https://doi.org/10.1140/epjp/i2016-16206-4
Regular Article
On infinite series concerning zeros of Bessel functions of the first kind
1
Department of Physics & Astronomy, University of Bologna, Via Irnerio 46, Bologna, Italy
2
INFN, Sezione di Bologna, Via Irnerio 46, Bologna, Italy
* e-mail: andrea.giusti@bo.infn.it
Received:
20
February
2016
Accepted:
22
May
2016
Published online:
22
June
2016
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.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2016
