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

✍ Scribed by Prof. Dr. Wolfram Koepf (auth.)

• Publisher: Vieweg+Teubner Verlag
• Year: 1998
• Tongue: English
• Leaves: 241
• Series: Advanced Lectures in Mathematics
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Content:
Front Matter....Pages I-X
Introduction....Pages 1-3
The Gamma Function....Pages 4-10
Hypergeometric Identities....Pages 11-30
Hypergeometric Database....Pages 31-43
Holonomic Recurrence Equations....Pages 44-60
Gosper’s Algorithm....Pages 61-79
The Wilf-Zeilberger Method....Pages 80-92
Zeilberger’s Algorithm....Pages 93-123
Extensions of the Algorithms....Pages 124-139
Petkovšek’s Algorithm....Pages 140-163
Differential Equations for Sums....Pages 164-182
Hyperexponential Antiderivatives....Pages 183-193
Holonomic Equations for Integrals....Pages 194-206
Rodrigues Formulas and Generating Functions....Pages 207-213
Back Matter....Pages 214-230