{"title":"Turán-Type Inequalities for Gaussian Hypergeometric Functions, and Baricz's Conjecture","authors":"Song-Liang Qiu, Xiao-Yan Ma, Xue-Yan Xiang","doi":"arxiv-2408.15723","DOIUrl":null,"url":null,"abstract":"In 2007, \\'A. Baricz put forward a conjecture concerning Tur\\'an-type\ninequalities for Gaussian hypergeometric functions (see Conjecture \\ref{ConjA}\nin Section \\ref{Sec1}). In this paper, the authors disprove this conjecture\nwith several methods, and present Tur\\'an-type double inequalities for Gaussian\nhypergeometric functions, and sharp bounds for complete and generalized\nelliptic integrals of the first kind.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"3 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Classical Analysis and ODEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.15723","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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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