Zeros of Gegenbauer and Hermite polynomials and connection coefficients

被引：25

作者：

Area, I

Dimitrov, DK

Godoy, E

Ronveaux, A

机构：

[1] Univ Vigo, ETSE Telecomunicac, Dept Matemat Aplicada 2, Vigo 36200, Spain

[2] Univ Estadual Paulista, IBILCE, Dept Ciencias Computacao & Estatist, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil

[3] Univ Vigo, ETSI Ind, Dept Matemat Aplicada 2, Vigo 36200, Spain

[4] Univ Catholique Louvain, Dept Math, Unite Anal Math & Mecan, B-1348 Louvain, Belgium

来源：

MATHEMATICS OF COMPUTATION | 2004年 / 73卷 / 248期

关键词：

orthogonal polynomials; zeros of Gegenbauer polynomials; zeros of Hermite polynomials; connection coefficients;

D O I：

10.1090/S0025-5718-04-01642-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, sharp upper limit for the zeros of the ultraspherical polynomials are obtained via a result of Obrechkoff and certain explicit connection coefficients for these polynomials. As a consequence, sharp bounds for the zeros of the Hermite polynomials are obtained.

引用

页码：1937 / 1951

页数：15

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