# Formula:KLS:14.09:19

$\displaystyle {\displaystyle \frac{1}{\qPochhammer{\expe^{\iunit(\theta+\phi)}t}{q}{\infty}}\ \qHyperrphis{2}{1}@@{a\expe^{\iunit(\theta+2\phi)},a\expe^{\iunit\theta}}{a^2}{q}{\expe^{-\iunit(\theta+\phi)}t} {}=\sum_{n=0}^{\infty}\frac{\qMeixnerPollaczek{n}@{x}{a}{q}}{\qPochhammer{a^2}{q}{n}}t^n }$

## Substitution(s)

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

## 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
$\displaystyle {\displaystyle P_{n}}$  : $\displaystyle {\displaystyle q}$ -Meixner-Pollaczek polynomial : http://drmf.wmflabs.org/wiki/Definition:qMeixnerPollaczek
$\displaystyle {\displaystyle \mathrm{cos}}$  : cosine function : http://dlmf.nist.gov/4.14#E2