Dynamics of a Ramanujan-type continued fraction with cyclic coefficients
type: Item
instance of: scholarly article
title: Dynamics of a Ramanujan-type continued fraction with cyclic coefficients
zbMATH Open document ID: 1171.11043
author: D. Russell Luke
author: Jonathan M. Borwein
published in: The Ramanujan Journal
publication date: 2008-11-18T00:00:00Z
review text: Let \(a\equiv(a_n)^\infty_{n=1}\) be a sequence of nonzero complex-valued scalars bounded above and below, and let \(b>1\). By \(S_1(a,b)\) is denoted the continued fraction \[ S_1(a,b):=\frac{1^b a_1^2}{1+\frac{2^ba_2^2}{1+\frac {3^ba^2_3}{1+\ddots}}}\tag{1} \] This is a generalization of a continued fraction studied by Ramanujan. In the present study the authors establish sufficient conditions for the divergence of \(S_1(a,b)\) with cyclic sequences of complex parameters \(a=(a_n)^\infty_{n=1}\) of period \(c<\infty\).
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 11J70
zbMATH DE Number: 5367288
zbMATH Keywords: continued fractions
zbMATH Keywords: Ramanujan AGM relation
zbMATH Keywords: difference equations
zbMATH Keywords: matrix analysis
Wikidata QID: Q56935576
MaRDI profile type: Publication
full work available at URL: s11139-007-9096-7
OpenAlex ID: W2118135367
cites work: Q3331506
cites work: On the Ramanujan AGM Fraction, II: The Complex-Parameter Case
cites work: Dynamics of a continued fraction of Ramanujan with random coefficients
cites work: On the Ramanujan AGM Fraction, I: The Real-Parameter Case
cites work: On the dynamics of certain recurrence relations
cites work: Continued fractions with applications
cites work: Invertibly convergent infinite products of matrices
DOI: 10.1007/S11139-007-9096-7
description: scientific article; zbMATH DE number 5367288