A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres
Abstract
We consider Poisson's equation on the ndimensional 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 odddimensional cases.
 Publication:

SIGMA
 Pub Date:
 August 2016
 DOI:
 10.3842/SIGMA.2016.079
 arXiv:
 arXiv:1508.06689
 Bibcode:
 2016SIGMA..12..079C
 Keywords:

 hyperspherical geometry;
 fundamental solution;
 Laplace's equation;
 separation of variables;
 hypergeometric functions;
 Mathematical Physics;
 Mathematics  Analysis of PDEs;
 Mathematics  Classical Analysis and ODEs;
 35A08;
 35J05;
 32Q10;
 31C12;
 33C05;
 33C20
 EPrint:
 SIGMA 12 (2016), 079, 20 pages