New steps in walks with small steps in the quarter plane

Irina Kurkova, Kilian Raschel

Published 2013-07-02, updated 2014-09-20Version 2

In this article we obtain new expressions for the generating functions counting (non-singular) walks with small steps in the quarter plane. Those are given in terms of infinite series, while in the literature, the standard expressions use solutions to boundary value problems. We illustrate our results with three examples (an algebraic case, a transcendental D-finite case, and an infinite group model).