On the asymptotic behavior of the best \(L_{\infty}\)-approximation by polynomials
type: Item
instance of: scholarly article
title: On the asymptotic behavior of the best \(L_{\infty}\)-approximation by polynomials
zbMATH Open document ID: 0634.41022
DOI: 10.1007/BF01890576
published in: Constructive Approximation
publication date: 1987-01-01T00:00:00Z
review text: Let \(E_ n(f)\) denote the Chebyshev distance (with respect to the interval [-1,1]) between f and the set of polynomials of degree not exceeding n. This paper proves that for a wide class of entire functions (containing exp(cx), cos(cx) and the Bessel functions \(J_ k(x))\) the quantity \(2^{n-1}n!E_{n-1}(f)/f^{(n)}(0)\) possesses a complete asymptotic expansion (provided n is always even (resp. always odd) if f is even (resp. odd)).
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 4032292
zbMATH Keywords: Chebyshev distance
zbMATH Keywords: entire functions
zbMATH Keywords: Bessel functions
author: H. Fiedler
MaRDI profile type: Publication
cites work: Q5531436
cites work: Approximation of monomials by lower degree polynomials
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description: scientific article; zbMATH DE number 4032292