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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