A system associated with the confluent hypergeometric function Φ₃ and a certain linear ordinary differential equation with two irregular singular points

The confluent hypergeometric function Φ₃ satisfies a system of partial differential equations on P¹(C) × P¹ (C) with the singular loci x = 0, x = ∞, y = ∞ of irregular type and y = 0 of regular type. We obtain asymptotic expansions and Stokes multipliers of linearly independent solutions near the singular loci x = 0 and x = ∞. Applying the results we also clarify the global behaviour of the solutions of a third order linear ordinary differential equation with two irregular singular points.