On a convergence of the rational-trigonometric-polynomial approximations realized by the roots of the Laguerre polynomials

The paper considers a problem of approximation of functions by means of their finite number of Fourier coefficients. Convergence acceleration of approximations by the truncated Fourier series is achieved by application of polynomial and rational correction functions. Rational corrections include unknown parameters whose determination is a crucial problem. We consider an approach connected with the roots of the Laguerre polynomials and study the rates of convergence of such approximations.