# Formula:KLS:14.25:13

$\displaystyle {\displaystyle w(x;a;q)\AlSalamCarlitzII{a}{n}@{x}{q}=a^n(q-1)^nq^{-\binomial{n}{2}} \left(\qderiv{q}\right)^n\left[w(x;a;q)\right] }$

## Substitution(s)

$\displaystyle {\displaystyle w(x;a;q)=\frac{1}{\qPochhammer{x,a^{-1}x}{q}{\infty}}}$

## 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

$\displaystyle {\displaystyle V^{(n)}_{\alpha}}$  : Al-Salam-Carlitz II polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamCarlitzII
$\displaystyle {\displaystyle \binom{n}{k}}$  : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
$\displaystyle {\displaystyle \mathcal{D}_q^n}$  : $\displaystyle {\displaystyle q}$ -derivative : http://drmf.wmflabs.org/wiki/Definition:qderiv
$\displaystyle {\displaystyle (a;q)_n}$  : $\displaystyle {\displaystyle q}$ -Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1