\[\frac{2\Gamma\left(\tfrac{1}{2}\right)\Gamma\left(a+b+\tfrac{1}{2}\right)}{%
\Gamma\left(a+\tfrac{1}{2}\right)\Gamma\left(b+\tfrac{1}{2}\right)}F\left(a,b;%
\tfrac{1}{2};z\right)=F\left(2a,2b;a+b+\tfrac{1}{2};\tfrac{1}{2}-\tfrac{1}{2}%
\sqrt{z}\right)+F\left(2a,2b;a+b+\tfrac{1}{2};\tfrac{1}{2}+\tfrac{1}{2}\sqrt{z%
}\right),\]