M. Abramowitz and I. A. , Stegun : Handbook of mathematical functions, formulas, graphs, and mathematical tables, Appl. Math. Series U.S. National Bureau of Standards, vol.55, 1964.

R. C. Ackerberg and R. E. Malley, Boundary Layer Problems Exhibiting Resonance, Studies in Applied Mathematics, vol.23, issue.3, pp.277-295, 1970.
DOI : 10.1002/sapm1970493277

W. Balser, From divergent power series to analytic functions, Lecture Notes in Mathematics, vol.1582, 2003.
DOI : 10.1007/BFb0073564

E. Benoît, A. Hamidi, and A. , Fruchard : On combined asymptotic expansions in singular perturbations, Electron. J. Diff. Eqns, No, vol.51, pp.1-27, 2002.

S. Bodine and R. Schäfke, On the summability of formal solutions in Liouville-Green theory, J. Dyn. Control Syst, vol.8, 2002.

M. Canalis-durand, J. Mozo-fernandez, and R. Schäfke, Monomial summability and doubly singular differential equations, Journal of Differential Equations, vol.233, issue.2, pp.485-511, 2007.
DOI : 10.1016/j.jde.2006.11.005

URL : https://hal.archives-ouvertes.fr/hal-00124889

M. Canalis-durand, J. Ramis, R. Schäfke, and Y. , Sibuya : Gevrey solutions of singularly perturbed differential equations, J. Reine Angew. Math, vol.518, pp.95-129, 2000.

A. Fruchard and R. Schäfke, Exceptional complex solutions of the forced Van der Pol equation, Funkcialaj Ekvacioj, vol.42, issue.2, pp.201-223, 1999.

A. Fruchard and R. Schäfke, De nouveaux développements asymptotiques combinés pour la perturbation singulière, pp.227-264, 2003.

A. Fruchard and R. Schäfke, Surstabilit?? et r??sonance, Annales de l???institut Fourier, vol.53, issue.1, pp.227-264, 2003.
DOI : 10.5802/aif.1943

A. Fruchard and R. Schäfke, Composite asymptotic expansions, Lecture Notes in Mathematics, vol.2066, 2013.
DOI : 10.1007/978-3-642-34035-2

URL : https://hal.archives-ouvertes.fr/hal-01320625

R. J. Hanson, Reduction theorems for systems of ordinary differential equations with a turning point, Journal of Mathematical Analysis and Applications, vol.16, issue.2, pp.280-301, 1966.
DOI : 10.1016/0022-247X(66)90171-5

R. J. Hanson, Simplification of Second Order Systems of Ordinary Differential Equations with a Turning Point, SIAM Journal on Applied Mathematics, vol.16, issue.5, pp.1059-80, 1968.
DOI : 10.1137/0116086

R. J. Hanson and D. L. Russell, Classification and Reduction of Second Order Systems at a Turning Point, Journal of Mathematics and Physics, vol.68, issue.I, pp.74-92, 1967.
DOI : 10.1002/sapm196746174

P. F. Hsieh, A turning point problem for a system of linear ordinary differential equations of the third order, Archive for Rational Mechanics and Analysis, vol.106, issue.2, pp.117-148, 1965.
DOI : 10.1007/BF00282278

M. Kohno, S. Ohkohchi, and T. Kohmoto, On full uniform simplification of even order linear differential equations with a parameter, Hiroshima Math. J, vol.9, pp.747-767, 1979.

R. Y. Lee, On uniform simplification of linear differential equation in a full neighborhood of a turning point, Journal of Mathematical Analysis and Applications, vol.27, issue.3, pp.501-510, 1969.
DOI : 10.1016/0022-247X(69)90129-2

A. Liénard, Étude des oscillations entretenues. Revue générale d'électricité, pp.901-954, 1928.

E. Matzinger, Étude d'équations différentielles ordinaires singulièrement perturbées au voisinage d'un point tournant, Thèse, 2000.

E. Matzinger, ??tude des solutions surstables de l'??quation de Van der Pol, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.10, issue.4, pp.713-744, 2001.
DOI : 10.5802/afst.1010

E. Matzinger, Asymptotic behaviour of solutions near a turning point: The example of the Brusselator equation, Journal of Differential Equations, vol.220, issue.2, pp.478-510, 2006.
DOI : 10.1016/j.jde.2005.06.028

J. A. Mchugh, An historical survey of ordinary linear differential equations with a large parameter and turning points, Archive for History of Exact Sciences, vol.239, issue.2, pp.277-324, 2003.
DOI : 10.1007/BF00328046

S. Ohkohchi, Uniform simplification in a full neighborhood of a turning point, Hiroshima Math. J, vol.15, pp.493-580, 1985.

F. W. Schäfke and R. Schäfke, Zur Parameterabhängigkeit bei Differentialgleichungen, J. Reine Angew. Math, vol.361, pp.1-10, 1985.

Y. Sibuya, Simplification of a linear ordinary differential equation of the nth order at a turning point, Archive for Rational Mechanics and Analysis, vol.4, issue.1, pp.206-221, 1963.
DOI : 10.1007/BF01262693

Y. Sibuya, A boundary value problem in the complex plane, Lecture Notes in Mathematics, vol.14, pp.128-144, 1971.
DOI : 10.1307/mmj/1028999657

Y. Sibuya, Uniform simplification in a full neighborhood of a transition point. Memoirs Amer, Math. Soc, vol.149, 1974.

Y. Sibuya, Global theory of a second order linear ordinary differential equation with a polynomial coefficient, 1975.

Y. Sibuya, A Theorem Concerning Uniform Simplification at a Transition Point and the Problem of Resonance, SIAM Journal on Mathematical Analysis, vol.12, issue.5, pp.653-668, 1981.
DOI : 10.1137/0512057

Y. Sibuya, Linear differential equations in the complex domain, problems of analytic continuation, 1990.

C. Stenger, Sur une conjecture de Wolfgang Wasow en théorie des points tournants, Comptes Rendus Acad. Sc, vol.325, issue.1, pp.27-32, 1999.

W. Wasow, Asymptotic expansions for ordinary differential equations. Interscience, 1965.

W. Wasow, Linear turning point theory, 1985.
DOI : 10.1007/978-1-4612-1090-0