Hypergeometric Summation An Algorithmic Approach to Summation and Special Function Identities /
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,...
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| Language: | English |
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London :
Springer London : Imprint: Springer,
2014.
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| Edition: | 2nd ed. 2014. |
| Series: | Universitext,
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| Online Access: | https://doi.org/10.1007/978-1-4471-6464-7 |
Table of Contents:
- Introduction
- The Gamma Function
- Hypergeometric Identities
- Hypergeometric Database
- Holonomic Recurrence Equations
- Gosper’s Algorithm
- The Wilf-Zeilberger Method
- Zeilberger’s Algorithm
- Extensions of the Algorithms
- Petkovˇsek’s and Van Hoeij’s Algorithm
- Differential Equations for Sums
- Hyperexponential Antiderivatives
- Holonomic Equations for Integrals
- Rodrigues Formulas and Generating Functions.