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Mellin-Barnes representations of Feynman diagrams, linear systems of differential equations, and polynomial solutions

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arxiv 1205.1697 v2 pith:TMWQBORY submitted 2012-05-08 hep-th math-phmath.MP

classification hep-thmath-phmath.MP
keywords differentialdiagramsequationsfeynmansystemslinearmellin-barnesrepresentations
verification ladder T0 review T1 audit T2 compute T3 formal
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We argue that the Mellin-Barnes representations of Feynman diagrams can be used for obtaining linear systems of homogeneous differential equations for the original Feynman diagrams with arbitrary powers of propagators without recourse to the integration-by-parts technique. These systems of differential equations can be used (i) for the differential reductions to sets of basic functions and (ii) for counting the numbers of master integrals.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Resonance and Differential Reduction of Feynman Integrals

    hep-th 2026-06 unverdicted novelty 7.0 of 10

    The paper develops reduction operators from resonance in GKZ systems to contract edges in Feynman graphs for one-loop, sunrise, and banana graphs, closing differential equation systems to master integrals.

  2. Numerical computation of Fox functions

    hep-ph 2025-06 conditional novelty 6.0 of 10

    A numerical toolkit, based on Sinc methods plus contiguity shifts of lambda, is presented for evaluating multivariate Fox functions representing Feynman integrals.

  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. Feynman Fox integrals in the physical region

    hep-ph 2025-06 conditional novelty 5.0 of 10

    A recipe is given that expresses physical-region Feynman integrals as Fox functions on vertical Mellin-Barnes contours with the correct cut structure, but the claimed imaginary-part correctness is not yet verified.

  5. Numerical analytical continuation of multivariate hypergeometric functions

    math-ph 2026-05 unverdicted novelty 4.0 of 10

    A general numerical framework is described for high-precision evaluation and analytic continuation of multivariate hypergeometric functions via Pfaffian systems and the Frobenius method.

  6. $\texttt{PrecisionLauricella}$: 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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