In this article we introduce a stability concept for the coercivity of multivariate polynomials f ∈ R[x]. In particular, we consider perturbations of f by polynomials up to the so-called degree of stable coercivity, and we analyze this stability concept in terms of the corresponding Newton polytopes at infinity. For coercive polynomials f ∈ R[x] we also introduce the order of coercivity as a me...

Polynomials orthogonal with respect to a perturbation of the Freud weight function by the addition of a mass point at zero are considered. These polynomials, called Freud-type orthogonal polynomials, satisfy a second order linear differential equation with varying polynomial coefficients. It plays an important role in the electrostatic interpretation for the distribution of zeros of the corresp...