$$E_n\left(x\right)=\frac{{\left(-z\right)}^{n-1}}{\left(n-1\right)!}\left(\psi \left(n\right)-\log \left(z\right)\right)-\sum _{k=\mathrm{0,}k\ne n-1}^{\infty }\frac{{\left(-1\right)}^k{z}^k}{\left(k-n+1\right)k!}$$