The convergence of diagonal Padé approximants and the Padé conjecture
type: Item
instance of: scholarly article
title: The convergence of diagonal Padé approximants and the Padé conjecture
zbMATH Open document ID: 0888.41008
DOI: 10.1016/S0377-0427(97)00162-3
published in: Journal of Computational and Applied Mathematics
publication date: 1998-06-07T00:00:00Z
review text: The Baker-Gammel-Wills conjecture says that if the function \(f\) is meromorphic in the unit disc \(D\), then there exists an infinite subsequence of diagonal Padé approximants \([n/n]\) converging to \(f\) locally uniformly in \(D\{\)poles of \(f\)\}. The author formulates some special and weaker versions of the above conjecture and analyses the role played by ``spurious poles'' of the approximants, i.e. poles of \([n/n]\) that do not correspond to poles of \(f\). Two types of convergence is considered: locally uniform convergence and convergence in capacity.
Mathematics Subject Classification ID: 41A21
Mathematics Subject Classification ID: 30E10
zbMATH DE Number: 1115938
zbMATH Keywords: convergence of Padé approximants
zbMATH Keywords: Padé conjecture
Wikidata QID: Q123142509
author: Herbert Stahl
reviewed by: Jacek Gilewicz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1115938