Classical orthogonal polynomials of a discrete variable and representations of the three-dimensional rotation group (Q1101590)

The authors construct a general theory of classical orthogonal polynomials of one discrete variable, which is defined on certain classes of nonuniform networks. These polynomials are solutions of a difference equation of second order, which is a difference analog of the hypergeometric equation. Difference derivatives of polynomials under consideration satisfy the difference equation of the same type. A Rodrigues formula and orthogonality relations are derived. As particular cases, the authors obtain Krawtchouk, Meixner, Charlier, Hahn, Racah and dual Hahn polynomials of a discrete variable. Authors discuss also the relation of classical orthogonal polynomials of a discrete variable to the representation theory for the group SO(3).