On a Class of Integrals Involving a Bessel Function Times Gegenbauer Polynomials

On a Class of Integrals Involving a Bessel Function Times Gegenbauer Polynomials

We provide information and explicit formulae for a class of integrals involving Bessel functions and Gegenbauer polynomials. We present a simple proof of an old formula of Gegenbauer. Some interesting special cases and applications of this result are obtained. In particular, we give a short proof of...

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Main Author: Stamatis Koumandos
Format: Article
Language:English
Published: Hindawi Limited 2007-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2007/73750
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spelling doaj-a7cc67f58f5e4a789e7067a760a7a91f2020-11-24T22:47:52ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/7375073750On a Class of Integrals Involving a Bessel Function Times Gegenbauer PolynomialsStamatis Koumandos0Department of Mathematics and Statistics, University of Cyprus, P. O. Box 20537, Nicosia 1678, CyprusWe provide information and explicit formulae for a class of integrals involving Bessel functions and Gegenbauer polynomials. We present a simple proof of an old formula of Gegenbauer. Some interesting special cases and applications of this result are obtained. In particular, we give a short proof of a recent result of A. A. R. Neves et al. regarding the analytical evaluation of an integral of a Bessel function times associated Legendre functions. These integrals arise in problems of vector diffraction in electromagnetic theory.http://dx.doi.org/10.1155/2007/73750
collection DOAJ
language English
format Article
sources DOAJ
author Stamatis Koumandos
spellingShingle Stamatis Koumandos
On a Class of Integrals Involving a Bessel Function Times Gegenbauer Polynomials
International Journal of Mathematics and Mathematical Sciences
author_facet Stamatis Koumandos
author_sort Stamatis Koumandos
title On a Class of Integrals Involving a Bessel Function Times Gegenbauer Polynomials
title_short On a Class of Integrals Involving a Bessel Function Times Gegenbauer Polynomials
title_full On a Class of Integrals Involving a Bessel Function Times Gegenbauer Polynomials
title_fullStr On a Class of Integrals Involving a Bessel Function Times Gegenbauer Polynomials
title_full_unstemmed On a Class of Integrals Involving a Bessel Function Times Gegenbauer Polynomials
title_sort on a class of integrals involving a bessel function times gegenbauer polynomials
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2007-01-01
description We provide information and explicit formulae for a class of integrals involving Bessel functions and Gegenbauer polynomials. We present a simple proof of an old formula of Gegenbauer. Some interesting special cases and applications of this result are obtained. In particular, we give a short proof of a recent result of A. A. R. Neves et al. regarding the analytical evaluation of an integral of a Bessel function times associated Legendre functions. These integrals arise in problems of vector diffraction in electromagnetic theory.
url http://dx.doi.org/10.1155/2007/73750
work_keys_str_mv AT stamatiskoumandos onaclassofintegralsinvolvingabesselfunctiontimesgegenbauerpolynomials
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