  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. For $N=2$, the proof is
much simpler than that of the former work, and significantly enlarges the range
of validity.
