Open AccessApproximation of the function |sin x| s by the partial sums of the trigonmometric rational fourier series
Author(s) -
N. Yu. Kazlouskaya,
Ya. A. Rovba
Publication year - 2021
Publication title -
doklady nacionalʹnoj akademii nauk belarusi
Language(s) - English
Resource type - Journals
eISSN - 2524-2431
pISSN - 1561-8323
DOI - 10.29235/1561-8323-2021-65-1-11-17
Subject(s) - fourier series , mathematics , trigonometric polynomial , rational function , trigonometric series , series (stratigraphy) , mathematical analysis , conjugate fourier series , function (biology) , fourier transform , polynomial , discrete fourier series , trigonometric functions , fourier analysis , representation (politics) , trigonometry , fractional fourier transform , geometry , paleontology , short time fourier transform , evolutionary biology , politics , political science , law , biology
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.