M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, American Journal of Physics, vol.34, issue.2, 1970.
DOI : 10.1119/1.1972842

W. Balser, Zum einzigkeitssatz in der invariantentheorie meromorpher differentialgleichungen, Journal für die Reine und Angewandte Mathematik, p.51, 1980.

W. Balser, Convergent power series expansions for the Birkho¤ invariants of meromorphic di¤erential equations, Yokohama Mathematical Journal, vol.32, pp.15-29, 1984.

W. Balser, Summation of Formal Power Series Through Iterated Laplace Integrals., MATHEMATICA SCANDINAVICA, vol.70, pp.161-171, 1992.
DOI : 10.7146/math.scand.a-12392

W. Balser, Calculation of the Stokes' multipliers for a polynomial system of rank 1 having distinct eigenvalues at in?nity, Hiroshima Mathematical Journal, vol.23, issue.230, p.223, 1993.

W. Balser, Formal power series and linear systems of meromorphic ordinary di¤erential equations, 2000.

W. Balser, B. L. Braaksma, J. Ramis, and Y. Sibuya, Multisummability of formal power series solutions of linear ordinary di¤erential equations, pp.27-45, 1991.

W. Balser, W. B. Jurkat, and D. A. Lutz, A general theory of invariants for meromorphic di¤erential equations ; Part I, formal invariants, Funkcialaj Ekvacioj, vol.22, issue.221, 1979.

W. Balser, W. B. Jurkat, and D. A. Lutz, A general theory of invariants for meromorphic di¤erential equations ; Part II, proper invariants, Funkcialaj Ekvacioj, vol.22, pp.257-283, 1979.

W. Balser, W. B. Jurkat, and D. A. Lutz, Birkhoff invariants and stokes' multipliers for meromorphic linear differential equations, Journal of Mathematical Analysis and Applications, vol.71, issue.1, pp.48-94, 1979.
DOI : 10.1016/0022-247X(79)90217-8

W. Balser, W. B. Jurkat, and D. A. Lutz, Transfer of connection problems for ?rst level solutions of meromorphic di¤erential equations and associated Laplace transforms, Journal für die Reine und Angewandte Mathematik, vol.344, issue.170, p.149, 1982.

W. Balser, W. B. Jurkat, and D. A. Lutz, Transfer of connection problems for meromorphic di¤erential equations of rank r 2 and representations of 391

M. Barkatou, F. Chyzak, M. Loday-richaud, M. Barkatou, and E. G. Birkho¤, An algorithm computing the regular formal solutions of a system of linear di¤erential equations Singular points of ordinary linear di¤erential equations, Translations of the, Birkho¤, Equivalent singular points of ordinary linear di¤erential equations Annales Scienti?ques de l'E.N.S, pp.569-587, 1909.

]. E. Eme-sériebo28 and . Borel, Leçons sur les séries divergentes, Gauthier-Villars, Paris, 1928, réimpression éd, Multisummability and Stokes multipliers of linear meromorphic di¤erential equations, p.1899, 1988.

B. Candelpergher, Une introduction à la résurgence, Gazette des Mathématiciens, vol.42, issue.64, p.36, 1989.

D. V. Chudnovsky and G. V. Chudnovsky, Computer assisted number theory with applications, Lecture Notes in Mathematics, vol.19, issue.15, p.1240, 1987.
DOI : 10.1007/BF01086034

D. V. Chudnovsky and G. V. Chudnovsky, Computer algebra in the service of mathematical physics and number theory (computers in mathematics, Lecture Notes in Pure and Applied Math, pp.125-232, 1986.

B. Candelpergher, J. Nosmas, and F. Pham, Approche de la résurgence, Theory of ordinary di¤erential equations, 1955.

E. Delabaered70-]-p and . Deligne, Asymptotique complexe : méthodes résurgentes Equations di¤érentielles à points singuliers réguliers Monodromy groups in algebraic geometry, exposés n 13 et 14, D73] P. Deligne, p.164, 1970.

J. Ecalle, Les fonctions résurgentes, tome I : les algèbres de fonctions résurgentes , Publications Mathématiques d'Orsay, p.5, 1981.

J. Ecalle, Les fonctions résurgentes, tome II : les fonctions résurgentes appliquées à l'itération, Publications Mathématiques d'Orsay, p.6, 1981.

. [. Ecalle, Les fonctions résurgentes, tome III : l'équation du pont et la classi?cation analytique des objets locaux, Publications Mathématiques d'Orsay, n 85 05, Résurgence et accélération, Cours de 3 eme cycleE92] J. Ecalle, Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac, 1985.

I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series and products Réductibilité d'un système di¤érentiel linéaire, p.17, 1983.

. [. Hilali, Solutions formelles de systèmes di¤érentiels linéaires au voisinage d'un point singulier Immink, A note on the relationship between Stokes multipliers and formal solutions of analytic di¤erential equations, Thèse, p.792, 1956.

]. W. Jurkat, D. A. Lutz, and A. Peyerimho¤, Birkhoff invariants and effective calculations for meromorphic linear differential equations. I, Journal of Mathematical Analysis and Applications, vol.53, issue.2, p.438, 1976.
DOI : 10.1016/0022-247X(76)90122-0

]. W. Jurkat, D. A. Lutz, and A. Peyerimho¤, Birkho¤ invariants and e¤ective calculations for meromorphic linear di¤erential equations II, Houston Journal of Mathematics, vol.2, issue.2, pp.207-238, 1976.

]. M. Ka83 and . Kashiwara, Systems of microdi¤erential equations, Progress in Mathematics, vol.34, 1983.

]. E. Bibliographie-[-le00 and . Leroy, Sur les séries divergentes et les fonctions dé?nies par un développement de Taylor, pp.317-430, 1900.

[. Loday-richaud, Stokes phenomenon, multisummability and di¤erential Galois groups, Annales de l'Institut Fourier, pp.849-906, 1994.

[. Loday-richaud, Solutions formelles des systèmes di¤érentiels linéaires méromorphes et sommation, Expositiones Mathematicae, vol.13, p.116162, 1995.

[. Loday-richaud, Rank reduction, normal forms and stokes matrices, Expositiones Mathematicae, vol.19, issue.3, p.229, 2001.
DOI : 10.1016/S0723-0869(01)80003-7

URL : http://doi.org/10.1016/s0723-0869(01)80003-7

]. D. Lu72, . A. Lutzlu79-]-d, and . Lutz, On the reduction of rank of linear di¤erential systems Birkho¤ invariants and meromorphic di¤erential equations, Equations di¤érentielles et systèmes de Pfa¤ dans le champ complexe (R. Gérard et J.-P. Ramis) connection coe¢ cients for meromorphic di¤erential equations, Complex Variables, p.145, 1972.

B. Malgrange, Sur les points singuliers des équations di¤érentielles, L'Enseignement Mathématique, p.176, 1974.

B. Malgrange, Remarques sur les équations di¤érentielles à points singuliers irréguliers, Lecture Notes in Mathematics, Equations di¤érentielles et systèmes de Pfa¤ dans le champ complexe, p.86, 1979.
DOI : 10.1007/bfb0062817

URL : http://archive.numdam.org/article/SEDP_1977-1978____A1_0.pdf

B. Malgrange-aux-travaux-de, J. Ecalle, and L. Mathématique, Introduction, pp.261-282, 1985.
DOI : 10.1007/978-94-017-8993-6_1

B. Malgrange, Equations di¤érentielles linéaires et transformation de Fourier : une introduction, 1989.

B. Malgrange, Fourier transform and di¤erential equations, Recent Developments in Quantum Mechanics, p.48, 1991.

B. Malgrange, Equations di¤érentielles à coe¢ cients polynomiaux, Progress in Mathematics, vol.96, 1991.

B. Malgrange and J. Ramis, Fonctions multisommables, Annales de l'Institut Fourier, p.368, 1992.

J. Martinet and J. Ramis, Problèmes de modules pour des équations di¤érentielles non linéaires du premier ordre, Publications Mathématiques de l'I, pp.63-164, 1982.

J. Martinet and J. Ramis, Théorie de Galois di¤érentielle et resommation, Computer Algebra and Di¤erential Equations, E. Tournier, éd, vol.117, p.214, 1989.

J. Martinet and J. Moser, Elementary acceleration and multisummability, Annales de l'Institut Henri Poincaré The order of a singularity in Fuchs' theory, Ne19] F. Nevanlinna, Zur theorie der asymptotischen potenzreihen, p.81, 1919.

F. W. Olver, Asymptotics and special functions, AKP Classics, Sur les intégrales irrégulières des équations linéaires Ramis, Les séries k-sommables et leurs applications, 1928.

]. [-ra84 and . Ramis, Théorèmes d'indices Gevrey pour les équations di¤érentielles ordinaires, Memoirs of the, 1984.

M. Sato, T. Kawai, and M. Kashiwara, Microfunctions and pseudo-di¤erential equations Sur les solutions régulières d'un système d'équations di¤érentielles, Lecture Notes in Mathematics Annales Scienti?ques de l'E.N.S, vol.287, issue.529, pp.391-404, 1973.

D. Sauzin, Resurgent functions and splitting problems, à paraître dans RIMS Koukyuroku, Kyoto [Si76] Y. Sibuya, Linear di¤erential equations in the complex domain : problems of analytic continuation, 1976.

]. L. Bibliographiesla60 and . Slater, Sibuya, Linear di¤erential equations in the complex domain : problems of analytic continuation, Translations of Mathematical Monographs, Con ?uent hypergeometric functions, 1960.

]. L. Sla66 and . Slater, Generalized hypergeometric functions, 1966.

]. H. Tu55 and . Turrittin, Convergent solutions for ordinary linear homogeneous differential equations in the neighborhood of an irregular singular point, Turrittin, Reducing the rank of ordinary di¤erential equations, pp.271-274, 1955.

J. Van-der-hoeven, Fast evaluation of holonomic functions, Theoretical Computer Science, vol.210, issue.1, 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, E¢ cient accelero-summation of holonomic functions, Prépublication, 2005.

W. Wasow, Asymptotic expansions for ordinary di¤erential equations, 1965.

G. N. Watson, A theory of asymptotic series, Philosophical Transactions of the Royal Society of London, série A, volume CCXI, p.313, 1911.