User:Rongator/sandbox

The Delves Lyness method is a way to locate the zeros of an analytic function numerically.

Given an area bounded by the curve $$C $$
 * $$N = \oint_C {f'(z) \over f(z)}\,dz.$$

More generally,
 * $$ p_k = \sum_{n=0}^{N}x_n^k = \oint_C z^k{f'(z) \over f(z)}\,dz.$$

The line integrals may be computed numerically to determine the value of the sums $$p_k$$. Then the Newton-Girard formulas may be used to construct a polynomial with complex zeros at the same location as $$f(z)$$. These zeros are then