zโข(1โˆ’z)โข(dFโก(a,b;c;z)/dz)=(cโˆ’a)โขFโก(aโˆ’1,b;c;z)+(aโˆ’c+bโขz)โขFโก(a,b;c;z)=(cโˆ’b)โขFโก(a,bโˆ’1;c;z)+(bโˆ’c+aโขz)โขFโก(a,b;c;z),