{"title":"巴塞尔问题之外，第一部分","authors":"K. Williams","doi":"10.1080/0025570X.2023.2176099","DOIUrl":null,"url":null,"abstract":"Summary In the 18th century, the problem of finding the sum of the reciprocals of the squares was known as the Basel problem. It was first solved by Euler, who, in 1735, showed the sum evaluated to . We go beyond the Basel problem by evaluating the sum of where , for some integers b and a. In particular, we examine the special cases and .","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Beyond the Basel Problem, Part I\",\"authors\":\"K. Williams\",\"doi\":\"10.1080/0025570X.2023.2176099\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Summary In the 18th century, the problem of finding the sum of the reciprocals of the squares was known as the Basel problem. It was first solved by Euler, who, in 1735, showed the sum evaluated to . We go beyond the Basel problem by evaluating the sum of where , for some integers b and a. In particular, we examine the special cases and .\",\"PeriodicalId\":18344,\"journal\":{\"name\":\"Mathematics Magazine\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-02-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics Magazine\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/0025570X.2023.2176099\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics Magazine","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/0025570X.2023.2176099","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Summary In the 18th century, the problem of finding the sum of the reciprocals of the squares was known as the Basel problem. It was first solved by Euler, who, in 1735, showed the sum evaluated to . We go beyond the Basel problem by evaluating the sum of where , for some integers b and a. In particular, we examine the special cases and .
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