT
ap-1416	55	25	.	.	PUNCT
ap-1416	56	1	the	the	DET
ap-1416	56	2	thick	thick	ADJ
ap-1416	56	3	black	black	ADJ
ap-1416	56	4	dots	dot	NOUN
ap-1416	56	5	mark	mark	VERB
ap-1416	56	6	the	the	DET
ap-1416	56	7	roots	root	NOUN
ap-1416	56	8	of	of	ADP
ap-1416	56	9	q	q	NOUN
ap-1416	56	10	,	,	PUNCT
ap-1416	56	11	the	the	DET
ap-1416	56	12	green	green	PROPN
ap-1416	56	13	dots	dot	NOUN
ap-1416	56	14	mark	mark	VERB
ap-1416	56	15	the	the	DET
ap-1416	56	16	roots	root	NOUN
ap-1416	56	17	of	of	ADP
ap-1416	56	18	van	van	PROPN
ap-1416	56	19	vleck	vleck	PROPN
ap-1416	56	20	polynomials	polynomial	NOUN
ap-1416	56	21	.	.	PUNCT
ap-1416	57	1	the	the	DET
ap-1416	57	2	right	right	ADJ
ap-1416	57	3	part	part	NOUN
ap-1416	57	4	:	:	PUNCT
ap-1416	57	5	the	the	DET
ap-1416	57	6	thick	thick	ADJ
ap-1416	57	7	green	green	ADJ
ap-1416	57	8	dot	dot	NOUN
ap-1416	57	9	marks	mark	NOUN
ap-1416	57	10	one	one	NUM
ap-1416	57	11	of	of	ADP
ap-1416	57	12	the	the	DET
ap-1416	57	13	51	51	NUM
ap-1416	57	14	van	van	PROPN
ap-1416	57	15	vleck	vleck	NOUN
ap-1416	57	16	polynomials	polynomial	NOUN
ap-1416	57	17	and	and	CCONJ
ap-1416	57	18	the	the	DET
ap-1416	57	19	small	small	ADJ
ap-1416	57	20	red	red	ADJ
ap-1416	57	21	dots	dot	NOUN
ap-1416	57	22	mark	mark	VERB
ap-1416	57	23	50	50	NUM
ap-1416	57	24	roots	root	NOUN
ap-1416	57	25	of	of	ADP
ap-1416	57	26	the	the	DET
ap-1416	57	27	corresponding	correspond	VERB
ap-1416	57	28	stieltjes	stieltjes	NOUN
ap-1416	57	29	polynomial	polynomial	ADJ
ap-1416	57	30	the	the	DET
ap-1416	57	31	roots	root	NOUN
ap-1416	57	32	can	can	AUX
ap-1416	57	33	be	be	AUX
ap-1416	57	34	asymptotically	asymptotically	ADV
ap-1416	57	35	localized	localize	VERB
ap-1416	57	36	.	.	PUNCT
ap-1416	58	1	for	for	ADP
ap-1416	58	2	any	any	DET
ap-1416	58	3	ε	ε	PROPN
ap-1416	58	4	>	>	X
ap-1416	58	5	0	0	PUNCT
ap-1416	58	6	there	there	PRON
ap-1416	58	7	exist	exist	VERB
ap-1416	58	8	nε	nε	NOUN
ap-1416	58	9	such	such	ADJ
ap-1416	58	10	that	that	SCONJ
ap-1416	58	11	for	for	ADP
ap-1416	58	12	any	any	DET
ap-1416	58	13	n	n	PRON
ap-1416	58	14	≥	≥	NOUN
ap-1416	58	15	nε	nε	VERB
ap-1416	58	16	any	any	DET
ap-1416	58	17	root	root	NOUN
ap-1416	58	18	of	of	ADP
ap-1416	58	19	any	any	DET
ap-1416	58	20	v	v	NOUN
ap-1416	58	21	as	as	ADV
ap-1416	58	22	well	well	ADV
ap-1416	58	23	as	as	ADP
ap-1416	58	24	any	any	DET
ap-1416	58	25	root	root	NOUN
ap-1416	58	26	of	of	ADP
ap-1416	58	27	the	the	DET
ap-1416	58	28	corresponding	corresponding	NOUN
ap-1416	58	29	s	s	PART
ap-1416	58	30	lie	lie	NOUN
ap-1416	58	31	in	in	ADP
ap-1416	58	32	the	the	DET
ap-1416	58	33	ε	ε	PROPN
ap-1416	58	34	-	-	PUNCT
ap-1416	58	35	neighbourhood	neighbourhood	NOUN
ap-1416	58	36	(	(	PUNCT
ap-1416	58	37	in	in	ADP
ap-1416	58	38	the	the	DET
ap-1416	58	39	usual	usual	ADJ
ap-1416	58	40	euclidean	euclidean	ADJ
ap-1416	58	41	distance	distance	NOUN
ap-1416	58	42	on	on	ADP
ap-1416	58	43	c	c	NOUN
ap-1416	58	44	)	)	PUNCT
ap-1416	58	45	of	of	ADP
ap-1416	58	46	the	the	DET
ap-1416	58	47	convex	convex	PROPN
ap-1416	58	48	hull	hull	NOUN
ap-1416	58	49	of	of	ADP
ap-1416	58	50	a1	a1	PROPN
ap-1416	58	51	,	,	PUNCT
ap-1416	58	52	a2	a2	PROPN
ap-1416	58	53	,	,	PUNCT
ap-1416	58	54	a3	a3	NOUN
ap-1416	58	55	.	.	PUNCT
ap-1416	59	1	this	this	DET
ap-1416	59	2	result	result	NOUN
ap-1416	59	3	shows	show	VERB
ap-1416	59	4	that	that	SCONJ
ap-1416	59	5	the	the	DET
ap-1416	59	6	asymptotic	asymptotic	ADJ
ap-1416	59	7	behaviour	behaviour	NOUN
ap-1416	59	8	of	of	ADP
ap-1416	59	9	roots	root	NOUN
ap-1416	59	10	is	be	AUX
ap-1416	59	11	determined	determine	VERB
ap-1416	59	12	by	by	ADP
ap-1416	59	13	q	q	NOUN
ap-1416	59	14	,	,	PUNCT
ap-1416	59	15	i.e.	i.e.	X
ap-1416	59	16	it	it	PRON
ap-1416	59	17	is	be	AUX
ap-1416	59	18	not	not	PART
ap-1416	59	19	influenced	influence	VERB
ap-1416	59	20	by	by	ADP
ap-1416	59	21	p	p	NOUN
ap-1416	59	22	for	for	ADP
ap-1416	59	23	sufficiently	sufficiently	ADV
ap-1416	59	24	large	large	ADJ
ap-1416	59	25	n.	n.	NOUN
ap-1416	59	26	for	for	ADP
ap-1416	59	27	a	a	DET
ap-1416	59	28	more	more	ADV
ap-1416	59	29	detailed	detailed	ADJ
ap-1416	59	30	description	description	NOUN
ap-1416	59	31	of	of	ADP
ap-1416	59	32	asymptotic	asymptotic	ADJ
ap-1416	59	33	distribution	distribution	NOUN
ap-1416	59	34	we	we	PRON
ap-1416	59	35	associate	associate	VERB
ap-1416	59	36	to	to	ADP
ap-1416	59	37	each	each	DET
ap-1416	59	38	polynomial	polynomial	NOUN
ap-1416	59	39	pn	pn	VERB
ap-1416	59	40	a	a	DET
ap-1416	59	41	finite	finite	ADJ
ap-1416	59	42	real	real	ADJ
ap-1416	59	43	measure	measure	NOUN
ap-1416	59	44	μn	μn	ADP
ap-1416	60	1	=	=	SYM
ap-1416	60	2	1	1	NUM
ap-1416	60	3	n	n	NUM
ap-1416	60	4	n∑	n∑	NOUN
ap-1416	60	5	j=1	j=1	NOUN
ap-1416	60	6	δ(z	δ(z	NOUN
ap-1416	60	7	−	−	PROPN
ap-1416	60	8	zj	zj	PROPN
ap-1416	60	9	)	)	PUNCT
ap-1416	60	10	,	,	PUNCT
ap-1416	60	11	where	where	SCONJ
ap-1416	60	12	δ(z	δ(z	NOUN
ap-1416	60	13	−	−	PROPN
ap-1416	60	14	zj	zj	PROPN
ap-1416	60	15	)	)	PUNCT
ap-1416	60	16	is	be	AUX
ap-1416	60	17	the	the	DET
ap-1416	60	18	dirac	dirac	NOUN
ap-1416	60	19	measure	measure	NOUN
ap-1416	60	20	supported	support	VERB
ap-1416	60	21	at	at	ADP
ap-1416	60	22	the	the	DET
ap-1416	60	23	root	root	PROPN
ap-1416	60	24	zj	zj	PROPN
ap-1416	60	25	.	.	PUNCT
ap-1416	61	1	this	this	DET
ap-1416	61	2	probability	probability	NOUN
ap-1416	61	3	measure	measure	NOUN
ap-1416	61	4	is	be	AUX
ap-1416	61	5	referred	refer	VERB
ap-1416	61	6	to	to	ADP
ap-1416	61	7	as	as	ADP
ap-1416	61	8	the	the	DET
ap-1416	61	9	root	root	NOUN
ap-1416	61	10	-	-	PUNCT
ap-1416	61	11	counting	count	VERB
ap-1416	61	12	measure	measure	NOUN
ap-1416	61	13	of	of	ADP
ap-1416	61	14	the	the	DET
ap-1416	61	15	polynomial	polynomial	ADJ
ap-1416	61	16	pn	pn	PROPN
ap-1416	61	17	.	.	PUNCT
ap-1416	62	1	now	now	ADV
ap-1416	62	2	,	,	PUNCT
ap-1416	62	3	two	two	NUM
ap-1416	62	4	questions	question	NOUN
ap-1416	62	5	are	be	AUX
ap-1416	62	6	to	to	PART
ap-1416	62	7	be	be	AUX
ap-1416	62	8	answered	answer	VERB
ap-1416	62	9	.	.	PUNCT
ap-1416	63	1	does	do	VERB
ap-1416	63	2	the	the	DET
ap-1416	63	3	sequence	sequence	NOUN
ap-1416	63	4	{	{	PUNCT
ap-1416	63	5	μn	μn	NOUN
ap-1416	63	6	}	}	PUNCT
ap-1416	63	7	converge	converge	NOUN
ap-1416	63	8	(	(	PUNCT
ap-1416	63	9	in	in	ADP
ap-1416	63	10	the	the	DET
ap-1416	63	11	weak	weak	ADJ
ap-1416	63	12	sense	sense	NOUN
ap-1416	63	13	)	)	PUNCT
ap-1416	63	14	to	to	ADP
ap-1416	63	15	a	a	DET
ap-1416	63	16	91	91	NUM
ap-1416	63	17	acta	acta	PROPN
ap-1416	63	18	polytechnica	polytechnica	PROPN
ap-1416	63	19	vol	vol	NOUN
ap-1416	63	20	.	.	PUNCT
ap-1416	64	1	51	51	NUM
ap-1416	64	2	no	no	INTJ
ap-1416	64	3	.	.	PUNCT
ap-1416	65	1	4/2011	4/2011	NUM
ap-1416	65	2	limiting	limiting	NOUN
ap-1416	65	3	measure	measure	NOUN
ap-1416	65	4	μ	μ	PROPN
ap-1416	65	5	and	and	CCONJ
ap-1416	65	6	if	if	SCONJ
ap-1416	65	7	so	so	ADV
ap-1416	65	8	what	what	PRON
ap-1416	65	9	does	do	AUX
ap-1416	65	10	μ	μ	NOUN
ap-1416	65	11	look	look	VERB
ap-1416	65	12	like	like	ADP
ap-1416	65	13	?	?	PUNCT
ap-1416	66	1	we	we	PRON
ap-1416	66	2	may	may	AUX
ap-1416	66	3	ask	ask	VERB
ap-1416	66	4	these	these	DET
ap-1416	66	5	questions	question	NOUN
ap-1416	66	6	when	when	SCONJ
ap-1416	66	7	pn	pn	PROPN
ap-1416	66	8	=	=	PROPN
ap-1416	66	9	spn	spn	PROPN
ap-1416	66	10	.	.	PUNCT
ap-1416	67	1	the	the	DET
ap-1416	67	2	first	first	ADJ
ap-1416	67	3	question	question	NOUN
ap-1416	67	4	is	be	AUX
ap-1416	67	5	answered	answer	VERB
ap-1416	67	6	positively	positively	ADV
ap-1416	67	7	[	[	X
ap-1416	67	8	11	11	NUM
ap-1416	67	9	,	,	PUNCT
ap-1416	67	10	12	12	NUM
ap-1416	67	11	]	]	PUNCT
ap-1416	67	12	.	.	PUNCT
ap-1416	68	1	the	the	DET
ap-1416	68	2	sequence	sequence	NOUN
ap-1416	68	3	{	{	PUNCT
ap-1416	68	4	μn	μn	NOUN
ap-1416	68	5	}	}	PUNCT
ap-1416	68	6	of	of	ADP
ap-1416	68	7	the	the	DET
ap-1416	68	8	root	root	NOUN
ap-1416	68	9	-	-	PUNCT
ap-1416	68	10	counting	count	VERB
ap-1416	68	11	measures	measure	NOUN
ap-1416	68	12	of	of	ADP
ap-1416	68	13	its	its	PRON
ap-1416	68	14	spectral	spectral	ADJ
ap-1416	68	15	polynomials	polynomial	NOUN
ap-1416	68	16	converges	converge	VERB
ap-1416	68	17	to	to	ADP
ap-1416	68	18	a	a	DET
ap-1416	68	19	probability	probability	NOUN
ap-1416	68	20	measure	measure	NOUN
ap-1416	68	21	μ	μ	NOUN
ap-1416	68	22	supported	support	VERB
ap-1416	68	23	on	on	ADP
ap-1416	68	24	the	the	DET
ap-1416	68	25	union	union	NOUN
ap-1416	68	26	of	of	ADP
ap-1416	68	27	three	three	NUM
ap-1416	68	28	curves	curve	NOUN
ap-1416	68	29	located	locate	VERB
ap-1416	68	30	inside	inside	ADP
ap-1416	68	31	convq	convq	PROPN
ap-1416	68	32	and	and	CCONJ
ap-1416	68	33	connecting	connect	VERB
ap-1416	68	34	the	the	DET
ap-1416	68	35	three	three	NUM
ap-1416	68	36	roots	root	NOUN
ap-1416	68	37	of	of	ADP
ap-1416	68	38	q	q	NOUN
ap-1416	68	39	with	with	ADP
ap-1416	68	40	a	a	DET
ap-1416	68	41	certain	certain	ADJ
ap-1416	68	42	interior	interior	ADJ
ap-1416	68	43	point	point	NOUN
ap-1416	68	44	,	,	PUNCT
ap-1416	68	45	cf	cf	NOUN
ap-1416	68	46	.	.	PUNCT
ap-1416	68	47	figure	figure	NOUN
ap-1416	68	48	2	2	NUM
ap-1416	68	49	.	.	PUNCT
ap-1416	69	1	moreover	moreover	ADV
ap-1416	69	2	,	,	PUNCT
ap-1416	69	3	μ	μ	PROPN
ap-1416	69	4	depends	depend	VERB
ap-1416	69	5	only	only	ADV
ap-1416	69	6	on	on	ADP
ap-1416	69	7	q.	q.	NOUN
ap-1416	69	8	the	the	DET
ap-1416	69	9	support	support	NOUN
ap-1416	69	10	of	of	ADP
ap-1416	69	11	μ	μ	PROPN
ap-1416	69	12	is	be	AUX
ap-1416	69	13	a	a	DET
ap-1416	69	14	union	union	NOUN
ap-1416	69	15	of	of	ADP
ap-1416	69	16	three	three	NUM
ap-1416	69	17	curve	curve	NOUN
ap-1416	69	18	segments	segment	NOUN
ap-1416	69	19	γi	γi	NOUN
ap-1416	69	20	,	,	PUNCT
ap-1416	69	21	i	i	PRON
ap-1416	69	22	∈	∈	PROPN
ap-1416	69	23	{	{	PUNCT
ap-1416	69	24	1	1	NUM
ap-1416	69	25	,	,	PUNCT
ap-1416	69	26	2	2	NUM
ap-1416	69	27	,	,	PUNCT
ap-1416	69	28	3	3	NUM
ap-1416	69	29	}	}	PUNCT
ap-1416	69	30	.	.	PUNCT
ap-1416	70	1	they	they	PRON
ap-1416	70	2	may	may	AUX
ap-1416	70	3	be	be	AUX
ap-1416	70	4	described	describe	VERB
ap-1416	70	5	as	as	ADP
ap-1416	70	6	the	the	DET
ap-1416	70	7	set	set	NOUN
ap-1416	70	8	of	of	ADP
ap-1416	70	9	all	all	DET
ap-1416	70	10	b	b	PROPN
ap-1416	70	11	∈	∈	PROPN
ap-1416	70	12	convq	convq	PROPN
ap-1416	70	13	satisfying∫	satisfying∫	PROPN
ap-1416	70	14	ak	ak	PROPN
ap-1416	70	15	aj	aj	PROPN
ap-1416	70	16	√	√	PROPN
ap-1416	70	17	b	b	PROPN
ap-1416	70	18	−	−	PROPN
ap-1416	70	19	t	t	PROPN
ap-1416	70	20	(	(	PUNCT
ap-1416	70	21	t	t	PROPN
ap-1416	70	22	−	−	PROPN
ap-1416	71	1	a1)(t	a1)(t	PROPN
ap-1416	71	2	−	−	PROPN
ap-1416	71	3	a2)(t	a2)(t	PROPN
ap-1416	71	4	−	−	PROPN
ap-1416	71	5	a3	a3	NOUN
ap-1416	71	6	)	)	PUNCT
ap-1416	71	7	dt	dt	PUNCT
ap-1416	72	1	∈	∈	PROPN
ap-1416	72	2	r	r	NOUN
ap-1416	72	3	,	,	PUNCT
ap-1416	72	4	here	here	ADV
ap-1416	72	5	j	j	PROPN
ap-1416	72	6	and	and	CCONJ
ap-1416	72	7	k	k	PROPN
ap-1416	72	8	are	be	AUX
ap-1416	72	9	the	the	DET
ap-1416	72	10	remaining	remain	VERB
ap-1416	72	11	two	two	NUM
ap-1416	72	12	indices	index	NOUN
ap-1416	72	13	in	in	ADP
ap-1416	72	14	{	{	PUNCT
ap-1416	72	15	1	1	NUM
ap-1416	72	16	,	,	PUNCT
ap-1416	72	17	2	2	NUM
ap-1416	72	18	,	,	PUNCT
ap-1416	72	19	3	3	NUM
ap-1416	72	20	}	}	PUNCT
ap-1416	72	21	in	in	ADP
ap-1416	72	22	any	any	DET
ap-1416	72	23	order	order	NOUN
ap-1416	72	24	and	and	CCONJ
ap-1416	72	25	the	the	DET
ap-1416	72	26	integration	integration	NOUN
ap-1416	72	27	is	be	AUX
ap-1416	72	28	taken	take	VERB
ap-1416	72	29	over	over	ADP
ap-1416	72	30	the	the	DET
ap-1416	72	31	straight	straight	ADJ
ap-1416	72	32	interval	interval	NOUN
ap-1416	72	33	connecting	connect	VERB
ap-1416	72	34	aj	aj	PROPN
ap-1416	72	35	and	and	CCONJ
ap-1416	72	36	ak	ak	PROPN
ap-1416	72	37	.	.	PROPN
ap-1416	73	1	we	we	PRON
ap-1416	73	2	can	can	AUX
ap-1416	73	3	see	see	VERB
ap-1416	73	4	that	that	PRON
ap-1416	73	5	ai	ai	VERB
ap-1416	73	6	belong	belong	VERB
ap-1416	73	7	to	to	ADP
ap-1416	73	8	γi	γi	NOUN
ap-1416	73	9	and	and	CCONJ
ap-1416	73	10	that	that	SCONJ
ap-1416	73	11	these	these	DET
ap-1416	73	12	three	three	NUM
ap-1416	73	13	curves	curve	NOUN
ap-1416	73	14	connect	connect	VERB
ap-1416	73	15	the	the	DET
ap-1416	73	16	corresponding	correspond	VERB
ap-1416	73	17	ai	ai	VERB
ap-1416	73	18	with	with	ADP
ap-1416	73	19	a	a	DET
ap-1416	73	20	common	common	ADJ
ap-1416	73	21	point	point	NOUN
ap-1416	73	22	within	within	ADP
ap-1416	73	23	convq	convq	PROPN
ap-1416	73	24	.	.	PUNCT
ap-1416	74	1	take	take	VERB
ap-1416	74	2	a	a	DET
ap-1416	74	3	segment	segment	NOUN
ap-1416	74	4	of	of	ADP
ap-1416	74	5	γi	γi	NOUN
ap-1416	74	6	connecting	connect	VERB
ap-1416	74	7	ai	ai	VERB
ap-1416	74	8	with	with	ADP
ap-1416	74	9	the	the	DET
ap-1416	74	10	common	common	ADJ
ap-1416	74	11	intersection	intersection	NOUN
ap-1416	74	12	point	point	NOUN
ap-1416	74	13	of	of	ADP
ap-1416	74	14	all	all	DET
ap-1416	74	15	γ	γ	NOUN
ap-1416	74	16	’s	’s	NOUN
ap-1416	74	17	.	.	PUNCT
ap-1416	75	1	let	let	VERB
ap-1416	75	2	us	we	PRON
ap-1416	75	3	denote	denote	VERB
ap-1416	75	4	the	the	DET
ap-1416	75	5	union	union	NOUN
ap-1416	75	6	of	of	ADP
ap-1416	75	7	these	these	DET
ap-1416	75	8	three	three	NUM
ap-1416	75	9	segments	segment	NOUN
ap-1416	75	10	by	by	ADP
ap-1416	75	11	γq	γq	ADP
ap-1416	75	12	.	.	PUNCT
ap-1416	76	1	then	then	ADV
ap-1416	76	2	the	the	DET
ap-1416	76	3	support	support	NOUN
ap-1416	76	4	of	of	ADP
ap-1416	76	5	the	the	DET
ap-1416	76	6	limiting	limit	VERB
ap-1416	76	7	root	root	NOUN
ap-1416	76	8	-	-	PUNCT
ap-1416	76	9	counting	count	VERB
ap-1416	76	10	measure	measure	NOUN
ap-1416	76	11	μ	μ	PROPN
ap-1416	76	12	coincides	coincide	VERB
ap-1416	76	13	with	with	ADP
ap-1416	76	14	γq	γq	NOUN
ap-1416	76	15	.	.	PUNCT
ap-1416	77	1	knowing	know	VERB
ap-1416	77	2	the	the	DET
ap-1416	77	3	support	support	NOUN
ap-1416	77	4	of	of	ADP
ap-1416	77	5	μ	μ	NOUN
ap-1416	77	6	it	it	PRON
ap-1416	77	7	is	be	AUX
ap-1416	77	8	also	also	ADV
ap-1416	77	9	possible	possible	ADJ
ap-1416	77	10	to	to	PART
ap-1416	77	11	define	define	VERB
ap-1416	77	12	its	its	PRON
ap-1416	77	13	density	density	NOUN
ap-1416	77	14	along	along	ADP
ap-1416	77	15	the	the	DET
ap-1416	77	16	support	support	NOUN
ap-1416	77	17	using	use	VERB
ap-1416	77	18	the	the	DET
ap-1416	77	19	linear	linear	ADJ
ap-1416	77	20	differential	differential	NOUN
ap-1416	77	21	equation	equation	NOUN
ap-1416	77	22	satisfied	satisfy	VERB
ap-1416	77	23	by	by	ADP
ap-1416	77	24	its	its	PRON
ap-1416	77	25	cauchy	cauchy	ADJ
ap-1416	77	26	transform	transform	NOUN
ap-1416	77	27	[	[	X
ap-1416	77	28	11	11	NUM
ap-1416	77	29	]	]	PUNCT
ap-1416	77	30	q(z)c′′	q(z)c′′	PROPN
ap-1416	77	31	ν	ν	NOUN
ap-1416	77	32	(	(	PUNCT
ap-1416	77	33	z	z	NOUN
ap-1416	77	34	)	)	PUNCT
ap-1416	77	35	+	+	NUM
ap-1416	77	36	q′(z)c′	q′(z)c′	NUM
ap-1416	77	37	ν(z	ν(z	NOUN
ap-1416	77	38	)	)	PUNCT
ap-1416	78	1	+	+	CCONJ
ap-1416	78	2	q′′(z	q′′(z	NOUN
ap-1416	78	3	)	)	PUNCT
ap-1416	78	4	8	8	NUM
ap-1416	78	5	cν(z	cν(z	NOUN
ap-1416	78	6	)	)	PUNCT
ap-1416	79	1	+	+	CCONJ
ap-1416	79	2	q′′′(z	q′′′(z	X
ap-1416	79	3	)	)	PUNCT
ap-1416	79	4	24	24	NUM
ap-1416	79	5	=	=	SYM
ap-1416	79	6	0	0	X
ap-1416	79	7	.	.	PUNCT
ap-1416	80	1	in	in	ADP
ap-1416	80	2	the	the	DET
ap-1416	80	3	case	case	NOUN
ap-1416	80	4	when	when	SCONJ
ap-1416	80	5	q(z	q(z	PROPN
ap-1416	80	6	)	)	PUNCT
ap-1416	80	7	has	have	VERB
ap-1416	80	8	all	all	DET
ap-1416	80	9	real	real	ADJ
ap-1416	80	10	zeros	zero	NOUN
ap-1416	80	11	,	,	PUNCT
ap-1416	80	12	the	the	DET
ap-1416	80	13	density	density	NOUN
ap-1416	80	14	is	be	AUX
ap-1416	80	15	explicitly	explicitly	ADV
ap-1416	80	16	given	give	VERB
ap-1416	80	17	in	in	ADP
ap-1416	80	18	[	[	X
ap-1416	80	19	3	3	NUM
ap-1416	80	20	]	]	PUNCT
ap-1416	80	21	.	.	PUNCT
ap-1416	81	1	the	the	DET
ap-1416	81	2	cauchy	cauchy	PROPN
ap-1416	81	3	transform	transform	VERB
ap-1416	81	4	cν(z	cν(z	NOUN
ap-1416	81	5	)	)	PUNCT
ap-1416	81	6	and	and	CCONJ
ap-1416	81	7	the	the	DET
ap-1416	81	8	logarithmic	logarithmic	ADJ
ap-1416	81	9	potential	potential	ADJ
ap-1416	81	10	potν(z	potν(z	PROPN
ap-1416	81	11	)	)	PUNCT
ap-1416	81	12	of	of	ADP
ap-1416	81	13	a	a	DET
ap-1416	81	14	(	(	PUNCT
ap-1416	81	15	complex	complex	ADV
ap-1416	81	16	-	-	PUNCT
ap-1416	81	17	valued	value	VERB
ap-1416	81	18	)	)	PUNCT
ap-1416	81	19	measure	measure	NOUN
ap-1416	81	20	ν	ν	NOUN
ap-1416	81	21	supported	support	VERB
ap-1416	81	22	in	in	ADP
ap-1416	81	23	c	c	PROPN
ap-1416	81	24	are	be	AUX
ap-1416	81	25	given	give	VERB
ap-1416	81	26	by	by	ADP
ap-1416	81	27	:	:	PUNCT
ap-1416	81	28	cν(z	cν(z	NOUN
ap-1416	81	29	)	)	PUNCT
ap-1416	82	1	=	=	SYM
ap-1416	82	2	∫	∫	PROPN
ap-1416	82	3	c	c	NOUN
ap-1416	82	4	dν(ξ	dν(ξ	PROPN
ap-1416	82	5	)	)	PUNCT
ap-1416	83	1	z	z	NOUN
ap-1416	83	2	−	−	PROPN
ap-1416	83	3	ξ	ξ	PROPN
ap-1416	83	4	and	and	CCONJ
ap-1416	83	5	potν(z	potν(z	PROPN
ap-1416	83	6	)	)	PUNCT
ap-1416	84	1	=	=	SYM
ap-1416	85	1	∫	∫	PROPN
ap-1416	85	2	c	c	NOUN
ap-1416	85	3	log	log	PROPN
ap-1416	86	1	|z	|z	PROPN
ap-1416	87	1	−	−	PROPN
ap-1416	87	2	ξ|	ξ|	PROPN
ap-1416	87	3	dν(ξ	dν(ξ	NUM
ap-1416	87	4	)	)	PUNCT
ap-1416	87	5	.	.	PUNCT
ap-1416	88	1	cν(z	cν(z	NOUN
ap-1416	88	2	)	)	PUNCT
ap-1416	88	3	is	be	AUX
ap-1416	88	4	analytic	analytic	ADJ
ap-1416	88	5	outside	outside	ADP
ap-1416	88	6	the	the	DET
ap-1416	88	7	support	support	NOUN
ap-1416	88	8	of	of	ADP
ap-1416	88	9	ν	ν	NOUN
ap-1416	88	10	[	[	X
ap-1416	88	11	5	5	NUM
ap-1416	88	12	]	]	PUNCT
ap-1416	88	13	.	.	PUNCT
ap-1416	89	1	in	in	ADP
ap-1416	89	2	[	[	X
ap-1416	89	3	11	11	NUM
ap-1416	89	4	]	]	PUNCT
ap-1416	89	5	we	we	PRON
ap-1416	89	6	were	be	AUX
ap-1416	89	7	able	able	ADJ
ap-1416	89	8	to	to	PART
ap-1416	89	9	find	find	VERB
ap-1416	89	10	an	an	DET
ap-1416	89	11	additional	additional	ADJ
ap-1416	89	12	probability	probability	NOUN
ap-1416	89	13	measure	measure	NOUN
ap-1416	89	14	ν	ν	X
ap-1416	89	15	which	which	PRON
ap-1416	89	16	is	be	AUX
ap-1416	89	17	easily	easily	ADV
ap-1416	89	18	described	describe	VERB
ap-1416	89	19	and	and	CCONJ
ap-1416	89	20	from	from	ADP
ap-1416	89	21	which	which	PRON
ap-1416	89	22	the	the	DET
ap-1416	89	23	measure	measure	NOUN
ap-1416	89	24	μ	μ	PROPN
ap-1416	89	25	is	be	AUX
ap-1416	89	26	obtained	obtain	VERB
ap-1416	89	27	by	by	ADP
ap-1416	89	28	the	the	DET
ap-1416	89	29	inverse	inverse	NOUN
ap-1416	89	30	balayage	balayage	NOUN
ap-1416	89	31	,	,	PUNCT
ap-1416	89	32	i.e.	i.e.	X
ap-1416	89	33	the	the	DET
ap-1416	89	34	support	support	NOUN
ap-1416	89	35	of	of	ADP
ap-1416	89	36	μ	μ	PROPN
ap-1416	89	37	will	will	AUX
ap-1416	89	38	be	be	AUX
ap-1416	89	39	contained	contain	VERB
ap-1416	89	40	in	in	ADP
ap-1416	89	41	the	the	DET
ap-1416	89	42	support	support	NOUN
ap-1416	89	43	of	of	ADP
ap-1416	89	44	the	the	DET
ap-1416	89	45	measure	measure	NOUN
ap-1416	89	46	ν	ν	NOUN
ap-1416	90	1	and	and	CCONJ
ap-1416	90	2	they	they	PRON
ap-1416	90	3	have	have	VERB
ap-1416	90	4	the	the	DET
ap-1416	90	5	same	same	ADJ
ap-1416	90	6	logarithmic	logarithmic	ADJ
ap-1416	90	7	potential	potential	NOUN
ap-1416	90	8	outside	outside	ADP
ap-1416	90	9	the	the	DET
ap-1416	90	10	support	support	NOUN
ap-1416	90	11	of	of	ADP
ap-1416	90	12	the	the	DET
ap-1416	90	13	latter	latter	ADJ
ap-1416	90	14	one	one	NUM
ap-1416	90	15	.	.	PUNCT
ap-1416	91	1	this	this	DET
ap-1416	91	2	measure	measure	NOUN
ap-1416	91	3	is	be	AUX
ap-1416	91	4	uniquely	uniquely	ADV
ap-1416	91	5	determined	determine	VERB
ap-1416	91	6	by	by	ADP
ap-1416	91	7	the	the	DET
ap-1416	91	8	choice	choice	NOUN
ap-1416	91	9	of	of	ADP
ap-1416	91	10	a	a	DET
ap-1416	91	11	root	root	NOUN
ap-1416	91	12	of	of	ADP
ap-1416	91	13	q(z	q(z	PROPN
ap-1416	91	14	)	)	PUNCT
ap-1416	91	15	,	,	PUNCT
ap-1416	91	16	and	and	CCONJ
ap-1416	91	17	thus	thus	ADV
ap-1416	91	18	we	we	PRON
ap-1416	91	19	in	in	ADP
ap-1416	91	20	fact	fact	NOUN
ap-1416	91	21	have	have	AUX
ap-1416	91	22	constructed	construct	VERB
ap-1416	91	23	three	three	NUM
ap-1416	91	24	different	different	ADJ
ap-1416	91	25	measures	measure	NOUN
ap-1416	91	26	νi	νi	ADP
ap-1416	91	27	having	have	VERB
ap-1416	91	28	the	the	DET
ap-1416	91	29	same	same	ADJ
ap-1416	91	30	measure	measure	NOUN
ap-1416	91	31	μ	μ	PROPN
ap-1416	91	32	as	as	ADP
ap-1416	91	33	their	their	PRON
ap-1416	91	34	inverse	inverse	NOUN
ap-1416	91	35	balayage	balayage	NOUN
ap-1416	91	36	.	.	PUNCT
ap-1416	92	1	let	let	VERB
ap-1416	92	2	us	we	PRON
ap-1416	92	3	try	try	VERB
ap-1416	92	4	to	to	PART
ap-1416	92	5	formulate	formulate	VERB
ap-1416	92	6	similar	similar	ADJ
ap-1416	92	7	results	result	NOUN
ap-1416	92	8	for	for	ADP
ap-1416	92	9	the	the	DET
ap-1416	92	10	asymptotic	asymptotic	ADJ
ap-1416	92	11	root	root	NOUN
ap-1416	92	12	behaviour	behaviour	NOUN
ap-1416	92	13	of	of	ADP
ap-1416	92	14	stieltjes	stieltjes	PROPN
ap-1416	92	15	polynomials	polynomial	VERB
ap-1416	92	16	.	.	PUNCT
ap-1416	93	1	to	to	ADP
ap-1416	93	2	this	this	DET
ap-1416	93	3	end	end	NOUN
ap-1416	93	4	we	we	PRON
ap-1416	93	5	must	must	AUX
ap-1416	93	6	formulate	formulate	VERB
ap-1416	93	7	in	in	ADP
ap-1416	93	8	more	more	ADJ
ap-1416	93	9	detail	detail	NOUN
ap-1416	93	10	which	which	DET
ap-1416	93	11	sequence	sequence	NOUN
ap-1416	93	12	of	of	ADP
ap-1416	93	13	polynomials	polynomial	NOUN
ap-1416	93	14	we	we	PRON
ap-1416	93	15	are	be	AUX
ap-1416	93	16	studying	study	VERB
ap-1416	93	17	.	.	PUNCT
ap-1416	94	1	take	take	VERB
ap-1416	94	2	a	a	DET
ap-1416	94	3	sequence	sequence	NOUN
ap-1416	94	4	of	of	ADP
ap-1416	94	5	monic	monic	ADJ
ap-1416	94	6	(	(	PUNCT
ap-1416	94	7	the	the	DET
ap-1416	94	8	leading	lead	VERB
ap-1416	94	9	coefficient	coefficient	NOUN
ap-1416	94	10	is	be	AUX
ap-1416	94	11	1	1	NUM
ap-1416	94	12	)	)	PUNCT
ap-1416	94	13	van	van	PROPN
ap-1416	94	14	vleck	vleck	NOUN
ap-1416	94	15	polynomials	polynomial	VERB
ap-1416	94	16	{	{	PUNCT
ap-1416	94	17	ṽn	ṽn	ADV
ap-1416	94	18	}	}	PUNCT
ap-1416	94	19	converging	converge	VERB
ap-1416	94	20	to	to	ADP
ap-1416	94	21	some	some	DET
ap-1416	94	22	monic	monic	ADJ
ap-1416	94	23	linear	linear	PROPN
ap-1416	94	24	polynomial	polynomial	ADJ
ap-1416	94	25	ṽ	ṽ	PROPN
ap-1416	94	26	.	.	PUNCT
ap-1416	95	1	the	the	DET
ap-1416	95	2	existence	existence	NOUN
ap-1416	95	3	of	of	ADP
ap-1416	95	4	a	a	DET
ap-1416	95	5	linear	linear	ADJ
ap-1416	95	6	polynomial	polynomial	ADJ
ap-1416	95	7	ṽ	ṽ	PROPN
ap-1416	95	8	is	be	AUX
ap-1416	95	9	ensured	ensure	VERB
ap-1416	95	10	by	by	ADP
ap-1416	95	11	the	the	DET
ap-1416	95	12	existence	existence	NOUN
ap-1416	95	13	of	of	ADP
ap-1416	95	14	the	the	DET
ap-1416	95	15	limit	limit	NOUN
ap-1416	95	16	of	of	ADP
ap-1416	95	17	the	the	DET
ap-1416	95	18	sequence	sequence	NOUN
ap-1416	95	19	of	of	ADP
ap-1416	95	20	(	(	PUNCT
ap-1416	95	21	unique	unique	ADJ
ap-1416	95	22	)	)	PUNCT
ap-1416	95	23	roots	root	NOUN
ap-1416	95	24	νn	νn	PRON
ap-1416	95	25	,	,	PUNCT
ap-1416	95	26	in	in	ADP
ap-1416	95	27	of	of	ADP
ap-1416	95	28	{	{	PUNCT
ap-1416	95	29	ṽn	ṽn	NOUN
ap-1416	95	30	}	}	PUNCT
ap-1416	95	31	.	.	PUNCT
ap-1416	96	1	the	the	DET
ap-1416	96	2	above	above	ADV
ap-1416	96	3	mentioned	mention	VERB
ap-1416	96	4	results	result	NOUN
ap-1416	96	5	guarantee	guarantee	VERB
ap-1416	96	6	the	the	DET
ap-1416	96	7	existence	existence	NOUN
ap-1416	96	8	of	of	ADP
ap-1416	96	9	plenty	plenty	NOUN
ap-1416	96	10	of	of	ADP
ap-1416	96	11	such	such	ADJ
ap-1416	96	12	converging	converge	VERB
ap-1416	96	13	sequences	sequence	NOUN
ap-1416	96	14	in	in	ADP
ap-1416	96	15	convq	convq	PROPN
ap-1416	96	16	and	and	CCONJ
ap-1416	96	17	the	the	DET
ap-1416	96	18	limit	limit	NOUN
ap-1416	96	19	ν̃	ν̃	PROPN
ap-1416	96	20	of	of	ADP
ap-1416	96	21	these	these	DET
ap-1416	96	22	roots	root	NOUN
ap-1416	96	23	must	must	AUX
ap-1416	96	24	necessarily	necessarily	ADV
ap-1416	96	25	belong	belong	VERB
ap-1416	96	26	to	to	ADP
ap-1416	96	27	γq	γq	NOUN
ap-1416	96	28	.	.	PUNCT
ap-1416	97	1	having	having	AUX
ap-1416	97	2	chosen	choose	VERB
ap-1416	97	3	{	{	PUNCT
ap-1416	97	4	ṽn	ṽn	PROPN
ap-1416	97	5	}	}	PUNCT
ap-1416	97	6	we	we	PRON
ap-1416	97	7	take	take	VERB
ap-1416	97	8	any	any	DET
ap-1416	97	9	sequence	sequence	NOUN
ap-1416	97	10	of	of	ADP
ap-1416	97	11	the	the	DET
ap-1416	97	12	corresponding	correspond	VERB
ap-1416	97	13	{	{	PUNCT
ap-1416	97	14	sn	sn	NOUN
ap-1416	97	15	,	,	PUNCT
ap-1416	97	16	in	in	ADP
ap-1416	97	17	}	}	PUNCT
ap-1416	97	18	,	,	PUNCT
ap-1416	97	19	deg	deg	X
ap-1416	97	20	sn	sn	PROPN
ap-1416	97	21	,	,	PUNCT
ap-1416	97	22	in	in	ADP
ap-1416	97	23	=	=	PUNCT
ap-1416	97	24	n	n	X
ap-1416	97	25	whose	whose	DET
ap-1416	97	26	corresponding	correspond	VERB
ap-1416	97	27	sequence	sequence	NOUN
ap-1416	97	28	{	{	PUNCT
ap-1416	97	29	ṽn	ṽn	X
ap-1416	97	30	}	}	PUNCT
ap-1416	97	31	has	have	VERB
ap-1416	97	32	a	a	DET
ap-1416	97	33	limit	limit	NOUN
ap-1416	97	34	.	.	PUNCT
ap-1416	98	1	if	if	SCONJ
ap-1416	98	2	we	we	PRON
ap-1416	98	3	denote	denote	VERB
ap-1416	98	4	by	by	ADP
ap-1416	98	5	μn	μn	PROPN
ap-1416	98	6	,	,	PUNCT
ap-1416	98	7	in	in	ADP
ap-1416	98	8	the	the	DET
ap-1416	98	9	root	root	NOUN
ap-1416	98	10	-	-	PUNCT
ap-1416	98	11	counting	count	VERB
ap-1416	98	12	measure	measure	NOUN
ap-1416	98	13	of	of	ADP
ap-1416	98	14	the	the	DET
ap-1416	98	15	corresponding	corresponding	ADJ
ap-1416	98	16	stieltjes	stieltjes	NOUN
ap-1416	98	17	polynomial	polynomial	ADJ
ap-1416	98	18	,	,	PUNCT
ap-1416	98	19	we	we	PRON
ap-1416	98	20	have	have	AUX
ap-1416	98	21	proved	prove	VERB
ap-1416	98	22	that	that	SCONJ
ap-1416	98	23	the	the	DET
ap-1416	98	24	sequence	sequence	NOUN
ap-1416	98	25	{	{	PUNCT
ap-1416	98	26	μn	μn	NOUN
ap-1416	98	27	,	,	PUNCT
ap-1416	98	28	in	in	ADP
ap-1416	98	29	}	}	PUNCT
ap-1416	98	30	converges	converge	VERB
ap-1416	98	31	weakly	weakly	ADV
ap-1416	98	32	to	to	ADP
ap-1416	98	33	the	the	DET
ap-1416	98	34	unique	unique	ADJ
ap-1416	98	35	probability	probability	NOUN
ap-1416	98	36	measure	measure	NOUN
ap-1416	98	37	μ	μ	PROPN
ap-1416	98	38	ṽ	ṽ	PROPN
ap-1416	98	39	whose	whose	DET
ap-1416	98	40	cauchy	cauchy	NOUN
ap-1416	98	41	transform	transform	VERB
ap-1416	98	42	c	c	PROPN
ap-1416	98	43	ṽ	ṽ	PROPN
ap-1416	98	44	(	(	PUNCT
ap-1416	98	45	z	z	NOUN
ap-1416	98	46	)	)	PUNCT
ap-1416	98	47	satisfies	satisfy	VERB
ap-1416	98	48	the	the	DET
ap-1416	98	49	equation	equation	NOUN
ap-1416	98	50	c2	c2	PROPN
ap-1416	98	51	ṽ	ṽ	PROPN
ap-1416	98	52	(	(	PUNCT
ap-1416	98	53	z	z	NOUN
ap-1416	98	54	)	)	PUNCT
ap-1416	99	1	=	=	SYM
ap-1416	99	2	ṽ	ṽ	PROPN
ap-1416	99	3	(	(	PUNCT
ap-1416	99	4	z	z	NOUN
ap-1416	99	5	)	)	PUNCT
ap-1416	99	6	q(z	q(z	PROPN
ap-1416	99	7	)	)	PUNCT
ap-1416	99	8	almost	almost	ADV
ap-1416	99	9	everywhere	everywhere	ADV
ap-1416	99	10	in	in	ADP
ap-1416	99	11	c.	c.	NOUN
ap-1416	99	12	in	in	ADP
ap-1416	99	13	order	order	NOUN
ap-1416	99	14	to	to	PART
ap-1416	99	15	formulate	formulate	VERB
ap-1416	99	16	further	further	ADJ
ap-1416	99	17	results	result	NOUN
ap-1416	99	18	we	we	PRON
ap-1416	99	19	used	use	VERB
ap-1416	99	20	[	[	X
ap-1416	99	21	12	12	NUM
ap-1416	99	22	]	]	PUNCT
ap-1416	99	23	the	the	DET
ap-1416	99	24	notion	notion	NOUN
ap-1416	99	25	of	of	ADP
ap-1416	99	26	the	the	DET
ap-1416	99	27	quadratic	quadratic	ADJ
ap-1416	99	28	differential	differential	NOUN
ap-1416	99	29	(	(	PUNCT
ap-1416	99	30	cf	cf	NOUN
ap-1416	99	31	.	.	PUNCT
ap-1416	100	1	also	also	ADV
ap-1416	100	2	[	[	X
ap-1416	100	3	7,8	7,8	NUM
ap-1416	100	4	]	]	PUNCT
ap-1416	100	5	)	)	PUNCT
ap-1416	100	6	.	.	PUNCT
ap-1416	101	1	we	we	PRON
ap-1416	101	2	avoid	avoid	VERB
ap-1416	101	3	this	this	DET
ap-1416	101	4	way	way	NOUN
ap-1416	101	5	of	of	ADP
ap-1416	101	6	formulating	formulate	VERB
ap-1416	101	7	the	the	DET
ap-1416	101	8	results	result	NOUN
ap-1416	101	9	,	,	PUNCT
ap-1416	101	10	because	because	SCONJ
ap-1416	101	11	it	it	PRON
ap-1416	101	12	would	would	AUX
ap-1416	101	13	necessarily	necessarily	ADV
ap-1416	101	14	exceed	exceed	VERB
ap-1416	101	15	the	the	DET
ap-1416	101	16	scope	scope	NOUN
ap-1416	101	17	if	if	SCONJ
ap-1416	101	18	this	this	DET
ap-1416	101	19	paper	paper	NOUN
ap-1416	101	20	.	.	PUNCT
ap-1416	102	1	instead	instead	ADV
ap-1416	102	2	,	,	PUNCT
ap-1416	102	3	we	we	PRON
ap-1416	102	4	limit	limit	VERB
ap-1416	102	5	ourselves	ourselves	PRON
ap-1416	102	6	to	to	ADP
ap-1416	102	7	presenting	present	VERB
ap-1416	102	8	a	a	DET
ap-1416	102	9	typical	typical	ADJ
ap-1416	102	10	example	example	NOUN
ap-1416	102	11	,	,	PUNCT
ap-1416	102	12	cf	cf	NOUN
ap-1416	102	13	.	.	PUNCT
ap-1416	103	1	the	the	DET
ap-1416	103	2	right	right	ADJ
ap-1416	103	3	part	part	NOUN
ap-1416	103	4	of	of	ADP
ap-1416	103	5	figure	figure	NOUN
ap-1416	103	6	2	2	NUM
ap-1416	103	7	.	.	PUNCT
ap-1416	104	1	the	the	DET
ap-1416	104	2	support	support	NOUN
ap-1416	104	3	of	of	ADP
ap-1416	104	4	the	the	DET
ap-1416	104	5	limit	limit	NOUN
ap-1416	104	6	measure	measure	NOUN
ap-1416	104	7	consists	consist	VERB
ap-1416	104	8	of	of	ADP
ap-1416	104	9	singular	singular	ADJ
ap-1416	104	10	trajectories	trajectory	NOUN
ap-1416	104	11	of	of	ADP
ap-1416	104	12	the	the	DET
ap-1416	104	13	quadratic	quadratic	ADJ
ap-1416	104	14	differential	differential	NOUN
ap-1416	104	15	.	.	PUNCT
ap-1416	105	1	they	they	PRON
ap-1416	105	2	run	run	VERB
ap-1416	105	3	close	close	ADV
ap-1416	105	4	to	to	ADP
ap-1416	105	5	the	the	DET
ap-1416	105	6	roots	root	NOUN
ap-1416	105	7	shown	show	VERB
ap-1416	105	8	in	in	ADP
ap-1416	105	9	red	red	PROPN
ap-1416	105	10	.	.	PUNCT
ap-1416	106	1	in	in	ADP
ap-1416	106	2	this	this	DET
ap-1416	106	3	particular	particular	ADJ
ap-1416	106	4	case	case	NOUN
ap-1416	106	5	,	,	PUNCT
ap-1416	106	6	one	one	NUM
ap-1416	106	7	trajectory	trajectory	NOUN
ap-1416	106	8	joins	join	VERB
ap-1416	106	9	two	two	NUM
ap-1416	106	10	zeros	zero	NOUN
ap-1416	106	11	of	of	ADP
ap-1416	106	12	q	q	NOUN
ap-1416	106	13	and	and	CCONJ
ap-1416	106	14	the	the	DET
ap-1416	106	15	other	other	ADJ
ap-1416	106	16	one	one	NOUN
ap-1416	106	17	joins	join	VERB
ap-1416	106	18	the	the	DET
ap-1416	106	19	third	third	ADJ
ap-1416	106	20	zero	zero	NUM
ap-1416	106	21	of	of	ADP
ap-1416	106	22	q	q	NOUN
ap-1416	106	23	with	with	ADP
ap-1416	106	24	the	the	DET
ap-1416	106	25	root	root	NOUN
ap-1416	106	26	of	of	ADP
ap-1416	106	27	the	the	DET
ap-1416	106	28	limiting	limit	VERB
ap-1416	106	29	van	van	PROPN
ap-1416	106	30	vleck	vleck	NOUN
ap-1416	106	31	polynomial	polynomial	NOUN
ap-1416	106	32	.	.	PUNCT
ap-1416	107	1	3	3	NUM
ap-1416	107	2	bispectral	bispectral	ADJ
ap-1416	107	3	problems	problem	NOUN
ap-1416	107	4	concerning	concern	VERB
ap-1416	107	5	the	the	DET
ap-1416	107	6	situation	situation	NOUN
ap-1416	107	7	when	when	SCONJ
ap-1416	107	8	k	k	PROPN
ap-1416	107	9	=	=	SYM
ap-1416	107	10	4	4	NUM
ap-1416	107	11	certain	certain	ADJ
ap-1416	107	12	general	general	ADJ
ap-1416	107	13	statements	statement	NOUN
ap-1416	107	14	have	have	AUX
ap-1416	107	15	already	already	ADV
ap-1416	107	16	been	be	AUX
ap-1416	107	17	published	publish	VERB
ap-1416	107	18	(	(	PUNCT
ap-1416	107	19	e.g.	e.g.	ADV
ap-1416	107	20	in	in	ADP
ap-1416	107	21	[	[	X
ap-1416	107	22	6	6	NUM
ap-1416	107	23	,	,	PUNCT
ap-1416	107	24	7	7	NUM
ap-1416	107	25	]	]	NUM
ap-1416	107	26	)	)	PUNCT
ap-1416	107	27	.	.	PUNCT
ap-1416	108	1	in	in	ADP
ap-1416	108	2	the	the	DET
ap-1416	108	3	case	case	NOUN
ap-1416	108	4	when	when	SCONJ
ap-1416	108	5	the	the	DET
ap-1416	108	6	roots	root	NOUN
ap-1416	108	7	of	of	ADP
ap-1416	108	8	van	van	PROPN
ap-1416	108	9	vleck	vleck	PROPN
ap-1416	108	10	and	and	CCONJ
ap-1416	108	11	stieltjes	stieltjes	PROPN
ap-1416	108	12	polynomials	polynomial	NOUN
ap-1416	108	13	are	be	AUX
ap-1416	108	14	real	real	ADJ
ap-1416	108	15	we	we	PRON
ap-1416	108	16	can	can	AUX
ap-1416	108	17	still	still	ADV
ap-1416	108	18	rely	rely	VERB
ap-1416	108	19	on	on	ADP
ap-1416	108	20	the	the	DET
ap-1416	108	21	result	result	NOUN
ap-1416	108	22	of	of	ADP
ap-1416	108	23	stieltjes	stieltjes	NOUN
ap-1416	108	24	mentioned	mention	VERB
ap-1416	108	25	above	above	ADV
ap-1416	108	26	,	,	PUNCT
ap-1416	108	27	which	which	PRON
ap-1416	108	28	make	make	VERB
ap-1416	108	29	ordering	ordering	NOUN
ap-1416	108	30	of	of	ADP
ap-1416	108	31	stieltjes	stieltjes	NOUN
ap-1416	108	32	polynomials	polynomial	NOUN
ap-1416	108	33	possible	possible	ADJ
ap-1416	108	34	.	.	PUNCT
ap-1416	109	1	the	the	DET
ap-1416	109	2	situation	situation	NOUN
ap-1416	109	3	is	be	AUX
ap-1416	109	4	shown	show	VERB
ap-1416	109	5	in	in	ADP
ap-1416	109	6	figure	figure	NOUN
ap-1416	109	7	3	3	NUM
ap-1416	109	8	.	.	PUNCT
ap-1416	109	9	when	when	SCONJ
ap-1416	109	10	complex	complex	ADJ
ap-1416	109	11	roots	root	NOUN
ap-1416	109	12	come	come	VERB
ap-1416	109	13	into	into	ADP
ap-1416	109	14	play	play	NOUN
ap-1416	109	15	,	,	PUNCT
ap-1416	109	16	the	the	DET
ap-1416	109	17	picture	picture	NOUN
ap-1416	109	18	is	be	AUX
ap-1416	109	19	less	less	ADV
ap-1416	109	20	clear	clear	ADJ
ap-1416	109	21	.	.	PUNCT
ap-1416	110	1	figure	figure	NOUN
ap-1416	110	2	3	3	NUM
ap-1416	110	3	suggests	suggest	VERB
ap-1416	110	4	that	that	SCONJ
ap-1416	110	5	the	the	DET
ap-1416	110	6	asymptotic	asymptotic	ADJ
ap-1416	110	7	root	root	NOUN
ap-1416	110	8	distribution	distribution	NOUN
ap-1416	110	9	of	of	ADP
ap-1416	110	10	van	van	PROPN
ap-1416	110	11	vleck	vleck	PROPN
ap-1416	110	12	polynomials	polynomial	NOUN
ap-1416	110	13	has	have	VERB
ap-1416	110	14	a	a	DET
ap-1416	110	15	more	more	ADV
ap-1416	110	16	complicated	complicated	ADJ
ap-1416	110	17	structure	structure	NOUN
ap-1416	110	18	than	than	ADP
ap-1416	110	19	before	before	ADV
ap-1416	110	20	.	.	PUNCT
ap-1416	111	1	on	on	ADP
ap-1416	111	2	the	the	DET
ap-1416	111	3	other	other	ADJ
ap-1416	111	4	hand	hand	NOUN
ap-1416	111	5	,	,	PUNCT
ap-1416	111	6	the	the	DET
ap-1416	111	7	structure	structure	NOUN
ap-1416	111	8	of	of	ADP
ap-1416	111	9	the	the	DET
ap-1416	111	10	asymptotic	asymptotic	ADJ
ap-1416	111	11	root	root	NOUN
ap-1416	111	12	distribution	distribution	NOUN
ap-1416	111	13	of	of	ADP
ap-1416	111	14	stieltjes	stieltjes	NOUN
ap-1416	111	15	polynomials	polynomial	NOUN
ap-1416	111	16	bears	bear	VERB
ap-1416	111	17	some	some	DET
ap-1416	111	18	resemblance	resemblance	NOUN
ap-1416	111	19	to	to	ADP
ap-1416	111	20	the	the	DET
ap-1416	111	21	k	k	PROPN
ap-1416	111	22	=	=	SYM
ap-1416	111	23	3	3	NUM
ap-1416	111	24	case	case	NOUN
ap-1416	111	25	.	.	PUNCT
ap-1416	112	1	there	there	PRON
ap-1416	112	2	are	be	VERB
ap-1416	112	3	still	still	ADV
ap-1416	112	4	several	several	ADJ
ap-1416	112	5	questions	question	NOUN
ap-1416	112	6	open	open	ADJ
ap-1416	112	7	.	.	PUNCT
ap-1416	113	1	in	in	ADP
ap-1416	113	2	addition	addition	NOUN
ap-1416	113	3	,	,	PUNCT
ap-1416	113	4	many	many	ADJ
ap-1416	113	5	other	other	ADJ
ap-1416	113	6	unsolved	unsolved	ADJ
ap-1416	113	7	problems	problem	NOUN
ap-1416	113	8	can	can	AUX
ap-1416	113	9	be	be	AUX
ap-1416	113	10	found	find	VERB
ap-1416	113	11	for	for	ADP
ap-1416	113	12	higher	high	ADJ
ap-1416	113	13	linear	linear	ADJ
ap-1416	113	14	differential	differential	ADJ
ap-1416	113	15	equations	equation	NOUN
ap-1416	113	16	with	with	ADP
ap-1416	113	17	polynomial	polynomial	ADJ
ap-1416	113	18	coefficients	coefficient	NOUN
ap-1416	113	19	.	.	PUNCT
ap-1416	114	1	92	92	NUM
ap-1416	114	2	acta	acta	PROPN
ap-1416	114	3	polytechnica	polytechnica	PROPN
ap-1416	114	4	vol	vol	NOUN
ap-1416	114	5	.	.	PUNCT
ap-1416	114	6	51	51	NUM
ap-1416	114	7	no	no	NOUN
ap-1416	114	8	.	.	PUNCT
ap-1416	115	1	4/2011	4/2011	NUM
ap-1416	115	2	−5	−5	ADV
ap-1416	115	3	0	0	NUM
ap-1416	115	4	5	5	NUM
ap-1416	115	5	10	10	NUM
ap-1416	115	6	−3	−3	ADJ
ap-1416	115	7	−2	−2	NOUN
ap-1416	115	8	−1	−1	NOUN
ap-1416	115	9	0	0	NUM
ap-1416	115	10	1	1	NUM
ap-1416	115	11	2	2	NUM
ap-1416	115	12	0	0	NUM
ap-1416	115	13	1	1	NUM
ap-1416	115	14	2	2	NUM
ap-1416	115	15	3	3	NUM
ap-1416	115	16	4	4	NUM
ap-1416	115	17	−3	−3	NOUN
ap-1416	115	18	−2	−2	NOUN
ap-1416	115	19	−1	−1	NOUN
ap-1416	115	20	0	0	NUM
ap-1416	115	21	1	1	NUM
ap-1416	115	22	2	2	NUM
ap-1416	115	23	0	0	NUM
ap-1416	115	24	1	1	NUM
ap-1416	115	25	2	2	NUM
ap-1416	115	26	3	3	NUM
ap-1416	115	27	4	4	NUM
ap-1416	115	28	fig	fig	NOUN
ap-1416	115	29	.	.	PUNCT
ap-1416	116	1	3	3	NUM
ap-1416	116	2	:	:	PUNCT
ap-1416	116	3	the	the	DET
ap-1416	116	4	left	left	ADJ
ap-1416	116	5	part	part	NOUN
ap-1416	116	6	:	:	PUNCT
ap-1416	116	7	the	the	DET
ap-1416	116	8	location	location	NOUN
ap-1416	116	9	of	of	ADP
ap-1416	116	10	roots	root	NOUN
ap-1416	116	11	for	for	ADP
ap-1416	116	12	q(x	q(x	NOUN
ap-1416	116	13	)	)	PUNCT
ap-1416	116	14	=	=	PUNCT
ap-1416	117	1	(	(	PUNCT
ap-1416	117	2	x	x	X
ap-1416	117	3	+	+	NUM
ap-1416	117	4	5)(x	5)(x	NUM
ap-1416	117	5	+	+	CCONJ
ap-1416	117	6	1)(x	1)(x	NUM
ap-1416	117	7	−	−	PROPN
ap-1416	117	8	5)(x	5)(x	NUM
ap-1416	117	9	−	−	PROPN
ap-1416	117	10	12	12	NUM
ap-1416	117	11	)	)	PUNCT
ap-1416	117	12	,	,	PUNCT
ap-1416	117	13	p	p	X
ap-1416	117	14	=	=	NOUN
ap-1416	117	15	0	0	NUM
ap-1416	117	16	,	,	PUNCT
ap-1416	117	17	and	and	CCONJ
ap-1416	117	18	n	n	CCONJ
ap-1416	117	19	=	=	SYM
ap-1416	117	20	6	6	NUM
ap-1416	117	21	.	.	PUNCT
ap-1416	118	1	the	the	DET
ap-1416	118	2	dots	dot	NOUN
ap-1416	118	3	have	have	VERB
ap-1416	118	4	the	the	DET
ap-1416	118	5	same	same	ADJ
ap-1416	118	6	meaning	meaning	NOUN
ap-1416	118	7	as	as	ADP
ap-1416	118	8	in	in	ADP
ap-1416	118	9	fig	fig	NOUN
ap-1416	118	10	.	.	PUNCT
ap-1416	119	1	1	1	X
ap-1416	119	2	.	.	X
ap-1416	119	3	the	the	DET
ap-1416	119	4	right	right	ADJ
ap-1416	119	5	upper	upper	ADJ
ap-1416	119	6	part	part	NOUN
ap-1416	119	7	:	:	PUNCT
ap-1416	119	8	the	the	DET
ap-1416	119	9	union	union	NOUN
ap-1416	119	10	of	of	ADP
ap-1416	119	11	roots	root	NOUN
ap-1416	119	12	of	of	ADP
ap-1416	119	13	(	(	PUNCT
ap-1416	119	14	quadratic	quadratic	ADJ
ap-1416	119	15	)	)	PUNCT
ap-1416	119	16	van	van	PROPN
ap-1416	119	17	vleck	vleck	NOUN
ap-1416	119	18	polynomials	polynomial	NOUN
ap-1416	119	19	for	for	ADP
ap-1416	119	20	q(z	q(z	PROPN
ap-1416	119	21	)	)	PUNCT
ap-1416	119	22	=	=	PUNCT
ap-1416	120	1	(	(	PUNCT
ap-1416	120	2	z	z	NOUN
ap-1416	120	3	+	+	NOUN
ap-1416	120	4	1)(z	1)(z	NUM
ap-1416	120	5	−	−	NOUN
ap-1416	120	6	2)(z	2)(z	NUM
ap-1416	120	7	−	−	NUM
ap-1416	120	8	2	2	NUM
ap-1416	120	9	−	−	NOUN
ap-1416	120	10	4i)(z	4i)(z	NUM
ap-1416	120	11	+	+	CCONJ
ap-1416	120	12	3	3	NUM
ap-1416	120	13	−	−	NOUN
ap-1416	120	14	2i	2i	NUM
ap-1416	120	15	)	)	PUNCT
ap-1416	120	16	,	,	PUNCT
ap-1416	120	17	p	p	NOUN
ap-1416	120	18	=	=	NOUN
ap-1416	120	19	0	0	NUM
ap-1416	120	20	,	,	PUNCT
ap-1416	120	21	and	and	CCONJ
ap-1416	120	22	n	n	CCONJ
ap-1416	120	23	=	=	NUM
ap-1416	120	24	20	20	NUM
ap-1416	120	25	.	.	PUNCT
ap-1416	121	1	the	the	DET
ap-1416	121	2	lower	low	ADJ
ap-1416	121	3	part	part	NOUN
ap-1416	121	4	:	:	PUNCT
ap-1416	121	5	roots	root	NOUN
ap-1416	121	6	of	of	ADP
ap-1416	121	7	a	a	DET
ap-1416	121	8	particular	particular	ADJ
ap-1416	121	9	stieltjes	stieltjes	NOUN
ap-1416	121	10	polynomial	polynomial	ADJ
ap-1416	121	11	(	(	PUNCT
ap-1416	121	12	in	in	ADP
ap-1416	121	13	red	red	NOUN
ap-1416	121	14	)	)	PUNCT
ap-1416	121	15	and	and	CCONJ
ap-1416	121	16	the	the	DET
ap-1416	121	17	roots	root	NOUN
ap-1416	121	18	of	of	ADP
ap-1416	121	19	the	the	DET
ap-1416	121	20	corresponding	correspond	VERB
ap-1416	121	21	van	van	PROPN
ap-1416	121	22	vleck	vleck	NOUN
ap-1416	121	23	polynomial	polynomial	NOUN
ap-1416	121	24	(	(	PUNCT
ap-1416	121	25	in	in	ADP
ap-1416	121	26	green	green	ADJ
ap-1416	121	27	)	)	PUNCT
ap-1416	121	28	acknowledgement	acknowledgement	NOUN
ap-1416	121	29	this	this	DET
ap-1416	121	30	work	work	NOUN
ap-1416	121	31	has	have	AUX
ap-1416	121	32	been	be	AUX
ap-1416	121	33	supported	support	VERB
ap-1416	121	34	by	by	ADP
ap-1416	121	35	the	the	DET
ap-1416	121	36	czech	czech	PROPN
ap-1416	121	37	ministry	ministry	PROPN
ap-1416	121	38	of	of	ADP
ap-1416	121	39	education	education	PROPN
ap-1416	121	40	,	,	PUNCT
ap-1416	121	41	youth	youth	NOUN
ap-1416	121	42	and	and	CCONJ
ap-1416	121	43	sports	sport	NOUN
ap-1416	121	44	within	within	ADP
ap-1416	121	45	the	the	DET
ap-1416	121	46	project	project	NOUN
ap-1416	121	47	lc06002	lc06002	NOUN
ap-1416	121	48	and	and	CCONJ
ap-1416	121	49	by	by	ADP
ap-1416	121	50	gacr	gacr	NOUN
ap-1416	121	51	grant	grant	NOUN
ap-1416	121	52	p203/11/0701	p203/11/0701	PROPN
ap-1416	121	53	.	.	PUNCT
ap-1416	122	1	references	reference	NOUN
ap-1416	122	2	[	[	X
ap-1416	122	3	1	1	NUM
ap-1416	122	4	]	]	X
ap-1416	122	5	bourget	bourget	PROPN
ap-1416	122	6	,	,	PUNCT
ap-1416	122	7	a.	a.	PROPN
ap-1416	122	8	,	,	PUNCT
ap-1416	122	9	mcmillen	mcmillen	PROPN
ap-1416	122	10	,	,	PUNCT
ap-1416	122	11	t.	t.	PROPN
ap-1416	122	12	:	:	PUNCT
ap-1416	122	13	on	on	ADP
ap-1416	122	14	the	the	DET
ap-1416	122	15	distribution	distribution	NOUN
ap-1416	122	16	and	and	CCONJ
ap-1416	122	17	interlacing	interlacing	NOUN
ap-1416	122	18	of	of	ADP
ap-1416	122	19	the	the	DET
ap-1416	122	20	zeros	zero	NOUN
ap-1416	122	21	of	of	ADP
ap-1416	122	22	stieltjes	stieltjes	PROPN
ap-1416	122	23	polynomials	polynomial	NOUN
ap-1416	122	24	,	,	PUNCT
ap-1416	122	25	proc	proc	NOUN
ap-1416	122	26	.	.	PUNCT
ap-1416	123	1	ams	ams	PROPN
ap-1416	123	2	138	138	NUM
ap-1416	123	3	(	(	PUNCT
ap-1416	123	4	2010	2010	NUM
ap-1416	123	5	)	)	PUNCT
ap-1416	123	6	,	,	PUNCT
ap-1416	123	7	3	3	NUM
ap-1416	123	8	267–3	267–3	NUM
ap-1416	123	9	275	275	NUM
ap-1416	123	10	.	.	PUNCT
ap-1416	124	1	[	[	X
ap-1416	124	2	2	2	NUM
ap-1416	124	3	]	]	X
ap-1416	124	4	bourget	bourget	PROPN
ap-1416	124	5	,	,	PUNCT
ap-1416	124	6	a.	a.	PROPN
ap-1416	124	7	,	,	PUNCT
ap-1416	124	8	mcmillen	mcmillen	PROPN
ap-1416	124	9	,	,	PUNCT
ap-1416	124	10	t.	t.	PROPN
ap-1416	124	11	,	,	PUNCT
ap-1416	124	12	vargas	vargas	PROPN
ap-1416	124	13	,	,	PUNCT
ap-1416	124	14	a.	a.	NOUN
ap-1416	124	15	:	:	PUNCT
ap-1416	124	16	interlacing	interlacing	NOUN
ap-1416	124	17	and	and	CCONJ
ap-1416	124	18	nonorthogonality	nonorthogonality	NOUN
ap-1416	124	19	of	of	ADP
ap-1416	124	20	spectral	spectral	ADJ
ap-1416	124	21	polynomials	polynomial	NOUN
ap-1416	124	22	for	for	ADP
ap-1416	124	23	the	the	DET
ap-1416	124	24	lamé	lamé	NOUN
ap-1416	124	25	operator	operator	NOUN
ap-1416	124	26	,	,	PUNCT
ap-1416	124	27	proc	proc	NOUN
ap-1416	124	28	.	.	PUNCT
ap-1416	125	1	ams	am	NOUN
ap-1416	125	2	137	137	NUM
ap-1416	125	3	(	(	PUNCT
ap-1416	125	4	2009	2009	NUM
ap-1416	125	5	)	)	PUNCT
ap-1416	125	6	,	,	PUNCT
ap-1416	125	7	1	1	NUM
ap-1416	125	8	699	699	NUM
ap-1416	125	9	-	-	SYM
ap-1416	125	10	1710	1710	NUM
ap-1416	125	11	.	.	PUNCT
ap-1416	126	1	[	[	X
ap-1416	126	2	3	3	NUM
ap-1416	126	3	]	]	X
ap-1416	126	4	borcea	borcea	NOUN
ap-1416	126	5	,	,	PUNCT
ap-1416	126	6	j.	j.	PROPN
ap-1416	126	7	,	,	PUNCT
ap-1416	126	8	shapiro	shapiro	PROPN
ap-1416	126	9	,	,	PUNCT
ap-1416	126	10	b.	b.	PROPN
ap-1416	126	11	:	:	PUNCT
ap-1416	126	12	root	root	NOUN
ap-1416	126	13	asymptotics	asymptotic	NOUN
ap-1416	126	14	of	of	ADP
ap-1416	126	15	spectral	spectral	ADJ
ap-1416	126	16	polynomials	polynomial	NOUN
ap-1416	126	17	for	for	ADP
ap-1416	126	18	the	the	DET
ap-1416	126	19	lamé	lamé	NOUN
ap-1416	126	20	operator	operator	NOUN
ap-1416	126	21	,	,	PUNCT
ap-1416	126	22	commun	commun	PROPN
ap-1416	126	23	.	.	PUNCT
ap-1416	126	24	math	math	NOUN
ap-1416	126	25	.	.	PUNCT
ap-1416	127	1	phys	phy	NOUN
ap-1416	127	2	.	.	PUNCT
ap-1416	128	1	282	282	NUM
ap-1416	128	2	(	(	PUNCT
ap-1416	128	3	2008	2008	NUM
ap-1416	128	4	)	)	PUNCT
ap-1416	128	5	,	,	PUNCT
ap-1416	128	6	323–337	323–337	NUM
ap-1416	128	7	.	.	PUNCT
ap-1416	129	1	[	[	X
ap-1416	129	2	4	4	NUM
ap-1416	129	3	]	]	PUNCT
ap-1416	129	4	cotfas	cotfas	NOUN
ap-1416	129	5	,	,	PUNCT
ap-1416	129	6	n.	n.	NOUN
ap-1416	129	7	:	:	PUNCT
ap-1416	129	8	systems	system	NOUN
ap-1416	129	9	of	of	ADP
ap-1416	129	10	orthogonal	orthogonal	ADJ
ap-1416	129	11	polynomials	polynomial	NOUN
ap-1416	129	12	defined	define	VERB
ap-1416	129	13	by	by	ADP
ap-1416	129	14	hypergeometric	hypergeometric	ADJ
ap-1416	129	15	type	type	NOUN
ap-1416	129	16	equations	equation	NOUN
ap-1416	129	17	with	with	ADP
ap-1416	129	18	application	application	NOUN
ap-1416	129	19	to	to	ADP
ap-1416	129	20	quantum	quantum	ADJ
ap-1416	129	21	mechanics	mechanic	NOUN
ap-1416	129	22	,	,	PUNCT
ap-1416	129	23	cent	cent	NOUN
ap-1416	129	24	.	.	PUNCT
ap-1416	130	1	eur	eur	PROPN
ap-1416	130	2	.	.	PUNCT
ap-1416	131	1	j.	j.	PROPN
ap-1416	131	2	phys	phys	PROPN
ap-1416	131	3	.	.	PUNCT
ap-1416	132	1	2	2	NUM
ap-1416	132	2	(	(	PUNCT
ap-1416	132	3	2004	2004	NUM
ap-1416	132	4	)	)	PUNCT
ap-1416	132	5	,	,	PUNCT
ap-1416	132	6	456–466	456–466	NUM
ap-1416	132	7	.	.	PUNCT
ap-1416	133	1	[	[	X
ap-1416	133	2	5	5	NUM
ap-1416	133	3	]	]	X
ap-1416	133	4	garnett	garnett	PROPN
ap-1416	133	5	,	,	PUNCT
ap-1416	133	6	j.	j.	PROPN
ap-1416	133	7	:	:	PUNCT
ap-1416	133	8	analytic	analytic	ADJ
ap-1416	133	9	capacity	capacity	NOUN
ap-1416	133	10	and	and	CCONJ
ap-1416	133	11	measure	measure	NOUN
ap-1416	133	12	.	.	PUNCT
ap-1416	134	1	lecture	lecture	NOUN
ap-1416	134	2	notes	note	NOUN
ap-1416	134	3	in	in	ADP
ap-1416	134	4	mathematics	mathematics	PROPN
ap-1416	134	5	297	297	NUM
ap-1416	134	6	,	,	PUNCT
ap-1416	134	7	springerverlag	springerverlag	NOUN
ap-1416	134	8	,	,	PUNCT
ap-1416	134	9	berlin	berlin	PROPN
ap-1416	134	10	-	-	PUNCT
ap-1416	134	11	new	new	PROPN
ap-1416	134	12	york	york	PROPN
ap-1416	134	13	,	,	PUNCT
ap-1416	134	14	1972	1972	NUM
ap-1416	134	15	.	.	PUNCT
ap-1416	135	1	[	[	X
ap-1416	135	2	6	6	NUM
ap-1416	135	3	]	]	SYM
ap-1416	135	4	holst	holst	NOUN
ap-1416	135	5	,	,	PUNCT
ap-1416	135	6	t.	t.	PROPN
ap-1416	135	7	,	,	PUNCT
ap-1416	135	8	shapiro	shapiro	PROPN
ap-1416	135	9	,	,	PUNCT
ap-1416	135	10	b.	b.	PROPN
ap-1416	135	11	:	:	PUNCT
ap-1416	135	12	on	on	ADP
ap-1416	135	13	higher	high	ADJ
ap-1416	135	14	heine	heine	PROPN
ap-1416	135	15	-	-	PUNCT
ap-1416	135	16	stieltjes	stieltjes	NOUN
ap-1416	135	17	polynomials	polynomial	NOUN
ap-1416	135	18	,	,	PUNCT
ap-1416	135	19	to	to	PART
ap-1416	135	20	appear	appear	VERB
ap-1416	135	21	in	in	ADP
ap-1416	135	22	isr	isr	PROPN
ap-1416	135	23	.	.	PUNCT
ap-1416	136	1	j.	j.	PROPN
ap-1416	136	2	math	math	PROPN
ap-1416	136	3	.	.	PUNCT
ap-1416	137	1	183	183	NUM
ap-1416	137	2	(	(	PUNCT
ap-1416	137	3	2011	2011	NUM
ap-1416	137	4	)	)	PUNCT
ap-1416	137	5	,	,	PUNCT
ap-1416	138	1	321–347	321–347	NUM
ap-1416	138	2	.	.	PUNCT
ap-1416	139	1	[	[	X
ap-1416	139	2	7	7	X
ap-1416	139	3	]	]	X
ap-1416	139	4	mart́ınez	mart́ınez	PROPN
ap-1416	139	5	-	-	PUNCT
ap-1416	139	6	finkelshtein	finkelshtein	NOUN
ap-1416	139	7	,	,	PUNCT
ap-1416	139	8	a.	a.	PROPN
ap-1416	139	9	,	,	PUNCT
ap-1416	139	10	rakhmanov	rakhmanov	PROPN
ap-1416	139	11	,	,	PUNCT
ap-1416	139	12	e.	e.	PROPN
ap-1416	139	13	a.	a.	PROPN
ap-1416	139	14	:	:	PUNCT
ap-1416	139	15	on	on	ADP
ap-1416	139	16	asymptotic	asymptotic	ADJ
ap-1416	139	17	behavior	behavior	NOUN
ap-1416	139	18	of	of	ADP
ap-1416	139	19	heine	heine	PROPN
ap-1416	139	20	-	-	PUNCT
ap-1416	139	21	stieltjes	stieltjes	PROPN
ap-1416	139	22	and	and	CCONJ
ap-1416	139	23	van	van	PROPN
ap-1416	139	24	vleck	vleck	PROPN
ap-1416	139	25	polynomials	polynomial	NOUN
ap-1416	139	26	,	,	PUNCT
ap-1416	139	27	contemporary	contemporary	ADJ
ap-1416	139	28	mathematics	mathematic	NOUN
ap-1416	139	29	507	507	NUM
ap-1416	139	30	(	(	PUNCT
ap-1416	139	31	2010	2010	NUM
ap-1416	139	32	)	)	PUNCT
ap-1416	139	33	,	,	PUNCT
ap-1416	139	34	209–232	209–232	NUM
ap-1416	139	35	.	.	PUNCT
ap-1416	140	1	[	[	X
ap-1416	140	2	8	8	NUM
ap-1416	140	3	]	]	X
ap-1416	140	4	mart́ınez	mart́ınez	PROPN
ap-1416	140	5	-	-	PUNCT
ap-1416	140	6	finkelshtein	finkelshtein	NOUN
ap-1416	140	7	,	,	PUNCT
ap-1416	140	8	a.	a.	PROPN
ap-1416	140	9	,	,	PUNCT
ap-1416	140	10	rakhmanov	rakhmanov	PROPN
ap-1416	140	11	,	,	PUNCT
ap-1416	140	12	e.	e.	PROPN
ap-1416	140	13	a.	a.	PROPN
ap-1416	140	14	:	:	PUNCT
ap-1416	140	15	critical	critical	ADJ
ap-1416	140	16	measures	measure	NOUN
ap-1416	140	17	,	,	PUNCT
ap-1416	140	18	quadratic	quadratic	ADJ
ap-1416	140	19	differentials	differential	NOUN
ap-1416	140	20	,	,	PUNCT
ap-1416	140	21	and	and	CCONJ
ap-1416	140	22	weak	weak	ADJ
ap-1416	140	23	limits	limit	NOUN
ap-1416	140	24	of	of	ADP
ap-1416	140	25	zeros	zero	NOUN
ap-1416	140	26	of	of	ADP
ap-1416	140	27	stieltjes	stieltjes	PROPN
ap-1416	140	28	polynomials	polynomial	NOUN
ap-1416	140	29	,	,	PUNCT
ap-1416	140	30	comm	comm	NOUN
ap-1416	140	31	.	.	PUNCT
ap-1416	141	1	math	math	NOUN
ap-1416	141	2	.	.	PUNCT
ap-1416	142	1	physics	physics	NOUN
ap-1416	142	2	302	302	NUM
ap-1416	142	3	(	(	PUNCT
ap-1416	142	4	2011	2011	NUM
ap-1416	142	5	)	)	PUNCT
ap-1416	142	6	,	,	PUNCT
ap-1416	142	7	53–111	53–111	NUM
ap-1416	142	8	.	.	PUNCT
ap-1416	143	1	[	[	X
ap-1416	143	2	9	9	NUM
ap-1416	143	3	]	]	PUNCT
ap-1416	143	4	pólya	pólya	ADV
ap-1416	143	5	:	:	PUNCT
ap-1416	143	6	,	,	PUNCT
ap-1416	143	7	g.	g.	PROPN
ap-1416	143	8	sur	sur	PROPN
ap-1416	143	9	un	un	PROPN
ap-1416	143	10	théorème	théorème	PROPN
ap-1416	143	11	de	de	PROPN
ap-1416	143	12	stieltjes	stieltjes	PROPN
ap-1416	143	13	,	,	PUNCT
ap-1416	143	14	c.	c.	PROPN
ap-1416	143	15	r.	r.	PROPN
ap-1416	143	16	acad	acad	PROPN
ap-1416	143	17	.	.	PUNCT
ap-1416	144	1	sci	sci	PROPN
ap-1416	144	2	.	.	PROPN
ap-1416	145	1	paris	paris	PROPN
ap-1416	145	2	155	155	NUM
ap-1416	145	3	(	(	PUNCT
ap-1416	145	4	1912	1912	NUM
ap-1416	145	5	)	)	PUNCT
ap-1416	145	6	,	,	PUNCT
ap-1416	145	7	76–769	76–769	NOUN
ap-1416	145	8	.	.	PUNCT
ap-1416	146	1	[	[	X
ap-1416	146	2	10	10	NUM
ap-1416	146	3	]	]	X
ap-1416	146	4	shapiro	shapiro	PROPN
ap-1416	146	5	,	,	PUNCT
ap-1416	146	6	b.	b.	PROPN
ap-1416	146	7	:	:	PUNCT
ap-1416	146	8	algebro	algebro	ADJ
ap-1416	146	9	-	-	PUNCT
ap-1416	146	10	geometric	geometric	ADJ
ap-1416	146	11	aspects	aspect	NOUN
ap-1416	146	12	of	of	ADP
ap-1416	146	13	heine	heine	PROPN
ap-1416	146	14	-	-	PUNCT
ap-1416	146	15	stieltjes	stieltjes	PROPN
ap-1416	146	16	theory	theory	NOUN
ap-1416	146	17	,	,	PUNCT
ap-1416	146	18	j.	j.	PROPN
ap-1416	146	19	london	london	PROPN
ap-1416	146	20	math	math	PROPN
ap-1416	146	21	.	.	PUNCT
ap-1416	147	1	soc	soc	PROPN
ap-1416	147	2	.	.	PUNCT
ap-1416	148	1	83	83	NUM
ap-1416	148	2	(	(	PUNCT
ap-1416	148	3	2011	2011	NUM
ap-1416	148	4	)	)	PUNCT
ap-1416	148	5	,	,	PUNCT
ap-1416	148	6	36–56	36–56	NUM
ap-1416	148	7	.	.	PUNCT
ap-1416	149	1	93	93	NUM
ap-1416	149	2	acta	acta	PROPN
ap-1416	149	3	polytechnica	polytechnica	PROPN
ap-1416	149	4	vol	vol	NOUN
ap-1416	149	5	.	.	PUNCT
ap-1416	150	1	51	51	NUM
ap-1416	150	2	no	no	INTJ
ap-1416	150	3	.	.	PUNCT
ap-1416	150	4	4/2011	4/2011	NUM
ap-1416	151	1	[	[	X
ap-1416	151	2	11	11	NUM
ap-1416	151	3	]	]	X
ap-1416	151	4	shapiro	shapiro	PROPN
ap-1416	151	5	,	,	PUNCT
ap-1416	151	6	b.	b.	PROPN
ap-1416	151	7	,	,	PUNCT
ap-1416	151	8	tater	tater	NOUN
ap-1416	151	9	,	,	PUNCT
ap-1416	151	10	m.	m.	NOUN
ap-1416	151	11	:	:	PUNCT
ap-1416	151	12	on	on	ADP
ap-1416	151	13	spectral	spectral	ADJ
ap-1416	151	14	polynomials	polynomial	NOUN
ap-1416	151	15	of	of	ADP
ap-1416	151	16	the	the	DET
ap-1416	151	17	heun	heun	NOUN
ap-1416	151	18	equation	equation	NOUN
ap-1416	151	19	.	.	PUNCT
ap-1416	152	1	i	i	PRON
ap-1416	152	2	,	,	PUNCT
ap-1416	152	3	j.	j.	PROPN
ap-1416	152	4	approx	approx	PROPN
ap-1416	152	5	.	.	PUNCT
ap-1416	153	1	theory	theory	NOUN
ap-1416	153	2	162	162	NUM
ap-1416	153	3	(	(	PUNCT
ap-1416	153	4	2010	2010	NUM
ap-1416	153	5	)	)	PUNCT
ap-1416	153	6	,	,	PUNCT
ap-1416	153	7	766–781	766–781	NUM
ap-1416	153	8	.	.	PUNCT
ap-1416	154	1	[	[	X
ap-1416	154	2	12	12	NUM
ap-1416	154	3	]	]	X
ap-1416	154	4	shapiro	shapiro	PROPN
ap-1416	154	5	,	,	PUNCT
ap-1416	154	6	b.	b.	PROPN
ap-1416	154	7	,	,	PUNCT
ap-1416	154	8	takemura	takemura	VERB
ap-1416	154	9	,	,	PUNCT
ap-1416	154	10	k.	k.	PROPN
ap-1416	154	11	,	,	PUNCT
ap-1416	154	12	tater	tater	NOUN
ap-1416	154	13	,	,	PUNCT
ap-1416	154	14	m.	m.	NOUN
ap-1416	154	15	:	:	PUNCT
ap-1416	154	16	on	on	ADP
ap-1416	154	17	spectral	spectral	ADJ
ap-1416	154	18	polynomials	polynomial	NOUN
ap-1416	154	19	of	of	ADP
ap-1416	154	20	the	the	DET
ap-1416	154	21	heun	heun	PROPN
ap-1416	154	22	equation	equation	NOUN
ap-1416	154	23	.	.	PUNCT
ap-1416	155	1	ii	ii	PROPN
ap-1416	155	2	,	,	PUNCT
ap-1416	155	3	arxiv:0904.0650	arxiv:0904.0650	NOUN
ap-1416	155	4	.	.	PUNCT
ap-1416	156	1	[	[	X
ap-1416	156	2	13	13	NUM
ap-1416	156	3	]	]	X
ap-1416	156	4	szegő	szegő	PROPN
ap-1416	156	5	,	,	PUNCT
ap-1416	156	6	g.	g.	NOUN
ap-1416	156	7	:	:	PUNCT
ap-1416	156	8	orthogonal	orthogonal	ADJ
ap-1416	156	9	polynomials	polynomial	NOUN
ap-1416	156	10	.	.	PUNCT
ap-1416	157	1	1975	1975	NUM
ap-1416	157	2	,	,	PUNCT
ap-1416	157	3	ams	am	NOUN
ap-1416	157	4	,	,	PUNCT
ap-1416	157	5	pronidence	pronidence	PROPN
ap-1416	157	6	,	,	PUNCT
ap-1416	157	7	r.i	r.i	PROPN
ap-1416	157	8	.	.	PROPN
ap-1416	158	1	[	[	X
ap-1416	158	2	14	14	NUM
ap-1416	158	3	]	]	X
ap-1416	158	4	whittaker	whittaker	PROPN
ap-1416	158	5	,	,	PUNCT
ap-1416	158	6	e.	e.	PROPN
ap-1416	158	7	t.	t.	PROPN
ap-1416	158	8	,	,	PUNCT
ap-1416	158	9	watson	watson	PROPN
ap-1416	158	10	,	,	PUNCT
ap-1416	158	11	g.	g.	PROPN
ap-1416	158	12	:	:	PUNCT
ap-1416	158	13	a	a	DET
ap-1416	158	14	course	course	NOUN
ap-1416	158	15	of	of	ADP
ap-1416	158	16	modern	modern	ADJ
ap-1416	158	17	analysis	analysis	NOUN
ap-1416	158	18	.	.	PUNCT
ap-1416	159	1	reprint	reprint	NOUN
ap-1416	159	2	of	of	ADP
ap-1416	159	3	the	the	DET
ap-1416	159	4	4th	4th	ADJ
ap-1416	159	5	edition	edition	NOUN
ap-1416	159	6	,	,	PUNCT
ap-1416	159	7	1996	1996	NUM
ap-1416	159	8	,	,	PUNCT
ap-1416	159	9	cambridge	cambridge	PROPN
ap-1416	159	10	univ	univ	PROPN
ap-1416	159	11	.	.	PUNCT
ap-1416	160	1	press	press	PROPN
ap-1416	160	2	,	,	PUNCT
ap-1416	160	3	uk	uk	PROPN
ap-1416	160	4	.	.	PROPN
ap-1416	160	5	boris	boris	PROPN
ap-1416	160	6	shapiro	shapiro	PROPN
ap-1416	160	7	e	e	PROPN
ap-1416	160	8	-	-	NOUN
ap-1416	160	9	mail	mail	NOUN
ap-1416	160	10	:	:	PUNCT
ap-1416	160	11	shapiro@math.su.se	shapiro@math.su.se	ADJ
ap-1416	160	12	department	department	NOUN
ap-1416	160	13	of	of	ADP
ap-1416	160	14	mathematics	mathematics	PROPN
ap-1416	160	15	stockholm	stockholm	PROPN
ap-1416	160	16	university	university	PROPN
ap-1416	160	17	,	,	PUNCT
ap-1416	160	18	se-106	se-106	NOUN
ap-1416	160	19	91	91	NUM
ap-1416	160	20	stockholm	stockholm	PROPN
ap-1416	160	21	,	,	PUNCT
ap-1416	160	22	sweden	sweden	ADJ
ap-1416	160	23	miloš	miloš	ADJ
ap-1416	160	24	tater	tater	NOUN
ap-1416	160	25	e	e	NOUN
ap-1416	160	26	-	-	NOUN
ap-1416	160	27	mail	mail	NOUN
ap-1416	160	28	:	:	PUNCT
ap-1416	160	29	tater@ujf.cas.cz	tater@ujf.cas.cz	NOUN
ap-1416	160	30	department	department	PROPN
ap-1416	160	31	of	of	ADP
ap-1416	160	32	theoretical	theoretical	ADJ
ap-1416	160	33	physics	physics	PROPN
ap-1416	160	34	nuclear	nuclear	PROPN
ap-1416	160	35	physics	physics	PROPN
ap-1416	160	36	institute	institute	PROPN
ap-1416	160	37	as	as	ADP
ap-1416	160	38	cr	cr	PROPN
ap-1416	160	39	v.v.i	v.v.i	PROPN
ap-1416	160	40	.	.	PUNCT
ap-1416	160	41	cz-250	cz-250	VERB
ap-1416	160	42	68	68	NUM
ap-1416	160	43	řež	řež	NOUN
ap-1416	160	44	,	,	PUNCT
ap-1416	160	45	czech	czech	PROPN
ap-1416	160	46	republic	republic	NOUN
ap-1416	160	47	94	94	NUM