\[\Gamma\left(-a,ze^{\pm\pi i}\right)=\frac{e^{z}e^{\mp\pi\mathrm{i}a}}{\Gamma%
\left(1+a\right)}\int_{0}^{\infty}\frac{t^{a}e^{-zt}}{t-1}\,\mathrm{d}t,\]