\[F\left({a,\tfrac{1}{3}a+\tfrac{1}{3}\atop\tfrac{2}{3}a+\tfrac{2}{3}};z\right)=%
\left(1+\sqrt{z}\right)^{-2a}\*F\left({a,\tfrac{2}{3}a+\tfrac{1}{6}\atop\tfrac%
{4}{3}a+\tfrac{1}{3}};\frac{4\sqrt{z}}{(1+\sqrt{z})^{2}}\right).\]