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 ${\sum }_{m\ge 0}{x}_m{P}_m(s)$ where the functions $P_m$ are polynomials with their roots on the line $\{\mathrm{\Re }(s)=1\mathrm{/}2\}$, the coefficients $x_m$ being finite linear combinations of the Euler constant $\gamma$ and the values $\zeta (2),\zeta (3),\dots ,\zeta (m+1)\mathrm{.}$