Formula:KLS:14.20:03

$\displaystyle {\displaystyle \sum_{k=0}^{\infty}\frac{(aq)^k}{\qPochhammer{q}{q}{k}}\littleqLaguerre{m}@{q^k}{a}{q}\littleqLaguerre{n}@{q^k}{a}{q}= \frac{(aq)^n}{\qPochhammer{aq}{q}{\infty}}\frac{\qPochhammer{q}{q}{n}}{\qPochhammer{aq}{q}{n}}\,\Kronecker{m}{n} }$

Constraint(s)

$\displaystyle {\displaystyle 0

Proof

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Symbols List

$\displaystyle {\displaystyle \Sigma}$  : 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
$\displaystyle {\displaystyle p_{n}}$  : little $\displaystyle {\displaystyle q}$ -Laguerre / Wall polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqLaguerre
$\displaystyle {\displaystyle \delta_{m,n}}$  : Kronecker delta : http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r4