English

On Kapteyn-Kummer Series' Integral Form

Classical Analysis and ODEs 2016-03-22 v2

Abstract

In this short research note we obtain double definite integral expressions for the Kapteyn type series built by Kummer's MM (or confluent hypergeometric 1F1{}_1F_1) 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 Ma\v{s}irevi\'c.

Keywords

Cite

@article{arxiv.1603.01085,
  title  = {On Kapteyn-Kummer Series' Integral Form},
  author = {Tibor K. Pogány and Árpád Baricz and Anikó Szakál},
  journal= {arXiv preprint arXiv:1603.01085},
  year   = {2016}
}
R2 v1 2026-06-22T13:03:02.513Z