\[\mathbf{F}\left({a,b\atop\tfrac{3}{2}};z\right)=\frac{2^{a+b-(\ifrac{5}{2})}}{%
\pi\sqrt{z}}\Gamma\left(a-\tfrac{1}{2}\right)\Gamma\left(b-\tfrac{1}{2}\right)%
\*(z-1)^{(-a-b+(\ifrac{3}{2}))/2}\*\left({\mathrm{e}}^{\pm\pi\mathrm{i}(a+b-(%
\ifrac{3}{2}))}P^{-a-b+(\ifrac{3}{2})}_{a-b-(\ifrac{1}{2})}\left(-\sqrt{z}%
\right)-P^{-a-b+(\ifrac{3}{2})}_{a-b-(\ifrac{1}{2})}\left(\sqrt{z}\right)%
\right),\]