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arXiv · 2409.06546

A family of integrals related to values of the Riemann zeta function

Rahul Kumar·Paul Levrie·Jean-Christophe Pain·Victor Scharaschkin
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Abstract

We propose a relation between values of the Riemann zeta function $\zeta$ and a family of integrals. This results in an integral representation for $\zeta(2p)$, where $p$ is a positive integer, and an expression of $\zeta(2p+1)$ involving one of the above mentioned integrals together with a harmonic-number sum. Simplification of the latter eventually leads to an integral representation of $\zeta(2p + 1)$.

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Rahul Kumar, Paul Levrie, Jean-Christophe Pain, Victor Scharaschkin. 2024-09-10. A family of integrals related to values of the Riemann zeta function. https://arxiv.org/abs/2409.06546

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