On some refinements for inequalities involving zero-balanced hypergeometric function

Tie-Hong Zhao; Zai-Yin He; Yu-Ming Chu; Tie-Hong Zhao; Zai-Yin He; Yu-Ming Chu

doi:10.3934/math.2020418

AIMS Mathematics

2020, Volume 5, Issue 6: 6479-6495. doi: 10.3934/math.2020418

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Research article

On some refinements for inequalities involving zero-balanced hypergeometric function

1.
Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, P. R. China
2.
School of Mathematics, Hunan University, Changsha 410082, P. R. China
3.
Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China
4.
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, P. R. China

Received: 08 June 2020 Accepted: 13 August 2020 Published: 19 August 2020
MSC : 33E05, 33C05

In the article, we present an elegant double inequality for the ratio of the zero-balanced hypergeometric functions, which improve and refine some previously known results and also give a positive answer the question by proposed by Ismail.
- Gaussian hypergeometric function,
- zero-balanced,
- complete elliptic integral,
- generalized elliptic integral
Citation: Tie-Hong Zhao, Zai-Yin He, Yu-Ming Chu. On some refinements for inequalities involving zero-balanced hypergeometric function[J]. AIMS Mathematics, 2020, 5(6): 6479-6495. doi: 10.3934/math.2020418

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Abstract

In the article, we present an elegant double inequality for the ratio of the zero-balanced hypergeometric functions, which improve and refine some previously known results and also give a positive answer the question by proposed by Ismail.

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