{"title":"A Trigonometric Quadrature Rule for Cauchy Integrals with Jacobi Weight","authors":"Philsu Kim","doi":"10.1006/jath.2000.3513","DOIUrl":null,"url":null,"abstract":"In this paper, we consider a quadrature rule for Cauchy integrals of the form I(wf;s)=[formula]w(t)f(t)/(t-s)dt, -1-1/2. Using the change of variables t=cosy, s=cosx and subtracting out the singularity, we propose a trigonometric quadrature rule. We obtain the error bounds independent of the set of values of poles and construct an automatic quadrature of nonadaptive type.","PeriodicalId":202056,"journal":{"name":"J. Approx. Theory","volume":"33 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"J. Approx. Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1006/jath.2000.3513","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
Abstract
In this paper, we consider a quadrature rule for Cauchy integrals of the form I(wf;s)=[formula]w(t)f(t)/(t-s)dt, -1-1/2. Using the change of variables t=cosy, s=cosx and subtracting out the singularity, we propose a trigonometric quadrature rule. We obtain the error bounds independent of the set of values of poles and construct an automatic quadrature of nonadaptive type.
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