ON MELLIN-BARNES INTEGRAL REPRESENTATIONS FOR GKZ HYPERGEOMETRIC FUNCTIONS
Saiei-Jaeyeong Matsubara-Heo · Kyushu Journal of Mathematics · 2020
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.A = c.h.{0, a(1), . . ., a(N )} and vol Z ( A ) is the Euclidean volume of A multiplied by n! so that the standard simplex has a volume one.Here, c.h. stands for the convex hull.The GKZ system M A (c) naturally has a formal series solution φ v (z) associated to any vector v ∈ C N ×1 2010