Geodesic
Markov's formula for numerical integration and its application in orthogonal expansions
Numerical methods and programming, Tome 2 (2001) no. 1, pp. 131-158.

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Some properties of Chebyshev's series are discussed. These series are used as the basis for numerical analytical methods of solving Cauchy problems for systems of ordinary differential equations. Particular attention has been given to the calculation of Chebyshev's coefficients with the aid of numerical integration. A Markov quadrature formula with a single node and a weight function that corresponds to the orthogonal system of Chebyshev's polynomial of the first kind is derived. Properties of partial sums of Chebyshev's series with coefficients obtained by Markov's formula are described.
Keywords: approximation of functions, orthogonal expansions, Chebyshev's series
Mots-clés : Markov's quadrature formula. 
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     author = {S. K. Tatevyan and N. A. Sorokin and S. F. Zaletkin},
     title = {Markov's formula for numerical integration and its application in orthogonal expansions},
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     pages = {131--158},
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     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2001_2_1_a9/}
}
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S. K. Tatevyan; N. A. Sorokin; S. F. Zaletkin. Markov's formula for numerical integration and its application in orthogonal expansions. Numerical methods and programming, Tome 2 (2001) no. 1, pp. 131-158. http://geodesic.mathdoc.fr/item/VMP_2001_2_1_a9/