In this volume we will present some applications of special functions in computer science. This largely consists of adaptations of articles that have appeared in the literature. Here they are presented in a format made accessible for the non-expert by providing some context. The material on group representations and Young tableaux is introductory in nature. However, the algebraic approach of Chapter 2 is original to the authors and has
not appeared previously. Similarly, the material and approach based on Appell states, so formulated, is presented here for the first time.