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