Hypergeometric functions in several variables, arising from connection problems for meromorphic differential equations (Q1067056)

In an earlier paper, the author introduced a class of hypergeometric functions in several complex variables by means of their power series expansion about the origin. These functions arose naturally from connection problems of certain systems of differential equations. This paper is devoted to an analysis of the properties of these functions. In detail, we show that they satisfy partial differential equations and have integral representations which provide their analytic continuation, with respect to every variable, into a complex plane with a cut from one to infinity along the positive real axis. Moreover, we analyze the behavior of the functions at the singularities one and infinity and show how they change under analytic continuation across the cut.