Generalization of Risch's Algorithm to Special Functions

Symbolic integration deals with the evaluation of integrals in closed form. We present an overview of Risch’s algorithm including recent developments. The algorithms discussed are suited for both indefinite and definite integration. They can also be used to compute linear relations among integrals and to find identities for special functions given by parameter integrals. The aim of this presentation1 is twofold: to introduce the reader to some basic ideas of differential algebra in the context of integration and to raise awareness in the physics community of computer algebra algorithms for indefinite and definite integration.