Authors: Simić, Slavko 
Vuorinen, Matti
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Landen inequalities for zero-balanced hypergeometric functions
Journal: Abstract and Applied Analysis
Volume: 2012
Issue Date: 19-Apr-2012
Rank: M21a
ISSN: 1085-3375
DOI: 10.1155/2012/932061
Abstract: 
For zero-balanced Gaussian hypergeometric functions F (a, b; a + b; x), a, b>0, we determine maximal regions of a b 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.
Publisher: Hindawi
Project: Academy of Finland, Project no. 2600066611

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