Formula:KLS:14.29:16

<< Formula:KLS:14.29:15

formula in Discrete q-Hermite II

Formula:KLS:14.29:17 >>

${\displaystyle{\displaystyle{\displaystyle\frac{\left(-xt;q\right)_{\infty}}{\left(-t^{2};q^{2}\right)_{\infty}}=\sum_{n=0}^{\infty}\frac{q^{\binomial{n}{2}}}{\left(q;q\right)_{n}}\tilde{h}_{n}\!\left(x;q\right)t^{n}}}}$

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
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}}}}$ : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
${\displaystyle{\displaystyle{\displaystyle\tilde{h}_{n}}}}$ : 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:14.29:15

formula in Discrete q-Hermite II

Formula:KLS:14.29:17 >>