A new expansion of the Riemann zeta function

After a brief introduction to Ramanujan's method of summation, we give an expansion of the Riemann Zeta function in the critical strip as a convergent series $\sum_{m\geq 0}x_m P_m(s)$ where the functions $P_m$ are polynomials with their roots on the line $\{\Re(s)=1/2\}$, the coefficients $x_m$ being finite linear combinations of the Euler constant $\gamma$ and the values $\zeta(2),\zeta(3),\dots,\zeta(m+1).$