Quantum q-Krawtchouk polynomials

Template:Italic title In mathematics, the quantum q-Krawtchouk polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Template:Harvs give a detailed list of their properties.

Definition

The polynomials are given in terms of basic hypergeometric functions by

$K_n^{qtm}(q^{-x};p,N;q)={}_2{\varphi }_1[\begin{array}{c}{q}^{-n},q^{-x}\\ q^{-N}\end{array};q;p{q}^{n+1}]n=0,1,2,\mathrm{...},N.$

References

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