A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres

Symmetry Integrability and Geometry-Methods and Applications

article

Richard Chapling¹ 

[1] Department of Applied Mathematics and Theoretical Physics, University of Cambridge

关键词: hyperspherical geometry;    fundamental solution;    Laplace’s equation;    separation of variables;    hypergeometric functions;   

DOI  :  10.3842/SIGMA.2016.079

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown