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arXiv · 1209.6047

Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems

Howard S. Cohl
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Abstract

We develop complex Jacobi, Gegenbauer and Chebyshev polynomial expansions for the kernels associated with power-law fundamental solutions of the polyharmonic equation on d-dimensional Euclidean space. From these series representations we derive Fourier expansions in certain rotationally-invariant coordinate systems and Gegenbauer polynomial expansions in Vilenkin's polyspherical coordinates. We compare both of these expansions to generate addition theorems for the azimuthal Fourier coefficients.

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Howard S. Cohl. 2012-09-26. Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems. https://doi.org/10.3842/sigma.2013.042

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