Discrete q-Hermite polynomials

In mathematics, the discrete "q"-Hermite polynomials are two closely related families "h""n"("x";"q") and "ĥ""n"("x";"q") of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by . give a detailed list of their properties. "h""n"("x";"q") is also called discrete q-Hermite I polynomials and "ĥ""n"("x";"q") is also called discrete q-Hermite II polynomials.
Definition.
The discrete "q"-Hermite polynomials are given in terms of basic hypergeometric functions and the Al-Salam–Carlitz polynomials by 
and are related by