### 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 language | English |
---|---|

Title of host publication | Lecture Notes in Mathematics |

Publisher | Springer Verlag |

Pages | 113-138 |

Number of pages | 26 |

DOIs | |

Publication status | Published - Jan 1 2017 |

### Publication series

Name | Lecture Notes in Mathematics |
---|---|

Volume | 2207 |

ISSN (Print) | 0075-8434 |

### Fingerprint

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*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

}

TY - CHAP

T1 - Schlömilch series

AU - Baricz, A.

AU - Jankov Maširević, Dragana

AU - Pogány, Tibor K.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85044661866&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044661866&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-74350-9_4

DO - 10.1007/978-3-319-74350-9_4

M3 - Chapter

AN - SCOPUS:85044661866

T3 - Lecture Notes in Mathematics

SP - 113

EP - 138

BT - Lecture Notes in Mathematics

PB - Springer Verlag

ER -