Asymptotic expansions and Stokes multipliers of the confluent hypergeometric function Φ_2 Ⅱ. Behaviour near (∞,∞) in P~1(C) x P~1(C)

摘要

Observing that (x - y)z_(xy) - β′z_x + βz_y = 0, we can verify that (z,xz_x,yz_y) satisfies a Pfaffian system which possesses the singular loci x = 0, y = 0, x = y of regular type and x = ∞, y = ∞ of irregular type, and that the solutions of (1.2) constitute a three-dimensional vector space over C. In the previous paper, we defined linearly independent solutions z_+, z_0, z_- admitting integral representations. Modifying the paths of integration, we obtained monodromy matrices with respect to them.