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