Hypergeometric Summation An Algorithmic Approach to Summation and Special Function Identities /

• Κύριος συγγραφέας: Koepf, Wolfram (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: London : Springer London : Imprint: Springer, 2014.
• Έκδοση: 2nd ed. 2014.
• Σειρά: Universitext,
• Θέματα: Mathematics.; Differential equations.; Special functions.; Algorithms.; Computer software.; Combinatorics.; Mathematical Software.; Special Functions.; Ordinary Differential Equations.

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,...

Πίνακας περιεχομένων:

• 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.