Opposite Antipodal Fundamental Solution of Laplace's Equation in Hyperspherical Geometry
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Opposite Antipodal Fundamental Solution of Laplace's Equation in Hyperspherical Geometry
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| Creator |
Cohl, H.S.
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| Description |
Due to the isotropy of d-dimensional hyperspherical space, one expects there to exist a spherically symmetric opposite antipodal fundamental solution for its corresponding Laplace-Beltrami operator. The R-radius hypersphere SdR with R>0, represents a Riemannian manifold with positive-constant sectional curvature. We obtain a spherically symmetric opposite antipodal fundamental solution of Laplace's equation on this manifold in terms of its geodesic radius. We give several matching expressions for this fundamental solution including a definite integral over reciprocal powers of the trigonometric sine, finite summation expressions over trigonometric functions, Gauss hypergeometric functions, and in terms of the Ferrers function of the second with degree and order given by d/2−1 and 1−d/2 respectively, with real argument x∈(−1,1).
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| Date |
2019-02-16T20:48:17Z
2019-02-16T20:48:17Z 2011 |
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| Type |
Article
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| Identifier |
Opposite Antipodal Fundamental Solution of Laplace's Equation in Hyperspherical Geometry / H.S. Cohl // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 39 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 35A08; 35J05; 32Q10; 31C12; 33C05 DOI: https://doi.org/10.3842/SIGMA.2011.108 http://dspace.nbuv.gov.ua/handle/123456789/148085 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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