Zeros of Padé error functions for functions with smooth Maclaurin coefficients
type: Item
instance of: scholarly article
title: Zeros of Padé error functions for functions with smooth Maclaurin coefficients
zbMATH Open document ID: 0836.41015
author: R. K. Kovacheva
published in: Journal of Approximation Theory
publication date: 1996-03-12T00:00:00Z
full work available at URL: http://hdl.handle.net/10525/3312
review text: Let \(\pi_{n,m}\) be the \((n, m)\) Padé approximant for the function \(f\) defined by its Maclaurin series \(f= \sum_{k=0}^\infty a_k z^k\). This series is assumed to satisfy the Lubinsky smoothness condition, i.e., \(\eta_n= a_{n+1} a_{n-1}/ a^2_n\to \eta\neq \infty\) as \(n\to \infty\). This paper deals with the asymptotics of (a properly normalized form of) the error function \(e_{n,m}= f- \pi_{n,m}\) as \(n\to \infty\) with \(m\) fixed. Several results are given when \(\eta_n\) converges to \(\eta\), \(|\eta|\leq 1\) in a sufficiently smooth way. As a result, the asymptotic distribution of the zeros of the error are obtained.
reviewed by: Adhemar Bultheel
Mathematics Subject Classification ID: 41A21
zbMATH DE Number: 846926
zbMATH Keywords: Padé approximation
zbMATH Keywords: distribution of zeros
zbMATH Keywords: Lubinsky smoothness condition
MaRDI profile type: Publication
OpenAlex ID: W1971834641
DOI: 10.1006/JATH.1995.1127
description: scientific article; zbMATH DE number 846926