Formal Power Series

with coefficients ak ∈ C (k ∈ Z ) are important in many branches of mathematics. Maple supports the computation of truncated series with its series command, and through the powerseries package [6] infinite series are available. In the latter case, the series is represented as a table of coefficients that have already been determined together with a function for computing additional coefficients. This is known as lazy evaluation. But these tools fail, if one is interested in an explicit formula for the coefficients ak. In this article we will describe the Maple implementation of an algorithm presented in [8]–[13] which computes an exact formal power series (FPS) of a given function. This procedure will enable the user to reproduce most of the results of the extensive bibliography on series [7]. We will give an overview of the algorithm and then present some parts of it in more detail. This package is available through the Maple-share library with the name FPS. We will flavor this procedure with the following example.