Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities

In this book modern algorithmic techniques for summation, most of which have been introduced within the last decade, are developed and carefully implemented in the computer algebra system Maple.
The algorithms of Gosper, Zeilberger and Petkovsek on hypergeometric summation and recurrence equations and their q-analogues are covered, and similar algorithms on differential equations are considered. An equivalent theory of hyperexponential integration due to Almkvist and Zeilberger completes the book.
The combination of all results considered gives work with orthogonal polynomials and (hypergeometric type) special functions a solid algorithmic foundation. Hence, many examples from this very active field are given.
The book is designed for use in the framework of a seminar and it is also suitable for an advanced lecture course in this area.