Eine verallgemeinerte Fuchs'sche Theorie

In this paper the solutions of the differential equation (D) w^m + a_m–1 (Z) W^m–1. + a_o(Z)=0 are discussed. In the definitions 1,2,3 functions are given measuring the growth of the coefficients resp. of the solutions of (D). Theorem 1 shows, that the l-fold iterated order of growth of the coefficients equals to the (l+1)-fold iterated order of growth of the solutions. In the case l==o theorem 1 passes over to the well known FUCHSian theory of regular singular points. Using proximate order theorem 4 gives an improved version of theorem 1.

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Herrn Professor Dr.R.Nevanlinna zum 75. Geburtstag gewidmet