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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.
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Bostan, A., Kauers, M.: The complete generating function for Gessel walks is algebraic. Proc. Amer. Math. Soc
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Bousquet-Mélou, M., Mishna, M.: Walks with small steps in the quarter plane. Contemp. Math
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Fayolle, G., Raschel, K.: On the holonomy or algebraicity of generating functions counting lattice walks in the quarter-plane. Markov Process. Related Fields
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Flajolet, P., Sedgewick, R.: Analytic combinatorics. Cambridge University Press, Cambridge (2009) Zbl 1165.05001 MR 2483235
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Kurkova, I., Raschel, K.: Explicit expression for the generating function counting Gessel’s walks. Adv. in Appl. Math., to appear
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Computing walks in a quadrant: a computer algebra approach via creative telescoping
Bostan, A., Chyzak, F., Kauers, M., Pech, L., van Hoeij, M.: · 2011
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