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

• 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
• 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.

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...