Linear approximations to continued fractions \(K(z_ n/1)\)
type: Item
instance of: scholarly article
title: Linear approximations to continued fractions \(K(z_ n/1)\)
zbMATH Open document ID: 0662.30002
DOI: 10.1016/0377-0427(87)90159-2
author: Haakon Waadeland
published in: Journal of Computational and Applied Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The author considers continued fractions \(K^{\infty}_ 1(\frac{a_ n+\epsilon_ nz}{1})=F(z)\) where \(K^{\infty}_ 1(\frac{a_ n}{1})\) and its tails \(K^{\infty}_ N(\frac{a_ n}{1})\) are supposed known and converging to finite values. Under proper conditions on the variable quantities involved - the \(a_ n\) lie in a parabolic region - it is proven that F(z) is holomorphic in some disk \(| z| <1/\theta\) and F'(0) is evaluated as an infinite series which \(F(1)-K^{\infty}_ 1(\frac{a_ n}{1})\) is estimated. The proof is based on previous papers of the author. Applications to convergence acceleration and some examples are considered.
Mathematics Subject Classification ID: 30B70
Mathematics Subject Classification ID: 40A15
zbMATH DE Number: 4081892
zbMATH Keywords: convergence acceleration
MaRDI profile type: Publication
full work available at URL: 0377-0427(87)90159-2
OpenAlex ID: W2030558625
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description: scientific article; zbMATH DE number 4081892