{"title":"评价Ramanujan的嵌套根：一种序列方法","authors":"K. Sarma, Pijush Pratim Sarmah","doi":"10.1080/0025570X.2023.2231337","DOIUrl":null,"url":null,"abstract":"Rewriting a nested radical in this form is commonly known as denesting. Denesting a nested radical is often very difficult. Many papers have been written on simplifying radicals. For example, consider the papers by Landau [3], Osler [4], and Zippel [6], and the references contained therein. The great Indian mathematician Srinivasa Ramanujan Aiyangar also contributed a lot in this direction. In his unique way, Ramanujan observed several striking relationships among certain nested radicals. Here are some examples (note that the final example uses the standard notation for a continued fraction):","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Evaluating Ramanujan’s Nested Radicals: A Sequential Approach\",\"authors\":\"K. Sarma, Pijush Pratim Sarmah\",\"doi\":\"10.1080/0025570X.2023.2231337\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Rewriting a nested radical in this form is commonly known as denesting. Denesting a nested radical is often very difficult. Many papers have been written on simplifying radicals. For example, consider the papers by Landau [3], Osler [4], and Zippel [6], and the references contained therein. The great Indian mathematician Srinivasa Ramanujan Aiyangar also contributed a lot in this direction. In his unique way, Ramanujan observed several striking relationships among certain nested radicals. Here are some examples (note that the final example uses the standard notation for a continued fraction):\",\"PeriodicalId\":18344,\"journal\":{\"name\":\"Mathematics Magazine\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-07-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics Magazine\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/0025570X.2023.2231337\",\"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.2023.2231337","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Evaluating Ramanujan’s Nested Radicals: A Sequential Approach
Rewriting a nested radical in this form is commonly known as denesting. Denesting a nested radical is often very difficult. Many papers have been written on simplifying radicals. For example, consider the papers by Landau [3], Osler [4], and Zippel [6], and the references contained therein. The great Indian mathematician Srinivasa Ramanujan Aiyangar also contributed a lot in this direction. In his unique way, Ramanujan observed several striking relationships among certain nested radicals. Here are some examples (note that the final example uses the standard notation for a continued fraction):
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