# Formula:KLS:14.22:04

$\displaystyle {\displaystyle \sum_{k=0}^{\infty}\frac{a^k}{\qPochhammer{q}{q}{k}}q^{\binomial{k+1}{2}}\qBesselPoly{m}@{q^k}{a}{q}\qBesselPoly{n}@{q^k}{a}{q} {}=\qPochhammer{q}{q}{n}\qPochhammer{-aq^n}{q}{\infty}\frac{a^nq^{\binomial{n+1}{2}}}{(1+aq^{2n})}\,\Kronecker{m}{n} }$

## Constraint(s)

$\displaystyle {\displaystyle a>0}$

## 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

$\displaystyle {\displaystyle \Sigma}$  : 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
$\displaystyle {\displaystyle \binom{n}{k}}$  : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
$\displaystyle {\displaystyle y_{n}}$  : $\displaystyle {\displaystyle q}$ -Bessel polynomial : http://drmf.wmflabs.org/wiki/Definition:qBessel
$\displaystyle {\displaystyle \delta_{m,n}}$  : Kronecker delta : http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r4