Volkmer, H.
, Alexander, B.
and Cohl, H.
(2023),
Internal and external harmonics in bi-cyclide coordinates, Journal of Physics A: Mathematical and Theoretical, [online], https://doi.org/10.1088/1751-8121/ace301, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=935937
(Accessed October 14, 2025)
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Internal and external harmonics in bi-cyclide coordinates
Published
Author(s)
Hans Volkmer, Brandon Alexander,
Abstract
The Laplace equation in three-dimensional Euclidean space is R-separable in bi-cyclide coordinates leading to harmonic functions expressed in terms of Lamé–Wangerin functions called internal and external bi-cyclide harmonics. An expansion for a 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 expansions in bi-spherical and prolate spheroidal coordinates.Citation
Journal of Physics A: Mathematical and Theoretical
Volume
56
Pub Type
Journals
Download Paper
Keywords
Laplace’s equation, fundamental solution, separable curvilinear coordinate system, bi-cyclide coordinates, Lamé-Wangerin functions.
Citation
Issues
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Created July 20, 2023, Updated March 27, 2024