English

Expansions for a fundamental solution of Laplace's equation on ${\mathbb R^3}$ in 5-cyclidic harmonics

Classical Analysis and ODEs 2013-11-15 v1 Mathematical Physics math.MP

Abstract

We derive eigenfunction expansions for a fundamental solution of Laplace's equation in three-dimensional Euclidean space in 5-cyclidic coordinates. There are three such expansions in terms of internal and external 5-cyclidic harmonics of first, second and third kind. The internal and external 5-cyclidic harmonics are expressed by solutions of a Fuchsian differential equation with five regular singular points.

Keywords

Cite

@article{arxiv.1311.3514,
  title  = {Expansions for a fundamental solution of Laplace's equation on ${\mathbb R^3}$ in 5-cyclidic harmonics},
  author = {Howard S. Cohl and Hans Volkmer},
  journal= {arXiv preprint arXiv:1311.3514},
  year   = {2013}
}