\[p_{n}\left(x;a,b,\overline{a},\overline{b}\right)=\frac{{\mathrm{i}}^{n}{\left%
(a+\overline{a}\right)_{n}}{\left(a+\overline{b}\right)_{n}}}{n!}\*{{}_{3}F_{2%
}}\left({-n,n+2\Re\left(a+b\right)-1,a+\mathrm{i}x\atop a+\overline{a},a+%
\overline{b}};1\right).\]