A note on the zeros of Freud–Sobolev orthogonal polynomials

We prove that the zeros of a certain family of Sobolev orthogonal polynomials involving the Freud weight function e - x 4 on R are real, simple, and interlace with the zeros of the Freud polynomials, i.e., those polynomials orthogonal with respect to the weight function e - x 4 . Some numerical examples are shown.