(z⁢ⅆⅆ⁡z⁡z)n⁢(zc-a-1⁢(1-z)a+b-c⁢F⁡(a,b;c;z))=(c-a)n⁢zc-a+n-1⁢(1-z)a-n+b-c⁢F⁡(a-n,b;c;z).