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

Publisher Website
Google Scholar
Abstract
Our purpose is to investigate lateral and central connection problems for systems of linear differential equations near an irregular singularity. In Part I [SIAM J. Math. Anal., 12 (1981), pp. 691–721] we showed how the lateral connection problem can be solved using some associated functions constructed from a formal fundamental solution. Here, we generalize the associated functions by introducing a complex parameter and show how certain values of these functions can be used to construct solutions in so-called Floquet form. We also show how the coefficients of the formal series can be asymptotically represented using other associated functions and how the central connection problems for the Floquet solution can be solved. We conclude with an application of the main results to the global solution of a rationalized form of Mathieu’s equation that has two irregular singularities.