“…This question, which has both mathematical and physical interest, has a somehow classical flavour and goes back to lord Rayleigh in 1874 [20] (in fact, the sum (1.3) as a function of α is usually called the Rayleigh function). Since then, many papers have been published which study, with different approaches, these and many other series along with identities and other properties; see, for instance, [23,15,14,3,10] or [19, formula 11 in § 5.7.33] (and the list is by no means exhaustive). However, identities relating (1.3) or any other sum involving the zeros of Bessel functions with some kind of "Bernoulli" or "Euler numbers" seem to be unknown.…”