Monotonicity properties and bounds for the complete <em>p</em>-elliptic integrals

Xi-Fan Huang; Miao-Kun Wang; Hao Shao; Yi-Fan Zhao; Yu-Ming Chu; Xi-Fan Huang; Miao-Kun Wang; Hao Shao; Yi-Fan Zhao; Yu-Ming Chu

doi:10.3934/math.2020453

AIMS Mathematics

2020, Volume 5, Issue 6: 7071-7086. doi: 10.3934/math.2020453

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Research article

Monotonicity properties and bounds for the complete p-elliptic integrals

1.
Department of Mathematics, Huzhou University, Huzhou 313000, China
2.
College of Science, Hunan City University, Yiyang 413000, China
3.
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, China

Received: 15 June 2020 Accepted: 03 September 2020 Published: 10 September 2020
MSC : 33E05, 33F05

In the article, we establish some monotonicity properties for certain functions involving the complete p-elliptic integrals of the first and second kinds, and find several sharp bounds for the p-elliptic integrals. Our results are the generalizations and improvements of some previously known results for the classical complete elliptic integrals.
- complete elliptic integral,
- complete p-elliptic integral,
- generalized trigonometric function,
- monotonicity,
- bound
Citation: Xi-Fan Huang, Miao-Kun Wang, Hao Shao, Yi-Fan Zhao, Yu-Ming Chu. Monotonicity properties and bounds for the complete p-elliptic integrals[J]. AIMS Mathematics, 2020, 5(6): 7071-7086. doi: 10.3934/math.2020453

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Abstract

In the article, we establish some monotonicity properties for certain functions involving the complete p-elliptic integrals of the first and second kinds, and find several sharp bounds for the p-elliptic integrals. Our results are the generalizations and improvements of some previously known results for the classical complete elliptic integrals.

References

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