Cohl, H.
, Volkmer, H.
and Bi, L.
(2022),
Expansion for a fundamental solution of Laplace's equation in flat-ring cyclide coordinates, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), [online], https://doi.org/10.3842/SIGMA.2022.041, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=933839
(Accessed October 14, 2025)
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Expansion for a fundamental solution of Laplace's equation in flat-ring cyclide coordinates
Published
Author(s)
, Hans Volkmer, Lijuan Bi
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 Lame functions. In a limiting case we obtain the expansion of the fundamental solution in toroidal coordinates.Citation
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume
18
Pub Type
Journals
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Keywords
Laplace’s equation, fundamental solution, separable curvilinear coordinate system, flat-ring cyclide coordinates, special functions, orthogonal polynomials.
Citation
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Created June 3, 2022, Updated March 27, 2024