Continuous q-Jacobi polynomials

The polynomials are given in terms of basic hypergeometric functions and the q-Pochhammer symbol by

${\displaystyle P_{n}^{(\alpha ,\beta )}(x;q)={\frac {(q^{n+1};q)_{n}}{(q;q)_{n}}}{}_{4}\phi _{3}\left[{\begin{matrix}q^{-n},q^{n+\alpha +\beta +1},q^{{\frac {1}{2}}\alpha +{\frac {1}{4}}e^{i\theta }},q^{{\frac {1}{2}}\alpha +{\frac {1}{4}}e^{-i\theta }}\\q^{n+1},-q^{{\frac {1}{2}}(\alpha +\beta +1)},-q^{{\frac {1}{2}}(\alpha +\beta +2)}\end{matrix}};q,q\right]\qquad x=\cos \,\theta .}$

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