Formula:KLS:14.13:27

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formula in q-Meixner

Formula:KLS:14.14:01 >>

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

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
${\displaystyle{\displaystyle{\displaystyle M_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Meixner polynomial : http://drmf.wmflabs.org/wiki/Definition:qMeixner

Bibliography

Equation in Section 14.13 of KLS.

URL links

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