Continuous q-Hermite polynomial

The continuous $q$-Hermite polynomials are defined by $$\left\{ \begin{array}{ll} H_0(x|q)=1 \\ H_1(x|q)=2x \\ H_{n+1}(x|q) = 2xH_n(x|q) - (1-q^n)H_{n-1}(x|q). \end{array} \right.$$

References

On the q-Hermite polynomials and their relationship with some other families of orthogonal polynomials