Formula:KLS:14.16:26

<< Formula:KLS:14.16:25

formula in Affine q-Krawtchouk

Affine q-Krawtchouk >>

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

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

Bibliography

Equation in Section 14.16 of KLS.

URL links

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<< Formula:KLS:14.16:25

formula in Affine q-Krawtchouk

Affine q-Krawtchouk >>