PFAFFIAN SYSTEMS OF CONFLUENT HYPERGEOMETRIC FUNCTIONS OF TWO VARIABLES

Abstract

We study Pfaffian systems of confluent hypergeometric functions of two variables with rank three, by using rational twisted cohomology groups associated with Euler-type integral representations of them. We give bases of the cohomology groups, whose intersection matrices depend only on parameters. Each connection matrix of our Pfaffian systems admits a decomposition into five parts, each of which is the product of a constant matrix and a rational 1-form on the space of variables.