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

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Abstract

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

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Acknowledgements

We are grateful to the anonymous referees for valuable suggestions.

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    Michael I. Ganzburg

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  1. Michael I. Ganzburg
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Correspondence to Michael I. Ganzburg.

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Communicated by Vladimir V. Andrievskii.

Dedicated to the memory of Stephan Ruscheweyh.

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Ganzburg, M.I. Asymptotic Behaviour of the Error of Polynomial Approximation of Functions Like \(\vert x\vert ^{{\alpha }+i{\beta }}\). Comput. Methods Funct. Theory 21, 73–94 (2021). https://doi.org/10.1007/s40315-021-00364-x

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