Abstract
The generalized Siewert-Burniston method for the determination of the zeros of an analytic function inside a simple closed contourC in the complex plane is modified to be applicable to the determination of both the zeros and the poles of a meromorphic function insideC. The method is based again on the solution of a homogeneous Riemann-Hilbert boundary value problem onC and the values of the meromorphic function onC are sufficient for the application of the method.
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