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Symmetry, Integrability and Geometry: Methods and Applications, 2022, Volume 18, 041, 31 pp.
DOI: https://doi.org/10.3842/SIGMA.2022.041 (Mi sigma1835) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates

Lijuan Bia, Howard S. Cohlb, Hans Volkmerc

a Department of Mathematics, The Ohio State University at Newark, Newark, OH 43055, USA
b Applied and Computational Mathematics Division, National Institute of Standards and Technology, Mission Viejo, CA 92694, USA
c Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201-0413, USA
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DOI: https://doi.org/10.3842/SIGMA.2022.041
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 Lamé functions. In a limiting case we obtain the expansion of the fundamental solution in toroidal coordinates.
Keywords: Laplace's equation, fundamental solution, separable curvilinear coordinate system, flat-ring cyclide coordinates, special functions, orthogonal polynomials.
Received: November 20, 2021; in final form May 18, 2022; Published online June 3, 2022
Bibliographic databases:
Document Type: Article
MSC: 35A08, 35J05, 33C05, 33C10, 33C15, 33C20, 33C45, 33C47, 33C55, 33C75
Language: English
Citation: Lijuan Bi, Howard S. Cohl, Hans Volkmer, “Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates”, SIGMA, 18 (2022), 041, 31 pp.
Citation in format AMSBIB
\Bibitem{BiCohVol22}
\by Lijuan~Bi, Howard~S.~Cohl, Hans~Volkmer
\paper Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates
\jour SIGMA
\yr 2022
\vol 18
\papernumber 041
\totalpages 31
\mathnet{http://mi.mathnet.ru/sigma1835}
\crossref{https://doi.org/10.3842/SIGMA.2022.041}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4432921}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85133835113}
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