Meromorphic solutions of linear differential systems, Painlevé type functions

We consider the n n matrix linear differential systems in the complex plane. We find necessary and sufficient conditions under which these systems have meromorphic fundamental solutions. Using the operator identity method we construct a set of systems which have meromorphic solutions. We prove that the well known operator with the sine kernel generates a class of meromorphic Painlev type functions. The fifth Painlev function belongs to this class. Hence we obtain a new and simple proof that the fifth Painlev function is meromorphic.