An algorithm to compute the exponential part of a formal fundamental matrix solution of a linear differential system

Babbitt, D. G., Varadarajan, V. S.: Formal reduction of meromorphic differential equations: a group theoretic view. Pacific J Math109(1), 1–80 (1983)

Chen, G.: An algorithm for computing the formal solutions of differential systems in the neighborhood of an irregular singular point. ISSAC90, 231–235

Balser, W., Jurkat, W. B., Lutz, D. A.: A general thoery of invariants for meromorphic differential equations; Part I, Formal invariants, Funkcial. Ekvac.22, 197–227 (1979)

Barkatou, M. A.: An algorithm for computing a companion block diagonal form for a system of linear differential equations. AAECC4, 185–195 (1993)

Barkatou, M. A.: Rational Newton Algorithm for computing formal solutions of linear differential equations, Proc. International Symposium on Algebraic Computation 1988. Berlin, Heidelberg, New York: Springer Lecture Notes in Computer Science vol. 358 (1989)

Cope, F.: Formal solutions of irregular linear differential equations. Am. J. Math.58, 130–140 (1936)

Deligne, P.: Equations différentielles à points singuliers réguliers. Lectures Notes in Mathematics, Vol.163. Berlin, Heidelberg, New York: Springer 1970

Hilali, A.: Solutions formelles de systèmes différentiels linéaires au voisinage d’un point singulier. Thèse de l’université Joseph Fourier Grenoble France, Juin 1987, pp. 71–103

Hilali, A., Wazner, A.: Un algorithme de calcul de l’invariant de Katz d’un système différentiel linéaire. Annales de l’Institut Fourier, Tome XXXVI-Fasicule3, 67–83 (1986)

Levelt, A. H. M.: Stabilizing differential operators: a method for computing invariants at irregular singularities. In: Singer, M. (ed), Differential Equations and Computer Algebra, Computational Mathematics and Applications, 181–228. New York: Academic Press 1991

Lutz, D. A., Schäfke, R.: On the identification and stability of formal invariants for singular differential equations. Linear Algebra And Its Applications72, 1–46 (1985)

Malgrange, B.: Sur le réduction formelle des équations différentielles à singularités irrégulières, Preprint Grenoble 1979

Moser, J.: The order of a singularity in Fuchs’ theory, Math. Z.72, 379–398 (1960)

Ramis, J. P.: Théorèmes d’indices Gevrey pour les équations différentielles ordinaires. Pub. IRMA, Strasbourg FRANCE, pp. 57–60 (1981)

Sommeling, R.: Characteristic classes for irregular singularies. PhD thesis, University of Nijmegen, 1993

Tournier, E.: Solutions formelles d’équations différentielles. Thèse de l’université Joseph Fourier Grenoble France, Avril 1987

Robba, P.: Lemmes de Hensel pour les opérateurs différentiels. Application à la réduction formelle des équations différentielles. L’Enseigenment Mathématique, Ser. II,26, 279–311 (1980)

Turritin, H. L.: Convergent solutions of ordinary linear homogeneous differential equations in the neighborhood of an irregular singular point. Acta Matm.93, 27–66 (1955)

Wasow, W.: Asymptotic Expansions For Ordinary Differential Equations. Interscience Publishers New-York 1965