Formula:KLS:14.28:15

<< Formula:KLS:14.28:13

formula in Discrete q-Hermite I

Formula:KLS:14.28:16 >>

${\displaystyle{\displaystyle{\displaystyle w(x;q)h_{n}\!\left(x;q\right)=(q-1)^{n}q^{\frac{1}{2}n(n-3)}\left(\mathcal{D}_{q^{-1}}\right)^{n}\left[w(x;q)\right]}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle w(x;q)=\left(qx,-qx;q\right)_{\infty}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle h_{n}}}}$ : discrete ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hermite I polynomial : http://drmf.wmflabs.org/wiki/Definition:discrqHermiteI
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

Bibliography

Equation in Section 14.28 of KLS.

URL links

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<< Formula:KLS:14.28:13

formula in Discrete q-Hermite I

Formula:KLS:14.28:16 >>