Jacobi theta 3

Let $q \in \mathbb{C}$ with $|q|<1$. The Jacobi $\vartheta_3$ function is defined by $$\vartheta_3(z,q)=1+2\displaystyle\sum_{k=1}^{\infty} q^{k^2} \cos(2kz),$$ where $\cos$ denotes the cosine function.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 16.27.3