research-article

A non-holonomic systems approach to special function identities

Authors:

Frédéric Chyzak,

Bruno SalvyAuthors Info & Claims

ISSAC '09: Proceedings of the 2009 international symposium on Symbolic and algebraic computation

Pages 111 - 118

https://doi.org/10.1145/1576702.1576720

Published: 28 July 2009 Publication History

Abstract

We extend Zeilberger's approach to special function identities to cases that are not holonomic. The method of creative telescoping is thus applied to definite sums or integrals involving Stirling or Bernoulli numbers, incomplete Gamma function or polylogarithms, which are not covered by the holonomic framework. The basic idea is to take into account the dimension of appropriate ideals in Ore algebras. This unifies several earlier extensions and provides algorithms for summation and integration in classes that had not been accessible to computer algebra before.

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Cited By

Teguia Tabuguia B(2024)Hypergeometric-type sequencesJournal of Symbolic Computation10.1016/j.jsc.2024.102328(102328)Online publication date: Apr-2024
https://doi.org/10.1016/j.jsc.2024.102328
Nummelin VBlanchette JDahmen S(2023)Recurrence-Driven Summations in Automated DeductionFrontiers of Combining Systems10.1007/978-3-031-43369-6_2(23-40)Online publication date: 13-Sep-2023
https://doi.org/10.1007/978-3-031-43369-6_2
Kauers MKauers M(2023)Summation and IntegrationD-Finite Functions10.1007/978-3-031-34652-1_5(393-509)Online publication date: 22-May-2023
https://doi.org/10.1007/978-3-031-34652-1_5
Show More Cited By

Index Terms

A non-holonomic systems approach to special function identities
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms

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cover image ACM Conferences

ISSAC '09: Proceedings of the 2009 international symposium on Symbolic and algebraic computation

July 2009

402 pages

ISBN:9781605586090

DOI:10.1145/1576702

General Chairs:
Jeremy Johnson
Drexel University, USA
,
Hyungju Park
Korea Institute for Advanced Study, Korea
,
Program Chair:
Erich Kaltofen
North Carolina State University, USA

Copyright © 2009 ACM.

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Published: 28 July 2009

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ISSAC '09: International Symposium on Symbolic and Algebraic Computation

July 28 - 31, 2009

Seoul, Republic of Korea

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Cited By

Teguia Tabuguia B(2024)Hypergeometric-type sequencesJournal of Symbolic Computation10.1016/j.jsc.2024.102328(102328)Online publication date: Apr-2024
https://doi.org/10.1016/j.jsc.2024.102328
Nummelin VBlanchette JDahmen S(2023)Recurrence-Driven Summations in Automated DeductionFrontiers of Combining Systems10.1007/978-3-031-43369-6_2(23-40)Online publication date: 13-Sep-2023
https://doi.org/10.1007/978-3-031-43369-6_2
Kauers MKauers M(2023)Summation and IntegrationD-Finite Functions10.1007/978-3-031-34652-1_5(393-509)Online publication date: 22-May-2023
https://doi.org/10.1007/978-3-031-34652-1_5
Kauers MKauers M(2023)OperatorsD-Finite Functions10.1007/978-3-031-34652-1_4(287-391)Online publication date: 22-May-2023
https://doi.org/10.1007/978-3-031-34652-1_4
Kauers MKauers M(2023)The Differential Case in One VariableD-Finite Functions10.1007/978-3-031-34652-1_3(185-286)Online publication date: 22-May-2023
https://doi.org/10.1007/978-3-031-34652-1_3
Kauers MKauers M(2023)The Recurrence Case in One VariableD-Finite Functions10.1007/978-3-031-34652-1_2(81-183)Online publication date: 22-May-2023
https://doi.org/10.1007/978-3-031-34652-1_2
Kauers MKauers M(2023)Background and Fundamental ConceptsD-Finite Functions10.1007/978-3-031-34652-1_1(1-80)Online publication date: 22-May-2023
https://doi.org/10.1007/978-3-031-34652-1_1
Raab C(2022)Comments on Risch’s On the Integration of Elementary Functions which are Built Up Using Algebraic OperationsIntegration in Finite Terms: Fundamental Sources10.1007/978-3-030-98767-1_6(217-229)Online publication date: 7-Jun-2022
https://doi.org/10.1007/978-3-030-98767-1_6
Schneider C(2021)Term Algebras, Canonical Representations and Difference Ring Theory for Symbolic SummationAnti-Differentiation and the Calculation of Feynman Amplitudes10.1007/978-3-030-80219-6_17(423-485)Online publication date: 10-Jul-2021
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Chen SDu LWang RZhu C(2020)On the existence of telescopers for rational functions in three variablesJournal of Symbolic Computation10.1016/j.jsc.2020.08.006Online publication date: Aug-2020
https://doi.org/10.1016/j.jsc.2020.08.006
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