Hypergeometric Summation

An Algorithmic Approach to Summation and Special Function Identities

  • Wolfram Koepf

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Wolfram Koepf
    Pages 1-10
  3. Wolfram Koepf
    Pages 11-33
  4. Wolfram Koepf
    Pages 35-48
  5. Wolfram Koepf
    Pages 49-77
  6. Wolfram Koepf
    Pages 79-101
  7. Wolfram Koepf
    Pages 103-116
  8. Wolfram Koepf
    Pages 117-151
  9. Wolfram Koepf
    Pages 153-168
  10. Wolfram Koepf
    Pages 169-204
  11. Wolfram Koepf
    Pages 205-225
  12. Wolfram Koepf
    Pages 227-237
  13. Wolfram Koepf
    Pages 239-254
  14. Wolfram Koepf
    Pages 255-269
  15. Back Matter
    Pages 271-279

About this book


Modern algorithmic techniques for summation, most of which were introduced in the 1990s, are developed here and carefully implemented in the computer algebra system Maple™.

The algorithms of Fasenmyer, Gosper, Zeilberger, Petkovšek and van Hoeij for hypergeometric summation and recurrence equations, efficient multivariate summation as well as q-analogues of the above algorithms are covered. Similar algorithms concerning differential equations are considered. An equivalent theory of hyperexponential integration due to Almkvist and Zeilberger completes the book.

The combination of these results gives orthogonal polynomials and (hypergeometric and q-hypergeometric) special functions a solid algorithmic foundation. Hence, many examples from this very active field are given.

The materials covered are suitable for an introductory course on algorithmic summation and will appeal to students and researchers alike.


Algorithmic Summation Antidifference Basic Hypergeometric Series Differential Equation Fasenmyer Algorithm Generating Function Gosper Algorithm Hypergeometric Series Non-commutative Factorization Operator Equation Petkovsek Algorithm Recurrence Equation Rodrigues Formulas Van Hoeij Algorithm Zeilberger Algorithm

Authors and affiliations

  • Wolfram Koepf
    • 1
  1. 1.University of KasselKasselGermany

Bibliographic information