A sharp double inequality involving generalized complete elliptic integral of the first kind

1.
Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, P. R. China
2.
Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China
3.
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, P. R. China

Received: 31 March 2020 Accepted: 13 May 2020 Published: 21 May 2020
MSC : 33C05, 33E05

In the article, we establish a sharp double inequality involving the ratio of generalized complete elliptic integrals of the first kind, which is the improvement and generalization of some previously known results.
- Gaussian hypergeometric function,
- generalized elliptic integral,
- gamma function,
- psi function
Citation: Tie-Hong Zhao, Miao-Kun Wang, Yu-Ming Chu. A sharp double inequality involving generalized complete elliptic integral of the first kind[J]. AIMS Mathematics, 2020, 5(5): 4512-4528. doi: 10.3934/math.2020290

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Abstract

In the article, we establish a sharp double inequality involving the ratio of generalized complete elliptic integrals of the first kind, which is the improvement and generalization of some previously known results.

References

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