Generalized elliptic integrals and modular equations

269 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

On l'Hospital-type rules for monotonicity. (2006, background): “In view of what has been said here, it should not be surprising that a very wide variety of applications of these l’Hospital-type rules for monotonicity patterns were given: in areas of analytic inequalities [5, 15, 16, 19], approximation theory [17], differential geometry [10, 11, 12, 21], informat”
A Power Mean Inequality involving the complete elliptic integrals (2013, background): “The complete elliptic integrals play a very important role in the study of conformal invariants [7], quasiconformal mappings [5, 6, 7, 12] and Ramanujan’s modular equations [4].”
Turán type inequalities for hypergeometric functions (2008, background): “The decreasing homeomorphism µ a : (0 , 1) → (0 , ∞ ) , deﬁned by , where a ∈ (0 , 1) , is the so-called generalized Gr¨otzsch ring function, which appears in Ramanujan’s generalized modular equations (see for example [3]).”
Turán type inequalities for generalized complete elliptic integrals (2007, background): “where a ∈ (0,1), is the so-called generalized Grotzsch ring function, which appears in Ramanujan’s generalized modular equations (see for example [ 3 ]).”