Algebraic Functions

Abstract

The next station in our tour through various classes of formal power series is the class of algebraic power series. These power series share the property that they can be described as solutions of a polynomial equation. A deep theory has been developed for these power series mainly because of the important role they play in the field of algebraic geometry for locally describing algebraic curves and surfaces in the neighborhood of a specific point. But the significance of algebraic power series is by no means restricted to algebraic geometry. In combinatorics, for example, they turn out to play a prominent role as well, as they do appear as generating functions for a number of important combinatorial objects.