An extension of the `1/9'-problem
type: Item
instance of: scholarly article
title: An extension of the `1/9'-problem
zbMATH Open document ID: 1204.30027
author: Thomas Schmelzer
author: Herbert Stahl
published in: Journal of Computational and Applied Mathematics
publication date: 2009-11-04T00:00:00Z
review text: Let \(u_0\) and \(u_1\) be rational functions. The authors considers rational approximation of the function \[ f(z)=u_0(z)+u_1(z)e^z \] on the negative half-axis. The main result is that \[ \lim_{n\to\infty}\|f-r^*_{n,n+k}\|^{1/n}=\frac{1}{9.28902549...}=H, \] where \(H\) is the Halpern constant from the solution of the `\(1/9\)'-problem by \textit{A. A. Gonchar} and \textit{E. A. Rakhmanov} [Math. USSR, Sb. 62, No. 2, 305--348 (1989); translation from Mat. Sb., Nov. Ser. 134 (176), No. 3(11), 306--352 (1987 Zbl 0663.30039)].
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 41A20
zbMATH DE Number: 5624895
zbMATH Keywords: rational approximation
zbMATH Keywords: complex approximation
zbMATH Keywords: `\(1/9\)'-problem
reviewed by: Vladimir V. Peller
MaRDI profile type: Publication
full work available at URL: j.cam.2009.02.084
OpenAlex ID: W1966656858
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DOI: 10.1016/J.CAM.2009.02.084
description: scientific article; zbMATH DE number 5624895