Continued fractions and series
type: Item
instance of: scholarly article
title: Continued fractions and series
zbMATH Open document ID: 0832.11002
author: Laura E. Clemens
author: Kathy D. Merrill
author: David W. Roeder
published in: Journal of Number Theory
publication date: 1996-03-07T00:00:00Z
review text: Generally it is difficult to compute the simple continued fraction expansion for a real irrational number which is defined by some other expression. But there are some known results on infinite series of rational numbers of rather peculiar type whose sequence of partial denominators in their continued fraction shows a definite pattern, being periodic or palindromic in some portions. See \textit{A. J. van der Poorten} and \textit{J. Shallit} [J. Number Theory 40, 237-250 (1992; Zbl 0753.11005)]\ for one of the recent papers in this field. In the paper under review the authors tie together previous results and provide many more interesting examples. They also show that Newton's method, with suitable initial values, produces convergents for the simple continued fraction expansion of quadratic irrationals.
reviewed by: Günter Köhler
Mathematics Subject Classification ID: 11A55
Mathematics Subject Classification ID: 11J70
zbMATH DE Number: 809127
zbMATH Keywords: simple continued fraction expansion
zbMATH Keywords: infinite series of rational numbers
zbMATH Keywords: Newton's method
zbMATH Keywords: convergents
MaRDI profile type: Publication
full work available at URL: jnth.1995.1121
OpenAlex ID: W1996134041
DOI: 10.1006/JNTH.1995.1121
description: scientific article; zbMATH DE number 809127