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Mellin-Barnes representations of Feynman diagrams, linear systems of differential equations, and polynomial solutions
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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.
Forward citations
Cited by 6 Pith papers
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Resonance and Differential Reduction of Feynman Integrals
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.
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Numerical computation of Fox functions
A numerical toolkit, based on Sinc methods plus contiguity shifts of lambda, is presented for evaluating multivariate Fox functions representing Feynman integrals.
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High-precision numerical evaluation of Lauricella functions
A Mathematica package computes high-precision epsilon-expansions of Lauricella functions using one-dimensional Frobenius series and interpolation.
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Feynman Fox integrals in the physical region
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.
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Numerical analytical continuation of multivariate hypergeometric functions
A general numerical framework is described for high-precision evaluation and analytic continuation of multivariate hypergeometric functions via Pfaffian systems and the Frobenius method.
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$\texttt{PrecisionLauricella}$: package for numerical computation of Lauricella functions depending on a parameter
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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