Formula:KLS:14.14:24

<< Formula:KLS:14.14:23

formula in Quantum q-Krawtchouk

Formula:KLS:14.15:01 >>

${\displaystyle{\displaystyle{\displaystyle K^{\mathrm{qtm}}_{n}\!\left(q^{x};p,N;q^{-1}\right)=\left(p^{-1}q;q\right)_{n}\left(-\frac{p}{q}\right)^{n}q^{-\binomial{n}{2}}K^{\mathrm{Aff}}_{n}\!\left(q^{x-N};p^{-1},N;q\right)}}}$

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

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
${\displaystyle{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}}}}$ : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
${\displaystyle{\displaystyle{\displaystyle K^{\mathrm{Aff}}_{n}}}}$ : affine ${\displaystyle{\displaystyle{\displaystyle q}}}$-Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:AffqKrawtchouk

Bibliography

Equation in Section 14.14 of KLS.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:KLS:14.14:23

formula in Quantum q-Krawtchouk

Formula:KLS:14.15:01 >>