{"title":"用梯形法则求解析函数积分的有效方法","authors":"S. Rice","doi":"10.1002/J.1538-7305.1973.TB01986.X","DOIUrl":null,"url":null,"abstract":"Definite integrals of analytic functions can often be evaluated efficiently by the trapezoidal rule after a suitable transformation. Here the work of Moran1 and Schwartz2 along this line is extended. First the dependence of the error on the spacing is discussed, and then several types of transformations are described and applied to integrals of technical interest.","PeriodicalId":55391,"journal":{"name":"Bell System Technical Journal","volume":"41 1","pages":"707-722"},"PeriodicalIF":0.0000,"publicationDate":"1973-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"74","resultStr":"{\"title\":\"Efficient evaluation of integrals of analytic functions by the trapezoidal rule\",\"authors\":\"S. Rice\",\"doi\":\"10.1002/J.1538-7305.1973.TB01986.X\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Definite integrals of analytic functions can often be evaluated efficiently by the trapezoidal rule after a suitable transformation. Here the work of Moran1 and Schwartz2 along this line is extended. First the dependence of the error on the spacing is discussed, and then several types of transformations are described and applied to integrals of technical interest.\",\"PeriodicalId\":55391,\"journal\":{\"name\":\"Bell System Technical Journal\",\"volume\":\"41 1\",\"pages\":\"707-722\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1973-05-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"74\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bell System Technical Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1002/J.1538-7305.1973.TB01986.X\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bell System Technical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/J.1538-7305.1973.TB01986.X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Efficient evaluation of integrals of analytic functions by the trapezoidal rule
Definite integrals of analytic functions can often be evaluated efficiently by the trapezoidal rule after a suitable transformation. Here the work of Moran1 and Schwartz2 along this line is extended. First the dependence of the error on the spacing is discussed, and then several types of transformations are described and applied to integrals of technical interest.
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