Internal and external harmonics in bi-cyclide coordinates
Classical Analysis and ODEs
2023-08-02 v1
Abstract
The Laplace equation in three dimensional Euclidean space is -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.
Cite
@article{arxiv.2303.02235,
title = {Internal and external harmonics in bi-cyclide coordinates},
author = {Brandon Alexander and Howard S. Cohl and Hans Volkmer},
journal= {arXiv preprint arXiv:2303.02235},
year = {2023}
}