Definite integrals involving Bessel functions expressed as a series of special functions

Abstract

Series involving hypergeometric functions are used to derive, extend and evaluate integrals involving the product of two Bessel functions of the first kind $J_u(az)$ $J_v(bz)$ with order $u,v$, studied by Landau et al. The method used in this work is contour integration.

arXiv commentarXiv admin note: substantial text overlap with arXiv:2412.10395