{"title":"广义伯恩斯坦函数的近似值","authors":"Stamatis Koumandos, Henrik Laurberg Pedersen","doi":"arxiv-2409.02536","DOIUrl":null,"url":null,"abstract":"We establish sharp inequalities involving the incomplete Beta and Gamma\nfunctions. These inequalities arise in the approximation of generalized\nBernstein functions by higher order Thorin-Bernstein functions. Furthermore,\nnew properties of a related function, namely\n$x^{\\lambda}\\Gamma(x)/\\Gamma(x+\\lambda)$ are derived.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"267 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Approximations of generalized Bernstein functions\",\"authors\":\"Stamatis Koumandos, Henrik Laurberg Pedersen\",\"doi\":\"arxiv-2409.02536\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We establish sharp inequalities involving the incomplete Beta and Gamma\\nfunctions. These inequalities arise in the approximation of generalized\\nBernstein functions by higher order Thorin-Bernstein functions. Furthermore,\\nnew properties of a related function, namely\\n$x^{\\\\lambda}\\\\Gamma(x)/\\\\Gamma(x+\\\\lambda)$ are derived.\",\"PeriodicalId\":501145,\"journal\":{\"name\":\"arXiv - MATH - Classical Analysis and ODEs\",\"volume\":\"267 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-04\",\"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-2409.02536\",\"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-2409.02536","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We establish sharp inequalities involving the incomplete Beta and Gamma
functions. These inequalities arise in the approximation of generalized
Bernstein functions by higher order Thorin-Bernstein functions. Furthermore,
new properties of a related function, namely
$x^{\lambda}\Gamma(x)/\Gamma(x+\lambda)$ are derived.
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