Schlömilch Series

  • Árpád Baricz
  • Dragana Jankov Maširević
  • Tibor K. Pogány
Part of the Lecture Notes in Mathematics book series (LNM, volume 2207)


This chapter is devoted to the study of integral representations of Schlömilch series built by Bessel functions of the first kind and modified Bessel functions of the second kind. Closed expressions for some special Schlömilch series together with their connection to Mathieu series are also investigated. The chapter ends with an integral representation formula for number theoretical summation by Popov, which also covers the theta-transform identity coming from functional equation for the Epstein Zeta function.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Árpád Baricz
    • 1
    • 2
  • Dragana Jankov Maširević
    • 3
  • Tibor K. Pogány
    • 1
    • 4
  1. 1.John von Neumann Faculty of Informatics, Institute of Applied MathematicsÓbuda UniversityBudapestHungary
  2. 2.Department of EconomicsBabeş–Bolyai UniversityCluj–NapocaRomania
  3. 3.Department of MathematicsJosip Juraj Strossmayer University of OsijekOsijekCroatia
  4. 4.Faculty of Maritime StudiesUniversity of RijekaRijekaCroatia

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