  A relevant result independently obtained by Rayleigh and Sneddon on an
identity on series involving the zeros of Bessel functions of the first kind is
derived by an alternative method based on Laplace transforms. Our method leads
to a Bernstein function of time, expressed by Dirichlet series, that allows us
to recover the Rayleigh-Sneddon sum. We also consider another method arriving
at the same result based on a relevant formula by Calogero. Moreover, we also
provide an electrical example in which this sum results to be extremely useful
in order to recover the analytical expression for the response of the system to
a certain external input.
