On the recursive sequence \(x_{n+1}=\frac{A}{\prod^ k_{i=0}x_{n-i}}+\frac{1}{\prod^{2(k+1)}_{j=k+2}x_{n-j}}\).
type: Item
instance of: scholarly article
title: On the recursive sequence \(x_{n+1}=\frac{A}{\prod^ k_{i=0}x_{n-i}}+\frac{1}{\prod^{2(k+1)}_{j=k+2}x_{n-j}}\).
zbMATH Open document ID: 1054.39008
author: Stevo Stević
published in: Taiwanese Journal of Mathematics
publication date: 2004-06-22T00:00:00Z
review text: For the difference equation in the title with \(A>1\) it is shown that every positive solution converges to a \((k+2)\)-periodic solution. By means of the substitution \(y_n= x_nx_{n-1}\cdots x_{n-k-1}\) this implies that every positive solution of \(y_{n+1}= A+ y_n/y_{n-k-1}\) converges to \(A+1\).
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A20
zbMATH DE Number: 2076839
zbMATH Keywords: difference equation
zbMATH Keywords: positive solution
zbMATH Keywords: periodic solution
reviewed by: Lothar Berg
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500575062
OpenAlex ID: W4236960087
DOI: 10.11650/TWJM/1500575062
description: scientific article; zbMATH DE number 2076839