An electrostatic interpretation of the zeros of the Freud-type orthogonal polynomials (Q2388694)

The paper deals with so-called Freud-type orthogonal polynomials which are orthogonal on the real line with respect to the Freud weight function \(e^{-x^4}\) together with a point mass distribution at zero. These polynomials satisfy a second-order linear differential equation with polynomial coefficients depending on the degree of the polynomials. This differential equation is derived explicitly by using a combination of a (degree) lowering and a (degree) raising operator for these Freud-type orthogonal polynomials. The second-order differential equation leads to an electrostatic model in the presence of a varying external potential. The asymptotic behavior of the position of movable constant charges involved in the external field is obtained.