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On coefficients of Kapteyn-type series

Mathematica Slovaca

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Abstract

Quite recently Jankov and Pogány [JANKOV, D.—POGÁNY, T. K.: Integral representation of Schlömilch series, J. Classical Anal. 1 (2012) 75–84] derived a double integral representation of the Kapteyn-type series of Bessel functions. Here we completely describe the class of functions Λ = {α}, which generate the mentioned integral representation in the sense that the restrictions \(\alpha |_\mathbb{N} = (\alpha _n )_{n \in \mathbb{N}} \) is the sequence of coefficients of the input Kapteyn-type series.

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Authors and Affiliations

  1. Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 3, 31000, Osijek, Croatia

    Dragana Jankov

  2. Faculty of Maritime Studies, University of Rijeka, Studentska 2, 51000, Rijeka, Croatia

    Tibor Pogány

Authors
  1. Dragana Jankov
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  2. Tibor Pogány
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Corresponding author

Correspondence to Dragana Jankov.

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Communicated by Ján Borsík

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Jankov, D., Pogány, T. On coefficients of Kapteyn-type series. Math. Slovaca 64, 403–410 (2014). https://doi.org/10.2478/s12175-014-0213-y

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  • DOI: https://doi.org/10.2478/s12175-014-0213-y

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