Let
$\displaystyle f(s)=\frac{1}{2}s(s-1)\pi^{-\frac{s}{2}}\Gamma(\frac{1}{2}s)\zeta(s)$.
Prove that $\displaystyle \underset{s\rightarrow o}{\lim}\, f(s)=\underset{s\rightarrow1}{\lim\,}f(s)=\frac{1} {2}$, and that f has no zeros outside the strip $\displaystyle 0\leq\sigma\leq1$.