Proof of a Bessel Function Integral

Bessel functions are widely encountered in research and are essential components of introductory undergraduate courses on mathematical physics. Here, I present a result for the integral of a product of a Bessel function and an exponential, using the method of introducing parameters into the problem to generate some symmetries. I then present an overview of other techniques that use this idea of increasing the parameter or dimensional space in order to make a problem easier to solve.