On Mellin-Barnes integral representations for GKZ hypergeometric functions

TL;DR

This paper develops explicit Mellin-Barnes integral representations for GKZ hypergeometric functions, constructing integration contours and demonstrating how analytic continuation yields a basis of solutions.

Contribution

It provides a new explicit construction of Mellin-Barnes integrals and contours for GKZ hypergeometric functions, enhancing understanding of their solution spaces.

Findings

Explicit integration contours are constructed for GKZ hypergeometric functions.

Analytic continuation of these integrals forms a basis of solutions.

The method clarifies the structure of solutions to GKZ equations.

Abstract

We consider Mellin-Barnes integral representations of GKZ hypergeometric equations. We construct integration contours in an explicit way and show that suitable analytic continuations give rise to a basis of solutions.