A Generalization of the Orlando Formula — Symbolic Manipulation Approach
In this paper some new results on polynomials whose roots are linear combinations (with fixed integer coefficients) of the roots of other polynomial are presented. This research is motivated by a new method for calculation of a generalized integral criterion with the integrand function being an arbitrary polynomial of the transient error.
The well known Orlando formula establishes the useful relation between the Hurwitz determinants and the polynomial whose roots are sums of the roots of a given polynomial. However, this is only a special case of the formulae derived in this paper.
In the paper two approaches are presented. The first one uses a recursive procedure based on resultants and Hurwitz determinants, and the second exploits the theory of symmetric functions. Both methods are implemented as symbolic manipulation algorithms in Maple V. The results obtained are illustrated with an example of application.
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