Orthogonal polynomials for self-dual weights

Abstract

A class of orthogonal polynomials relative to special discrete weights is considered. These self-dual weights which are completely determined by their finite support appear in the polynomial approximation of a function over this set, in the barycentric form of classical Lagrange interpolation polynomial as well as in mathematical statistics and statistical physics. Orthogonal polynomials possess remarkable symmetry reflected in the properties of their coefficients in the three-term recurrence relations, some of which have an explicit form. Formulas for the expected values are derived.