\[\zeta\left(s,a\right)=\frac{1}{2}a^{-s}+\frac{a^{1-s}}{s-1}+2\int_{0}^{\infty}%
\frac{\sin\left(s\operatorname{arctan}\left(x/a\right)\right)}{(a^{2}+x^{2})^{%
s/2}(e^{2\pi x}-1)}\,\mathrm{d}x,\]