Cohl, H.
(2013),
Fourier, Gegenbauer and Jacobi expansions for a power-law fundamental solution of the polyharmonic equation and polyspherical addition theorems, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=912042
(Accessed September 12, 2024)
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Fourier, Gegenbauer and Jacobi expansions for a power-law fundamental solution of the polyharmonic equation and polyspherical addition theorems
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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.Citation
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume
9
Pub Type
Journals
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Keywords
fundamental solutions, polyharmonic equation, Jacobi polynomials, Gegenbauer polynomials, Chebyshev polynomials, eigenfunction expansions, separation of variables, addition theorems
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Created June 5, 2013, Updated June 2, 2021