  The Euler-Koszul complex is the fundamental tool in the homological study of
A-hypergeometric differential systems and functions. We compare Euler-Koszul
homology with D-module direct images from the torus to the base space through
orbits in the corresponding toric variety. Our approach generalizes a result by
Gel'fand et al. and yields a simpler, more algebraic proof.
  In the process we extend the Euler-Koszul functor a category of infinite
toric modules and describe multigraded localizations of Euler-Koszul homology.
