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This article is cited in 4 scientific papers (total in 4 papers)
A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres
Richard Chapling Department of Applied Mathematics and Theoretical Physics,
University of Cambridge, Cambridge, England
Abstract:
We consider Poisson's equation on the $n$-dimensional sphere in the situation where the inhomogeneous term has zero integral. Using a number of classical and modern hypergeometric identities, we integrate this equation to produce the form of the fundamental solutions for any number of dimensions in terms of generalised hypergeometric functions, with different closed forms for even and odd-dimensional cases.
Keywords:
hyperspherical geometry; fundamental solution; Laplace's equation; separation of variables; hypergeometric functions.
Received: November 23, 2015; in final form August 4, 2016; Published online August 10, 2016
Citation:
Richard Chapling, “A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres”, SIGMA, 12 (2016), 079, 20 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1161 https://www.mathnet.ru/eng/sigma/v12/p79
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Abstract page: | 151 | Full-text PDF : | 36 | References: | 27 |
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