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.
| ISBN: | 9781447164630 |
| Publication date: | 25th June 2014 |
| Author: | Wolfram Koepf |
| Publisher: | Springer an imprint of Springer London |
| Format: | Paperback |
| Pagination: | 279 pages |
| Series: | Universitext |
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.
Paperback. Not Available.
Hypergeometric Summation was written by Wolfram Koepf and published by Springer an imprint of Springer London
Hypergeometric Summation has 279 pages
Yes it is part of Universitext series