Bäcklund transformations for discrete Painlevé equations: Discrete PII-PV

Abstract

Transformation properties of discrete Painlevé equations are investigated by using an algorithmic method. This method yields explicit transformations which relates the solutions of discrete Painlevé equations, discrete PII-PV, with different values of parameters. The particular solutions which are expressible in terms of the discrete analogue of the classical special functions of discrete Painlevé equations can also be obtained from these transformations. © 2005 Elsevier Ltd. All rights reserved.