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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| Дата: | 2016 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147845 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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dspace |
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irk-123456789-1478452019-02-17T01:27:47Z A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres Chapling, R. 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. 2016 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147845 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Chapling, R. |
| spellingShingle |
Chapling, R. A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Chapling, R. |
| author_sort |
Chapling, R. |
| title |
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_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_sort |
hypergeometric integral with applications to the fundamental solution of laplace's equation on hyperspheres |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147845 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT chaplingr ahypergeometricintegralwithapplicationstothefundamentalsolutionoflaplacesequationonhyperspheres AT chaplingr hypergeometricintegralwithapplicationstothefundamentalsolutionoflaplacesequationonhyperspheres |
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2023-05-20T17:28:39Z |
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2023-05-20T17:28:39Z |
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1796153385717596160 |