{"title":"A new asymptotic expansion and sharp inequality for the volume of the unit ball in R^n","authors":"Xiao Zhang, Chao-Ping Chen","doi":"10.47443/ejm.2022.032","DOIUrl":null,"url":null,"abstract":"For n ∈ { 1 , 2 , . . . } , let Ω n = π n/ 2 / Γ( n 2 + 1) be the volume of the unit ball in R n . In this paper, we give a new asymptotic expansion for Ω n . Based on the obtained result, we also establish a sharp double inequality for Ω n .","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2022-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Electronic Journal of Mathematics Education","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47443/ejm.2022.032","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"EDUCATION & EDUCATIONAL RESEARCH","Score":null,"Total":0}
引用次数: 0
Abstract
For n ∈ { 1 , 2 , . . . } , let Ω n = π n/ 2 / Γ( n 2 + 1) be the volume of the unit ball in R n . In this paper, we give a new asymptotic expansion for Ω n . Based on the obtained result, we also establish a sharp double inequality for Ω n .
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