Generalized Ellipsoidal and Sphero-Conal Harmonics
Classical Analysis and ODEs
2008-04-24 v1 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.math/0610718,
title = {Generalized Ellipsoidal and Sphero-Conal Harmonics},
author = {Hans Volkmer},
journal= {arXiv preprint arXiv:math/0610718},
year = {2008}
}
Comments
This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/