Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems
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 co...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2013 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2013
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149201 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862735427033628672 |
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| author | Cohl, H.S. |
| author_facet | Cohl, H.S. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T19:48:05Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149201 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:48:05Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Cohl, H.S. 2019-02-19T18:33:49Z 2019-02-19T18:33:49Z 2013 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. 1815-0659 2010 Mathematics Subject Classification: 35A08; 31B30; 31C12; 33C05; 42A16 DOI: http://dx.doi.org/10.3842/SIGMA.2013.042 https://nasplib.isofts.kiev.ua/handle/123456789/149201 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems Article published earlier |
| spellingShingle | Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems Cohl, H.S. |
| title | Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems |
| title_full | Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems |
| title_fullStr | Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems |
| title_full_unstemmed | Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems |
| title_short | Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems |
| title_sort | fourier, gegenbauer and jacobi expansions for a power-law fundamental solution of the polyharmonic equation and polyspherical addition theorems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149201 |
| work_keys_str_mv | AT cohlhs fouriergegenbauerandjacobiexpansionsforapowerlawfundamentalsolutionofthepolyharmonicequationandpolysphericaladditiontheorems |