Landen Inequalities for Zero-Balanced Hypergeometric Functions



: Simic S, Vuorinen M

Publisher: HINDAWI PUBLISHING CORPORATION

: 2012

: Abstract and Applied Analysis

: ABSTRACT AND APPLIED ANALYSIS

: ABSTR APPL ANAL

: 93261

: 11

: 1085-3375

DOI: https://doi.org/10.1155/2012/932061


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 is an element of (0, 1). Thereby an exhausting answer is given to the open problem from the work by Anderson et al., 1990.



Last updated on 2024-26-11 at 15:31