Formula:KLS:14.29:01

<< Discrete q-Hermite I

formula in Discrete q-Hermite II

Formula:KLS:14.29:02 >>

${\displaystyle{\displaystyle{\displaystyle\tilde{h}_{n}\!\left(x;q\right)={\mathrm{i}^{-n}}V^{(-1)}_{n}\!\left(\mathrm{i}x;q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\tilde{h}_{n}}}}$ : discrete ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hermite II polynomial : http://drmf.wmflabs.org/wiki/Definition:discrqHermiteII
${\displaystyle{\displaystyle{\displaystyle\mathrm{i}}}}$ : imaginary unit : http://dlmf.nist.gov/1.9.i
${\displaystyle{\displaystyle{\displaystyle V^{(n)}_{\alpha}}}}$ : Al-Salam-Carlitz II polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamCarlitzII

Bibliography

Equation in Section 14.29 of KLS.

URL links

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<< Discrete q-Hermite I

formula in Discrete q-Hermite II

Formula:KLS:14.29:02 >>