Notes on the complete elliptic integral of the first kind

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Abstract

In the article, we present several monotonicity properties and bounds for the complete elliptic integral of the first kind. As applications, we find sharp bounds for the arithmetic-geometric mean.

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Yang, Z. H., Qian, W. M., Zhang, W., & Chu, Y. M. (2020). Notes on the complete elliptic integral of the first kind. Mathematical Inequalities and Applications, 23(1), 77–93. https://doi.org/10.7153/mia-2020-23-07

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