Formula:KLS:14.14:06

<< Formula:KLS:14.14:05

formula in Quantum q-Krawtchouk

Formula:KLS:14.14:07 >>

${\displaystyle{\displaystyle{\displaystyle K^{\mathrm{qtm}}_{n}\!\left(q^{-x};p,N;q\right)=\frac{p^{n}q^{n^{2}}}{\left(q^{-N};q\right)_{n}}{\widehat{K}^{\mathrm{qtm}}}_{n}\!\left(q^{-x}\right)}}}$

Proof

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Symbols List

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

Bibliography

Equation in Section 14.14 of KLS.

URL links

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<< Formula:KLS:14.14:05

formula in Quantum q-Krawtchouk

Formula:KLS:14.14:07 >>