Algebraic approach to univariate polynomial derivation (Q2059919)

The authors propose an algebraic approach to polynomial derivation based on the notion of Fibonacci, Tribonacci, Quatronacci, Pentanacci, \(\ldots\), \(N\)-acci sequences. Starting from \(n\) roots of a univariate polynomial of \(n\)-th degree, combining the first, the second, and up to the \(n\)-th class, new polynomials are generated. Each class of polynomials obtained in such a way is fully determined by its roots. The arithmetic means of the corresponding coefficients are proportional to the values of the coefficients obtained by the derivation of the initial univariate polynomial.