Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems

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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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dc.contributor.author	Cohl, H.S.
dc.date.accessioned	2019-02-19T18:33:49Z
dc.date.available	2019-02-19T18:33:49Z
dc.date.issued	2013
dc.identifier.citation	Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems / H.S. Cohl // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 35 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 35A08; 31B30; 31C12; 33C05; 42A16
dc.identifier.other	DOI: http://dx.doi.org/10.3842/SIGMA.2013.042
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/149201
dc.description.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.	uk_UA
dc.description.sponsorship	I would like to thank A.F.M. Tom ter Elst and Heather Macbeth for valuable discussions. I would like to express my gratitude to the anonymous referees and an editor at SIGMA whose helpful comments improved this paper. Part of this work was conducted while H.S. Cohl was a National Research Council Research Postdoctoral Associate in the Applied and Computational Mathematics Division at the National Institute of Standards and Technology, Gaithersburg, Maryland, USA.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA