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arXiv · 2103.09376

Asymptotic Behaviour of the Error of Polynomial Approximation of Functions Like $\vert x\vert^{\alpha+i\beta}$

Michael I. Ganzburg
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Abstract

New asymptotic relations between the $L_p$-errors of best approximation of univariate functions by algebraic polynomials and entire functions of exponential type are obtained for $p\in (0,\iy]$. General asymptotic relations are applied to functions $\vert x\vert^{\al+i\be},\,\vert x\vert^{\al}\cos(\be\log\vert x\vert)$, and $\vert x\vert^{\al}\sin(\be\log\vert x\vert)$.

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Michael I. Ganzburg. 2021-03-17. Asymptotic Behaviour of the Error of Polynomial Approximation of Functions Like $\vert x\vert^{\alpha+i\beta}$. https://arxiv.org/abs/2103.09376

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