Geodesic
On the fundamental matrix of a Pfaffian system of Fuchsian type
Izvestiya. Mathematics, Tome 11 (1977) no. 5, pp. 1031-1054 Cet article a éte moissonné depuis la source Math-Net.Ru

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A necessary and sufficient condition is given in order that a completely integrable Pfaffian system with regular singular point, given on a polydisk $D^n$, be of Fuchsian type. It is proved that the system is Fuchsian if and only if the space of solutions is “weakly singular”. In the one-dimensional case, this problem was studied by A. H. M. Levelt (RZhMat., 1963, 12B56). For higher dimensions, a similar attempt was made by R. Gérard (RZhMat., 1970, IA553), but his paper contains an error. Bibliography: 4 titles. 
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A. A. Bolibrukh. On the fundamental matrix of a Pfaffian system of Fuchsian type. Izvestiya. Mathematics, Tome 11 (1977) no. 5, pp. 1031-1054. http://geodesic.mathdoc.fr/item/IM2_1977_11_5_a6/

[1] Koddington E. A., Levinson N., Teoriya obyknovennykh differentsialnykh uravnenii, IL, M., 1958

[2] Levelt A. H. M., “Hypergeometric functions”, Koninkl. Nederl. Akad. Van Wet., Indagation Mathematical, XXIII:4 (1961), 361–401 | MR

[3] Gérard R., “Theorie de Fuchs sur une variété analytique complexe”, J. Math. Pur. Appliq., 47:4 (1968), 321–404 | MR | Zbl

[4] Yoshida M., Takano K., “Local theory of Fuchsian systems, I”, Proc. Japan Acad., LI (1975), 219–223 | DOI | MR