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This article is cited in 9 scientific papers (total in 9 papers)
Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems
Howard S. Cohl Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD, 20899-8910, USA
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.
Keywords:
fundamental solutions; polyharmonic equation; Jacobi polynomials; Gegenbauer polynomials; Chebyshev polynomials; eigenfunction expansions; separation of variables; addition theorems.
Received: November 29, 2012; in final form May 28, 2013; Published online June 5, 2013
Citation:
Howard S. Cohl, “Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems”, SIGMA, 9 (2013), 042, 26 pp.
Linking options:
https://www.mathnet.ru/eng/sigma825 https://www.mathnet.ru/eng/sigma/v9/p42
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Abstract page: | 168 | Full-text PDF : | 44 | References: | 26 |
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