An Exact Integral-to-Sum Relation for Products of Bessel Functions

Abstract

A useful identity relating the infinite sum of two Bessel functions to their infinite integral was discovered in Dominici et al. (2012). Here, we extend this result to products of $N$ Bessel functions, and show it can be straightforwardly proven using the Abel-Plana theorem, or the Poisson summation formula. For $N=2$, the proof is much simpler than that of Dominici et al., and significantly enlarges the range of validity.