Some Integrals Involving Bessel Functions Some Integrals Involving Bessel Functions

A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized hypergeometric function with subsequent reduction to special cases. Connection is made with Weber's second exponential integral and Laplace transforms of products of three Bessel functions. 1. Introduction The aim of this work is to derive a number of infinite integrals involving Bessel functions which appear to be new. The approach is, beginning with an expression for the product of two Bessel functions as a sum of Gauss functions, to integrate and perform a resummation to obtain other hyper-geometric functions, and then to reduce these to more familiar form. In particular we exploit the relation between Bessel functions and the function