On zeros of discrete orthogonal polynomials

Ilia Krasikov; Alexander Zarkh

doi:10.1016/j.jat.2008.04.015

On zeros of discrete orthogonal polynomials

Ilia Krasikov^*, Alexander Zarkh

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We exploit difference equations to establish sharp inequalities on the extreme zeros of the classical discrete orthogonal polynomials, Charlier, Krawtchouk, Meixner and Hahn. We also provide lower bounds on the minimal distance between their consecutive zeros.

Original language	English
Pages (from-to)	121-141
Number of pages	21
Journal	Journal of Approximation Theory
Volume	156
Issue number	2
DOIs	https://doi.org/10.1016/j.jat.2008.04.015
State	Published - Feb 2009
Externally published	Yes

Keywords

Charlier polynomials
Discrete orthogonal polynomials
Hahn polynomials
Krawtchouk polynomials
Meixner polynomials
Zeros

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10.1016/j.jat.2008.04.015

Cite this

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title = "On zeros of discrete orthogonal polynomials",

abstract = "We exploit difference equations to establish sharp inequalities on the extreme zeros of the classical discrete orthogonal polynomials, Charlier, Krawtchouk, Meixner and Hahn. We also provide lower bounds on the minimal distance between their consecutive zeros.",

keywords = "Charlier polynomials, Discrete orthogonal polynomials, Hahn polynomials, Krawtchouk polynomials, Meixner polynomials, Zeros",

author = "Ilia Krasikov and Alexander Zarkh",

note = "Funding Information: This work was supported by the EC Marie Curie programme NET-ACE (MEST-CT-2004-6724). ",

year = "2009",

month = feb,

doi = "10.1016/j.jat.2008.04.015",

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AU - Zarkh, Alexander

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PY - 2009/2

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AB - We exploit difference equations to establish sharp inequalities on the extreme zeros of the classical discrete orthogonal polynomials, Charlier, Krawtchouk, Meixner and Hahn. We also provide lower bounds on the minimal distance between their consecutive zeros.

KW - Charlier polynomials

KW - Discrete orthogonal polynomials

KW - Hahn polynomials

KW - Krawtchouk polynomials

KW - Meixner polynomials

KW - Zeros

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SN - 0021-9045

VL - 156

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JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

IS - 2

ER -

On zeros of discrete orthogonal polynomials

Abstract

Keywords

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