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.
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页数：16
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