A Formal Comparison of the Delves—Lyness and Burniston—Siewert Methods for Locating the Zeros of Analytic Functions

Abstract

The classical Delves—Lyness and Burniston—Siewert methods for the derivation of closed-form integral formulae for the zeros of analytic functions in the complex plane are compared. Although the two methods have different starting points and yield different algorithms, it is shown that when applied to the problem of locating the zeros of an analytic function inside a simple closed contour, the Delves—Lyness method is formally equivalent to a special case of the Burniston—Siewert method.