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Inequalities for Extreme Zeros of Some Classical Orthogonal and q-orthogonal Polynomials
Published online by Cambridge University Press: 28 January 2013
Abstract
Let {pn}∞n=0 be a sequence of orthogonal polynomials. We briefly review properties of pn that have been used to derive upper and lower bounds for the largest and smallest zero of pn. Bounds for the extreme zeros of Laguerre, Jacobi and Gegenbauer polynomials that have been obtained using different approaches are numerically compared and new bounds for extreme zeros of q-Laguerre and little q-Jacobi polynomials are proved.
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- 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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