\[\mathbf{F}\left({a,b\atop c};x+\mathrm{i}0\right)-\mathbf{F}\left({a,b\atop c}%
;x-\mathrm{i}0\right)=\frac{2\pi\mathrm{i}}{\Gamma\left(a\right)\Gamma\left(b%
\right)}(x-1)^{c-a-b}\mathbf{F}\left({c-a,c-b\atop c-a-b+1};1-x\right),\]