Determination of poles of sectionally meromorphic functions

摘要

The numerical methods of Abd-Ellal, Delves and Reid for locating poles of meromorphic functions inside smooth closed contours C in the complex plane are generalized to apply to sectionally meromorphic functions satisfying a homogeneous or nonhomogeneous Riemann-Hilbert boundary value problem on the simple closed contours of their discontinuity (which may intersect C). In the first case, the zeros of the meromorphic functions can be determined as well. Two simple illustrations of the present generalization are also presented.