Representations for the extreme zeros of orthogonal polynomials

Erik A. van Doorn; N.D. van Foreest; Alexander I. Zeifman

doi:10.1016/j.cam.2009.02.051

Representations for the extreme zeros of orthogonal polynomials

Erik A. van Doorn, N.D. van Foreest, Alexander I. Zeifman

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Abstract

We establish some representations for the smallest and largest zeros of orthogonal polynomials in terms of the parameters in the three-terms recurrence relation. As a corollary we obtain representations for the endpoints of the true interval of orthogonality. Implications of these results for the decay parameter of a birth death process (with killing) are displayed.

Original language	English
Pages (from-to)	847-851
Number of pages	5
Journal	Journal of computational and applied mathematics
Volume	233
Issue number	3
DOIs	https://doi.org/10.1016/j.cam.2009.02.051
Publication status	Published - 2009

Keywords

Three-terms recurrence relation
EWI-15998
MSC-60J80
MSC-42C05
Interval of orthogonality
IR-67864
Birth-death process
Decay parameter
METIS-263992

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Cite this

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title = "Representations for the extreme zeros of orthogonal polynomials",

abstract = "We establish some representations for the smallest and largest zeros of orthogonal polynomials in terms of the parameters in the three-terms recurrence relation. As a corollary we obtain representations for the endpoints of the true interval of orthogonality. Implications of these results for the decay parameter of a birth death process (with killing) are displayed.",

keywords = "Three-terms recurrence relation, EWI-15998, MSC-60J80, MSC-42C05, Interval of orthogonality, IR-67864, Birth-death process, Decay parameter, METIS-263992",

author = "{van Doorn}, {Erik A.} and {van Foreest}, N.D. and Zeifman, {Alexander I.}",

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year = "2009",

doi = "10.1016/j.cam.2009.02.051",

language = "English",

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pages = "847--851",

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TY - JOUR

T1 - Representations for the extreme zeros of orthogonal polynomials

AU - van Doorn, Erik A.

AU - van Foreest, N.D.

AU - Zeifman, Alexander I.

N1 - eemcs-eprint-15998

PY - 2009

Y1 - 2009

N2 - We establish some representations for the smallest and largest zeros of orthogonal polynomials in terms of the parameters in the three-terms recurrence relation. As a corollary we obtain representations for the endpoints of the true interval of orthogonality. Implications of these results for the decay parameter of a birth death process (with killing) are displayed.

AB - We establish some representations for the smallest and largest zeros of orthogonal polynomials in terms of the parameters in the three-terms recurrence relation. As a corollary we obtain representations for the endpoints of the true interval of orthogonality. Implications of these results for the decay parameter of a birth death process (with killing) are displayed.

KW - Three-terms recurrence relation

KW - EWI-15998

KW - MSC-60J80

KW - MSC-42C05

KW - Interval of orthogonality

KW - IR-67864

KW - Birth-death process

KW - Decay parameter

KW - METIS-263992

U2 - 10.1016/j.cam.2009.02.051

DO - 10.1016/j.cam.2009.02.051

M3 - Article

SN - 0377-0427

VL - 233

SP - 847

EP - 851

JO - Journal of computational and applied mathematics

JF - Journal of computational and applied mathematics

IS - 3

ER -

Representations for the extreme zeros of orthogonal polynomials

Abstract

Keywords

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