# Asymptotic Behaviour of the Error of Polynomial Approximation of Functions Like |x|α+iβ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\vert x\vert ^{{\alpha }+i{\beta }}$$\end{document}

Asymptotic Behaviour of the Error of Polynomial Approximation of Functions Like... New asymptotic relations between the Lp\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L_p$$\end{document}-errors of polynomials approximation of univariate functions by algebraic polynomials and entire functions of exponential type are obtained for p∈(0,∞]\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$p\in (0,{\infty }]$$\end{document}. General asymptotic relations are applied to functions |x|α+iβ,|x|αcos(βlog|x|)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\vert x\vert ^{{\alpha }+i{\beta }},\,\vert x\vert ^{{\alpha }}\cos ({\beta }\log \vert x\vert )$$\end{document}, and |x|αsin(βlog|x|)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\vert x\vert ^{{\alpha }}\sin ({\beta }\log \vert x\vert )$$\end{document}. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

# Asymptotic Behaviour of the Error of Polynomial Approximation of Functions Like |x|α+iβ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\vert x\vert ^{{\alpha }+i{\beta }}$$\end{document}

, Volume 21 (1) – Mar 19, 2021
22 pages

/lp/springer-journals/asymptotic-behaviour-of-the-error-of-polynomial-approximation-of-0HuCbTP0xO
Publisher
Springer Journals
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-021-00364-x
Publisher site
See Article on Publisher Site

### Abstract

New asymptotic relations between the Lp\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L_p$$\end{document}-errors of polynomials approximation of univariate functions by algebraic polynomials and entire functions of exponential type are obtained for p∈(0,∞]\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$p\in (0,{\infty }]$$\end{document}. General asymptotic relations are applied to functions |x|α+iβ,|x|αcos(βlog|x|)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\vert x\vert ^{{\alpha }+i{\beta }},\,\vert x\vert ^{{\alpha }}\cos ({\beta }\log \vert x\vert )$$\end{document}, and |x|αsin(βlog|x|)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\vert x\vert ^{{\alpha }}\sin ({\beta }\log \vert x\vert )$$\end{document}.

### Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 19, 2021