\[F\left({-m,-\ell\atop n};z\right)\ln z-\sum_{k=1}^{n-1}\frac{(n-1)!(k-1)!}{(n-%
k-1)!{\left(m+1\right)_{k}}{\left(\ell+1\right)_{k}}}(-z)^{-k}+\sum_{k=0}^{%
\ell}\frac{{\left(-m\right)_{k}}{\left(-\ell\right)_{k}}}{{\left(n\right)_{k}}%
k!}z^{k}\left(\psi\left(1+m-k\right)+\psi\left(1+\ell-k\right)-\psi\left(1+k%
\right)-\psi\left(n+k\right)\right)+(-1)^{\ell}\ell\,!\sum_{k=\ell+1}^{m}\frac%
{(k-1-\ell)!{\left(-m\right)_{k}}}{{\left(n\right)_{k}}k!}z^{k},\]