Landen inequalities for Gaussian hypergeometric function (Q2063006)

The paper contains several Landen inequalities, and quadratic and cubic transformation inequalities for the general Gaussian hypergeometric function \(_2F_1(a, b; c ;x)\). The authors present Landen inequalities and other Ramanujan's quadratic, cubic transformation inequalities for the Gaussian hypergeometric function \(F(a,b;c;r)\) which are generalizations of known ones for two classes of hypergeometric functions \(F(a,b;a+b;r)\) and \(F(a,b;a+b+12;r)\), they improve and refine results given before.