Computation of the Stokes Multipliers of Okubo’s Confluent Hypergeometric System
نویسندگان
چکیده
The Stokes multipliers of Okubo’s confluent hypergeometric system can, in general, not be expressed in closed form using known special functions. Instead they may themselves be regarded as highly interesting new functions of the system’s parameters. In this article we study their dependence on the eigenvalues of the leading term. Doing so, we obtain several interesting representations in terms of power series in several variables. As an application we show that the Stokes multipliers may be obtained with help of the sum of a formal solution of a system of difference equations whose dimension is smaller than that of the hypergeometric one. AMS Subject Classifications: 34A25, 34A30, 33C99.
منابع مشابه
Nonlinear Difference Equations and Stokes Matrices
We study one scalar holomorphic function of finitely many complex variables which, under the assumption that one of the two coefficient matrices has all distinct eigenvalues, allows to calculate the Stokes multipliers of Okubo’s confluent hypergeometric system. Many properties of this function, including a nonlinear functional equation, are obtained. An open question is whether the function is ...
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