Generalized Ellipsoidal and Sphero-Conal Harmonics

被引：7

作者：

Volkmer, Hans ^{[1
]}

机构：

[1] Univ Wisconsin, Dept Math Sci, Milwaukee, WI 53201 USA

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2006年 / 2卷

关键词：

generalized ellipsoidal harmonic; Stieltjes polynomials; Dunkl equation; Niven formula;

D O I：

10.3842/SIGMA.2006.071

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Classical ellipsoidal and sphero-conal harmonics are polynomial solutions of the Laplace equation that can be expressed in terms of Lame polynomials. Generalized ellipsoidal and sphero-conal harmonics are polynomial solutions of the more general Dunkl equation that can be expressed in terms of Stieltjes polynomials. Niven's formula connecting ellipsoidal and sphero-conal harmonics is generalized. Moreover, generalized ellipsoidal harmonics are applied to solve the Dirichlet problem for Dunkl's equation on ellipsoids.

引用

页数：16

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