We rst give a brief survey of some aspects of orthogonal polynomials. The three-term recurrence relation gives a tridiagonal matrix and the corresponding Ja-cobi operator gives useful information about the orthogonalizing measure and the asymptotic behavior of the zeros of the orthogonal polynomials. The Toda lattice and other similar dynamical systems (Langmuir lattice or Kac-Van Moerbeke latt...

Given an orthogonal polynomial sequence on the real line, another of polynomials can be found by composing them with a Möbius transformation. In this work, we study properties such Möbius-transformed in systematically way. We show that these are given curve complex plane respect to particular kind varying measure, and they enjoy several common line. Moreover, many easier derived from approach, ...

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...