A new, simple approach to the derivation of exact analytical formulae for the zeros of analytic functions

摘要

A very simple method for the construction of the polynomial whose zeros coincide with the zeros of an analytic function inside and along a simple closed contour in the complex plane, based on an appropriate application of the Cauchy theorem in complex analysis, is proposed. The present method was motivated by the classical Burniston-Siewert method, based on the theory of the Riemann-Hilbert boundary-value problem for the construction of the aforementioned polynomial, but, although essentially equivalent to the Burniston-Siewert method, it is much simpler.