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)
Pub Type: Journals
fundamental solutions, polyharmonic equation, Jacobi polynomials, Gegenbauer polynomials, Chebyshev polynomials, eigenfunction expansions, separation of variables, addition theorems