Universitext

Hypergeometric Summation

An Algorithmic Approach to Summation and Special Function Identities

Authors: Koepf, Wolfram

  • 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
see more benefits

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-1-4471-6464-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-1-4471-6463-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this Textbook

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.

About the authors

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.

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)


Video

Table of contents (13 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-1-4471-6464-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-1-4471-6463-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Hypergeometric Summation
Book Subtitle
An Algorithmic Approach to Summation and Special Function Identities
Authors
Series Title
Universitext
Copyright
2014
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
eBook ISBN
978-1-4471-6464-7
DOI
10.1007/978-1-4471-6464-7
Softcover ISBN
978-1-4471-6463-0
Series ISSN
0172-5939
Edition Number
2
Number of Pages
XVII, 279
Number of Illustrations and Tables
2 b/w illustrations, 3 illustrations in colour
Topics