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arXiv · 2408.15723

Tur\'an-Type Inequalities for Gaussian Hypergeometric Functions, and Baricz's Conjecture

Song-Liang Qiu·Xiao-Yan Ma·Xue-Yan Xiang
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Abstract

In 2007, \'A. Baricz put forward a conjecture concerning Tur\'an-type inequalities for Gaussian hypergeometric functions (see Conjecture \ref{ConjA} in Section \ref{Sec1}). In this paper, the authors disprove this conjecture with several methods, and present Tur\'an-type double inequalities for Gaussian hypergeometric functions, and sharp bounds for complete and generalized elliptic integrals of the first kind.

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Song-Liang Qiu, Xiao-Yan Ma, Xue-Yan Xiang. 2024-08-28. Tur\'an-Type Inequalities for Gaussian Hypergeometric Functions, and Baricz's Conjecture. https://arxiv.org/abs/2408.15723

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