Confluence of Singularities in Hypergeometric Systems

抄録

A system in a Birkhoff normal form with an irregular singularity of Poincaré rank 1 at the origin and a regular singularity at infinity is dual through the Borel–Laplace transform to a system in an Okubo form. Schäfke has showed that the Birkhoff system can also be obtained from the Okubo system by a simple limiting procedure. The Okubo system comes naturally with two kinds of mixed solution bases, both of which are shown to converge under the limit procedure to the canonical sectoral solutions of the limit Birkhoff system. We define Stokes matrices of the Okubo system as connection matrices between different branches of these mixed solution bases and use them to relate the monodromy matrices of the Okubo system to the usual Stokes matrices of the limit system at the irregular singularity. This is illustrated on the example of confluence in the generalized hypergeometric equation.