# Formula:KLS:14.21:04

$\displaystyle {\displaystyle \sum_{k=-\infty}^{\infty}\frac{q^{k\alpha+k}}{\qPochhammer{-cq^k}{q}{\infty}}\qLaguerre[\alpha]{m}@{cq^k}{q}\qLaguerre[\alpha]{n}@{cq^k}{q} {}=\frac{\qPochhammer{q,-cq^{\alpha+1},-c^{-1}q^{-\alpha}}{q}{\infty}} {\qPochhammer{q^{\alpha+1},-c,-c^{-1}q}{q}{\infty}}\frac{\qPochhammer{q^{\alpha+1}}{q}{n}}{\qPochhammer{q}{q}{n}q^n}\,\Kronecker{m}{n} }$

## Constraint(s)

$\displaystyle {\displaystyle \alpha>-1}$ &
$\displaystyle {\displaystyle c>0}$

## 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
$\displaystyle {\displaystyle \Sigma}$  : sum : http://drmf.wmflabs.org/wiki/Definition:sum
$\displaystyle {\displaystyle (a;q)_n}$  : $\displaystyle {\displaystyle q}$ -Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
$\displaystyle {\displaystyle L_n^{(\alpha)}}$  : $\displaystyle {\displaystyle q}$ -Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:qLaguerre
$\displaystyle {\displaystyle \delta_{m,n}}$  : Kronecker delta : http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r4