{"title":"Some New Optimal Bounds for Wallis Ratio","authors":"Yin Chen","doi":"10.9734/arjom/2023/v19i10739","DOIUrl":null,"url":null,"abstract":"Wallis ratio can be expressed as an asymptotic expansion using Stirling series and Bernoulli numbers. We prove the general inequalities for Wallis ratio for arbitrary number of terms in the asymptotic expansion. We show that the coefficients in the asymptotic expansion are the best possible.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asian Research Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.9734/arjom/2023/v19i10739","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
Wallis ratio can be expressed as an asymptotic expansion using Stirling series and Bernoulli numbers. We prove the general inequalities for Wallis ratio for arbitrary number of terms in the asymptotic expansion. We show that the coefficients in the asymptotic expansion are the best possible.
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