Convexity of the zeros of some orthogonal polynomials and related functions

Authors:
Kerstin Jordaan;Ferenc Tookos
Affiliations:
Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002, South Africa;Institute for Biomathematics and Biometry, GSF - Research Center for Environment and Health, Neuherberg, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 2
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Abstract

We study convexity properties of the zeros of some special functions that follow from the convexity theorem of Sturm. We prove results on the intervals of convexity for the zeros of Laguerre, Jacobi and ultraspherical polynomials, as well as functions related to them, using transformations under which the zeros remain unchanged. We give upper as well as lower bounds for the distance between consecutive zeros in several cases.