\[\gamma^{*}\left(a,z\right)=e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\Gamma\left(a%
+k+1\right)}=\frac{1}{\Gamma\left(a\right)}\sum_{k=0}^{\infty}\frac{(-z)^{k}}{%
k!(a+k)}.\]