\[\lim_{\tau\to 0}\frac{\left(a/\tau;q\right)_{n}}{\left(b/\tau;q\right)_{n}}=%
\lim_{\sigma\to\infty}\frac{\left(a\sigma;q\right)_{n}}{\left(b\sigma;q\right)%
_{n}}=\left(\frac{a}{b}\right)^{n},\]