Convexity of the zeros of some orthogonal polynomials and related functions

[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.

[发布日期] 2009-12-01

[效力级别]  Proceedings Paper

[关键词] Orthogonal polynomials;Zeros;Laguerre polynomials;Jacobi polynomials;Ultraspherical polynomials;Convexity