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}
}