1. Trans. Am. Math. Soc. 10, p. 436?470.
2. Loc. cit. Trans. Am. Math. Soc. 10 p. 446 and p. 453.
3. For these definitions see Schlesinger,Vorlesungen über lineare Differentialgleichungen, p. 181.
4. For an exposition of the elementary properties of matrices used in the present paper see Schlesinger, loc. cit.,Vorlesungen über lineare Differentialgleichungen, p. 18?19.
5. This definition is more satisfactory than the one used in my earlier paper (Trans. Am. Math. Soc., loc. cit. 10 p. 446 and p. 453.) where the functionsa ij (x) were merely restricted to be rational in character atx=?.