  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.
