In mathematics, the continuous q-Hermite polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme.
Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.
The polynomials are given in terms of basic hypergeometric functions by with the initial conditions From the above, one can easily calculate: where
x = cos θ
{\displaystyle \textstyle x=\cos \theta }