Monotonicity properties of the zeros of Freud and sub-range Freud polynomials: Analytic and empirical results

Freud and sub-range Freud polynomials are orthogonal with respect to the weight function $w(t)=\vert t\vert^\mu \exp (-\vert t\vert^\nu )$, $\mu >-1$, $\nu >0$, supported on the whole real line $\mathbb{R}$, resp. on strict subintervals thereof. The zeros of these polynomials are studied here as functions of $\nu$ and shown, analytically and empirically by computation, to collectively increase or decrease on appropriate intervals of the variable $\nu$.