A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres

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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, 2016, том 12
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Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12, випуск за цей рік
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dc.contributor.author	Chapling, R.
dc.date.accessioned	2019-02-16T09:13:58Z
dc.date.available	2019-02-16T09:13:58Z
dc.date.issued	2016
dc.identifier.citation	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.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 35A08; 35J05; 31C12; 33C05; 33C20
dc.identifier.other	DOI:10.3842/SIGMA.2016.079
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/147845
dc.description.abstract	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.	uk_UA
dc.description.sponsorship	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.	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	A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA