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Volume 64, Issue 2 (Apr 2014)

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On coefficients of Kapteyn-type series

Dragana Jankov
  • Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 3, 31000, Osijek, Croatia
  • Email:
/ Tibor Pogány
  • Faculty of Maritime Studies, University of Rijeka, Studentska 2, 51000, Rijeka, Croatia
  • Email:
Published Online: 2014-05-08 | DOI: https://doi.org/10.2478/s12175-014-0213-y

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.

MSC: Primary 40H05, 33C10; Secondary 40A30

Keywords: Kapteyn series of Bessel functions; Kapteyn-type series; integral representation

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About the article

Published Online: 2014-05-08

Published in Print: 2014-04-01


Citation Information: Mathematica Slovaca, ISSN (Online) 1337-2211, DOI: https://doi.org/10.2478/s12175-014-0213-y. Export Citation

© 2014 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

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