AIMS Mathematics, 2020, 5(5): 4512-4528. doi: 10.3934/math.2020290.

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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

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.
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Keywords 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. AIMS Mathematics, 2020, 5(5): 4512-4528. doi: 10.3934/math.2020290

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