A Natural Approximation to the Complete Elliptic Integral of the First Kind - Ling Zhu (Mathematics, 2022)
Let <semantics>K(r)</semantics> be the complete elliptic integral of the first kind. Then, the inequality <semantics>2K(r)/π>tanh−1(r)/sin−1<mfenced open="(" close=")">r</mfenced></semantics> holds for all <semantics>r∈(0,1)</semantics>. This conclusion does not match those in the existing literature.