A note on Hurwitzian numbers
type: Item
instance of: scholarly article
title: A note on Hurwitzian numbers
zbMATH Open document ID: 1032.11003
author: Hartono
author: Cor Kraaikamp
published in: Tokyo Journal of Mathematics
publication date: 2004-03-13T00:00:00Z
review text: The number \(x\) is called Hurwitzian if the regular continued fraction expansion of \(x\) can be written as \(x=[a_0;a_1,\dots,a_n,\overline{a_{n+1}(k), \dots,a_{n+p}(k)}]_{k=0}^\infty\), where \(a_{n+1}(k),\dots, a_{n+p}(k)\) are polynomials with rational coefficients which take positive integral values for \(k=0,1,2,\dots\), and at least one of them is not constant. In this note Hurwitzian numbers are defined for three other continued fraction expansions, namely, the nearest integer continued fraction expansion, the backward continued fraction expansion, and \textit{H. Nakada}'s \(\alpha\)-continued fraction expansions [Tokyo J. Math. 4, 399-426 (1981; Zbl 0479.10029)]. It is shown that their set of Hurwitzian numbers coincides with the classical set of Hurwitzian numbers.
reviewed by: Takao Komatsu
Mathematics Subject Classification ID: 11A55
Mathematics Subject Classification ID: 11Y65
Mathematics Subject Classification ID: 11B39
zbMATH DE Number: 1930970
zbMATH Keywords: Hurwitzian numbers
zbMATH Keywords: continued fractions
zbMATH Keywords: singularization
zbMATH Keywords: nearest integer continued fraction
zbMATH Keywords: backward continued fraction
zbMATH Keywords: \(\alpha\)-expansions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1244208859
OpenAlex ID: W2032498091
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DOI: 10.3836/TJM/1244208859
description: scientific article; zbMATH DE number 1930970