Monotonicity and concavity properties of the Gaussian hypergeometric functions, with applications

Miao-Kun Wang (), Tie-Hong Zhao (), Xue-Jing Ren (), Yu-Ming Chu () and Zai-Yin He ()
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Miao-Kun Wang: Huzhou University
Tie-Hong Zhao: Hangzhou Normal University
Xue-Jing Ren: Changzhou Institute of Technology
Yu-Ming Chu: Huzhou University
Zai-Yin He: Hunan University

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 4, 1105-1124

Abstract: Abstract This paper deals with the monotonicity and concavity properties of certain functions involving the Gaussian hypergeometric function. With these results, we not only obtain sharp bounds for the ratio of hypergeometric functions which extend recently discovered inequalities for k-balanced hypergeometric functions, and but also give an affirmative answer to an open problem proposed by Qiu and Vuorinen. In addition, as by-products, some monotonicity theorems for complete p-elliptic integrals and inequalities for generalized Grötzsch ring function are established.

Keywords: Gaussian hypergeometric function; Complete p-elliptic integrals; Ratio function; Monotonicity; Concavity; 33C05; 33E05 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00325-7

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