Monotonicity, convexity properties and inequalities involving Gaussian hypergeometric functions with applications

Ye-Cong Han; Chuan-Yu Cai; Ti-Ren Huang; Ye-Cong Han; Chuan-Yu Cai; Ti-Ren Huang

doi:10.3934/math.2022277

AIMS Mathematics

2022, Volume 7, Issue 4: 4974-4991. doi: 10.3934/math.2022277

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Monotonicity, convexity properties and inequalities involving Gaussian hypergeometric functions with applications

1.
Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, China
2.
Zhejiang Technical Institute of Economics, Hangzhou 310018, China

Received: 12 September 2021 Revised: 19 December 2021 Accepted: 21 December 2021 Published: 29 December 2021
MSC : 33C05, 33E05

In this paper, we mainly prove monotonicity and convexity properties of certain functions involving zero-balanced Gaussian hypergeometric function $ F(a, b; a+b; x) $. We generalize conclusions of elliptic integral to Gaussian hypergeometric function, and get some accurate inequalities about Gaussian hypergeometric function.
- Gaussian hypergeometric function,
- monotonicity,
- convexity
Citation: Ye-Cong Han, Chuan-Yu Cai, Ti-Ren Huang. Monotonicity, convexity properties and inequalities involving Gaussian hypergeometric functions with applications[J]. AIMS Mathematics, 2022, 7(4): 4974-4991. doi: 10.3934/math.2022277

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Abstract

In this paper, we mainly prove monotonicity and convexity properties of certain functions involving zero-balanced Gaussian hypergeometric function $ F(a, b; a+b; x) $. We generalize conclusions of elliptic integral to Gaussian hypergeometric function, and get some accurate inequalities about Gaussian hypergeometric function.

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