SIAM AG on Orthogonal Polynomials and Special Functions


Extract from OP-SF NET

Topic #8     -------------   OP-SF NET 5.4   ------------   July 15, 1998
From: Wolfram Koepf 
Subject: 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

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
as compressed zip files, or from my homepage
under "Research Activities, Projects"

- 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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