# Formula:KLS:14.10:111

$\displaystyle {\displaystyle \ctsqLegendreRahman{n}@{x}{q}=\qHyperrphis{4}{3}@@{q^{-n},q^{n+1},q^{\frac{1}{2}}\expe^{\iunit\theta},q^{\frac{1}{2}}\expe^{-\iunit\theta}}{q,-q,-q}{q}{q} }$

## 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

$\displaystyle {\displaystyle P_{n}}$  : continuous $\displaystyle {\displaystyle q}$ -Legendre-Rahman polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqLegendreRahman
$\displaystyle {\displaystyle {{}_{r}\phi_{s}}}$  : basic hypergeometric (or $\displaystyle {\displaystyle q}$ -hypergeometric) function : http://dlmf.nist.gov/17.4#E1
$\displaystyle {\displaystyle \mathrm{e}}$  : 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
$\displaystyle {\displaystyle \mathrm{cos}}$  : cosine function : http://dlmf.nist.gov/4.14#E2