Overview
- Provides a self-contained and easy-to-read introduction to algorithmic summation
- Presents the essential algorithms due to Fasenmyer, Gosper, Zeilberger and Petkovšek
- Studies the ideas of the state-of-the-art algorithm for hypergeometric term solutions of recurrence equations (van Hoeij algorithm)
- Includes the most efficient ideas for multiple summation
- Contains many examples from the field of orthogonal polynomials and special functions
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
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Table of contents (13 chapters)
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Front Matter
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Back Matter
Keywords
- 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
- ordinary differential equations
- combinatorics
About this book
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.
Reviews
“The book under review deals with the modern algorithmic techniques for hypergeometric summation, most of which were introduced in the 1990’s. … This well-written book should be recommended for anybody who is interested in binomial summations and special functions. It should also prove useful to researchers in mathematics and/or quantum physics working in topics which associate combinatorics of special (q-)functions … with current quantum mechanics issues.” (Christian Lavault, Mathematical Reviews, August, 2015)
Authors and Affiliations
About the author
Prof. Dr. Wolfram Koepf is Professor for Computational Mathematics at the University of Kassel. He started his research in geometric function theory, switching towards orthogonal polynomials and special functions and towards computer algebra. In the 1990s he has written several books about the use of computer algebra in math education, followed by the first edition of his monograph Hypergeometric Summation. In 2006 his German language text book Computeralgebra appeared. Between 2002 and 2010 he was the Chairman of the Fachgruppe Computeralgebra , the largest computer algebra group world-wide, in 2010 he served as the General Chair of the most important international computer algebra symposium ISSAC in Munich. Since 2010 he serves as PC chair of the conference series CASC. As a member of the executive committee of the German Mathematical Union (DMV) he is the responsible editor of the web resource Mathematik.de.
Bibliographic Information
Book Title: Hypergeometric Summation
Book Subtitle: An Algorithmic Approach to Summation and Special Function Identities
Authors: Wolfram Koepf
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-4471-6464-7
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London 2014
Softcover ISBN: 978-1-4471-6463-0Published: 25 June 2014
eBook ISBN: 978-1-4471-6464-7Published: 10 June 2014
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 2
Number of Pages: XVII, 279
Number of Illustrations: 2 b/w illustrations, 3 illustrations in colour
Topics: Algorithms, Mathematical Software, Special Functions, Ordinary Differential Equations, Combinatorics