engleski

On coefficients of Kapteyn-type series

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 (α_n)_{; ; ; n∈N}; ; ; is the sequence of coefficients of the input Kapteyn- type series.

Kapteyn series of Bessel functions ; Kapteyn-type series ; Integral representation

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