  We consider four types of representations of solutions of GKZ system: series
representations, Laplace integral representations, Euler integral
representations, and Residue integral representations which will be introduced
in this paper. In the former half of this paper, we provide a method for
constructing integration cycles for Laplace, Residue, and Euler integral
representations and relate them to series representations. In the latter half,
we reformulate our integral representations in terms of direct images of
$D$-modules and show their equivalence.
