In this book, modern algorithmic techniques for summation--most of which have been introduced within the last decade--are developed and carefully implemented via computer algebra system software (which can be downloaded from the Web; URL is given in the text). 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 volume. 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 as framework for a seminar on the topic, but is also suitable for use in an advanced lecture course.

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