Zur Konvergenzbeschleunigung von Reihen mit logarithmischer Konvergenz. (Acceleration of the convergence of logarithmically convergent series)
type: Item
instance of: scholarly article
title: Zur Konvergenzbeschleunigung von Reihen mit logarithmischer Konvergenz. (Acceleration of the convergence of logarithmically convergent series)
zbMATH Open document ID: 0718.65008
DOI: 10.4171/ZAA/409
author: Yanyan Li
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1990-01-01T00:00:00Z
review text: This paper discusses series \(\sum a_ n\) when \(a_ n=(n^{- \alpha}\ln^{\beta}n)(\gamma_ 0+O(1/n))\) and when \(a_ n=(n^{- 1}\ln^{\beta}n)(\gamma_ 0+\gamma_ 1n^{-1}+O(n^{-2})),\) where Re \(\alpha\) \(>1\), \(\beta\neq 0\) in the first case, Re \(\beta\) \(>1\) in the second case. The author obtains asymptotic expressions for the remainders and then applies a convergence accelerating process. This procedure can be more effective than, for example, the use of the Euler-Maclaurin formula.
Mathematics Subject Classification ID: 65B10
Mathematics Subject Classification ID: 65B05
Mathematics Subject Classification ID: 40A25
zbMATH DE Number: 4184910
zbMATH Keywords: logarithmically convergent series
zbMATH Keywords: asymptotic expressions
zbMATH Keywords: convergence accelerating process
zbMATH Keywords: Euler-Maclaurin formula
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/zaa/409
OpenAlex ID: W2380305696
description: scientific article