# Fungrim entry: e08bb4

$\theta_{1}^{4}\!\left(z, \tau\right) - \theta_{4}^{4}\!\left(z, \tau\right) = \theta_{2}^{4}\!\left(z, \tau\right) - \theta_{3}^{4}\!\left(z, \tau\right)$
Assumptions:$z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}$
TeX:
\theta_{1}^{4}\!\left(z, \tau\right) - \theta_{4}^{4}\!\left(z, \tau\right) = \theta_{2}^{4}\!\left(z, \tau\right) - \theta_{3}^{4}\!\left(z, \tau\right)

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
Pow${a}^{b}$ Power
JacobiTheta$\theta_{j}\!\left(z , \tau\right)$ Jacobi theta function
CC$\mathbb{C}$ Complex numbers
HH$\mathbb{H}$ Upper complex half-plane
Source code for this entry:
Entry(ID("e08bb4"),
Formula(Equal(Sub(Pow(JacobiTheta(1, z, tau), 4), Pow(JacobiTheta(4, z, tau), 4)), Sub(Pow(JacobiTheta(2, z, tau), 4), Pow(JacobiTheta(3, z, tau), 4)))),
Variables(z, tau),
Assumptions(And(Element(z, CC), Element(tau, HH))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-01-31 18:09:28.494564 UTC