Inequalities for the generalized elliptic integrals and modular functions (Q878496): Difference between revisions

Sharp inequalities for the Ramanujan's generalized modular functions are proved by using monotonicity and convexity of the generalized elliptic integrals. The authors study in details these properties of elliptic integrals and modular functions from a different point of view, developing Ramanujan's ideas in these topics. In particular, the authors apply the so-called monotone form of L'Hopital's rule. This approach allows to obtain some sharp inequalities for modular functions.