Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Fourier, Gegenbauer and Jacobi expansions for a power-law fundamental solution of the polyharmonic equation and polyspherical addition theorems

Published

Author(s)

Howard S. Cohl

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

Keywords

fundamental solutions, polyharmonic equation, Jacobi polynomials, Gegenbauer polynomials, Chebyshev polynomials, eigenfunction expansions, separation of variables, addition theorems

Citation

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 March 29, 2024)
Created June 5, 2013, Updated June 2, 2021