A New Generator of Third-Degree Linear Forms

This paper examines linear forms of the third-degree, i.e., when the associated Stieltjes function satisfies a cubic equation with polynomial coefficients.A generator for third-degree forms is constructed.In fact, we study the stability of the third-degree character under this transformation that generalizes the rational spectral transformation.Moreover, we prove the stability of thirddegree linear forms under standard algebraic operations.Several illustrative examples are shown.