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