Topic #8 ------------- OP-SF NET 5.4 ------------ July 15, 1998 ~~~~~~~~~~~~~ From: Wolfram KoepfSubject: Book on Hypergeometric Summation Hypergeometric Summation By Wolfram Koepf Verlag Vieweg, Braunschweig/Wiesbaden, 1998, 230 pp., DM 69.00, US$ 49.00, distributed in North-America by the AMS, ISBN 3-528-06950-3 In this book "Hypergeometric Summation. An Algorithmic Approach to Summation and Special Function Identities", 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 present book is designed for use in the framework of a seminar but is also suitable for an advanced lecture course in this area. Many exercises are included. The software to this book and worksheets with the sessions in the book and the solution of the exercises can be obtained from http://www.vieweg.de/welcome/downloads/supplements.htm as compressed zip files, or from my homepage http://www.imn.htwk-leipzig.de/~koepf under "Research Activities, Projects" (www.imn.htwk-leipzig.de/~koepf/research.html). Contents: - Preface - Introduction - The Gamma Function - Hypergeometric Identities q-Hypergeometric Identities - Hypergeometric Database q-Hypergeometric Database - Holonomic Recurrence Equations Multiple Summation q-Holonomic Recurrence Equations - Gosper's Algorithm Linearization of Gosper's Algorithm q-Gosper Algorithm - The Wilf-Zeilberger Method q-WZ method - Zeilberger's Algorithm q-Zeilberger Algorithm - Extensions of the Algorithms - Petkovsek's Algorithm q-Petkovsek Algorithm - Differential Equations for Sums q-Differential Equations for Sums - Hyperexponential Antiderivatives - Holonomic Equations for Integrals - Rodrigues Formulas and Generating Functions - Appendix: Installation of the Software - Bibliography - List of Symbols - Index Wolfram Koepf

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