Asymptotic two-point approximations by rational functions
type: Item
instance of: scholarly article
title: Asymptotic two-point approximations by rational functions
zbMATH Open document ID: 0889.41026
DOI: 10.1007/BF03322522
author: Lothar Berg
published in: Results in Mathematics
publication date: 1998-06-29T00:00:00Z
review text: For every function \(f(s)\) continuous in \(0\leq s\leq \infty\) possessing asymptotic power expansions both for \(s\to +0\) and for \(s\to+\infty\), the author in the paper under review proves the existence of a sequence of rational functions \(r_n(s)\) with positive denominators satisfying the property \(r_n(s)- f(s)= \begin{cases} O(s^n) \quad & \text{for } s\to +0 \\ O(s^{-n}) \quad & \text{for } s\to+ \infty \end{cases}\) for \(n\in \mathbb{N}_0\), converging uniformly in \([0, \infty]\) to \(f(s) \). Such functions can be considered as generalized two-points Padé approximants. Some illustrative examples are given. \{Reviewer's remark: To the list of references it could be convenient to add some closely related works, among others, e.g. \textit{A. Draux} [Polynômes orthogonaux formels -- applications (1983; Zbl 0504.42001)] and \textit{P. Gonzáles-Vera}, \textit{O. Njåstad}, [J. Comput. Appl. Math. 32, No. 1/2, 97-105 (1990; Zbl 0721.30026)]\}.
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 41A21
Mathematics Subject Classification ID: 33B20
zbMATH DE Number: 1112234
zbMATH Keywords: two-points Padé approximants
reviewed by: Nácere Hayek
MaRDI profile type: Publication
cites work: Zur Operatorenrechnung für Funktionen einer diskreten Veränderlichen
cites work: Laurent series and their Padé approximations
cites work: Q4765553
cites work: Q4137395
cites work: Approximation von Funktionen und ihre numerische Behandlung
cites work: Q4059363
cites work: Q3786878
cites work: Vorlesungen über asymptotische Reihen
cites work: Q4880419
cites work: Two-point Padé approximants for formal Stieltjes series
cites work: Q5343650
cites work: Q4028736
cites work: Q5509892
cites work: Q5284551
full work available at URL: https://doi.org/10.1007/bf03322522
OpenAlex ID: W2154461071
Recommended article: Q5752983
Recommended article: On approximation by rational functions
Recommended article: Approximation by Rational Functions
Recommended article: Approximation by rational functions
Recommended article: On rational approximations of functions
Recommended article: Q3762778
Recommended article: Approximation by rational functions along a half-axis
Recommended article: Q5512300
Recommended article: Rational approximation near zero sets of functions
description: scientific article; zbMATH DE number 1112234