Series over Bessel Functions as Series in Terms of Riemann’s Zeta Function

Slobodan B. Tričković () and Miomir S. Stanković
Additional contact information
Slobodan B. Tričković: Department of Mathematics, University of Niš, 18000 Niš, Serbia
Miomir S. Stanković: Mathematical Institute of the Serbian Academy of Sciences and Arts, 11000 Belgrade, Serbia

Mathematics, 2024, vol. 12, issue 19, 1-12

Abstract: Relying on the Hurwitz formula, we find closed-form formulas for the series over sine and cosine functions through the Hurwitz zeta functions, and using them and another summation formula for trigonometric series, we obtain a finite sum for some series over the Riemann zeta functions. We apply these results to the series over Bessel functions, expressing them first as series over the Riemann zeta functions.

Keywords: Riemann’s zeta function; Hurwitz’s zeta function; gamma function; harmonic numbers; Bessel functions; spherical Bessel functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/19/3000/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/19/3000/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:19:p:3000-:d:1486585

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().