most citedOn a Conjecture Concerning the Approximates of Complete Elliptic Integral of the First Kind by Inverse Hyperbolic Tangent

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math.CA2021★ 2 cited

On a Conjecture Concerning the Approximates of Complete Elliptic Integral of the First Kind by Inverse Hyperbolic Tangent

Song-Liang Qiu, Qi Bao, Xiao-Yan Ma +1

Let $\K$ be the complete elliptic integral of the first kind. In this paper, the authors prove that the function $r\mapsto r^{-2}\{[\log(2\K(r)/π)]/\log((\arth r)/r)-3/4\}$ is stri…