  The aim of this article is to introduce a unified method to obtain explicit
integral representations of the trivariate generating function counting the
walks with small steps which are confined to a quarter plane. For many models,
this yields for the first time an explicit expression of the counting
generating function. Moreover, the nature of the integrand of the integral
formulations is shown to be directly dependent on the finiteness of a naturally
attached group of birational transformations as well as on the sign of the
covariance of the walk
