{"title":"超实级数的积与柯西积的局限性","authors":"Jonathan Bartlett","doi":"10.33014/issn.2640-5652.3.2.bartlett.1","DOIUrl":null,"url":null,"abstract":"Cauchy products are used to take the products of convergent series. Here, we show the limitations of this approach in divergent series, including those that can be analyzed through the BGN method. Alternative approaches and formulas for divergent series are suggested, as well as their benefits and drawbacks.","PeriodicalId":114457,"journal":{"name":"Communications of the Blyth Institute","volume":"31 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The Products of Hyperreal Series and the Limitations of Cauchy Products\",\"authors\":\"Jonathan Bartlett\",\"doi\":\"10.33014/issn.2640-5652.3.2.bartlett.1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Cauchy products are used to take the products of convergent series. Here, we show the limitations of this approach in divergent series, including those that can be analyzed through the BGN method. Alternative approaches and formulas for divergent series are suggested, as well as their benefits and drawbacks.\",\"PeriodicalId\":114457,\"journal\":{\"name\":\"Communications of the Blyth Institute\",\"volume\":\"31 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-01-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications of the Blyth Institute\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33014/issn.2640-5652.3.2.bartlett.1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications of the Blyth Institute","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33014/issn.2640-5652.3.2.bartlett.1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Products of Hyperreal Series and the Limitations of Cauchy Products
Cauchy products are used to take the products of convergent series. Here, we show the limitations of this approach in divergent series, including those that can be analyzed through the BGN method. Alternative approaches and formulas for divergent series are suggested, as well as their benefits and drawbacks.
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