On Kapteyn-Kummer Series' Integral Form
Abstract
In this short research note we obtain double definite integral expressions for the Kapteyn type series built by Kummer's M (or confluent hypergeometric 1F1) functions. These kind of series unify in natural way the similar fashion results for Neumann-, Schl\"omilch- and Kapteyn-Bessel series recently established by Pog\'any, S\"uli, Baricz and Jankov Masirevi\'c.
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