On a class of integrals involving a Bessel function times Gegenbauer polynomials
Summary: 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 \textit{A. A. R. Neves} et al. [J. Phys. A, Math. Gen. 39, No. 18, L293--L296 (2006; Zbl 1099.33004)] 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.
scientific article; zbMATH DE number 5282439