{"title":"Series representations of positive integral powers of pi","authors":"Mingzhou Xu","doi":"arxiv-2405.12248","DOIUrl":null,"url":null,"abstract":"Using a pointwise version of Fej\\'{e}r's theorem about Fourier series, we\nobtain two formulae related to the series representations of positive integral\npowers of $\\pi$. We also check the correctness of our formulae by the\napplications of the R software.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"20 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - General Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2405.12248","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
Using a pointwise version of Fej\'{e}r's theorem about Fourier series, we
obtain two formulae related to the series representations of positive integral
powers of $\pi$. We also check the correctness of our formulae by the
applications of the R software.
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