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arXiv · 1110.6619

Landen inequalities for zero-balanced hypergeometric functions

Slavko Simić·Matti Vuorinen
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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 $x\in (0,1)$. Thereby an exhausting answer is given to an open problem.

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Slavko Simić, Matti Vuorinen. 2011-10-30. Landen inequalities for zero-balanced hypergeometric functions. https://arxiv.org/abs/1110.6619

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