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 third-degree linear forms under standard algebraic operations. Several illustrative examples are shown.