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