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arXiv · 1910.08651

Hypergeometric Series Representations of Feynman Integrals by GKZ Hypergeometric Systems

René Pascal Klausen
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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 $\Delta_G$ 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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René Pascal Klausen. 2019-10-18. Hypergeometric Series Representations of Feynman Integrals by GKZ Hypergeometric Systems. https://doi.org/10.1007/jhep04(2020)121

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