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arXiv · 2303.02235

Internal and external harmonics in bi-cyclide coordinates

Brandon Alexander·Howard S. Cohl·Hans Volkmer
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Abstract

The Laplace equation in three dimensional Euclidean space is $R$-separable in bi-cyclide coordinates leading to harmonic functions expressed in terms of Lam\'e-Wangerin functions called internal and external bi-cyclide harmonics. An expansion for the fundamental solution of Laplace's equation in products of internal and external bi-cyclide harmonics is derived. In limiting cases this expansion reduces to known expansion in bi-spherical and prolate spheroidal coordinates.

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Brandon Alexander, Howard S. Cohl, Hans Volkmer. 2023-03-03. Internal and external harmonics in bi-cyclide coordinates. https://doi.org/10.1088/1751-8121/ace301

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