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Application of Krein’s series to calculation of sums containing zeros of the Bessel functions

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Abstract

The Bessel functions of the first kind, J v (z), with v > −1 are considered. On the basis of the general theorem on the representation of the reciprocal of an entire function in the form of Krein’s series, an expansion of the function 1/J v (z) in simple fractions is obtained. This result is used to calculate the sums of series of a certain structure that contain powers of positive zeros of Bessel functions.

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Authors and Affiliations

  1. National Nuclear Research University MEPhI, Kashirskoe sh. 31, Moscow, 115409, Russia

    V. B. Sherstyukov & E. V. Sumin

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  1. V. B. Sherstyukov
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  2. E. V. Sumin
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Correspondence to V. B. Sherstyukov.

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Original Russian Text © V.B. Sherstyukov, E.V. Sumin, 2015, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2015, Vol. 55, No. 4, pp. 575–581.

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Sherstyukov, V.B., Sumin, E.V. Application of Krein’s series to calculation of sums containing zeros of the Bessel functions. Comput. Math. and Math. Phys. 55, 572–579 (2015). https://doi.org/10.1134/S0965542515040120

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