Landen inequalities for zero-balanced hypergeometric functions

2011/10/30 by Slavko Simić, Simić, Slavko, Матти Вуоринен +2
Mathematics · #26D06 #33C05 #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials #math.CA #msc:26D06 #msc:33C05

paper · pdf · doi:10.48550/arxiv.1110.6619

9 pages

arxiv created 2011/10/30 · openalex publication_date 2011/10/30 · arxiv updated 2011/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 an open problem.

Related

• Inequalities for Zero-Balanced Gaussian hypergeometric function
• Turán-Type Inequalities for Gaussian Hypergeometric Functions, and Baricz's Conjecture
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• Limits of elliptic hypergeometric integrals