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arXiv · 1311.3514

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

Howard S. Cohl·Hans Volkmer
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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.

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Howard S. Cohl, Hans Volkmer. 2013-11-14. Expansions for a fundamental solution of Laplace's equation on ${\mathbb R^3}$ in 5-cyclidic harmonics. https://arxiv.org/abs/1311.3514

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