Generalized Ellipsoidal and Sphero-Conal Harmonics

Details Generalized Ellipsoidal and Sphero-Conal Harmonics Generalized Ellipsoidal and Sphero-Conal Harmonics

2006-10-24

arxiv.org/abs/math/0610718v1

SIGMA 2 (2006), 071, 16 pages

Mathematics

Classical Analysis and ODEs

This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Sym

Scientific paper

10.3842/SIGMA.2006.071

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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