Analytic solutions of q-P(A1) near its critical points

For transcendental functions that solve non-linear q-difference equations, the best descriptions available are the ones obtained by expansion near critical points at the origin and infinity. We describe such solutions of a q-discrete Painleve equation, with seven parameters whose initial value space is a rational surface of type A(1)((1)). The resultant expansions are shown to approach series expansions of the classical sixth Painleve equation in the continuum limit.