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
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
收藏
页码:1937 / 1951
页数:15
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