\[\sigma\left(z\right)=\frac{2\omega_{1}}{\pi}\exp\left(\frac{\pi^{2}z^{2}}{24%
\omega_{1}^{2}}\right)\sin\left(\frac{\pi z}{2\omega_{1}}\right)\*\left(1-%
\left(\frac{\pi^{2}z^{2}}{\omega_{1}^{2}}-4{\sin}^{2}\left(\frac{\pi z}{2%
\omega_{1}}\right)\right)q^{2}+O\left(q^{4}\right)\right),\]