Formula:KLS:14.19:20

$\displaystyle {\displaystyle \frac{\qPochhammer{q^{\alpha+\frac{1}{2}}t,q^{\alpha+1}t}{q}{\infty}} {\qPochhammer{q^{\frac{1}{2}\alpha+\frac{1}{4}}\expe^{\iunit\theta}t,q^{\frac{1}{2}\alpha+\frac{1}{4}}\expe^{-\iunit\theta}t}{q}{\infty}} =\sum_{n=0}^{\infty}\ctsqLaguerre{\alpha}{n}@{x}{q}t^n }$

Substitution(s)

$\displaystyle {\displaystyle x=\cos@@{\theta}}$

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

$\displaystyle {\displaystyle (a;q)_n}$  : $\displaystyle {\displaystyle q}$ -Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
$\displaystyle {\displaystyle \mathrm{e}}$  : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
$\displaystyle {\displaystyle \mathrm{i}}$  : imaginary unit : http://dlmf.nist.gov/1.9.i
$\displaystyle {\displaystyle \Sigma}$  : sum : http://drmf.wmflabs.org/wiki/Definition:sum
$\displaystyle {\displaystyle P^{(n)}_{\alpha}}$  : continuous $\displaystyle {\displaystyle q}$ -Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqLaguerre
$\displaystyle {\displaystyle \mathrm{cos}}$  : cosine function : http://dlmf.nist.gov/4.14#E2