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

Stamatis Koumandos

International Journal of Mathematics and Mathematical Sciences, 2007, vol. 2007, 1-5

Abstract:

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.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:073750

DOI: 10.1155/2007/73750

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