Special function solutions of the discrete Painlevé equations
type: Item
instance of: scholarly article
title: Special function solutions of the discrete Painlevé equations
zbMATH Open document ID: 0994.33500
DOI: 10.1016/S0898-1221(01)00180-8
author: T. Tamizhmani
author: K. M. Tamizhmani
author: A. Ramani
author: B. Grammaticos
publication date: 2002-06-13T00:00:00Z
review text: A review of special solutions of discrete (difference) and \(q\)-discrete Painlevé equations in terms of discrete special functions is given. It is shown that these solutions exist if the parameters of the Painlevé equation satisfy a particular constraint. The discrete special functions belong to the hypergeometric family, although in some cases they seem to go beyond the known discrete and \(q\)-discrete hypergeometric functions.
Mathematics Subject Classification ID: 33E17
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 65Q05
zbMATH DE Number: 1755277
zbMATH Keywords: Painlevé equation
zbMATH Keywords: discrete special function
zbMATH Keywords: affine Weyl groups
reviewed by: J. Saurer
MaRDI profile type: Publication
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full work available at URL: s0898-1221(01)00180-8
OpenAlex ID: W2018357620
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1755277