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Four Lectures on Euler Integrals

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arxiv 2306.13578 v2 pith:M6LSUIEG submitted 2023-06-23 math-ph hep-thmath.AGmath.MP

classification math-phhep-thmath.AGmath.MP
keywords integralseulerfouraffinealgebraamplitudesapplicationsarise
verification ladder T0 review T1 audit T2 compute T3 formal
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These lecture notes provide a self-contained introduction to Euler integrals, which are frequently encountered in applications. In particle physics, they arise as Feynman integrals or string amplitudes. Our four selected topics demonstrate the diverse mathematical techniques involved in the study of Euler integrals, including polyhedral geometry, very affine varieties, differential equations, and computational algebra.

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Cited by 4 Pith papers

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    The one-loop triangle in-in correlator of massless scalars in flat space is evaluated in closed form in terms of dilogarithms, with Landau analysis revealing its physical singularities and a partial-energy factorisati...

  2. A double copy from twisted (co)homology at genus g

    hep-th 2025-09 conditional novelty 7.0 of 10

    A double-copy (KLT-type) formula for genus-g hypergeometric integrals is derived from twisted homology intersection numbers and verified numerically at genus two.

  3. High-precision numerical evaluation of Lauricella functions

    hep-th 2025-02 conditional novelty 6.0 of 10

    A Mathematica package computes high-precision epsilon-expansions of Lauricella functions using one-dimensional Frobenius series and interpolation.

  4. $\texttt{PrecisionLauricella}$: package for numerical computation of Lauricella functions depending on a parameter

    cs.MS 2025-02 conditional novelty 4.0 of 10

    PrecisionLauricella is a Mathematica package that computes epsilon-expansions of Lauricella F_A, F_B, and F_D functions for n up to 3 using Frobenius-series analytic continuation.

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