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

共 50 条

[31] Inequalities for the zeros of the associated ultraspherical polynomials
Siafarikas, PD
[J]. MATHEMATICAL INEQUALITIES & APPLICATIONS, 1999, 2 (02): : 233 - 241
[32] EXPANSION IN ULTRASPHERICAL POLYNOMIALS WITH NONNEGATIVE COEFFICIENTS
DUNKL, CF
[J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 20 (03): : A389 - A389
[33] ON THE COEFFICIENTS OF DIFFERENTIATED EXPANSIONS OF ULTRASPHERICAL POLYNOMIALS
KARAGEORGHIS, A
PHILLIPS, TN
[J]. APPLIED NUMERICAL MATHEMATICS, 1992, 9 (02) : 133 - 141
[34] ON THE ZEROS OF THE PARAMETRIC DERIVATIVES OF THE ULTRASPHERICAL POLYNOMIALS
KANTER, LH
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1951, 57 (01) : 69 - 69
[35] RECURRENT DETERMINANTS OF LEGENDRE AND OF ULTRASPHERICAL POLYNOMIALS
BECKENBACH, EF
SEIDEL, W
SZASZ, O
[J]. DUKE MATHEMATICAL JOURNAL, 1951, 18 (01) : 1 - 10
[36] INEQUALITIES FOR ULTRASPHERICAL POLYNOMIALS AND THE GAMMA FUNCTION
LORCH, L
[J]. JOURNAL OF APPROXIMATION THEORY, 1984, 40 (02) : 115 - 120
[37] ON THE COEFFICIENTS OF INTEGRATED EXPANSIONS OF ULTRASPHERICAL POLYNOMIALS
PHILLIPS, TN
KARAGEORGHIS, A
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1990, 27 (03) : 823 - 830
[38] On the Riesz transform associated with the ultraspherical polynomials
Dariusz Buraczewski
Teresa Martinez
José L. Torrea
Roman Urban
[J]. Journal d’Analyse Mathématique, 2006, 98 : 113 - 143
[39] Convexity of the largest zero of the ultraspherical polynomials
Kokologiannaki, CG
Siafarikas, PD
[J]. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 1996, 4 (03) : 275 - 278
[40] ON POSITIVE HARMONIC FUNCTIONS AND ULTRASPHERICAL POLYNOMIALS
SEIDEL, W
SZASZ, O
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1950, 56 (01) : 37 - 37

← 1 2 3 4 5 →