Monotonicity and inequalities related to complete elliptic integrals of the second kind

Fei Wang; Bai-Ni Guo; Feng Qi; Fei Wang; Bai-Ni Guo; Feng Qi

doi:10.3934/math.2020176

AIMS Mathematics

2020, Volume 5, Issue 3: 2732-2742. doi: 10.3934/math.2020176

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Research article

Monotonicity and inequalities related to complete elliptic integrals of the second kind

1.
Department of Mathematics, Zhejiang Institute of Mechanical and Electrical Engineering, Hangzhou 310053, Zhejiang, China
2.
School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, China
3.
School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China

Received: 28 December 2019 Accepted: 09 March 2020 Published: 17 March 2020
MSC : Primary 33E05; Secondary 26A48, 26D15, 33C75

In the paper, the authors present some monotonicity properties of certain functions defined in terms of the complete elliptic integrals of the second kind and some elementary functions and, consequently, improve several known inequalities for the complete elliptic integrals of the second kind.
- monotonicity,
- inequality,
- complete elliptic integral of the second kind
Citation: Fei Wang, Bai-Ni Guo, Feng Qi. Monotonicity and inequalities related to complete elliptic integrals of the second kind[J]. AIMS Mathematics, 2020, 5(3): 2732-2742. doi: 10.3934/math.2020176

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Abstract

In the paper, the authors present some monotonicity properties of certain functions defined in terms of the complete elliptic integrals of the second kind and some elementary functions and, consequently, improve several known inequalities for the complete elliptic integrals of the second kind.

References

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