G. E. Andrews, R. Askey, and R. Roy, Special functions, volume 71 of Encyclopedia of Mathematics and its Applications, 1999.

A. Aparicio-monforte and M. Kauers, Formal Laurent series in several variables, Expositiones Mathematicae, vol.31, issue.4, pp.350-367, 2013.
DOI : 10.1016/j.exmath.2013.01.004

URL : https://hal.archives-ouvertes.fr/hal-00825858

. Didierarqù-es, Dénombrements de chemins dans R 2 soumisàsoumisà contraintes, RAIRO Inform. Théor. Appl, vol.20, issue.4, pp.473-482, 1986.

A. Bostan, F. Chyzak, M. Van-hoeij, and L. Pech, Explicit formula for the generating series of diagonal 3D rook paths, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00780432

A. Bostan and M. Kauers, Unpublished notes, 2008.

A. Bostan and M. Kauers, Automatic classification of restricted lattice walks, 21st International Conference on Formal Power Series and Algebraic Combinatorics Discrete Math. Theor. Comput. Sci. Proc., AK, pp.201-215, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00780428

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.3063-3078, 2010.
DOI : 10.1090/S0002-9939-2010-10398-2

URL : https://hal.archives-ouvertes.fr/hal-00780429

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.
DOI : 10.1016/j.jcta.2013.09.005

URL : https://hal.archives-ouvertes.fr/hal-00697386

M. Bousquet-mélou, Counting Walks in the Quarter Plane, Mathematics and computer science, II (Versailles Trends Math, pp.49-67, 2002.
DOI : 10.1007/978-3-0348-8211-8_3

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, Algorithmic probability and combinatorics, pp.1-39, 2010.
DOI : 10.1090/conm/520/10252

M. Bousquet-mélou and M. Petkov?ek, 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

P. Cartier, Démonstration " automatique " d'identités et fonctions hypergéométriques

F. Chyzak, An extension of Zeilberger's fast algorithm to general holonomic functions, Discrete Mathematics, vol.217, issue.1-3, pp.115-134, 2000.
DOI : 10.1016/S0012-365X(99)00259-9

D. Denisov and V. Wachtel, Random walks in cones, The Annals of Probability, vol.43, issue.3, pp.992-1044, 2015.
DOI : 10.1214/13-AOP867

T. Fang and M. Van-hoeij, 2-descent for second order linear differential equations, Proceedings of the 36th international symposium on Symbolic and algebraic computation, ISSAC '11, pp.107-114, 2011.
DOI : 10.1145/1993886.1993907

G. Fayolle and K. , 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

G. Fayolle, R. Iasnogorodski, and V. Malyshev, Random walks in the quarter-plane Algebraic methods, boundary value problems and applications, Applications of Mathematics, vol.40, 1999.

P. Flajolet, Analytic models and ambiguity of context-free languages, Twelfth international colloquium on automata, languages and programming, pp.283-309, 1985.
DOI : 10.1016/0304-3975(87)90011-9

URL : https://hal.archives-ouvertes.fr/inria-00076071

P. Flajolet and A. Odlyzko, Singularity Analysis of Generating Functions, SIAM Journal on Discrete Mathematics, vol.3, issue.2, pp.216-240, 1990.
DOI : 10.1137/0403019

URL : https://hal.archives-ouvertes.fr/inria-00075725

P. Flajolet and R. Sedgewick, Analytic combinatorics, 2009.
DOI : 10.1017/CBO9780511801655

URL : https://hal.archives-ouvertes.fr/inria-00072739

I. M. 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

M. Ira, D. Gessel, and . Zeilberger, Random walk in a Weyl chamber Sur l'´ equation différentielle linéaire qui admet pour intégrale la série hypergéométrique, Proc. Amer. Math. Soc. Ann. Sci. ´ Ecole Norm. Sup, vol.11524, issue.10, pp.27-313, 1992.

D. Gouyou-beauchamps, Chemins sous-diagonaux et tableaux de Young, Combinatoiré enumérative, pp.112-125, 1985.
DOI : 10.4153/CJM-1962-032-x

R. K. Guy, C. Krattenthaler, and B. E. Sagan, Lattice paths, reflections, & dimension-changing bijections, Ars Combin, vol.34, pp.3-15, 1992.

K. Humphreys, A history and a survey of lattice path enumeration, Journal of Statistical Planning and Inference, vol.140, issue.8, pp.2237-2254, 2010.
DOI : 10.1016/j.jspi.2010.01.020

C. Koutschan, A Fast Approach to Creative Telescoping, Mathematics in Computer Science, vol.32, issue.3, pp.259-266, 2010.
DOI : 10.1007/s11786-010-0055-0

J. J. Kovacic, An algorithm for solving second order linear homogeneous differential equations, Journal of Symbolic Computation, vol.2, issue.1, pp.3-43, 1986.
DOI : 10.1016/S0747-7171(86)80010-4

C. Krattenthaler, Lattice Path Enumeration, Handbook of enumerative combinatorics, pp.589-678, 2015.
DOI : 10.1201/b18255-13

G. Kreweras, Sur une classe deprobì emes liés au treillis des partitions d'entiers, Cahiers du B.U.R.O, vol.6, pp.5-105, 1965.

I. Kurkova and K. Raschel, On the functions counting walks with small steps in the quarter plane, Publications math??matiques de l'IH??S, vol.14, issue.1, pp.69-114, 2012.
DOI : 10.1007/s10240-012-0045-7

URL : https://hal.archives-ouvertes.fr/hal-00628424

P. Lairez, Computing periods of rational integrals, Mathematics of Computation, vol.85, issue.300, pp.1719-1752, 2016.
DOI : 10.1090/mcom/3054

URL : https://hal.archives-ouvertes.fr/hal-00981114

L. Lipshitz, The diagonal of a D-finite power series is D-finite, Journal of Algebra, vol.113, issue.2, pp.373-378, 1988.
DOI : 10.1016/0021-8693(88)90166-4

S. Melczer and M. Mishna, Enumerating lattice paths with symmetries through multivariate diagonals, AofA 2014 Proc., AK, pp.1-12

S. Melczer and M. Mishna, Singularity Analysis Via the Iterated Kernel Method, Combinatorics, Probability and Computing, vol.17, issue.05, pp.861-888, 2014.
DOI : 10.1016/S0304-3975(02)00007-5

URL : https://hal.archives-ouvertes.fr/hal-01229731

S. Melczer and M. C. Wilson, Asymptotics of lattice walks via analytic combinatorics in several variables, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01394166

M. Mishna and A. Rechnitzer, Two non-holonomic lattice walks in the quarter plane, Theoretical Computer Science, vol.410, issue.38-40, pp.38-403616, 2009.
DOI : 10.1016/j.tcs.2009.04.008

M. Mishna, Classifying lattice walks restricted to the quarter plane, Journal of Combinatorial Theory, Series A, vol.116, issue.2, pp.460-477, 2009.
DOI : 10.1016/j.jcta.2008.06.011

K. Raschel, Counting walks in a quadrant: a unified approach via boundary value problems, Journal of the European Mathematical Society, vol.14, issue.3, pp.749-777, 2012.
DOI : 10.4171/JEMS/317

URL : https://hal.archives-ouvertes.fr/hal-00461853

A. Regev, Asymptotic values for degrees associated with strips of young diagrams, Advances in Mathematics, vol.41, issue.2, pp.115-136, 1981.
DOI : 10.1016/0001-8708(81)90012-8

N. J. Sloane, The On-Line Encyclopedia of Integer Sequences, 2010.
DOI : 10.1007/978-3-540-73086-6_12

J. Stienstra and F. Beukers, On the Picard-Fuchs equation and the formal brauer group of certain ellipticK3-surfaces, Mathematische Annalen, vol.126, issue.2, pp.269-304, 1985.
DOI : 10.1007/BF01455990

P. F. Stiller, Classical automorphic forms and hypergeometric functions, Journal of Number Theory, vol.28, issue.2, pp.219-232, 1988.
DOI : 10.1016/0022-314X(88)90067-4

K. Takeuchi, Commensurability classes of arithmetic triangle groups, J. Fac. Sci. Univ. Tokyo Sect. IA Math, vol.24, issue.1, pp.201-212, 1977.

. Mark-van-hoeij, Factorization of Differential Operators with Rational Functions Coefficients, Journal of Symbolic Computation, vol.24, issue.5, pp.537-561, 1997.
DOI : 10.1006/jsco.1997.0151

M. Van, H. , and V. J. Kunwar, Classifying (near)-Belyi maps with five exceptional points, 2016.

R. Vid¯-unas, Transformations of some Gauss hypergeometric functions, Journal of Computational and Applied Mathematics, vol.178, issue.1-2, pp.473-487, 2005.
DOI : 10.1016/j.cam.2004.09.053

D. Zeilberger, A holonomic systems approach to special functions identities, Journal of Computational and Applied Mathematics, vol.32, issue.3, pp.321-368, 1990.
DOI : 10.1016/0377-0427(90)90042-X

D. Zeilberger, The method of creative telescoping, Journal of Symbolic Computation, vol.11, issue.3, pp.195-204, 1991.
DOI : 10.1016/S0747-7171(08)80044-2