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BY-NC-ND 3.0 license Open Access Published by De Gruyter May 8, 2014

On coefficients of Kapteyn-type series

Dragana Jankov and Tibor Pogány
From the journal Mathematica Slovaca

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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Published Online: 2014-5-8
Published in Print: 2014-4-1

© 2014 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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