\[\wp\left(z\right)=\frac{1}{z^{2}}+8\int_{0}^{\infty}s\left(e^{-s}{\sinh}^{2}%
\left(\tfrac{1}{2}zs\right)f_{1}(s,\tau)+e^{i\tau s}{\sin}^{2}\left(\tfrac{1}{%
2}zs\right)f_{2}(s,\tau)\right)\,\mathrm{d}s,\]