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