Laplace, Residue, and Euler integral representations of GKZ hypergeometric functions

Understand

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.