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