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High Energy Physics - Theory, hep-th
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.
