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Numerical evaluation of iterated integrals related to elliptic Feynman integrals

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arxiv 2010.05271 v2 pith:SE6CGR6Q submitted 2020-10-11 hep-ph hep-thmath-phmath.MP

Moritz Walden , Stefan Weinzierl This is my paper · ORCID
classification hep-phhep-thmath-phmath.MP
keywords integralsiteratedellipticcoefficientfeynmanfunctionsimplementationincludes
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We report on an implementation within GiNaC to evaluate iterated integrals related to elliptic Feynman integrals numerically to arbitrary precision within the region of convergence of the series expansion of the integrand. The implementation includes iterated integrals of modular forms as well as iterated integrals involving the Kronecker coefficient functions $g^{(k)}(z,\tau)$. For the Kronecker coefficient functions iterated integrals in $d\tau$ and $dz$ are implemented. This includes elliptic multiple polylogarithms.

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Cited by 2 Pith papers

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  1. Analytic Regression of Feynman Integrals from High-Precision Numerical Sampling

    hep-th 2025-07 conditional novelty 6.0 of 10

    Multi-point lattice reduction on high-precision numerical samples can recover exact analytic expressions for multi-loop Feynman integrals with rational coefficients.

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    hep-ph 2024-12 conditional novelty 6.0 of 10

    Presents epsilon-factorised master integrals, boundary values, and numerical routines for the planar and non-planar electroweak double-box families relevant to NNLO Moller scattering.

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