\[\mathbf{F}\left({a,b\atop\tfrac{1}{2}(a+b+1)};z\right)=\left(-z(1-z)\right)^{%
\ifrac{(1-a-b)}{4}}\*P^{\ifrac{(1-a-b)}{2}}_{\ifrac{(a-b-1)}{2}}\left(1-2z%
\right),\]