{"title":"高斯帕的算法，精确的求和，以及离散的牛顿-莱布尼茨公式","authors":"S. Abramov, M. Petkovssek","doi":"10.1145/1073884.1073888","DOIUrl":null,"url":null,"abstract":"Sufficient conditions are given for validity of the discrete Newton-Leibniz formula when the indefinite sum is obtained either by Gosper's algorithm or by Accurate Summation algorithm. It is shown that sometimes a polynomial can be factored from the summand in such a way that the safe summation range is increased.","PeriodicalId":311546,"journal":{"name":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","volume":"154 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2005-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"15","resultStr":"{\"title\":\"Gosper's algorithm, accurate summation, and the discrete Newton-Leibniz formula\",\"authors\":\"S. Abramov, M. Petkovssek\",\"doi\":\"10.1145/1073884.1073888\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Sufficient conditions are given for validity of the discrete Newton-Leibniz formula when the indefinite sum is obtained either by Gosper's algorithm or by Accurate Summation algorithm. It is shown that sometimes a polynomial can be factored from the summand in such a way that the safe summation range is increased.\",\"PeriodicalId\":311546,\"journal\":{\"name\":\"Proceedings of the 2005 international symposium on Symbolic and algebraic computation\",\"volume\":\"154 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2005-07-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"15\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 2005 international symposium on Symbolic and algebraic computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/1073884.1073888\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 2005 international symposium on Symbolic and algebraic computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/1073884.1073888","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Gosper's algorithm, accurate summation, and the discrete Newton-Leibniz formula
Sufficient conditions are given for validity of the discrete Newton-Leibniz formula when the indefinite sum is obtained either by Gosper's algorithm or by Accurate Summation algorithm. It is shown that sometimes a polynomial can be factored from the summand in such a way that the safe summation range is increased.
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