{"title":"pi 的正积分幂的数列表示法","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":"{\"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}","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
摘要
利用关于傅里叶级数的 Fej\'{e}r's theorem 的点式版本,我们得到了两个与 $\pi$ 的正积分幂的级数表示有关的公式。我们还通过应用 R 软件检验了公式的正确性。
Series representations of positive integral powers of pi
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.