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Bounds for zeros of Meixner and Kravchuk polynomials

Part of: Nontrigonometric harmonic analysis

Published online by Cambridge University Press:  01 April 2014

A. Jooste  and
K. Jordaan
A. Jooste
Affiliation:
Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood Road, Pretoria, 0002, South Africa email alta.jooste@up.ac.za
K. Jordaan
Affiliation:
Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood Road, Pretoria, 0002, South Africa email kjordaan@up.ac.za

Abstract

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The zeros of certain different sequences of orthogonal polynomials interlace in a well-defined way. The study of this phenomenon and the conditions under which it holds lead to a set of points that can be applied as bounds for the extreme zeros of the polynomials. We consider different sequences of the discrete orthogonal Meixner and Kravchuk polynomials and use mixed three-term recurrence relations, satisfied by the polynomials under consideration, to identify bounds for the extreme zeros of Meixner and Kravchuk polynomials.

MSC classification

Secondary: 33C05: Classical hypergeometric functions, $_2F_1$ 33C20: Generalized hypergeometric series, $_pF_q$ 42C05: Orthogonal functions and polynomials, general theory

Information

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 17 , Issue 1 , 2014 , pp. 47 - 57
Copyright
© The Author(s) 2014 

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