θ 3 ( π z | τ ) = θ 3 ( 0 | τ ) exp ( − ∑ j = 1 ∞ 1 2 j β 2 j ( τ ) z 2 j ) \theta_{3}\left(\pi z | \tau\right)=\theta_{3}\left(0 | \tau\right)\exp\left(-\sum_{j=1}^{\infty}\frac{1}{2j}\beta_{2j}(\tau)z^{2j}\right)