On Kapteyn-Kummer Series' Integral Form

In this short research note we obtain double definite integral expressions for the Kapteyn type series built by Kummer's $M$ (or confluent hypergeometric ${}_1F_1$) functions. These kind of series unify in natural way the similar fashion results for Neumann-, Schlömilch- and Kapteyn-Bessel series recently established by Pogány, Süli, Baricz and Jankov Maširević.

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