Special function solutions for asymmetric discrete Painleve equations

We study the solutions of a family of discrete Painleve equations. The equa tions that we examine are given as a system of two first-order non-autonomo us mappings. The solutions we are interested in are the ones obtained whene ver the Painleve equation can be reduced to a discrete Riccati equation, wh ich can be linearized through a Cole-Hopf transformation. The special solut ions thus obtained involve generalizations or reductions of the hypergeomet ric (and q-hypergeometric) function.