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

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...

Full description

Saved in:
Bibliographic Details
Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2016
Main Author: Chapling, R.
Format: Article
Language:English
Published: Інститут математики НАН України 2016
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/147845
Tags: Add Tag
No Tags, Be the first to tag this record!
Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres / R. Chapling // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 16 назв. — англ.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
Description
Summary: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.
ISSN:1815-0659