Remainder Padé approximants for the exponential function
type: Item
instance of: scholarly article
title: Remainder Padé approximants for the exponential function
zbMATH Open document ID: 1102.41016
author: M. Prevost
author: T. Rivoal
published in: Constructive Approximation
publication date: 2006-12-20T00:00:00Z
review text: The authors study a new method for obtaining the complete Padé table the exponential function. The aim of this paper is to show that this table of Padé approximants for the function \(\exp(z)\) at \(z=0\) essentially coincide with the approximation obtained by the method described in [\textit{S. Fischler} and \textit{T. Rivoal}, Approximants de Padé et séries hypergéométriques équilibrées, J. Math. Pures. Appl. 82, 1369--1394 (2003; Zbl 1064.11053)]. The authors call it the remainder Padé approximants for \(\exp(z)\). The results deal more generally with simultaneous type II Padé approximations of a family of exponential functions. The proof uses certain discrete multiple orthogonal polynomials recently introduced by Arvesú, Coussement, and Van Assche which generalize the classical Charlier orthogonal polynomials.
reviewed by: Antonio López-Carmona
Mathematics Subject Classification ID: 41A21
Mathematics Subject Classification ID: 41A28
zbMATH DE Number: 5080852
zbMATH Keywords: Padé approximants
zbMATH Keywords: exponential function
MaRDI profile type: Publication
full work available at URL: s00365-006-0635-6
OpenAlex ID: W1963620544
DOI: 10.1007/S00365-006-0635-6
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description: scientific article; zbMATH DE number 5080852