An acoustical interpretation of the zeroes of ultraspherical polynomials

被引：1

作者：

Le Vey, Georges ^{[1
]}

机构：

[1] Ecole Mines Nantes, UMR CNRS 6597, IRCCyN, 4 Rue Alfred Kastler, F-44307 Nantes 1, France

来源：

COMPTES RENDUS MECANIQUE | 2016年 / 344卷 / 06期

关键词：

Acoustics; Acoustical resonators; Ultraspherical polynomials; Orthogonal polynomials roots; Resonance frequencies; Plane wave propagation;

D O I：

10.1016/j.crme.2016.01.005

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

In 1887, T.J. Stieltjes gave an electrostatical interpretation of the zeroes of Jacobi polynomials. This was extended later to Laguerre and Hermite polynomials by G. Szego. An analogous interpretation is given here for ultraspherical polynomials in terms of piecewise cylindrical acoustical resonators. (C) 2016 Academie des sciences. Published by Elsevier Masson SAS.

引用

页码：434 / 438

页数：5

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