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Approximation properties of the Vallée-Poussin means of partial sums of a mixed series of Legendre polynomials

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Abstract

We estimate the order of weighted approximations of functions and their derivatives by using the means of mixed series of Legendre polynomials. As the main result, we obtain estimates of the order of approximation of a function and its derivatives by the Vallé-Poussin means and their derivatives.

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Authors and Affiliations

  1. Daghestan Scientific Center, Russian Academy of Sciences, Moscow, Russia

    I. I. Sharapudinov

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  1. I. I. Sharapudinov
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Correspondence to I. I. Sharapudinov.

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Original Russian Text © I. I. Sharapudinov, 2008, published in Matematicheskie Zametki, 2008, Vol. 84, No. 3, pp. 452–471.

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Sharapudinov, I.I. Approximation properties of the Vallée-Poussin means of partial sums of a mixed series of Legendre polynomials. Math Notes 84, 417–434 (2008). https://doi.org/10.1134/S0001434608090125

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  • DOI: https://doi.org/10.1134/S0001434608090125

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