Pfaffian of Lauricella's hypergeometric system $F_A$

Abstract

We give a Pfaffian system of differential equations annihilating Lauricella's hypergeometric series $F_A(a,b,c;x)$ of $m$-variables. This system is integrable of rank $2^m$. To express the connection form of this system, we make use of the intersection form of twisted cohomology groups with respect to integrals representing solutions of this system.