A formula for $\zeta$(2n + 1) and some related expressions
Number Theory
2016-12-15 v4
Abstract
Using a polylogarithmic identity, we express the values of at odd integers as integrals over unit 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 , we prove two closed-form expressions concerning related integrals. Finally, another family of related one-dimensional integrals is studied.
Keywords
Cite
@article{arxiv.1608.03174,
title = {A formula for $\zeta$(2n + 1) and some related expressions},
author = {Thomas Sauvaget},
journal= {arXiv preprint arXiv:1608.03174},
year = {2016}
}
Comments
An erroneous claim of irrationality of all zeta(2n+1) has been withdrawn, with apologies. The resulting work is not intended for publication