\[\frac{\sin\left(\pi(c-a-b)\right)}{\pi}\mathbf{F}\left({a,b\atop c};z\right)=%
\frac{1}{\Gamma\left(c-a\right)\Gamma\left(c-b\right)}\mathbf{F}\left({a,b%
\atop a+b-c+1};1-z\right)-\frac{(1-z)^{c-a-b}}{\Gamma\left(a\right)\Gamma\left%
(b\right)}\mathbf{F}\left({c-a,c-b\atop c-a-b+1};1-z\right),\]