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Sharp Power Mean Inequalities for the Generalized Elliptic Integral of the First Kind

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Abstract

We establish two sharp inequalities involving the power mean and generalized elliptic integral of the first kind. As applications, the analogous inequalities concerning the complete p-elliptic integral of the first kind are also derived.

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Acknowledgements

The authors would like to express sincere thanks to the anonymous referee for carefully reading the manuscript and valuable comments and suggestions. This work was supported by the Natural Science Foundation of China (Grant Nos. 11701176, 11971142, 61673169), and the Science Foundation of Zhejiang Province (Grant No. YL19A010012).

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Authors and Affiliations

  1. Department of Mathematics, Huzhou University, Huzhou, 313000, China

    Miao-Kun Wang

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

    Zai-Yin He

  3. College of Science, Hunan City University, Yiyang, 413000, China

    Yu-Ming Chu

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

    Yu-Ming Chu

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  1. Miao-Kun Wang
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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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Communicated by Doron Lubinsky.

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Wang, MK., He, ZY. & Chu, YM. Sharp Power Mean Inequalities for the Generalized Elliptic Integral of the First Kind. Comput. Methods Funct. Theory 20, 111–124 (2020). https://doi.org/10.1007/s40315-020-00298-w

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