International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 73750, 5 pages
doi:10.1155/2007/73750

On a class of integrals involving a Bessel function times Gegenbauer polynomials

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.