Formula:KLS:14.28:13

<< Formula:KLS:14.28:12

formula in Discrete q-Hermite I

Formula:KLS:14.28:15 >>

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

Substitution(s)

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

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

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

We ask users to provide relevant URL links in this space.

<< Formula:KLS:14.28:12

formula in Discrete q-Hermite I

Formula:KLS:14.28:15 >>