Formula:KLS:14.29:12

<< Formula:KLS:14.29:11

formula in Discrete q-Hermite II

Formula:KLS:14.29:13 >>

${\displaystyle{\displaystyle{\displaystyle\mathcal{D}_{q}\tilde{h}_{n}\!\left(x;q\right)=\frac{q^{-n+1}(1-q^{n})}{1-q}\tilde{h}_{n-1}\!\left(qx;q\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle\tilde{h}_{n}}}}$ : discrete ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hermite II polynomial : http://drmf.wmflabs.org/wiki/Definition:discrqHermiteII

Bibliography

Equation in Section 14.29 of KLS.

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<< Formula:KLS:14.29:11

formula in Discrete q-Hermite II

Formula:KLS:14.29:13 >>