Convexity of the zeros of some orthogonal polynomials and related functions

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• 作者：Kerstin Jordaan ; Ferenc Tookos
• 关键词：Orthogonal polynomials ; Zeros ; Laguerre polynomials ; Jacobi polynomials ; Ultraspherical polynomials ; Convexity
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2009
• 出版时间：1 December 2009
• 年：2009
• 卷：233
• 期：3
• 页码：762-767
• 全文大小：365 K

文摘

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.