Approximation for the complete elliptic integral of the first kind

被引：0
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作者：
Wei-Mao Qian
Zai-Yin He
Yu-Ming Chu
机构：
[1] Huzhou Radio & Television University,School of Continuing Education
[2] Hunan University,School of Mathematics
[3] Huzhou University,Department of Mathematics
[4] Changsha University of Science & Technology,School of Mathematics and Statistics
来源：
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas | 2020年 / 114卷
关键词：
Complete elliptic integrals; Inverse trigonometric function; Inverse hyperbolic function; Arithmetic-geometric mean; 33E05; 26E60;
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摘要：
In the article, we present several sharp upper and lower bounds for the complete elliptic integral of the first kind in terms of inverse trigonometric and inverse hyperbolic functions. As consequences, some sharp bounds for the Gaussian arithmetic-geometric mean in terms of other bivariate means are also given.
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