\[\zeta\left(s\right)=\frac{\pi^{s/2}}{s(s-1)\Gamma\left(\frac{1}{2}s\right)}+%
\frac{\pi^{s/2}}{\Gamma\left(\frac{1}{2}s\right)}\*\int_{1}^{\infty}\left(x^{s%
/2}+x^{(1-s)/2}\right)\frac{\omega(x)}{x}\,\mathrm{d}x,\]