Rogers–Szegő polynomials

Rogers–Szegő polynomials are a sequence of orthogonal polynomials that arise in the theory of special functions, particularly in the context of approximation theory and the study of orthogonal functions. They are associated with certain weight functions over the unit circle and have applications in various areas including combinatorics, number theory, and mathematical physics. The Rogers–Szegő polynomials can be defined in terms of a generating function.