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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 4, Pages 575–581 (Mi zvmmf10185)  

This article is cited in 4 scientific papers (total in 4 papers)

Application of Kreins series to calculation of sums containing zeros of the Bessel functions

E. V. Sumin, V. B. Sherstyukov

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

Abstract: The Bessel functions of the first kind, $J_{\mathrm{v}}(z)$, with $\mathrm{v}>-1$ are considered. On the basis of the general theorem on the representation of the reciprocal of an entire function in the form of Kreins series, an expansion of the function $1/J_{\mathrm{v}}(z)$ 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.

Key words: meromorphic functions, Kreins series, summation relationships, zeros of Bessel functions, Rayleigh function.

DOI: https://doi.org/10.7868/S0044466915040134

Full text: PDF file (191 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:4, 572–579

Bibliographic databases:

UDC: 519.65
MSC: Primary 33C10; Secondary 30D10, 41A60
Received: 16.06.2014

Citation: E. V. Sumin, V. B. Sherstyukov, “Application of Kreins series to calculation of sums containing zeros of the Bessel functions”, Zh. Vychisl. Mat. Mat. Fiz., 55:4 (2015), 575–581; Comput. Math. Math. Phys., 55:4 (2015), 572–579

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. B. Sherstyukov, E. V. Sumin, “Reciprocal expansion of modified bessel function in simple fractions and obtaining general summation relationships containing its zeros”, VI International Conference Problems of Mathematical Physics and Mathematical Modelling, Journal of Physics Conference Series, 937, IOP Publishing Ltd, 2017, UNSP 012047  crossref  isi
    2. D. J. Masirevic, R. K. Parmar, T. K. Pogany, “$(p, q)$-extended Bessel and modified Bessel functions of the first kind”, Results Math., 72:1–2 (2017), 617–632  crossref  mathscinet  zmath  isi
    3. T. G. Pedersen, “Sum rules for zeros and intersections of Bessel functions from quantum mechanical perturbation theory”, Phys. Lett. A, 382:28 (2018), 1837–1841  crossref  isi
    4. V. B. Sherstyukov, “Asimptoticheskie svoistva tselykh funktsii s zadannym zakonom raspredeleniya kornei”, Kompleksnyi analiz. Tselye funktsii i ikh primeneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 161, VINITI RAN, M., 2019, 104–129  mathnet  mathscinet
  •      Computational Mathematics and Mathematical Physics
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