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Nested Integrals and Rationalizing Transformations

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Anti-Differentiation and the Calculation of Feynman Amplitudes

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Abstract

A brief overview of some computer algebra methods for computations with nested integrals is given. The focus is on nested integrals over integrands involving square roots. Rewrite rules for conversion to and from associated nested sums are discussed. We also include a short discussion comparing the holonomic systems approach and the differential field approach. For simplification to rational integrands, we give a comprehensive list of univariate rationalizing transformations, including transformations tuned to map the interval [0, 1] bijectively to itself.

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Acknowledgements

The author wants to thank Jakob Ablinger for useful discussions. The author is supported by the Austrian Science Fund (FWF) grant P 31952.

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Correspondence to Clemens G. Raab .

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Raab, C.G. (2021). Nested Integrals and Rationalizing Transformations. In: Blümlein, J., Schneider, C. (eds) Anti-Differentiation and the Calculation of Feynman Amplitudes. Texts & Monographs in Symbolic Computation. Springer, Cham. https://doi.org/10.1007/978-3-030-80219-6_16

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  • DOI: https://doi.org/10.1007/978-3-030-80219-6_16

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