Opposite Antipodal Fundamental Solution of Laplace's Equation in Hyperspherical Geometry

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 sec...

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Бібліографічні деталі
Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2011
Автор: Cohl, H.S.
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2011
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/148085
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати: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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Резюме: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).
ISSN:1815-0659