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Integration of unspecified functions and families of iterated integrals

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Clemens G. RaabAuthors Info & Claims

ISSAC '13: Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation

Pages 323 - 330

https://doi.org/10.1145/2465506.2465939

Published: 26 June 2013 Publication History

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Abstract

An algorithm for parametric elementary integration over differential fields constructed by a differentially transcendental extension is given. It extends current versions of Risch's algorithm to this setting and is based on some first ideas of Graham H. Campbell transferring his method to more formal grounds and making it parametric, which allows to compute relations among definite integrals. Apart from differentially transcendental functions, such as the gamma function or the zeta function, also unspecified functions and certain families of iterated integrals such as the polylogarithms can be modeled in such differential fields.

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Cited By

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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
Boulier FLemaire FLallemand JRegensburger GRosenkranz M(2019)Additive normal forms and integration of differential fractionsJournal of Symbolic Computation10.1016/j.jsc.2016.01.00277:C(16-38)Online publication date: 3-Jan-2019
https://dl.acm.org/doi/10.1016/j.jsc.2016.01.002
Koutschan CRanetbauer HRegensburger GWolfram M(2015)Symbolic Derivation of Mean-Field PDEs from Lattice-Based ModelsProceedings of the 2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)10.1109/SYNASC.2015.14(27-33)Online publication date: 21-Sep-2015
https://dl.acm.org/doi/10.1109/SYNASC.2015.14

Index Terms

Integration of unspecified functions and families of iterated integrals
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms

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Published In

ISSAC '13: Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation

June 2013

400 pages

ISBN:9781450320597

DOI:10.1145/2465506

General Chairs:
Michael Monagan
Simon Fraser University, Burnaby, Canada
,
Gene Cooperman
Northeastern University, Boston, USA
,
Program Chair:
Mark Giesbrecht
University of Waterloo, Waterloo, Canada

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Published: 26 June 2013

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ISSAC'13: International Symposium on Symbolic and Algebraic Computation

June 26 - 29, 2013

Maine, Boston, USA

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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
Boulier FLemaire FLallemand JRegensburger GRosenkranz M(2019)Additive normal forms and integration of differential fractionsJournal of Symbolic Computation10.1016/j.jsc.2016.01.00277:C(16-38)Online publication date: 3-Jan-2019
https://dl.acm.org/doi/10.1016/j.jsc.2016.01.002
Koutschan CRanetbauer HRegensburger GWolfram M(2015)Symbolic Derivation of Mean-Field PDEs from Lattice-Based ModelsProceedings of the 2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)10.1109/SYNASC.2015.14(27-33)Online publication date: 21-Sep-2015
https://dl.acm.org/doi/10.1109/SYNASC.2015.14

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Generalized Hermite Reduction, Creative Telescoping and Definite Integration of D-Finite Functions

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