J. Abad, F. J. Gómez, and J. Sesma, An algorithm to obtain global solutions of the double confluent Heun equation, Numerical Algorithms, vol.118, issue.1-4, pp.1-433, 2008.
DOI : 10.1007/s11075-008-9197-4

F. Bellard, Computation of 2700 billion decimal digits of Pi using a Desktop Computer, 2010.

D. J. Bernstein, Fast multiplication and its applications, Algorithmic Number Theory, pp.325-384, 2008.

A. Bostan, T. Cluzeau, and B. Salvy, Fast algorithms for polynomial solutions of linear differential equations, Proceedings of the 2005 international symposium on Symbolic and algebraic computation , ISSAC '05, pp.45-52, 2005.
DOI : 10.1145/1073884.1073893

URL : https://hal.archives-ouvertes.fr/hal-00078763

R. P. Brent, The complexity of multiple-precision arithmetic, The Complexity of Computational Problem Solving, pp.126-165, 1976.

R. P. Brent, A Fortran Multiple-Precision Arithmetic Package, ACM Transactions on Mathematical Software, vol.4, issue.1, pp.57-70, 1978.
DOI : 10.1145/355769.355775

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.8425

R. P. Brent and P. Zimmermann, Modern Computer Arithmetic. Version 0.4, 2009.
URL : https://hal.archives-ouvertes.fr/cel-01500109

P. Bürgisser, M. Clausen, and M. A. Shokrollahi, Algebraic complexity theory, 1997.
DOI : 10.1007/978-3-662-03338-8

H. Cheng, G. Hanrot, E. Thomé, E. Zima, and P. Zimmermann, Time-and space-efficient evaluation of some hypergeometric constants, Proceedings of the 2007 international symposium on Symbolic and algebraic computation , ISSAC '07, 2007.
DOI : 10.1145/1277548.1277561

URL : https://hal.archives-ouvertes.fr/inria-00126428

D. V. Chudnovsky and G. V. Chudnovsky, On expansion of algebraic functions in power and Puiseux series, II, Journal of Complexity, vol.3, issue.1, pp.271-2941, 1986.
DOI : 10.1016/0885-064X(87)90002-1

D. V. Chudnovsky and G. V. Chudnovsky, Computer algebra in the service of mathematical physics and number theory, Computers in mathematics, pp.109-232, 1986.

R. Dupont, Moyenne arithmético-géométrique, suites de Borchardt et applications, Thèse de doctorat, École polytechnique, 2006.

P. Falloon, P. Abbott, and J. Wang, Theory and computation of spheroidal wavefunctions, Journal of Physics A: Mathematical and General, vol.36, issue.20, pp.5477-5495, 2003.
DOI : 10.1088/0305-4470/36/20/309

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

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

L. Fousse, G. Hanrot, V. Lefèvre, P. Pélissier, and P. Zimmermann, MPFR, ACM Transactions on Mathematical Software, vol.33, issue.2, pp.1-13, 2007.
DOI : 10.1145/1236463.1236468

URL : https://hal.archives-ouvertes.fr/inria-00070266

X. Gourdon and P. Sebah, Binary splitting method, 2001.

B. Haible and T. Papanikolaou, Fast multiprecision evaluation of series of rational numbers, 1997.
DOI : 10.1007/BFb0054873

L. Heffter, Einleitung in die Theorie der linearen Differentialgleichungen, p.1894

O. M. Makarov, An algorithm for multiplying 3??3 matrices, USSR Computational Mathematics and Mathematical Physics, vol.26, issue.1, pp.179-180, 1987.
DOI : 10.1016/0041-5553(86)90203-X

L. Meunier and B. Salvy, ESF, Proceedings of the 2003 international symposium on Symbolic and algebraic computation , ISSAC '03, pp.199-206, 2003.
DOI : 10.1145/860854.860898

M. Mezzarobba, Génération automatique de procédures numériques pour les fonctions D-finies, 2007.

M. Mezzarobba and B. Salvy, Effective bounds for P-recursive sequences, Journal of Symbolic Computation, vol.45, issue.10
DOI : 10.1016/j.jsc.2010.06.024

URL : https://hal.archives-ouvertes.fr/inria-00376219

E. G. Poole, Introduction to the theory of linear differential equations, 1936.

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

É. Tournier, Solutions formelles d'équations différentielles, Thèse de doctorat, 1987.

J. Van-der-hoeven, Fast evaluation of holonomic functions, Theoretical Computer Science, vol.210, issue.1, pp.199-216, 1999.
DOI : 10.1016/S0304-3975(98)00102-9

URL : https://hal.archives-ouvertes.fr/hal-01374898

J. Van-der-hoeven, Fast Evaluation of Holonomic Functions Near and in Regular Singularities, Journal of Symbolic Computation, vol.31, issue.6, pp.717-743, 2001.
DOI : 10.1006/jsco.2000.0474

J. Van-der-hoeven, Majorants for formal power series, 2003.

J. Van-der-hoeven, Efficient accelero-summation of holonomic functions, Journal of Symbolic Computation, vol.42, issue.4, pp.389-428, 2007.
DOI : 10.1016/j.jsc.2006.12.005

J. Van-der-hoeven, On Effective Analytic Continuation, Mathematics in Computer Science, vol.1, issue.1, pp.111-175, 2007.
DOI : 10.1007/s11786-007-0006-6

J. Van-der-hoeven, Transséries et analyse complexe effective. Mémoire d'habilitation, 2007.

A. Waksman, On Winograd's Algorithm for Inner Products, IEEE Transactions on Computers, vol.19, issue.4, pp.360-361, 1970.
DOI : 10.1109/T-C.1970.222926

P. Zimmermann, The bit-burst algorithm. Slides of a talk at the workshop Computing by the Numbers: Algorithms, Precision, and Complexity " for R, 2006.