A hypergeometric integral with applications to the fundamental solution of Laplace's equation on hyperspheres

DOI10.3842/SIGMA.2016.079zbMath1348.35009arXiv1508.06689OpenAlexW1927409934MaRDI QIDQ308689

Richard Chapling

Publication date: 6 September 2016

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.06689

zbMATH Keywords

hypergeometric functionsfundamental solutionseparation of variablesLaplace's equationhyperspherical geometry

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Generalized hypergeometric series, ({}_pF_q) (33C20) Classical hypergeometric functions, ({}_2F_1) (33C05) Potential theory on Riemannian manifolds and other spaces (31C12)

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Cites Work

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• Fundamental solution of Laplace's equation in hyperspherical geometry
• The early history of the hypergeometric function
• Contiguous relations of hypergeometric series
• Fourier and Gegenbauer expansions for a fundamental solution of Laplace's equation in hyperspherical geometry
• Handbook of normal frames and coordinates
• Fourier and Gegenbauer expansions for a fundamental solution of the Laplacian in the hyperboloid model of hyperbolic geometry
• Introduction to Smooth Manifolds
• Closed forms of the Green's function and the generalized Green's function for the Helmholtz operator on theN-dimensional unit sphere
• The contiguous function relations for _{𝑝}𝐹_{𝑞} with application to Batemean’s 𝐽_{𝑛}^{𝑢,𝜈} and Rice’s 𝐻_{𝑛}(𝜁,𝑝,𝜈)

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