Monotonicity of zeros of polynomials orthogonal with respect to an even weight function

Loading...
Thumbnail Image

Authors

Jordaan, Kerstin Heidrun
Wang, H.
Zhou, J.

Journal Title

Journal ISSN

Volume Title

Publisher

Taylor and Francis

Abstract

The monotonicity properties of all the zeros with respect to a parameter of orthogonal polynomials associated with an even weight function are studied. The results we obtain extend the work of A. Markoff. The monotonicity of the zeros of Gegenbauer, Freud-type and symmetric Meixner-Pollaczek orthogonal polynomials as well as Al-Salam-Chihara q-orthogonal polynomials are investigated. For the Meixner-Pollaczek polynomials, a special case of a conjecture by Jordaan and To´okos which concerns the interlacing of their zeros between two different sequences of Meixner-Pollaczek polynomials is proved.

Description

Keywords

Freud-type orthogonal polynomial, Meixner-Pollaczek polynomials, Gegenbauer polynomials, Al-Salam-Chihara polynomials, Zeros, Monotonicity, Interlacing

Sustainable Development Goals

Citation

K. Jordaan, H. Wang & J. Zhou (2014) Monotonicity of zeros of polynomials orthogonal with respect to an even weight function, Integral Transforms and Special Functions, 25:9, 721-729, DOI: 10.1080/10652469.2014.904303.