This article is cited in 5 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.

MSC: 35A08; 35J05; 31C12; 33C05; 33C20

Received: November 23, 2015; in final form August 4, 2016; Published online August 10, 2016

Language: English

DOI: 10.3842/SIGMA.2016.079

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ArXiv: 1508.06689