\[E_{n}\left(z\right)=\frac{(-1)^{n}z^{n-1}}{(n-1)!}\ln z+\frac{e^{-z}}{(n-1)!}%
\sum_{k=1}^{n-1}(-z)^{k-1}\Gamma\left(n-k\right)+\frac{e^{-z}(-z)^{n-1}}{(n-1)%
!}\sum_{k=0}^{\infty}\frac{z^{k}}{k!}\psi\left(k+1\right),\]