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Approximation for the complete elliptic integral of the first kind

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

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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Acknowledgements

This work was supported by the Natural Science Foundation of China (Grant Nos. 61673169, 11301127, 11701176, 11626101, 11601485) and the Key Project of the Scientific Research of Zhejiang Open University in 2019 (Grant no. XKT-19Z02).

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Authors and Affiliations

  1. School of Continuing Education, Huzhou Radio & Television University, Huzhou, 313000, Zhejiang, China

    Wei-Mao Qian

  2. School of Mathematics, Hunan University, Changsha, 410082, Hunan, China

    Zai-Yin He

  3. Department of Mathematics, Huzhou University, Huzhou, 313000, Zhejiang, China

    Yu-Ming Chu

  4. School of Mathematics and Statistics, Changsha University of Science & Technology, Changsha, 410114, Hunan, China

    Yu-Ming Chu

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  1. Wei-Mao Qian
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  2. Zai-Yin He
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  3. Yu-Ming Chu
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Correspondence to Yu-Ming Chu.

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Qian, WM., He, ZY. & Chu, YM. Approximation for the complete elliptic integral of the first kind. RACSAM 114, 57 (2020). https://doi.org/10.1007/s13398-020-00784-9

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