A family of integrals related to values of the Riemann zeta function
Year: 2024
Type: article
Abstract: 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].
Institutions: Pennsylvania State University, University of Antwerp, KU Leuven, Commissariat à l'Énergie Atomique et aux Énergies Alternatives, Université Paris-Saclay, CEA Paris-Saclay - Etablissement de Saclay, CEA DAM Île-de-France, Laboratoire Matière en Conditions Extrêmes, The University of Queensland
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403002073