# A formula for ζ(2n + 1) and some related expressions

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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Cited literature [12 references]

https://hal.archives-ouvertes.fr/hal-01352764
Contributor : Thomas Sauvaget <>
Submitted on : Wednesday, December 14, 2016 - 1:43:10 PM
Last modification on : Monday, April 9, 2018 - 12:20:05 PM
Document(s) archivé(s) le : Wednesday, March 15, 2017 - 1:13:35 PM

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### Identifiers

• HAL Id : hal-01352764, version 4
• ARXIV : 1608.03174

### Citation

Thomas Sauvaget. A formula for ζ(2n + 1) and some related expressions. An erroneous claim of irrationality of all zeta(2n+1) has been withdrawn, with apologies. The res.. 2016. 〈hal-01352764v4〉

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