Landen Inequalities for Zero-Balanced Hypergeometric Functions

Abstract EN

For zero-balanced Gaussian hypergeometric functions F(a,b;a+b;x), a,b>0, we determine maximal regions of ab plane where well-known Landen identities for the complete elliptic integral of the first kind turn on respective inequalities valid for each x∈(0,1).

Thereby an exhausting answer is given to the open problem from the work by Anderson et al., 1990.