中文

Generalized Ellipsoidal and Sphero-Conal Harmonics

经典分析与常微分方程 2008-04-24 v1 数学物理 math.MP

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

@article{arxiv.math/0610718,
  title  = {Generalized Ellipsoidal and Sphero-Conal Harmonics},
  author = {Hans Volkmer},
  journal= {arXiv preprint arXiv:math/0610718},
  year   = {2008}
}

备注

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/