Asymptotic solution of a differential system related to the generalized hypergeometric equation

We introduce a first-order differential system Y'(x) = A(x)Y(x) on [a, infi nity) particular cases of which are equivalent to standard forms of the gen eralized hypergeometric equation. Our purpose is to obtain the asymptotic s olution of the system as x --> infinity by defining suitable transformation s of the solution vector Y and using ideas from a unified asymptotic theory of differential systems. Thus our methods place the system within the scop e of this unified theory, and they are independent of specialized propertie s of the Meijer G - function solutions of generalized hypergeometric equati ons. As such, our methods are also capable of extension to other situations not covered by these special functions.