On the Hadamard and Vandermonde determinants and the Bernoulli–Euler–Lagrange–Aitken method for calculating the roots of polynomials

The article develops an Euler–Lagrange method for calculating all the roots of an arbitrary polynomial $P(z)$ with complex coefficients. The method is based on calculating the limits of ratios of determinants (as in the Bernoulli–Aitken methods) constructed from the coefficients of the Taylor and Laurent series expansions of the function $P'(z)/P(z)$.