\[F\left({a,b\atop 2b};z\right)=\left(1-\tfrac{1}{2}z\right)^{-a}F\left({\tfrac{%
1}{2}a,\tfrac{1}{2}a+\tfrac{1}{2}\atop b+\tfrac{1}{2}};\left(\frac{z}{2-z}%
\right)^{2}\right),\]