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
Clasificación:Libro Electrónico
Autor principal: Koepf, Wolfram (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: London : Springer London : Imprint: Springer, 2014.
Edición:2nd ed. 2014.
Colección:Universitext,
Temas:
Algorithms.
Computer software.
Special functions.
Differential equations.
Discrete mathematics.
Mathematical Software.
Special Functions.
Differential Equations.
Discrete Mathematics.
Acceso en línea:Texto Completo

MARC

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245 1 0 |a Hypergeometric Summation  |h [electronic resource] :  |b An Algorithmic Approach to Summation and Special Function Identities /  |c by Wolfram Koepf. 
250 |a 2nd ed. 2014. 
264 1 |a London :  |b Springer London :  |b Imprint: Springer,  |c 2014. 
300 |a XVII, 279 p. 5 illus., 3 illus. in color.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
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490 1 |a Universitext,  |x 2191-6675 
505 0 |a 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. 
520 |a 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. 
650 0 |a Algorithms. 
650 0 |a Computer software. 
650 0 |a Special functions. 
650 0 |a Differential equations. 
650 0 |a Discrete mathematics. 
650 1 4 |a Algorithms. 
650 2 4 |a Mathematical Software. 
650 2 4 |a Special Functions. 
650 2 4 |a Differential Equations. 
650 2 4 |a Discrete Mathematics. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9781447164654 
776 0 8 |i Printed edition:  |z 9781447164630 
830 0 |a Universitext,  |x 2191-6675 
856 4 0 |u https://doi.uam.elogim.com/10.1007/978-1-4471-6464-7  |z Texto Completo 
912 |a ZDB-2-SMA 
912 |a ZDB-2-SXMS 
950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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