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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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Bibliographic Details
Main Author: Koepf, Wolfram
Format: eBook
Language:English
Published: London Springer London 2014, 2014
Edition:2nd ed. 2014
Series:Universitext
Subjects:
Special Functions
Algorithms
Computer Software
Discrete Mathematics
Differential Equations
Mathematical Software
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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

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