Take a sneak peek at the new NIST.gov and let us know what you think!
(Please note: some content may not be complete on the beta site.).
NIST Authors in Bold
|Author(s):||Howard S. Cohl;|
|Title:||Fourier, Gegenbauer and Jacobi expansions for a power-law fundamental solution of the polyharmonic equation and polyspherical addition theorems|
|Published:||June 05, 2013|
|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)|
|Keywords:||fundamental solutions, polyharmonic equation, Jacobi polynomials, Gegenbauer polynomials, Chebyshev polynomials, eigenfunction expansions, separation of variables, addition theorems|
|Research Areas:||Math, Modeling|
|PDF version:||Click here to retrieve PDF version of paper (758KB)|