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Computer Algebra in Quantum Field Theory pp 285–304Cite as

Generalization of Risch’s Algorithm to Special Functions

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Part of the book series: Texts & Monographs in Symbolic Computation ((TEXTSMONOGR))

Abstract

Symbolic integration deals with the evaluation of integrals in closed form. We present an overview of Risch’s algorithm including recent developments. The algorithms discussed are suited for both indefinite and definite integration. They can also be used to compute linear relations among integrals and to find identities for special functions given by parameter integrals. The aim of this presentation is twofold: to introduce the reader to some basic ideas of differential algebra in the context of integration and to raise awareness in the physics community of computer algebra algorithms for indefinite and definite integration.

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Acknowledgements

The author was supported by the Austrian Science Fund (FWF), grant no. W1214-N15 project DK6, by the strategic program “Innovatives OÖ 2010 plus” of the Upper Austrian Government, by DFG Sonderforschungsbereich Transregio 9 “Computergestützte Theoretische Teilchenphysik”, and by the Research Executive Agency (REA) of the European Union under the Grant Agreement number PITN-GA-2010-264564 (LHCPhenoNet).

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  1. Deutsches Elektronen-Synchrotron, DESY, Platanenallee 6, 15738, Zeuthen, Germany

    Clemens G. Raab

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  1. RISC, Johannes Kepler University, Linz, Austria

    Carsten Schneider

  2. DESY, Zeuthen, Germany

    Johannes Blümlein

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Raab, C.G. (2013). Generalization of Risch’s Algorithm to Special Functions. In: Schneider, C., Blümlein, J. (eds) Computer Algebra in Quantum Field Theory. Texts & Monographs in Symbolic Computation. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1616-6_12

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  • DOI: https://doi.org/10.1007/978-3-7091-1616-6_12

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  • Online ISBN: 978-3-7091-1616-6

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