Convexity of the zeros of some orthogonal polynomials and related functions

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:233

Article; Proceedings Paper

Jordaan, Kerstin¹  Tookos, Ferenc² 

[1] Univ Pretoria, Dept Math & Appl Math, ZA-0002 Pretoria, South Africa

[2] GSF Res Ctr Environm & Hlth, Inst Biomath & Biometry, Neuherberg, Germany

关键词: Orthogonal polynomials;    Zeros;    Laguerre polynomials;    Jacobi polynomials;    Ultraspherical polynomials;    Convexity;   

DOI  :  10.1016/j.cam.2009.02.045

来源: Elsevier

【 摘 要 】

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. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free