Euler and Laplace integral representations of GKZ hypergeometric functions. I (Q2225636)

The author introduces an integral representation of GKZ hypergeometric functions. which generalizes the Euler-Laplace integral representation. It is claimed that, when parameters \(\delta\) of the integrand are non-resonant, the \(\mathcal D\)-module corresponding to the Euler-Laplace integral is isomorphic to the GKZ hypergeometric system \(M_A(\delta)\), where \(A\) is a generalization of Cayley configuration. Moreover, an isomorphism between a certain rapid decay homology group and the holomorphic solutions of the GKZ hypergeometric system is established.