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arXiv · 1608.03174

A formula for $\zeta$(2n + 1) and some related expressions

Thomas Sauvaget
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Abstract

Using a polylogarithmic identity, we express the values of $\zeta$ at odd integers $2n+1$ as integrals over unit $n-$dimensional hypercubes of simple functions involving products of logarithms. We also prove a useful property of those functions as some of their variables are raised to a power. In the case $n=2$, we prove two closed-form expressions concerning related integrals. Finally, another family of related one-dimensional integrals is studied.

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Thomas Sauvaget. 2016-08-09. A formula for $\zeta$(2n + 1) and some related expressions. https://arxiv.org/abs/1608.03174

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