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arXiv · 2202.08918

Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates

Lijuan Bi·Howard S. Cohl·Hans Volkmer
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Abstract

We derive an expansion for the fundamental solution of Laplace's equation in flat-ring coordinates in three-dimensional Euclidean space. This expansion is a double series of products of functions that are harmonic in the interior and exterior of "flat rings". These internal and external flat-ring harmonic functions are expressed in terms of simply-periodic Lam\'e functions. In a limiting case we obtain the expansion of the fundamental solution in toroidal coordinates.

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Lijuan Bi, Howard S. Cohl, Hans Volkmer. 2022-02-17. Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates. https://doi.org/10.3842/sigma.2022.041

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