I. Adan, J. Van-leeuwaarden, and K. Raschel, The Compensation Approach for Walks With Small Steps in the Quarter Plane, Combinatorics, Probability and Computing, vol.4, issue.02, 2011.
DOI : 10.1016/j.aam.2010.11.004
URL : https://hal.archives-ouvertes.fr/hal-00551472

A. Bostan, F. Chyzak, M. Kauers, L. Pech, and M. Van-hoeij, Computing walks in a quadrant: a computer algebra approach via creative telescoping, 2011.

A. Bostan and M. Kauers, Automatic classification of restricted lattice walks, Proceedings of the 21st International Conference on Formal Power Series and Algebraic Combinatorics, pp.203-217, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00780428

A. Bostan and M. Kauers, The complete generating function for Gessel walks is algebraic, Proc. Amer, pp.3063-3078, 2010.
DOI : 10.1090/S0002-9939-2010-10398-2
URL : https://hal.archives-ouvertes.fr/hal-00780429

M. Bousquet-mélou, Walks in the quarter plane: Kreweras??? algebraic model, The Annals of Applied Probability, vol.15, issue.2, pp.1451-1491, 2005.
DOI : 10.1214/105051605000000052

M. Bousquet-mélou and M. Mishna, Walks with small steps in the quarter plane, Contemp. Math, vol.520, pp.1-40, 2010.
DOI : 10.1090/conm/520/10252

M. Bousquet-mélou and M. Petkovsek, Walks confined in a quadrant are not always D-finite, Theoretical Computer Science, vol.307, issue.2, pp.257-276, 2003.
DOI : 10.1016/S0304-3975(03)00219-6

W. Chen, E. Deng, R. Du, R. Stanley, and C. Yan, Crossings and nestings of matchings and partitions, Transactions of the American Mathematical Society, vol.359, issue.04, pp.1555-1575, 2007.
DOI : 10.1090/S0002-9947-06-04210-3

G. Fayolle, R. Iasnogorodski, and V. Malyshev, Random walks in the quarter-plane, 1999.
URL : https://hal.archives-ouvertes.fr/inria-00572276

G. Fayolle and K. Raschel, On the holonomy or algebraicity of generating functions counting lattice walks in the quarter-plane. Markov Process, pp.485-496, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00559676

P. Flajolet and R. Sedgewick, Analytic combinatorics, 2009.
DOI : 10.1017/CBO9780511801655
URL : https://hal.archives-ouvertes.fr/inria-00072739

L. Flatto, Two Parallel Queues Created by Arrivals with Two Demands II, SIAM Journal on Applied Mathematics, vol.45, issue.5, pp.861-878, 1985.
DOI : 10.1137/0145052

L. Flatto and S. Hahn, Two Parallel Queues Created by Arrivals with Two Demands I, SIAM Journal on Applied Mathematics, vol.44, issue.5, pp.1041-1053, 1984.
DOI : 10.1137/0144074

I. Gessel, A probabilistic method for lattice path enumeration, Journal of Statistical Planning and Inference, vol.14, issue.1, pp.49-58, 1986.
DOI : 10.1016/0378-3758(86)90009-1

G. Jones and D. Singerman, Complex Functions, 1987.
DOI : 10.1017/CBO9781139171915

M. Kauers, C. Koutschan, and D. Zeilberger, Proof of Ira Gessel's lattice path conjecture, Proc. Natl. Acad. Sci. USA, pp.11502-11505, 2009.
DOI : 10.1073/pnas.0901678106

I. Kurkova, K. Raschel, I. Kurkova, and K. Raschel, Explicit expression for the generating function counting Gessel's walks, Adv. in Appl. Math

G. Litvinchuk, Solvability theory of boundary value problems and singular integral equations with shift, 2000.
DOI : 10.1007/978-94-011-4363-9

V. Malyshev, Positive random walks and Galois theory, Nauk, vol.26, pp.227-228, 1971.

M. Mishna and A. Rechnitzer, Two non-holonomic lattice walks in the quarter plane, Theoretical Computer Science, vol.410, issue.38-40, pp.3616-3630, 2009.
DOI : 10.1016/j.tcs.2009.04.008

K. Raschel, Paths confined to a quadrant, 2010.
URL : https://hal.archives-ouvertes.fr/tel-00539964

K. Raschel, Green functions for killed random walks in the Weyl chamber of Sp(4), Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.47, issue.4
DOI : 10.1214/10-AIHP405
URL : https://hal.archives-ouvertes.fr/hal-00635414

G. Watson and E. Whittaker, A course of modern analysis, 1962.