Some integrals involving Bessel functions

TL;DR

This paper introduces new definite integrals involving Bessel functions, derived through novel integral representations and connections to classical integral transforms, expanding the mathematical toolkit for analyzing Bessel function products.

Contribution

It presents new integral representations for products of Bessel functions, linking them to hypergeometric functions and classical integral transforms, which was not previously documented.

Findings

Derived new integral representations for Bessel function products

Connected integrals to hypergeometric functions and Weber's integral

Provided reduction to special cases for practical computation

Abstract

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.