Abstract
In this paper, we establish a sufficient and necessary condition for a function involving the inverse hyperbolic tangent function as a best possible upper bound for the complete elliptic integral of the first kind. Equivalently, we obtain a lower bound involving the arithmetic mean and logarithmic mean for the Gauss arithmetic-geometric mean. This provides a positive answer to a conjecture proposed by Yang, Song and Chu in 2014.
Citation
Zhong-Xuan Mao. Lan-Xiang Yu. Jun-Yi Li. Jing-Feng Tian. "A best possible upper bound for the complete elliptic integral of the first kind." Bull. Belg. Math. Soc. Simon Stevin 30 (2) 246 - 259, september 2023. https://doi.org/10.36045/j.bbms.230228
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