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Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems
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- Фізико-технічні та математичні науки
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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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Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems
Інший ID:
2010 Mathematics Subject Classification: 35A08; 31B30; 31C12; 33C05; 42A16
DOI: http://dx.doi.org/10.3842/SIGMA.2013.042
DOI: http://dx.doi.org/10.3842/SIGMA.2013.042
Посилання:
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.
Підтримка:
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.
Дата:
2013
Переглядів:
471
Завантажень:
228
Анотація:
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.
