On the Reduction of Connection Problems for Differential Equations with an Irregular Singular Point to Ones with Only Regular Singularities, I

It is shown that a complete system of Stokes’ multipliers for a system of linear differential equations having an irregular singularity of Poincaré rank one can be calculated in terms of connection relations of certain associated functions near their regular singularities. Solutions of the differential equation are expressed as Laplace integrals of the associated functions, and the formal solutions can be summed as generalized factorial series in explicitly given half-planes of convergence.