\[\mathbf{F}\left({a,b\atop\tfrac{1}{2}};z\right)=\frac{2^{a+b-(\ifrac{3}{2})}}{%
\pi}\Gamma\left(a+\tfrac{1}{2}\right)\Gamma\left(b+\tfrac{1}{2}\right)\*(z-1)^%
{(-a-b+(\ifrac{1}{2}))/2}\*\left({\mathrm{e}}^{\pm\pi\mathrm{i}(a+b-(\ifrac{1}%
{2}))}P^{-a-b+(\ifrac{1}{2})}_{a-b-(\ifrac{1}{2})}\left(-\sqrt{z}\right)+P^{-a%
-b+(\ifrac{1}{2})}_{a-b-(\ifrac{1}{2})}\left(\sqrt{z}\right)\right),\]