Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates
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 interna...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2022 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2022
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211627 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates. Lijuan Bi, Howard S. Cohl and Hans Volkmer. SIGMA 18 (2022), 041, 31 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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 Lamé functions. In a limiting case, we obtain the expansion of the fundamental solution in toroidal coordinates.
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| ISSN: | 1815-0659 |