TRIGONOMETRIC RATIONAL FOURIER SERIES FOR |sin x|
Trigonometric polynomial Fourier series are widely used in various fields of science and practice. In particular, we know quite a lot of interesting representations for elementary functions as sums of corresponding Fourier series (see, for example, [1; 2]). Rational trigonometric Fourier series as a generalization of the corresponding polynomial series were constructed by M. M. Jrbashyan [3]. In [3] the Dini-Lipschitz and Jordan-Dirichlet criterions of the convergence of rational trigonometric Fourier series for the case when the poles of rational functions don’t have limit points on the unit circle were also obtained. In this paper we construct rational Fourier series for |sin x|.