The asymptotic accuracy of rational best approximations to \(e^ z\) on a disk
type: Item
instance of: scholarly article
title: The asymptotic accuracy of rational best approximations to \(e^ z\) on a disk
zbMATH Open document ID: 0545.41019
DOI: 10.1016/0021-9045(84)90013-3
published in: Journal of Approximation Theory
publication date: 1984-01-01T00:00:00Z
review text: D. Braess has recently proved the Meinardus conjecture regarding degree of approximation of \(e^ z\) on the unit interval by rational functions of type (m,n). The present paper uses Braess's method to prove an analogous result for approximation of \(e^ z\) on the unit disk: as \(m+n\) approaches \(\infty\), the best approximation error has the behavior \(E_{mn}\sim m!n!/(m+n)!(m+n+1)!.\)
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 30E10
zbMATH DE Number: 3867912
zbMATH Keywords: Meinardus conjecture
zbMATH Keywords: degree of approximation
zbMATH Keywords: Braess's method
author: Lloyd N. Trefethen
MaRDI profile type: Publication
full work available at URL: 0021-9045(84)90013-3
OpenAlex ID: W2066752236
cites work: On the conjecture of Meinardus on rational approximation of \(e^ x\), II
cites work: On the degree of best rational approximation to the exponential function
cites work: Near-circularity of the error curve in complex Chebyshev approximation
cites work: Rational Chebyshev approximation on the unit disk
description: scientific article; zbMATH DE number 3867912