The Frobenius-Harper technique in a general recurrence model

We present a general recurrence model which provides a conceptual framework for well-known problems such as ascents, peaks, turning points, Bernstein' s urn model, the Eggenberger-Polya um model and the hypergeometric distribu tion. Moreover, we show that the Frobenius-Harper technique, based on real roots of a generating function, can be applied to this general recurrence m odel (under simple conditions), and so a Berry-Esseen bound and local limit theorems can be found. This provides a simple and unified approach to asym ptotic theory for diverse problems hitherto treated separately.