Riemann's Zeta Function - another approach (RPL)

[Gerson W. Barbosa]

(07-16-2017 03:08 PM)Dieter Wrote:  

(07-10-2017 11:49 AM)Dieter Wrote:  It's not perfect until it's perfect. ;-)

Still not perfect, but at least less imperfect than the previous ones:

\[\zeta (s)\approx \frac{1}{1-2^{1- s}}\left ( \frac{1}{2\cdot \left (n+\frac{1}{2}+\frac{s+1}{8\cdot n}-\frac{ s+1}{16\cdot n^{2}}+ ? \right )^{s}} + \sum_{k=1}^{n} \frac{(-1)^{k}}{(n-k+1)^{s}} \right )\]