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