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