q-Krawtchouk polynomials

In mathematics, the 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.

Template:Harvtxt showed that the q-Krawtchouk polynomials are spherical functions for 3 different Chevalley groups over finite fields, and Template:Harvtxt showed that they are related to representations of the quantum group SU(2).

Definition

The polynomials are given in terms of basic hypergeometric functions by

$K_n(q^{-x};p,N;q)={}_3{\varphi }_2[\begin{array}{c}{q}^{-n},q^{-x},-p{q}^n\\ q^{-N},0\end{array};q,q],n=0,1,2,\mathrm{...},N.$

See also

• affine q-Krawtchouk polynomials
• dual q-Krawtchouk polynomials
• quantum q-Krawtchouk polynomials

Sources

• Template:Citation
• Template:Citation
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• Template:Cite thesis
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