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A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres
Інший ID:
2010 Mathematics Subject Classification: 35A08; 35J05; 31C12; 33C05; 33C20
DOI:10.3842/SIGMA.2016.079
DOI:10.3842/SIGMA.2016.079
Посилання:
A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres / R. Chapling // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 16 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications.
The full collection is available at http://www.emis.de/journals/SIGMA/OPSFA2015.html.
The author would like to thank David Stuart for suggesting a method for solving the odd case
recurrence relation, and Thomas Forster for some notational advice, as well as the referees
for numerous suggestions which improved the paper. We especially wish to acknowledge our
indebtedness to the first anonymous referee, without whose extraordinary and tireless attention,
and extensive suggestions and contributions, so many aspects of the paper would have been
considerably the poorer.
Дата:
2016
Переглядів:
585
Завантажень:
246
Анотація:
We consider Poisson's equation on the n-dimensional sphere in the situation where the inhomogeneous term has zero integral. Using a number of classical and modern hypergeometric identities, we integrate this equation to produce the form of the fundamental solutions for any number of dimensions in terms of generalised hypergeometric functions, with different closed forms for even and odd-dimensional cases.
