Hypergeometric Summation
An Algorithmic Approach to Summation and Special Function Identities
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Beschreibung
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.
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.
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
Autor*in
Wolfram Koepf
Themen in »Hypergeometric Summation«
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
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“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)
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