Turán-Type Inequalities for Gaussian Hypergeometric Functions, and Baricz's Conjecture

2024/08/28 by Song-Liang Qiu, Qiu, Song-Liang, Xiao-Yan Ma +3
Mathematics · Social Sciences · #Mathematical Inequalities and Applications #Point processes and geometric inequalities #Diverse Research Studies Overview

paper · pdf · doi:10.48550/arxiv.2408.15723

Abstract

In 2007, Á. Baricz put forward a conjecture concerning Turán-type inequalities for Gaussian hypergeometric functions (see Conjecture \refConjA in Section \refSec1). In this paper, the authors disprove this conjecture with several methods, and present Turán-type double inequalities for Gaussian hypergeometric functions, and sharp bounds for complete and generalized elliptic integrals of the first kind.

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