Abstract
We show that almost all Feynman integrals as well as their coefficients in a Laurent series in dimensional regularization can be written in terms of Horn hypergeometric functions. By applying the results of Gelfand-Kapranov-Zelevinsky (GKZ) we derive a formula for a class of hypergeometric series representations of Feynman integrals, which can be obtained by triangulations of the Newton polytope ∆G corresponding to the Lee- Pomeransky polynomial G. Those series can be of higher dimension, but converge fast for convenient kinematics, which also allows numerical applications. Further, we discuss possible difficulties which can arise in a practical usage of this approach and give strategies to solve them.
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Klausen, R.P. Hypergeometric series representations of Feynman integrals by GKZ hypergeometric systems. J. High Energ. Phys. 2020, 121 (2020). https://doi.org/10.1007/JHEP04(2020)121
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DOI: https://doi.org/10.1007/JHEP04(2020)121