[15] J. ÉCALLE, "Les fonctions résurgentes I", Tech. Report 81-05, Publ. Math. Orsay, 1981.

[16] ——, "Les fonctions résurgentes II", Tech. Report 81-06, Publ. Math. Orsay, 1981.

[17] ——, "Les fonctions resurgentes. III: L'équation du pont et la classification analytique des objets locaux", Tech. Report 85-05, Publ. Math. Orsay, 1985.

[18] ——, *Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac*, Hermann, 1992.

[19] F. FAUVET, F. RICHARD-JUNG & J. THOMANN, "Automatic computation of Stokes matrices", *Numer. Algorithms* **50** (2009), no. 2, p. 179-213.

[20] F. FAUVET & J. THOMANN, "Formal and numerical computations with resurgent functions", *Numerical Algorithms* **40** (2005), no. 4, p. 323-353.

[21] A. GOYER, "Algorithmes symboliques-numériques en algèbre différentielle", PhD Thesis, Université Paris-Saclay, 2025.

[22] D. GUZZETTI, "On Stokes Matrices in terms of Connection Coefficients", *Funkcialaj Ekvacioj* **59** (2016), no. 3, p. 383-433.

[23] D. HARVEY & J. VAN DER HOEVEN, "Integer multiplication in time $O(n \log n)$", *Annals of Mathematics* **193** (2021), no. 2, p. 563-617.

[24] J. VAN DER HOEVEN, "Fast Evaluation of Holonomic Functions Near and in Regular Singularities", *Journal of Symbolic Computation* **31** (2001), no. 6, p. 717-743.

[25] ——, "Effective real numbers in Mmxlib", in *ISSAC '06* (New York, NY, USA), ACM, 2006, p. 138-145.

[26] ——, "Efficient accelero-summation of holonomic functions", *Journal of Symbolic Computation* **42** (2007), no. 4, p. 389-428.

[27] ——, "Newton's method and FFT trading", *Journal of Symbolic Computation* **45** (2010), no. 8, p. 857-878.

[28] ——, "Uniformly fast evaluation of holonomic functions", 2016.

[29] E. L. INCE, *Ordinary Differential Equations*, Dover Publications, New York, 1944.

[30] F. JOHANSSON, *Using ball arithmetic*, FLINT documentation, https://flintlib.org/doc/using.html.

[31] ——, "Arb: Efficient Arbitrary-Precision Midpoint-Radius Interval Arithmetic", *IEEE Transactions on Computers* **66** (2017), no. 8, p. 1281-1292.

[32] ——, "Calcium: Computing in Exact Real and Complex Fields", in *ISSAC '21* (New York, NY, USA), ACM, 2021, p. 225-232.

[33] ——, "Arbitrary-precision computation of the gamma function", *Maple Transactions* **3** (2023), no. 1.

[34] F. JUNG, F. NAEGELE & J. THOMANN, "An algorithm of multisummation of formal power series, solutions of linear ODE equations", *Mathematics and Computers in Simulation* **42** (1996), no. 4-6, p. 409-425.

[35] W. B. JURKAT, D. A. LUTZ & A. PEYERIMHOFF, "Birkhoff invariants and effective calculations for meromorphic linear differential equations. II", *Houston J. Math.* **2** (1976), p. 207-238.

[36] M. LODAY-RICHAUD, "Calcul des invariants de Birkhoff des systèmes d'ordre deux", *Funkc. Ekvacioj, Ser. Int.* **33** (1990), no. 2, p. 161-225.

[37] ——, "Stokes phenomenon, multisummability and differential Galois groups", *Ann. Inst. Fourier (Grenoble)* **44** (1994), no. 3, p. 849-906.

[38] ——, "Rank reduction, normal forms and Stokes matrices", *Expo. Math.* **19** (2001), no. 3, p. 229-250.

[39] ——, *Divergent series, summability and resurgence. II*, Lecture Notes in Mathematics, vol. 2154, Springer, 2016, Simple and multiple summability, xxiii+272 pages.
[40] M. LODAY-RICHAUD & P. REMY, "Resurgence, Stokes phenomenon and alien derivatives for level-one linear differential systems", *J. Differential Equations* **250** (2011), no. 3, p. 1591-1630.

[41] D. A. LUTZ & R. SCHÄFKE, "Calculating connection coefficients for meromorphic differential equations", *Complex Variables, Theory Appl.* **34** (1997), no. 1-2, p. 145-170.

[42] B. MALGRANGE, "Remarques sur les équations différentielles à points singuliers irréguliers", in *Equations différentielles et systèmes de Pfaff dans le champ complexe*, Lect. Notes Math., vol. 712, 1979, p. 77-86.

[43] ——, "Fourier transform and differential equations", Recent developments in quantum mechanics, Proc. Conf., Braşov/Rom. 1989, Math. Phys. Stud. 12, 33-48, 1991.

[44] J. MARTINET & J.-P. RAMIS, "Problèmes de modules pour des équations différentielles non linéaires du premier ordre", *Publ. Math. IHES* **55** (1982), p. 63-164.

[45] M. MEZZAROBBA, "Rigorous Multiple-Precision Evaluation of D-Finite Functions in SageMath", https://hal.archives-ouvertes.fr/hal-01342769, 2016.

[46] ——, "Truncation Bounds for Differentially Finite Series", *Annales Henri Lebesgue* **2** (2019), p. 99-148.

[47] C. MITSCHI & D. SAUZIN, *Divergent series, summability and resurgence. I*, Lecture Notes in Mathematics, vol. 2153, Springer, 2016, Monodromy and resurgence, xxi+298 pages.

[48] J. J. MORALES-RUIZ & J.-P. RAMIS, "Integrability of dynamical systems through differential Galois theory: a practical guide", *Differential algebra, complex analysis and orthogonal polynomials* **509** (2010), p. 143-220.

[49] N. T. MÜLLER, "The iRRAM: Exact Arithmetic in C++", in *Computability and Complexity in Analysis* (G. Goos, J. Hartmanis, J. Van Leeuwen, J. Blanck, V. Bratka & P. Hertling, eds.), vol. 2064, Springer, Berlin, Heidelberg, 2001, p. 222-252.

[50] F. NAEGELE, "Autour de quelques équations fonctionnelles analytiques", PhD Thesis, Institut national polytechnique de Grenoble, 1995.

[51] F. W. OLVER, D. W. LOZIER, R. F. BOISVERT & C. W. CLARK (eds.), *Digital Library of Mathematical Functions*, National Institute of Standards and Technology, 2010, http://dlmf.nist.gov/.

[52] E. G. C. POOLE, *Introduction to the theory of linear differential equations*, Clarendon Press, New York, 1936.

[53] J.-P. RAMIS, "Epilogue: Stokes Phenomena. Dynamics, Classification Problems and Avatars", in *Handbook of Geometry and Topology of Singularities VI: Foliations* (F. Cano et al., eds.), Springer Nature Switzerland, Cham, 2024, p. 383-482.

[54] F. RICHARD-JUNG, "Stokes Phenomenon : graphical visualization and certified computation", in *SNC'11* (M. Moreno Maza, ed.), ACM, 2011.

[55] T. SCHMELZER & L. N. TREFETHEN, "Computing the Gamma Function Using Contour Integrals and Rational Approximations", *SIAM Journal on Numerical Analysis* **45** (2007), no. 2, p. 558-571.

[56] The PARI Group, Univ. Bordeaux, *PARI/GP version 2.17.2*, 2025.

[57] J. THOMANN, "Resommation des séries formelles", *Numerische Mathematik* **58** (1990), no. 1, p. 503-535.

[58] ——, "Procédés formels et numériques de sommation de séries solutions d'équations différentielles", *Expositiones Mathematicae* **13** (1995), p. 223-246.