\[\mathbf{F}\left({a,a+m\atop c};z\right)=\frac{(-z)^{-a}}{\Gamma\left(a+m\right%
)}\sum_{k=0}^{m-1}\frac{{\left(a\right)_{k}}(m-k-1)!}{k!\Gamma\left(c-a-k%
\right)}z^{-k}+\frac{(-z)^{-a}}{\Gamma\left(a\right)}\sum_{k=0}^{\infty}\frac{%
{\left(a+m\right)_{k}}}{k!(k+m)!\Gamma\left(c-a-k-m\right)}(-1)^{k}z^{-k-m}\*%
\left(\ln\left(-z\right)+\psi\left(k+1\right)+\psi\left(k+m+1\right)-\psi\left%
(a+k+m\right)-\psi\left(c-a-k-m\right)\right),\]