Formula:KLS:14.11:26

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formula in Big q-Laguerre

Formula:KLS:14.12:01 >>

${\displaystyle{\displaystyle{\displaystyle\AffqKrawtchouk{n}@{q^{-x}}{p}{N}{q}=\bigqLaguerre{n}@{q^{-x}}{p}{q^{-N-1}}{q}}}}$

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
${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:bigqLaguerre

Bibliography

Equation in Section 14.11 of KLS.

URL links

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