On Kapteyn-Kummer series' integral form

Tibor K. Pogány, A. Baricz, Anikó Szakál

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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-, Schlömilch- and Kapteyn-Bessel series recently established by Pogány, Süli, Baricz and Jankov Maširević.

Original languageEnglish
Title of host publicationSACI 2016 - 11th IEEE International Symposium on Applied Computational Intelligence and Informatics, Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages119-122
Number of pages4
ISBN (Electronic)9781509023790
DOIs
Publication statusPublished - Jul 7 2016
Event11th IEEE International Symposium on Applied Computational Intelligence and Informatics, SACI 2016 - Timisoara
Duration: May 12 2016May 14 2016

Other

Other11th IEEE International Symposium on Applied Computational Intelligence and Informatics, SACI 2016
CityTimisoara
Period5/12/165/14/16

Keywords

  • Dirichlet series
  • Integral representation
  • Kampé de Fériet function
  • Kapteyn series
  • Kummer function
  • Neumann series
  • Schlömilch series

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computer Science Applications
  • Control and Systems Engineering
  • Control and Optimization
  • Health Informatics

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  • Cite this

    Pogány, T. K., Baricz, A., & Szakál, A. (2016). On Kapteyn-Kummer series' integral form. In SACI 2016 - 11th IEEE International Symposium on Applied Computational Intelligence and Informatics, Proceedings (pp. 119-122). [7507352] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SACI.2016.7507352