An S-fraction and \(\ell n^ 2(1+x)\)
type: Item
instance of: scholarly article
title: An S-fraction and \(\ell n^ 2(1+x)\)
zbMATH Open document ID: 0675.33002
DOI: 10.1016/0377-0427(89)90081-2
author: L. R. Shenton
author: Adrienne W. Kemp
published in: Journal of Computational and Applied Mathematics
publication date: 1989-01-01T00:00:00Z
review text: \(\ell n^ 2(1+x)=\frac{1|}{| y}+\frac{-p_ 1q_ 1|}{| 1}+\frac{-p_ 2q_ 2|}{| y}+...\), where \( y=(1-x)/x^ 2,\quad p_{2s}+q_{2s-1}=0\), \(q_{2s+1}+q_{2s}=1\) \((s=1,2,...)\). This implies \(\ell n^ 2(1+x)<x^ 2/(1+x)\) and more complicated upper and lower bounds valid for \(x>-1\).
Mathematics Subject Classification ID: 33B10
Mathematics Subject Classification ID: 65D99
zbMATH DE Number: 4105349
zbMATH Keywords: continued fractions
zbMATH Keywords: logarithm
zbMATH Keywords: S-fraction
zbMATH Keywords: inequalities
reviewed by: Erwin O. Kreyszig
MaRDI profile type: Publication
full work available at URL: 0377-0427(89)90081-2
OpenAlex ID: W2073550039
cites work: Q5621398
cites work: Some remarks on uniform asymptotic expansions for Bessel functions
cites work: Analytic Inequalities
cites work: Q5559386
cites work: A Determinantal Expansion for a Class of Definite Integral
cites work: Q5508372
description: scientific article; zbMATH DE number 4105349