Abstract
We introduce a first-order differential system Y′(x) =A(x)Y(x) on [a, ∞) particular cases of which are equivalent to standard forms of the generalized hypergeometric equation. Our purpose is to obtain the asymptotic solution of the system as x → ∞ by defining suitable transformations of the solution vector Y and using ideas from a unified asymptotic theory of differential systems. Thus our methods place the system within the scope of this unified theory, and they are independent of specialized properties of the Meijer G-function solutions of generalized hypergeometric equations. As such, our methods are also capable of extension to other situations not covered by these special functions.
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