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Mathematica Slovaca

, Volume 64, Issue 2, pp 403–410 | Cite as

On coefficients of Kapteyn-type series

  • Dragana JankovEmail author
  • Tibor Pogány
Article

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.

Keywords

Kapteyn series of Bessel functions Kapteyn-type series integral representation 

2010 Mathematics Subject Classification

Primary 40H05, 33C10 Secondary 40A30 

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Copyright information

© Versita Warsaw and Springer-Verlag Wien 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OsijekOsijekCroatia
  2. 2.Faculty of Maritime StudiesUniversity of RijekaRijekaCroatia

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