# Illustrations of Jacobi theta functions

Related topics: Jacobi theta functions

## X-ray plots, variable argument

### Square lattice

Image: X-ray of $\theta_{1}\!\left(z , i\right)$ on $z \in \left[-2, 2\right] + \left[-2, 2\right] i$ Image: X-ray of $\theta_{2}\!\left(z , i\right)$ on $z \in \left[-2, 2\right] + \left[-2, 2\right] i$ Image: X-ray of $\theta_{3}\!\left(z , i\right)$ on $z \in \left[-2, 2\right] + \left[-2, 2\right] i$ Image: X-ray of $\theta_{4}\!\left(z , i\right)$ on $z \in \left[-2, 2\right] + \left[-2, 2\right] i$ ### Rectangular lattice

Image: X-ray of $\theta_{1}\!\left(z , \frac{1}{2} i\right)$ on $z \in \left[-2, 2\right] + \left[-2, 2\right] i$ Image: X-ray of $\theta_{2}\!\left(z , \frac{1}{2} i\right)$ on $z \in \left[-2, 2\right] + \left[-2, 2\right] i$ Image: X-ray of $\theta_{3}\!\left(z , \frac{1}{2} i\right)$ on $z \in \left[-2, 2\right] + \left[-2, 2\right] i$ Image: X-ray of $\theta_{4}\!\left(z , \frac{1}{2} i\right)$ on $z \in \left[-2, 2\right] + \left[-2, 2\right] i$ ### Nonrectangular lattice

Image: X-ray of $\theta_{1}\!\left(z , \frac{1}{4} + \frac{3}{4} i\right)$ on $z \in \left[-2, 2\right] + \left[-2, 2\right] i$ Image: X-ray of $\theta_{2}\!\left(z , \frac{1}{4} + \frac{3}{4} i\right)$ on $z \in \left[-2, 2\right] + \left[-2, 2\right] i$ Image: X-ray of $\theta_{3}\!\left(z , \frac{1}{4} + \frac{3}{4} i\right)$ on $z \in \left[-2, 2\right] + \left[-2, 2\right] i$ Image: X-ray of $\theta_{4}\!\left(z , \frac{1}{4} + \frac{3}{4} i\right)$ on $z \in \left[-2, 2\right] + \left[-2, 2\right] i$ ## X-ray plots, variable lattice parameter

### Zero argument (theta constants)

Image: X-ray of $\theta_{2}\!\left(0 , \tau\right)$ on $\tau \in \left[-\frac{5}{2}, \frac{5}{2}\right] + \left[0, 2\right] i$ Image: X-ray of $\theta_{3}\!\left(0 , \tau\right)$ on $\tau \in \left[-\frac{5}{2}, \frac{5}{2}\right] + \left[0, 2\right] i$ Image: X-ray of $\theta_{4}\!\left(0 , \tau\right)$ on $\tau \in \left[-\frac{5}{2}, \frac{5}{2}\right] + \left[0, 2\right] i$ ### Nonzero argument

Image: X-ray of $\theta_{1}\!\left(\frac{1}{3} + \frac{3}{4} i , \tau\right)$ on $\tau \in \left[-\frac{5}{2}, \frac{5}{2}\right] + \left[0, 2\right] i$ Image: X-ray of $\theta_{2}\!\left(\frac{1}{3} + \frac{3}{4} i , \tau\right)$ on $\tau \in \left[-\frac{5}{2}, \frac{5}{2}\right] + \left[0, 2\right] i$ Image: X-ray of $\theta_{3}\!\left(\frac{1}{3} + \frac{3}{4} i , \tau\right)$ on $\tau \in \left[-\frac{5}{2}, \frac{5}{2}\right] + \left[0, 2\right] i$ Image: X-ray of $\theta_{4}\!\left(\frac{1}{3} + \frac{3}{4} i , \tau\right)$ on $\tau \in \left[-\frac{5}{2}, \frac{5}{2}\right] + \left[0, 2\right] i$ Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC