Formula:KLS:14.16:02

<< Formula:KLS:14.16:01

formula in Affine q-Krawtchouk

Formula:KLS:14.16:03 >>

${\displaystyle{\displaystyle{\displaystyle\AffqKrawtchouk{n}@{q^{-x}}{p}{N}{q}=\frac{(-pq)^{n}q^{\binomial{n}{2}}}{\qPochhammer{pq}{q}{n}}\ {{}_{2}\phi_{1}}\!\left({q^{-n},q^{x-N}\atop q^{-N}};q,\frac{q^{-x}}{p}\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle K^{\mathrm{Aff}}_{n}}}}$ : affine ${\displaystyle{\displaystyle{\displaystyle q}}}$-Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:AffqKrawtchouk
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \binom{n}{k}}}  : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

Bibliography

Equation in Section 14.16 of KLS.

URL links

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<< Formula:KLS:14.16:01

formula in Affine q-Krawtchouk

Formula:KLS:14.16:03 >>