CAOP - Computer Algebra & Orthogonal Polynomials
Wolfram Koepf : Hypergeometric Summation . An Algorithmic Approach to Summation and Special Function Identities, Springer Universitext Series , 2014. XII, 253 pp., ISBN 978-1-4471-6463-0
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 func
CAOP - Computer Algebra & Orthogonal Polynomials