Special solutions of discrete Painleve equations through direct linearisation

We study the special solutions of discrete Painleve equations which can be expressed through the discrete equivalent of quadratures. The discrete Painleve equations examined are the ones which appear in the classification based on affine Weyl groups and which can be written as a system of two first-order mappings. The solutions obtained are the discrete equivalents of solutions which have been shown to exist for the continuous Painleve equations. (C) 2002 Published by Elsevier Science B.V.