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Research Article | Open Access

Monotonicity, convexity and inequalities involving zero-balanced Gaussian hypergeometric function

Li Xu1, Lu Chen2, Ti-Ren Huang3( )
Jinhua Radio and Television University, Jinhua 321000, China
Wuxi Vocational Institute of Commerce, Wuxi 214153, China
Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, China
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Abstract

We generalize several monotonicity and convexity properties as well as sharp inequalities for the complete elliptic integrals to the zero-balanced Gaussian hypergeometric function F ( a , b ; a + b ; x ).

Keywords

Gaussian hypergeometric functionmonotonicityconvexity and concavity
CLC number: 33C05, 26D20

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AIMS Mathematics
Volume 7 Issue 7,
July 2022
Pages 12471-12482
DOI: 10.3934/math.2022692

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Cite this article:
Xu L, Chen L, Huang T-R. Monotonicity, convexity and inequalities involving zero-balanced Gaussian hypergeometric function. AIMS Mathematics, 2022, 7(7): 12471-12482. https://doi.org/10.3934/math.2022692

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Received: 04 January 2022
Revised: 16 April 2022
Accepted: 21 April 2022
Published: 15 July 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)