On a class of special solutions of the Painlevé equations

We present a class of special solutions for continuous, discrete and q-discrete Painlevé equations. These solutions are expressed through quadratures or their discrete equivalents. The condition for their existence is a further constraint on the conditions for the existence of other special, linearisable, solutions of Painlevé equations. Thus, these solutions exist for equations that have at least two parameters. In most cases, the special solutions are expressed in terms of functions defined through quadratures.