Geodesic
Application of Markov’s quadrature in orthogonal expansions
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2009), pp. 18-22

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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. 
@article{VMUMM_2009_6_a2,
     author = {O. B. Arushanyan and S. F. Zaletkin},
     title = {Application of {Markov{\textquoteright}s} quadrature in orthogonal expansions},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {18--22},
     publisher = {mathdoc},
     number = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2009_6_a2/}
}
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O. B. Arushanyan; S. F. Zaletkin. Application of Markov’s quadrature in orthogonal expansions. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2009), pp. 18-22. http://geodesic.mathdoc.fr/item/VMUMM_2009_6_a2/