Continuous q-Hermite polynomials


In mathematics, the continuous q-Hermite polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. give a detailed list of their properties.

Definition

The polynomials are given in terms of basic hypergeometric functions and the Pochhammer symbol.

Recurrence and difference relations

with the initial conditions
From the above, one can easily calculate:

Rodrigues formula

Generating function

where.

Relation to other polynomials