\[{{}_{3}F_{2}}\left({a,1-a,c\atop d,2c-d+1};1\right)=\frac{\pi\Gamma\left(d%
\right)\Gamma\left(2c-d+1\right)2^{1-2c}}{\Gamma\left(c+\frac{1}{2}(a-d+1)%
\right)\Gamma\left(c+1-\frac{1}{2}(a+d)\right)\Gamma\left(\frac{1}{2}(a+d)%
\right)\Gamma\left(\frac{1}{2}(d-a+1)\right)},\]