Another observation on the distribution of values of continued fractions \(K(a_n/1)\)
type: Item
instance of: scholarly article
title: Another observation on the distribution of values of continued fractions \(K(a_n/1)\)
zbMATH Open document ID: 1041.30002
author: Walter M. Reid
published in: Rocky Mountain Journal of Mathematics
publication date: 2004-03-17T00:00:00Z
review text: It is known that the continued fractions \(K(a_n/1)\) takes limit values in the value region \(V=[-\rho,\rho]\) if the \(a_n\) are taken in the Worpitzky interval \(W=[-\rho(1-\rho),\rho(1-\rho)]\). \textit{L. Jacobsen}, \textit{W. J. Thron} and \textit{H. Waadeland} in [Numer. Math. 55, 711--733 (1989; Zbl 0704.40001)] and \textit{H. Waadeland} in [Probability distribution of continued fraction values. An invitation and an example, Commun. Anal. Theory Cont. Fractions 1, 40--45 (1992)] consider uniform distributions of the \(a_n\) in \(W\) and find the distribution of the limit values in \(V\). In this paper, the result is extended for distributions of \(a_n\) that are of the form \(b_0+b_1 | x| \). It turns out that also the limit values are distributed in a similar way with a slope that is greater than \(| b_1| \).
Mathematics Subject Classification ID: 30B70
Mathematics Subject Classification ID: 65D15
zbMATH DE Number: 2060101
zbMATH Keywords: continued fraction
zbMATH Keywords: probability distribution
reviewed by: Adhemar Bultheel
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181069975
OpenAlex ID: W2046587256
cites work: Some observations on the distribution of values of continued fractions
DOI: 10.1216/RMJM/1181069975
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description: scientific article; zbMATH DE number 2060101