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Hypergeometric summation: an algorithmic approach to summation and special function identities

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,...

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Detalles Bibliográficos
Autor principal: Koepf, Wolfram
Lenguaje:eng
Publicado: Springer 2014
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-1-4471-6464-7
http://cds.cern.ch/record/1742585
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author Koepf, Wolfram
author_facet Koepf, Wolfram
author_sort Koepf, Wolfram
collection CERN
description 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.
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spelling cern-17425852021-04-21T20:56:41Zdoi:10.1007/978-1-4471-6464-7http://cds.cern.ch/record/1742585engKoepf, WolframHypergeometric summation: an algorithmic approach to summation and special function identitiesMathematical Physics and MathematicsModern 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.Springeroai:cds.cern.ch:17425852014
spellingShingle Mathematical Physics and Mathematics
Koepf, Wolfram
Hypergeometric summation: an algorithmic approach to summation and special function identities
title Hypergeometric summation: an algorithmic approach to summation and special function identities
title_full Hypergeometric summation: an algorithmic approach to summation and special function identities
title_fullStr Hypergeometric summation: an algorithmic approach to summation and special function identities
title_full_unstemmed Hypergeometric summation: an algorithmic approach to summation and special function identities
title_short Hypergeometric summation: an algorithmic approach to summation and special function identities
title_sort hypergeometric summation: an algorithmic approach to summation and special function identities
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-1-4471-6464-7
http://cds.cern.ch/record/1742585
work_keys_str_mv AT koepfwolfram hypergeometricsummationanalgorithmicapproachtosummationandspecialfunctionidentities