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