A package on formal power series

TL;DR

This paper presents a implementation of algorithms developed by the author for converting between certain classes of functions and their equivalent representing series, and enables the user to reproduce most of the results of Hansen's extensive table of series.

Abstract

Formal Laurent-Puiseux series are important in many branches of mathematics. This paper presents a {\it Mathematica} implementation of algorithms developed by the author for converting between certain classes of functions and their equivalent representing series. The package {\tt PowerSeries} handles functions of rational, exponential, and hypergeometric type, and enables the user to reproduce most of the results of Hansen's extensive table of series. Subalgorithms of independent significance generate differential equations satisfied by a given function and recurrence equations satisfied by a given sequence.