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Abstract <p>The study of special series in Meixner polynomials, that was started in the author’s previous works, is continued. The present paper is devoted to the study of approximation properties of de la Vallée Poussin means for partial sums of the mentioned series. It is shown that for a function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(f\)</EquationSource> <!--RusMath2570068Gadzhimirzaev-m1--> </InlineEquation> the rate of the weighted approximation by de la Vallée Poussin means has the same order as the best weighted approximation of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(f\)</EquationSource> <!--RusMath2570068Gadzhimirzaev-m2--> </InlineEquation>.</p>

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Approximation Properties of de la Vallée Poussin Means for Partial Sums of a Special Series in Meixner Polynomials

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • R. M. Gadzhimirzaev

摘要

Abstract

The study of special series in Meixner polynomials, that was started in the author’s previous works, is continued. The present paper is devoted to the study of approximation properties of de la Vallée Poussin means for partial sums of the mentioned series. It is shown that for a function \(f\) the rate of the weighted approximation by de la Vallée Poussin means has the same order as the best weighted approximation of \(f\) .