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Illustrations of Jacobi theta functions

Table of contents: X-ray plots, variable argument - X-ray plots, variable lattice parameter

Related topics: Jacobi theta functions

X-ray plots, variable argument

Square lattice

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Image: X-ray of θ1 ⁣(z,i)\theta_{1}\!\left(z , i\right) on z[2,2]+[2,2]iz \in \left[-2, 2\right] + \left[-2, 2\right] i
a75407
Image: X-ray of θ2 ⁣(z,i)\theta_{2}\!\left(z , i\right) on z[2,2]+[2,2]iz \in \left[-2, 2\right] + \left[-2, 2\right] i
bac5fb
Image: X-ray of θ3 ⁣(z,i)\theta_{3}\!\left(z , i\right) on z[2,2]+[2,2]iz \in \left[-2, 2\right] + \left[-2, 2\right] i
8c9f96
Image: X-ray of θ4 ⁣(z,i)\theta_{4}\!\left(z , i\right) on z[2,2]+[2,2]iz \in \left[-2, 2\right] + \left[-2, 2\right] i

Rectangular lattice

56acfe
Image: X-ray of θ1 ⁣(z,12i)\theta_{1}\!\left(z , \frac{1}{2} i\right) on z[2,2]+[2,2]iz \in \left[-2, 2\right] + \left[-2, 2\right] i
e47bfb
Image: X-ray of θ2 ⁣(z,12i)\theta_{2}\!\left(z , \frac{1}{2} i\right) on z[2,2]+[2,2]iz \in \left[-2, 2\right] + \left[-2, 2\right] i
d98ccc
Image: X-ray of θ3 ⁣(z,12i)\theta_{3}\!\left(z , \frac{1}{2} i\right) on z[2,2]+[2,2]iz \in \left[-2, 2\right] + \left[-2, 2\right] i
7902fc
Image: X-ray of θ4 ⁣(z,12i)\theta_{4}\!\left(z , \frac{1}{2} i\right) on z[2,2]+[2,2]iz \in \left[-2, 2\right] + \left[-2, 2\right] i

Nonrectangular lattice

c4febd
Image: X-ray of θ1 ⁣(z,14+34i)\theta_{1}\!\left(z , \frac{1}{4} + \frac{3}{4} i\right) on z[2,2]+[2,2]iz \in \left[-2, 2\right] + \left[-2, 2\right] i
fa8e96
Image: X-ray of θ2 ⁣(z,14+34i)\theta_{2}\!\left(z , \frac{1}{4} + \frac{3}{4} i\right) on z[2,2]+[2,2]iz \in \left[-2, 2\right] + \left[-2, 2\right] i
80f43a
Image: X-ray of θ3 ⁣(z,14+34i)\theta_{3}\!\left(z , \frac{1}{4} + \frac{3}{4} i\right) on z[2,2]+[2,2]iz \in \left[-2, 2\right] + \left[-2, 2\right] i
0ce854
Image: X-ray of θ4 ⁣(z,14+34i)\theta_{4}\!\left(z , \frac{1}{4} + \frac{3}{4} i\right) on z[2,2]+[2,2]iz \in \left[-2, 2\right] + \left[-2, 2\right] i

X-ray plots, variable lattice parameter

Zero argument (theta constants)

ad8a9a
Image: X-ray of θ2 ⁣(0,τ)\theta_{2}\!\left(0 , \tau\right) on τ[52,52]+[0,2]i\tau \in \left[-\frac{5}{2}, \frac{5}{2}\right] + \left[0, 2\right] i
6636f2
Image: X-ray of θ3 ⁣(0,τ)\theta_{3}\!\left(0 , \tau\right) on τ[52,52]+[0,2]i\tau \in \left[-\frac{5}{2}, \frac{5}{2}\right] + \left[0, 2\right] i
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Image: X-ray of θ4 ⁣(0,τ)\theta_{4}\!\left(0 , \tau\right) on τ[52,52]+[0,2]i\tau \in \left[-\frac{5}{2}, \frac{5}{2}\right] + \left[0, 2\right] i

Nonzero argument

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Image: X-ray of θ1 ⁣(13+34i,τ)\theta_{1}\!\left(\frac{1}{3} + \frac{3}{4} i , \tau\right) on τ[52,52]+[0,2]i\tau \in \left[-\frac{5}{2}, \frac{5}{2}\right] + \left[0, 2\right] i
9b868d
Image: X-ray of θ2 ⁣(13+34i,τ)\theta_{2}\!\left(\frac{1}{3} + \frac{3}{4} i , \tau\right) on τ[52,52]+[0,2]i\tau \in \left[-\frac{5}{2}, \frac{5}{2}\right] + \left[0, 2\right] i
c2c002
Image: X-ray of θ3 ⁣(13+34i,τ)\theta_{3}\!\left(\frac{1}{3} + \frac{3}{4} i , \tau\right) on τ[52,52]+[0,2]i\tau \in \left[-\frac{5}{2}, \frac{5}{2}\right] + \left[0, 2\right] i
d3b45d
Image: X-ray of θ4 ⁣(13+34i,τ)\theta_{4}\!\left(\frac{1}{3} + \frac{3}{4} i , \tau\right) on τ[52,52]+[0,2]i\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.

2019-11-19 15:10:20.037976 UTC