We consider a new identity involving integrals and sums of Bessel functions.
The identity provides new ways to evaluate integrals of products of two Bessel
functions. The identity is remarkably simple and powerful since the summand and
integrand are of exactly the same form and the sum converges to the integral
relatively fast for most cases. A proof and numerical examples of the identity
are discussed.Comment: 10 pages, 2 figure