On difference Riccati equations and second order linear difference equations
type: Item
instance of: scholarly article
title: On difference Riccati equations and second order linear difference equations
zbMATH Open document ID: 1215.39021
author: Katsuya Ishizaki
published in: Aequationes Mathematicae
publication date: 2011-03-31T00:00:00Z
review text: The author considers second order linear difference equations and the associated difference Riccati equation in the complex domain, namely \[ \Delta^2y(z) + A(z)y(z)=0 \] and \[ \Delta f(z) = {{f(z)^2+A(z)}\over{f(z)-1}} \] where he defines \[ \Delta\varphi(z)=\varphi(z+1)-\varphi(z) \] with the standard iteration of the difference operator; \(A(z)\) is a meromorphic function. He considers: meromorphic solutions of the difference Riccati equation and the discrete analogue of the cross ratio; linear second order difference equations in the complex domain and growth problems for the solutions.
reviewed by: Vladimir Răsvan
Mathematics Subject Classification ID: 39A45
Mathematics Subject Classification ID: 39A13
Mathematics Subject Classification ID: 39A06
Mathematics Subject Classification ID: 30D15
zbMATH DE Number: 5872783
zbMATH Keywords: difference Riccati equations
zbMATH Keywords: linear difference equations
zbMATH Keywords: meromorphic functions
zbMATH Keywords: meromorphic solutions
MaRDI profile type: Publication
full work available at URL: s00010-010-0060-z
OpenAlex ID: W2041467983
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DOI: 10.1007/S00010-010-0060-Z
description: scientific article; zbMATH DE number 5872783