# Jacobi theta 4

Let $q \in \mathbb{C}$ with $|q|<1$. The Jacobi $\vartheta_4$ function is defined by $$\vartheta_4(z,q)=1+2\displaystyle\sum_{k=1}^{\infty} (-1)^k q^{k^2} \cos(2kz),$$ where $\cos$ denotes the cosine function.