\[\frac{B^{2n+1}_{2m+1}(q)}{B^{2n+1}_{1}(q)}=\frac{(-1)^{m}}{\left({\left(\tfrac%
{1}{2}\right)_{m+1}}\right)^{2}}\left(\frac{q}{4}\right)^{m+1}\frac{2\left(1+O%
\left(m^{-1}\right)\right)}{w_{\mbox{\tiny I}}(\frac{1}{2}\pi;b_{2n+1}\left(q%
\right),q)},\]