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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2016 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147845 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862696479564496896 |
|---|---|
| author | Chapling, R. |
| author_facet | Chapling, R. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T16:27:22Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147845 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:27:22Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Chapling, R. 2019-02-16T09:13:58Z 2019-02-16T09:13:58Z 2016 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. 1815-0659 2010 Mathematics Subject Classification: 35A08; 35J05; 31C12; 33C05; 33C20 DOI:10.3842/SIGMA.2016.079 https://nasplib.isofts.kiev.ua/handle/123456789/147845 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. This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications.
 The full collection is available at http://www.emis.de/journals/SIGMA/OPSFA2015.html.
 The author would like to thank David Stuart for suggesting a method for solving the odd case
 recurrence relation, and Thomas Forster for some notational advice, as well as the referees
 for numerous suggestions which improved the paper. We especially wish to acknowledge our
 indebtedness to the first anonymous referee, without whose extraordinary and tireless attention,
 and extensive suggestions and contributions, so many aspects of the paper would have been
 considerably the poorer. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres Article published earlier |
| spellingShingle | A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres Chapling, R. |
| title | A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres |
| title_full | A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres |
| title_fullStr | A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres |
| title_full_unstemmed | A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres |
| title_short | A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres |
| title_sort | hypergeometric integral with applications to the fundamental solution of laplace's equation on hyperspheres |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147845 |
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