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Inequalities for Extreme Zeros of Some Classical Orthogonal andq-orthogonal Polynomials

Published online by Cambridge University Press:  28 January 2013

K. Driver  and
K. Jordaan
K. Driver*
Affiliation:
Department of Mathematics and Applied Mathematics, University of Cape Town 7701, RSA
K. Jordaan
Affiliation:
Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002, RSA
*
∗ Corresponding author. E-mail: [email protected]
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Abstract

Let {pn}∞n=0 be a sequence of orthogonal polynomials. We brieflyreview properties of pn that have been usedto derive upper and lower bounds for the largest and smallest zero ofpn. Bounds for theextreme zeros of Laguerre, Jacobi and Gegenbauer polynomials that have been obtained usingdifferent approaches are numerically compared and new bounds for extreme zeros ofq-Laguerre and little q-Jacobi polynomials are proved.

Keywords

Bounds for extreme zeros of orthogonal and q-orthogonal polynomialscommon zeros of orthogonal polynomialsmonotonicityconvexityinterlacing of zerosseparation of zerosinequalities for zeros
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 1: Harmonic analysis , 2013 , pp. 48 - 59
Copyright
© EDP Sciences, 2013

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