Application of Markov's Quadrature in Orthogonal Expansions / O.B. Arushanyan and S.F. Zaletkin // Vestn. Mosk. Univ., Matem. Mekhan. 2009. № 6. P. 18-22 [Moscow Univ. Math. Bulletin. Vol. 64, No 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 shifted Chebyshev series. Approximation properties of a partial sum of a series with approximate coefficients are considered. This approach can be used to construct some numerical-analytic methods for solving ordinary differential equations.
Key words: Markov's quadratures, Fourier-Chebyshev series, Chebyshev shifted series,
orthogonal expansions, interpolation polynomials.