Formula:KLS:14.15:09

<< Formula:KLS:14.15:08

formula in q-Krawtchouk

Formula:KLS:14.15:10 >>

${\displaystyle{\displaystyle{\displaystyle K_{n}\!\left(q^{-x};p,N;q\right)=\frac{\left(-pq^{n};q\right)_{n}}{\left(q^{-N};q\right)_{n}}{\widehat{K}}_{n}\!\left(q^{-x}\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle K_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:qKrawtchouk
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle{\widehat{K}}_{n}}}}$ : monic ${\displaystyle{\displaystyle{\displaystyle q}}}$-Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:monicqKrawtchouk

Bibliography

Equation in Section 14.15 of KLS.

URL links

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<< Formula:KLS:14.15:08

formula in q-Krawtchouk

Formula:KLS:14.15:10 >>