S. A. Abramov, Indefinite sums of rational functions, Proceedings of the 1995 international symposium on Symbolic and algebraic computation - ISSAC '95, pp.303-308, 1995.

A. Bostan, M. Bousquet-mélou, M. Kauers, and S. Melczer, On 3-Dimensional Lattice Walks Confined to the Positive Octant, Annals of Combinatorics, vol.20, issue.4, pp.661-704, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01063886

O. Bernardi, M. Bousquet-mélou, and K. Raschel, Counting quadrant walks via Tutte's invariant method, An extended abstract to appear in Proceedings of FPSAC, Discrete Math. Theor. Comput. Sci. Proc, 2015.

K. Raschel, Counting walks in a quadrant: a unified approach via boundary value problems, Journal of the European Mathematical Society, pp.749-777, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00461853

M. Bousquet, -. Mélou, and M. Mishna, Walks with small steps in the quarter plane, Algorithmic probability and combinatorics, Contemp. Math, vol.520, pp.1-39, 2010.

A. Bostan, K. Raschel, and B. Salvy, Non-D-finite excursions in the quarter plane, Journal of Combinatorial Theory, Series A, vol.121, pp.45-63, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00697386

A. Bostan and M. Kauers, The complete generating function for Gessel walks is algebraic, Proceedings of the American Mathematical Society, vol.138, issue.09, pp.3063-3063, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00780429

S. Chen and M. F. Singer, Residues and telescopers for bivariate rational functions, Advances in Applied Mathematics, vol.49, issue.2, pp.111-133, 2012.

T. Dreyfus, C. Hardouin, J. Roques, and M. F. Singer, On the nature of the generating series of walks in the quarter plane, Inventiones mathematicae, vol.213, issue.1, pp.139-203, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01897314

T. Dreyfus, C. Hardouin, J. Roques, and M. F. Singer, On the nature of the generating series of walks in the quarter plane, Inventiones mathematicae, vol.213, issue.1, pp.139-203, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01897314

*. , We recall that the polar divisor of b 2 is the formal Z-linear combination of points of Et given by P ?E t n P P

D. K. Du, Q. Hou, and R. Wang, Infinite Orders and Non-D-finite Property of 3-Dimensional Lattice Walks, The Electronic Journal of Combinatorics, vol.23, issue.3, 2016.

J. Duistermaat, Elliptic Surfaces, Springer Monographs in Mathematics, vol.304, pp.179-327, 2010.

G. Fayolle, R. Iasnogorodski, and V. A. Malyshev, Random Walks in the Quarter-Plane, vol.40, 1999.
URL : https://hal.archives-ouvertes.fr/inria-00572276

G. Fayolle, R. Iasnogorodski, and V. Malyshev, Random walks in the quarter-plane: Algebraic methods, boundary value problems and applications, Computers & Mathematics with Applications, vol.38, issue.11-12, p.292, 1999.
URL : https://hal.archives-ouvertes.fr/hal-01651919

G. Fayolle, R. Iasnogorodski, and V. Malyshev, Criterion for the Finiteness of the Group in the Genus 0 Case, Probability Theory and Stochastic Modelling, vol.17, pp.171-182, 2017.

W. Fulton, An introduction to algebraic geometry, Notes written with the collaboration of Richard Weiss, 1989.

C. Hardouin, Hypertranscendance des systèmes aux différences diagonaux, Compositio Mathematica, vol.144, issue.3, pp.565-581, 2008.

C. Hardouin and M. F. Singer, Differential Galois theory of linear difference equations, Mathematische Annalen, vol.342, issue.2, pp.333-377, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01927297

K. Ishizaki, Hypertranscendency of meromorphic solutions of a linear functional equations, aequationes mathematicae, vol.56, issue.3, pp.271-283, 1998.

I. Kurkova and K. Raschel, On the functions counting walks with small steps in the quarter plane, Publications mathématiques de l'IHÉS, vol.116, issue.1, pp.69-114, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00628424

M. Mishna, Classifying lattice walks restricted to the quarter plane, Journal of Combinatorial Theory, Series A, vol.116, issue.2, pp.460-477, 2009.

S. Melczer and M. Mishna, Singularity Analysis Via the Iterated Kernel Method, Combinatorics, Probability and Computing, vol.23, issue.5, pp.861-888, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01229731

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.

K. Raschel, Counting walks in a quadrant: a unified approach via boundary value problems, Journal of the European Mathematical Society, issue.3, pp.749-777, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00461853