2nd ed. 2014, XVII, 279 p. 5 illus., 3 illus. in color.
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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
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.