Continuous big q-Hermite polynomials

In mathematics, the continuous big 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.

Definition

The polynomials are given in terms of basic hypergeometric functions. $H_n(x;a|q)=a^{-n}{}_3{\varphi }_2[\begin{array}{c}{q}^{-n},a{e}^{i\theta },a{e}^{-i\theta }\\ 0,0\end{array};q,q],x=\cos \theta .$

References

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