# Formula:KLS:01.08:12

$\displaystyle {\displaystyle \qPochhammer{a}{q}{n+k}=\qPochhammer{a}{q}{n}\qPochhammer{aq^n}{q}{k} }$

## Constraint(s)

$\displaystyle {\displaystyle a\neq 0}$ &
$\displaystyle {\displaystyle 0<|q|<1}$

## Substitution(s)

$\displaystyle {\displaystyle \qPochhammer{a}{q}{n}=\frac{\qPochhammer{a}{q}{\infty}}{\qPochhammer{aq^n}{q}{\infty}} =\qPochhammer{a^{-1}q^{1-n}}{q}{n}(-a)^nq^{\binomial{n}{2}}}$ &
$\displaystyle {\displaystyle \qPochhammer{a}{q}{\infty}=\prod_{k=0}^{\infty}(1-aq^k) =\qPochhammer{a}{q^2}{\infty}\qPochhammer{aq}{q^2}{\infty}}$

## 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

& : logical and
$\displaystyle {\displaystyle (a;q)_n}$  : $\displaystyle {\displaystyle q}$ -Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
$\displaystyle {\displaystyle \binom{n}{k}}$  : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
$\displaystyle {\displaystyle \Pi}$  : product : http://drmf.wmflabs.org/wiki/Definition:prod