Affine q-Krawtchouk polynomials

The polynomials are given in terms of basic hypergeometric functions by Roelof Koekoek, Hypergeometric Orthogonal Polynomials and its q-Analogues, p. 501, Springer, 2010

: $K^\{\backslash text\{aff\}\}\_n\; (q^\{-x\};p;N;q)\; =\; \{\}\_3\backslash phi\_2\backslash left(\; \backslash begin\{matrix\}$

q^{-n},0,q^{-x}\\

pq,q^{-N}\end{matrix};q,q\right), \qquad n=0,1,2,\ldots, N.

affine q-Krawtchouk polynomials → little q-Laguerre polynomials：

: $\backslash lim\_\{a\; \backslash to\; 1\}=K\_n^\backslash text\{aff\}(q^\{x-N\};p,N\backslash mid\; q)=p\_n(q^x;p,q)$.

{{Reflist}}

• {{Citation | last1=Gasper | first1=George | last2=Rahman | first2=Mizan | title=Basic hypergeometric series | publisher=Cambridge University Press | edition=2nd | series=Encyclopedia of Mathematics and its Applications | isbn=978-0-521-83357-8 | mr=2128719 | year=2004 | volume=96}}
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Category:Orthogonal polynomials

Category:Q-analogs

Category:Special hypergeometric functions