Dual q-Hahn polynomials

In mathematics, the dual q-Hahn 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. $R_n(q^{-x}+\gamma \delta q^{x+1},\gamma ,\delta ,N|q)={}_3{\varphi }_2[\begin{array}{c}{q}^{-n},q^{-x},\gamma \delta q^{x+1}\\ \gamma q,q^{-N}\end{array};q,q],n=0,1,2,\mathrm{...},N$

References

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