Application of Markov's quadrature in orthogonal expansions / O. B. Arushanyan, S. F. Zaletkin. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2009. ? 6. P. 18-22 [Moscow Univ. Math. Bulletin. Vol. 64, N 6, 2009. P. 244-248].

A method of using Markov's quadrature with a fixed node is proposed to calculate the coefficients of the expansion of a function in a Chebyshev shifted series. Approximation properties of a partial sum of the series with approximate coefficients are considered. This approach can be used to construct a number of numerical analytic methods for solving ordinary differential equations.

Key words: Markov's quadratures, Fourier–Chebyshev series, Chebyshev shifted series, orthogonal expansions, interpolation polynomials.