@article{BoKa10,
author = {Bostan, Alin and Kauers, Manuel},
title = {The complete generating function for {G}essel walks is algebraic},
note = {With an Appendix by Mark van Hoeij},
journal = {Proceedings of the American Mathematical Society},
year = {2010},
volume = {138},
number = {9},
month = {September},
pages = {3063--3078},
arxiv = {abs/0909.1965},
abstract = {Gessel walks are lattice walks in the quarter plane $\set N^2$ which start at the origin~$(0,0)\in\set N^2$ and consist only of steps chosen from the set $\{\leftarrow,\penalty0\swarrow,\penalty0\nearrow,\penalty0\rightarrow\}$. We prove that if $g(n;i,j)$ denotes the number of Gessel walks of length~$n$ which end at the point~$(i,j)\in\set N^2$, then the trivariate generating series $\displaystyle\smash{ G(t;x,y)=\sum_{n,i,j\geq 0} g(n;i,j)x^i y^j t^n }$ is an algebraic function.},
}