Stirling-Markov series transformations with increasingly rapid convergence rates
type: Item
instance of: scholarly article
title: Stirling-Markov series transformations with increasingly rapid convergence rates
zbMATH Open document ID: 0588.40002
DOI: 10.1016/0022-247X(86)90268-4
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: A series transformation based on an inverse factorial integral representation is given. The procedure yields a hierarchy of transformations. Transformations of higher rank convergence faster and apply to larger classes of series. The procedure can be considered as a specific formulation of Markov's transformation of series, and the rank 1 transformation includes typical examples of Markov's transformation. It is shown that the rank K transformation of any rational series converges exponentially fast with ratio \(\rho_ K=K^ K/(K+1)^{K+1}\). Since \(\rho_ K\) tends to zero as K increases, it follows that every rational series can be transformed to a series converging at an arbitrarily fast exponential rate. The generalization of the procedure to other integral transforms is discussed.
Mathematics Subject Classification ID: 40A05
zbMATH DE Number: 3944448
zbMATH Keywords: Markov's transformation of series
zbMATH Keywords: integral transforms
author: Davis K. Cope
MaRDI profile type: Publication
cites work: Q3231324
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full work available at URL: 0022-247x(86)90268-4
OpenAlex ID: W2041041592
description: scientific article; zbMATH DE number 3944448