\[\frac{1}{2\pi}\int_{0}^{\pi}C_{n}\left(\cos\theta;\beta\,|\,q\right)C_{m}\left%
(\cos\theta;\beta\,|\,q\right)\*{\left|\frac{\left({\mathrm{e}}^{2\mathrm{i}%
\theta};q\right)_{\infty}}{\left(\beta{\mathrm{e}}^{2\mathrm{i}\theta};q\right%
)_{\infty}}\right|}^{2}\,\mathrm{d}\theta=\frac{\left(\beta,\beta q;q\right)_{%
\infty}}{\left(\beta^{2},q;q\right)_{\infty}}\frac{(1-\beta)\left(\beta^{2};q%
\right)_{n}}{(1-\beta q^{n})\left(q;q\right)_{n}}\delta_{n,m},\]