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The Holonomic Toolkit

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Computer Algebra in Quantum Field Theory

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

Abstract

This is an overview over standard techniques for holonomic functions, written for readers who are new to the subject. We state the definition for holonomy in a couple of different ways, including some concrete special cases as well as a more abstract and more general version. We give a collection of standard examples and state several fundamental properties of holonomic objects. Two techniques which are most useful in applications are explained in some more detail: closure properties, which can be used to prove identities among holonomic functions, and guessing, which can be used to generate plausible conjectures for equations satisfied by a given function.

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Authors and Affiliations

  1. Research Institute for Symbolic Computation, Johannes Kepler University, A4040, Linz, Austria

    Manuel Kauers

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  1. Manuel Kauers
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Correspondence to Manuel Kauers .

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Editors and Affiliations

  1. RISC, Johannes Kepler University, Linz, Austria

    Carsten Schneider

  2. DESY, Zeuthen, Germany

    Johannes Blümlein

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Kauers, M. (2013). The Holonomic Toolkit. 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_5

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  • DOI: https://doi.org/10.1007/978-3-7091-1616-6_5

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  • Print ISBN: 978-3-7091-1615-9

  • Online ISBN: 978-3-7091-1616-6

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