Schlömilch series

A. Baricz, Dragana Jankov Maširević, Tibor K. Pogány

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

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.

Original languageEnglish
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Pages113-138
Number of pages26
DOIs
Publication statusPublished - Jan 1 2017

Publication series

NameLecture Notes in Mathematics
Volume2207
ISSN (Print)0075-8434

Fingerprint

Integral Representation
Series
Neumann function
Bessel function of the first kind
Modified Bessel Functions
Representation Formula
Integral Formula
Riemann zeta function
Summation
Functional equation
Cover
Transform
Closed

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Baricz, A., Jankov Maširević, D., & Pogány, T. K. (2017). Schlömilch series. In Lecture Notes in Mathematics (pp. 113-138). (Lecture Notes in Mathematics; Vol. 2207). Springer Verlag. https://doi.org/10.1007/978-3-319-74350-9_4

Schlömilch series. / Baricz, A.; Jankov Maširević, Dragana; Pogány, Tibor K.

Lecture Notes in Mathematics. Springer Verlag, 2017. p. 113-138 (Lecture Notes in Mathematics; Vol. 2207).

Research output: Chapter in Book/Report/Conference proceedingChapter

Baricz, A, Jankov Maširević, D & Pogány, TK 2017, Schlömilch series. in Lecture Notes in Mathematics. Lecture Notes in Mathematics, vol. 2207, Springer Verlag, pp. 113-138. https://doi.org/10.1007/978-3-319-74350-9_4
Baricz A, Jankov Maširević D, Pogány TK. Schlömilch series. In Lecture Notes in Mathematics. Springer Verlag. 2017. p. 113-138. (Lecture Notes in Mathematics). https://doi.org/10.1007/978-3-319-74350-9_4
Baricz, A. ; Jankov Maširević, Dragana ; Pogány, Tibor K. / Schlömilch series. Lecture Notes in Mathematics. Springer Verlag, 2017. pp. 113-138 (Lecture Notes in Mathematics).
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