A family of integrals related to values of the Riemann zeta function
We propose a relation between values of the Riemann zeta function [Formula: see text] and a family of integrals. This results in an integral representation for [Formula: see text], where p is a positive integer, and an expression of [Formula: see text] involving one of the above-mentioned integrals together with a harmonic-number sum. Simplification of the latter eventually leads to an integral representation of [Formula: see text].
Authors
- Victor Scharaschkin
- Paul Levrie (ORCID: https://orcid.org/0000-0003-1688-3656)
- Rahul Kumar (ORCID: https://orcid.org/0000-0002-2533-837X)
- Jean‐Christophe Pain (ORCID: https://orcid.org/0000-0002-7825-1315)
Institutions
- Pennsylvania State University (US)
- University of Antwerp (BE)
- The University of Queensland (AU)
- Commissariat à l'Énergie Atomique et aux Énergies Alternatives (FR)
- Université Paris-Saclay (FR)
- CEA DAM Île-de-France (FR)
- CEA Paris-Saclay (FR)
- KU Leuven (BE)
Publication Details
- Journal
- International Journal of Number Theory
- Published
- 2024-09-30
- DOI
- https://doi.org/10.1142/s1793042125500319
- Citations
- 2
- Primary Topic
- Advanced Mathematical Identities
- Type
- article
- Field-Weighted Citation Impact
- 2.54