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