{"title":"Approximation of the function |sin x| s by the partial sums of the trigonmometric rational fourier series","authors":"N. Y. Kazlouskaya, Y. A. Rovba","doi":"10.29235/1561-8323-2021-65-1-11-17","DOIUrl":null,"url":null,"abstract":"In the present article, the approximation of the function |sin x| s by the partial sums of the rational trigonometric Fourier series is considered. An integral representation, uniform and point estimates for the above-mentioned approximation were obtained. Based on them, several special cases of the selection of poles were studied. In the case of the approximation by the partial sums of the polynomial trigonometric Fourier series, an asymptotic equality was found. A detailed study is made of a fixed number of geometrically different poles.","PeriodicalId":11283,"journal":{"name":"Doklady of the National Academy of Sciences of Belarus","volume":"179 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady of the National Academy of Sciences of Belarus","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.29235/1561-8323-2021-65-1-11-17","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
In the present article, the approximation of the function |sin x| s by the partial sums of the rational trigonometric Fourier series is considered. An integral representation, uniform and point estimates for the above-mentioned approximation were obtained. Based on them, several special cases of the selection of poles were studied. In the case of the approximation by the partial sums of the polynomial trigonometric Fourier series, an asymptotic equality was found. A detailed study is made of a fixed number of geometrically different poles.
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