\[\Phi\left(-z,s,a\right)=\frac{1}{2\pi\mathrm{i}}\int_{\sigma-\mathrm{i}\infty}%
^{\sigma+\mathrm{i}\infty}\frac{\Gamma\left(1+t\right)\Gamma\left(-t\right)z^{%
t}}{\left(a+t\right)^{s}}\,\mathrm{d}t,\]