Rogers–Szegő polynomials

In mathematics, the Rogers–Szegő polynomials are a family of polynomials orthogonal on the unit circle introduced by Szegő (1926), who was inspired by the continuous q-Hermite polynomials studied by Leonard James Rogers. They are given by

where (q;q)n is the descending q-Pochhammer symbol.

Furthermore, the satisfy (for ) the recurrence relation

with and .