{"title":"形式如Σƒ(i)ti的有限和的求和公式","authors":"Xiaomin Chen, Ruiyue Lin","doi":"10.1109/IWACI.2010.5585207","DOIUrl":null,"url":null,"abstract":"In this paper, we discussed a kind of summation formula for the finite sum of form such as Σƒ(i)ti, which is based on two representations of a (n + 1) -th continuous differentiable function ƒ(z) by the Bernoulli function or the Eulerian function. For ƒ(z) be a polynomial in z of degree n, we educed an especial summation formula, which has wide applications in numerical calculation.","PeriodicalId":189187,"journal":{"name":"Third International Workshop on Advanced Computational Intelligence","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A summation formula for the finite sum of form such as Σƒ(i)ti\",\"authors\":\"Xiaomin Chen, Ruiyue Lin\",\"doi\":\"10.1109/IWACI.2010.5585207\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we discussed a kind of summation formula for the finite sum of form such as Σƒ(i)ti, which is based on two representations of a (n + 1) -th continuous differentiable function ƒ(z) by the Bernoulli function or the Eulerian function. For ƒ(z) be a polynomial in z of degree n, we educed an especial summation formula, which has wide applications in numerical calculation.\",\"PeriodicalId\":189187,\"journal\":{\"name\":\"Third International Workshop on Advanced Computational Intelligence\",\"volume\":\"4 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-09-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Third International Workshop on Advanced Computational Intelligence\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/IWACI.2010.5585207\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Third International Workshop on Advanced Computational Intelligence","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/IWACI.2010.5585207","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A summation formula for the finite sum of form such as Σƒ(i)ti
In this paper, we discussed a kind of summation formula for the finite sum of form such as Σƒ(i)ti, which is based on two representations of a (n + 1) -th continuous differentiable function ƒ(z) by the Bernoulli function or the Eulerian function. For ƒ(z) be a polynomial in z of degree n, we educed an especial summation formula, which has wide applications in numerical calculation.
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