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...
Main Author: | |
---|---|
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 |
id |
doaj-a7cc67f58f5e4a789e7067a760a7a91f |
---|---|
record_format |
Article |
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 |
_version_ |
1725680701309714432 |