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Hypergeometric summation : an algorithmic approach to summation and special function identities

Author: Wolfram Koepf
Publisher: Braunschweig : Vieweg, ©1998.
Series: Advanced lectures in mathematics.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"In this book modern algorithmic techniques for summation, most of which have been introduced within the last decade, are developed and carefully implemented in the computer algebra system Maple." "The algorithms of Gosper, Zeilberger and Petkovsek on hypergeometric summation and recurrence equations and their q-analogues are covered, and similar algorithms on differential equations are considered. An equivalent  Read more...
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Additional Physical Format: Online version:
Koepf, Wolfram.
Hypergeometric summation.
Braunschweig : Vieweg, ©1998
(OCoLC)707203555
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Wolfram Koepf
ISBN: 3528069503 9783528069506
OCLC Number: 40751779
Description: x, 230 pages ; 23 cm.
Contents: 1. The Gamma Function --
2. Hypergeometric Identities --
3. Hypergeometric Database --
4. Holonomic Recurrence Equations --
5. Gosper's Algorithm --
6. The Wilf-Zeilberger Method --
7. Zeilberger's Algorithm --
8. Extensions of the Algorithms --
9. Petkovsek's Algorithm --
10. Differential Equations for Sums --
11. Hyperexponential Antiderivatives --
12. Holonomic Equations for Integrals --
13. Rodrigues Formulas and Generating Functions --
Appendix: Installation of the Software.
Series Title: Advanced lectures in mathematics.
Responsibility: Wolfram Koepf.
More information:

Abstract:

"In this book modern algorithmic techniques for summation, most of which have been introduced within the last decade, are developed and carefully implemented in the computer algebra system Maple." "The algorithms of Gosper, Zeilberger and Petkovsek on hypergeometric summation and recurrence equations and their q-analogues are covered, and similar algorithms on differential equations are considered. An equivalent theory of hyperexponential integration due to Almkvist and Zeilberger completes the book." "The combination of all results considered gives work with orthogonal polynomials and (hypergeometric type) special functions a solid algorithmic foundation. Hence, many examples from this very active field are given." "The present book is designed for use in the framework of a seminar but is also suitable for an advanced lecture course in this area."--Jacket.

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