Formula:KLS:14.24:09

<< Formula:KLS:14.24:08

formula in Al-Salam-Carlitz I

Formula:KLS:14.24:10 >>

${\displaystyle{\displaystyle{\displaystyle\mathcal{D}_{q}U^{(a)}_{n}\!\left(x;q\right)=\frac{1-q^{n}}{1-q}U^{(a)}_{n-1}\!\left(x;q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\mathcal{D}_{q}^{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-derivative : http://drmf.wmflabs.org/wiki/Definition:qderiv
${\displaystyle{\displaystyle{\displaystyle U^{(n)}_{\alpha}}}}$ : Al-Salam-Carlitz I polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamCarlitzI

Bibliography

Equation in Section 14.24 of KLS.

URL links

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<< Formula:KLS:14.24:08

formula in Al-Salam-Carlitz I

Formula:KLS:14.24:10 >>