La relation entre $\zeta (4n-1)$, $\zeta (2p)$ et $\zeta (4n-1-2p)$

The functional relation of the Riemann zêta function provides us with neither the nature nor the expression of zêta at positive odd numbers. From the function $F(z)=\frac{z^{-2n}}{e^z-1}$, we find a functional relation involving $\zeta (4n-1)$, $\zeta (2p)$ and $\zeta (4n-1-2p)$. It is given by: \begin{equation} ζ(4n-1)=\frac{1}{2n-1}\sum_{p=1}^{2n-2}ζ(2p)ζ(4n-1-2p). \end{equation} $n=2,3,4,5,6,\mathrm{.}\mathrm{.}\mathrm{.}$ From this formula we introduce a new approach to study the nature of $\zeta$ on these integers.