Dual q-Krawtchouk polynomials

In mathematics, the dual q-Krawtchouk 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 by

$K_n(\lambda (x);c,N|q)={}_3{\varphi }_2(q^{-n},q^{-x},c{q}^{x-N};q^{-N},0|q;q),n=0,1,2,\mathrm{...},N,$

where $\lambda (x)=q^{-x}+c{q}^{x-N}.$

Further reading

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