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Fourier and Gegenbauer expansions for a fundamental solution of the Laplacian in the hyperboloid model of hyperbolic geometry

2012
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Journal of Physics A: Mathematical and Theoretical
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Due to the isotropy d-dimensional hyperbolic space, there exist a spherically symmetric fundamental solution for its corresponding Laplace-Beltrami operator. On the R-radius hyperboloid model of d-dimensional hyperbolic geometry with R>0 and d> 2, we compute azimuthal Fourier expansions for a fundamental solution of Laplace's equation. For d> 2, we compute a Gegenbauer polynomial expansion in geodesic polar coordinates for a fundamental solution of Laplace's equation on this negative-constant

doi:10.1088/1751-8113/45/14/145206
fatcat:gqlrprtcl5grnepgr35qbv547q