Meromorphic Solutions of Linear Differential Systems, Painlevé Type Functions
نویسنده
چکیده
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 Painlevé type functions. The fifth Painlevé function belongs to this class. Hence we obtain a new and simple proof that the fifth Painlevé function is meromorphic. Mathematics subject classification (2000): 34M05, 34M55, 47B38.
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