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