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＜電子ブック＞
Hypergeometric Summation : An Algorithmic Approach to Summation and Special Function Identities / by Wolfram Koepf
(Universitext. ISSN:21916675)

版	2nd ed. 2014.
出版者	(London : Springer London : Imprint: Springer)
出版年	2014
本文言語	英語
大きさ	XVII, 279 p. 5 illus., 3 illus. in color : online resource
著者標目	*Koepf, Wolfram author SpringerLink (Online service)
件　名	LCSH:Algorithms LCSH:Computer software LCSH:Special functions LCSH:Differential equations LCSH:Discrete mathematics FREE:Algorithms FREE:Mathematical Software FREE:Special Functions FREE:Differential Equations FREE:Discrete Mathematics
一般注記	Introduction -- The Gamma Function -- Hypergeometric Identities -- Hypergeometric Database -- Holonomic Recurrence Equations -- Gosper’s Algorithm -- The Wilf-Zeilberger Method -- Zeilberger’s Algorithm -- Extensions of the Algorithms -- Petkovˇsek’s and Van Hoeij’s Algorithm -- Differential Equations for Sums -- Hyperexponential Antiderivatives -- Holonomic Equations for Integrals -- Rodrigues Formulas and Generating 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 HTTP:URL=https://doi.org/10.1007/978-1-4471-6464-7

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