高斯超几何函数的 Turán 型不等式和 Baricz 猜想

arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-08-28 DOI:arxiv-2408.15723

Song-Liang Qiu, Xiao-Yan Ma, Xue-Yan Xiang

{"title":"高斯超几何函数的 Turán 型不等式和 Baricz 猜想","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":"{\"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}","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

摘要

2007年，Baricz提出了一个关于高斯超几何函数的Tur\'an-typeinequalities猜想（见第1节中的Conjecture \ref{ConjA}）。在本文中，作者用几种方法反证了这一猜想，并提出了高斯超几何函数的 Tur\'an-type 双不等式，以及第一类完全椭圆积分和广义椭圆积分的尖锐边界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

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

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Classical Analysis and ODEs

自引率

0.00%

发文量