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On infinite series concerning zeros of Bessel functions of the first kind

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Abstract.

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.

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Authors and Affiliations

  1. Department of Physics & Astronomy, University of Bologna, Via Irnerio 46, Bologna, Italy

    Andrea Giusti & Francesco Mainardi

  2. INFN, Sezione di Bologna, Via Irnerio 46, Bologna, Italy

    Andrea Giusti & Francesco Mainardi

Authors
  1. Andrea Giusti
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  2. Francesco Mainardi
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Correspondence to Andrea Giusti.

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Giusti, A., Mainardi, F. On infinite series concerning zeros of Bessel functions of the first kind. Eur. Phys. J. Plus 131, 206 (2016). https://doi.org/10.1140/epjp/i2016-16206-4

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  • DOI: https://doi.org/10.1140/epjp/i2016-16206-4

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