Аннотация:
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.
Ключевые слова:
hyperspherical geometry; fundamental solution; Laplace's equation; separation of variables; hypergeometric functions.
Поступила:23 ноября 2015 г.; в окончательном варианте 4 августа 2016 г.; опубликована 10 августа 2016 г.
Образец цитирования:
Richard Chapling, “A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres”, SIGMA, 12 (2016), 079, 20 pp.
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Эта публикация цитируется в следующих 4 статьяx:
Fatma Terzioglu, “Recovering a function from its integrals over conical surfaces through relations with the Radon transform”, Inverse Problems, 39:2 (2023), 024005
Ivan Kolář, “Nonlocal scalar fields in static spacetimes via heat kernels”, Phys. Rev. D, 105:8 (2022)
M. Kirchbach, T. Popov, J. A. Vallejo, “Color confinement at the boundary of the conformally compactified AdS(5)”, J. High Energy Phys., 2021, no. 9, 171
Howard S. Cohl, Thinh H. Dang, T. M. Dunster, “Fundamental Solutions and Gegenbauer Expansions of Helmholtz Operators in Riemannian Spaces of Constant Curvature”, SIGMA, 14 (2018), 136, 45 pp.
Цитирование в формате AMSBIB
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