Landen Inequalities for Zero‐Balanced Hypergeometric Functions

Slavko Simić and Matti Vuorinen

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

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 the open problem from the work by Anderson et al., 1990.

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

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:932061

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