Formula:KLS:14.29:17

<< Formula:KLS:14.29:16

formula in Discrete q-Hermite II

Formula:KLS:14.29:18 >>

${\displaystyle{\displaystyle{\displaystyle\left(-\mathrm{i}t;q\right)_{\infty}\cdot\qHyperrphis{1}{1}@@{\mathrm{i}x}{-\mathrm{i}t}{q}{\mathrm{i}t}=\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n(n-1)}}{\left(q;q\right)_{n}}\tilde{h}_{n}\!\left(x;q\right)t^{n}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle\mathrm{i}}}}$ : imaginary unit : http://dlmf.nist.gov/1.9.i
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle\tilde{h}_{n}}}}$ : discrete ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hermite II polynomial : http://drmf.wmflabs.org/wiki/Definition:discrqHermiteII

Bibliography

Equation in Section 14.29 of KLS.

URL links

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<< Formula:KLS:14.29:16

formula in Discrete q-Hermite II

Formula:KLS:14.29:18 >>