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We show that almost all Feynman integrals as well as their coefficients in aLaurent series in dimensional regularization can be written in terms of Hornhypergeometric functions. By applying the results ofGelfand-Kapranov-Zelevinsky (GKZ) we derive a formula for a class ofhypergeometric series representations of Feynman integrals, which can beobtained by triangulations of the Newton polytope $\Delta_G$ corresponding tothe Lee-Pomeransky polynomial $G$. Those series can be of higher dimension, butconverge fast for convenient kinematics, which also allows numericalapplications. Further, we discuss possible difficulties which can arise in apractical usage of this approach and give strategies to solve them.

Hypergeometric Series Representations of Feynman Integrals by GKZ Hypergeometric Systems