# Hypergeometric Summation

## An Algorithmic Approach to Summation and Special Function Identities

- 40 Citations
- 23k Downloads

Part of the Universitext book series (UTX)

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Textbook

- 40 Citations
- 23k Downloads

Part of the Universitext book series (UTX)

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

- DOI https://doi.org/10.1007/978-1-4471-6464-7
- Copyright Information Springer-Verlag London 2014
- Publisher Name Springer, London
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Print ISBN 978-1-4471-6463-0
- Online ISBN 978-1-4471-6464-7
- Series Print ISSN 0172-5939
- Series Online ISSN 2191-6675
- Buy this book on publisher's site