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

article

Howard S. Cohl¹ 

[1] Applied and Computational Mathematics Division, National Institute of Standards and Technology

关键词: fundamental solutions;    polyharmonic equation;    Jacobi polynomials;    Gegenbauer polynomials;    Chebyshev polynomials;    eigenfunction expansions;    separation of variables;    addition theorems;   

DOI  :  10.3842/SIGMA.2013.042

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown