Reflection coefficients counterpart of Cardan-Viete formulas

Polynomials can be represented by their coefficients or by their zeros. The link between these two representations is the Cardan-Viete formulas that let us express the coefficients as elementary symmetric functions in the zeros. In this paper, as a consequence of Levinson recursion, we present a counterpart to the Cardan-Viete formulas that expresses the polynomial coefficients or the regression vector of an autoregressive filter, when a lattice representation is considered, in terms of its reflection coefficients.