Y. André, G-functions and geometry, Aspects of Mathematics E13. Friedr. Vieweg & Sohn, 1989.
DOI : 10.1007/978-3-663-14108-2

D. H. Bailey, J. M. Borwein, N. J. Calkin, R. Girgensohn, D. R. Luke et al., Integer relation detection, Computing in Science & Engineering, vol.2, issue.1, pp.29-31, 2007.
DOI : 10.1109/5992.814653

C. Banderier and P. Flajolet, Basic analytic combinatorics of directed lattice paths, Theoretical Computer Science, vol.281, issue.1-2, pp.37-80, 2002.
DOI : 10.1016/S0304-3975(02)00007-5

B. Beckermann and G. Labahn, A Uniform Approach for the Fast Computation of Matrix-Type Pad?? Approximants, SIAM Journal on Matrix Analysis and Applications, vol.15, issue.3, pp.804-823, 1994.
DOI : 10.1137/S0895479892230031

A. Bostan, F. Chyzak, G. Lecerf, B. Salvy, and . Schost, Differential equations for algebraic functions, Proceedings of the 2007 international symposium on Symbolic and algebraic computation , ISSAC '07, pp.25-32, 2007.
DOI : 10.1145/1277548.1277553

URL : https://hal.archives-ouvertes.fr/inria-00138206

A. Bostan and M. Kauers, The complete generating function for Gessel walks is algebraic, Proceedings of the American Mathematical Society, vol.138, issue.09, 2009.
DOI : 10.1090/S0002-9939-2010-10398-2

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

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, 2008.
DOI : 10.1090/conm/520/10252

M. Bousquet-mélou and M. Petkov?ek, Linear recurrences with constant coefficients: the multivariate case, Discrete Mathematics, vol.225, issue.1-3, pp.51-7598, 2000.
DOI : 10.1016/S0012-365X(00)00147-3

R. Brak and A. J. Guttmann, Algebraic approximants: a new method of series analysis, Journal of Physics A: Mathematical and General, vol.23, issue.24, pp.1331-1337, 1990.
DOI : 10.1088/0305-4470/23/24/008

C. Brezinski, Algorithmes d'accélération de la convergence. ´ Editions Technip, Etude numérique, Collection Langages et Algorithmes de l'Informatique, 1978.

A. Chambert-loir, Théorèmes d'algébricité en géométrie diophantienne (d'après, pp.175-209, 2002.

D. V. Chudnovsky and G. V. Chudnovsky, Applications of Pad?? approximations to diophantine inequalities in values of G-functions, Number theory, pp.1983-84, 1985.
DOI : 10.3792/pjaa.59.281

M. Dettweiler and S. Reiter, On globally nilpotent differential equations. ArXiv:math/0605383, 2006.

B. Dwork, Differential Operators with Nilpotent p-Curvature, American Journal of Mathematics, vol.112, issue.5, pp.749-786, 1990.
DOI : 10.2307/2374806

B. Dwork, G. Gerotto, and F. J. Sullivan, An introduction to G-functions, Annals of Mathematics Studies, vol.133, 1994.

P. Flajolet, Analytic models and ambiguity of context-free languages, Theoretical Computer Science, vol.49, issue.2-3, pp.283-309, 1987.
DOI : 10.1016/0304-3975(87)90011-9

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

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

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

S. Garoufalidis, G-functions and multisum versus holonomic sequences, Advances in Mathematics, vol.220, issue.6, pp.1945-1955, 2009.
DOI : 10.1016/j.aim.2008.11.012

URL : http://doi.org/10.1016/j.aim.2008.11.012

T. Honda and R. Indam, Algebraic differential equations, Symposia Mathematica, pp.169-204, 1979.

N. M. Katz, Nilpotent connections and the monodromy theorem: Applications of a result of turrittin, Publications math??matiques de l'IH??S, vol.93, issue.1, pp.175-232, 1970.
DOI : 10.1007/BF02684688

M. Kauers, Guessing handbook, 2009.

M. Kauers, C. Koutschan, and D. Zeilberger, Proof of Ira Gessel's lattice path conjecture, Proceedings of the National Academy of Sciences, vol.106, issue.28, 2008.
DOI : 10.1073/pnas.0901678106

M. Kauers and D. Zeilberger, The quasi-holonomic ansatz and restricted lattice walks, Journal of Difference Equations and Applications, vol.1, issue.10-11, pp.10-111119, 2008.
DOI : 10.1007/s00026-007-0316-z

D. Krammer, An example of an arithmetic Fuchsian group, J. Reine Angew. Math, vol.473, pp.69-85, 1996.

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

C. Mallinger, Algorithmic manipulations and transformations of univariate holonomic functions and sequences. Master's thesis, 1996.

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

S. Plouffe, Plouffe's inverter

B. Salvy and P. Zimmermann, GFUN: a Maple package for the manipulation of generating and holonomic functions in one variable, ACM Transactions on Mathematical Software, vol.20, issue.2, pp.163-177, 1994.
DOI : 10.1145/178365.178368

URL : https://hal.archives-ouvertes.fr/hal-00917741

H. Schmitt, Operators with Nilpotent p-Curvature, Proceedings of the American Mathematical Society, vol.119, issue.3, pp.701-710, 1993.
DOI : 10.2307/2160503

J. Wimp and D. Zeilberger, Resurrecting the asymptotics of linear recurrences, Journal of Mathematical Analysis and Applications, vol.111, issue.1, pp.162-176, 1985.
DOI : 10.1016/0022-247X(85)90209-4