\[\theta_{3}\left(\pi z\middle|\tau\right)=\sum_{n=-\infty}^{\infty}p^{2n}q^{n^{%
2}}\\
=\prod_{n=1}^{\infty}\left(1-q^{2n}\right)\left(1+q^{2n-1}p^{2}\right)\left(1+%
q^{2n-1}p^{-2}\right),\]