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 ${\displaystyle h_{n}(x;q)}$ satisfy (for ${\displaystyle n\geq 1}$) the recurrence relation

with ${\displaystyle h_{0}(x;q)=1}$ and ${\displaystyle h_{1}(x;q)=1+x}$.

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