# Fungrim entry: 21dc98

$\theta_{4}\!\left(2 z , \tau\right) = \frac{\theta_{1}^{2}\!\left(z, \tau\right) \theta_{2}^{2}\!\left(z, \tau\right) + \theta_{3}^{2}\!\left(z, \tau\right) \theta_{4}^{2}\!\left(z, \tau\right)}{\theta_{4}\!\left(0 , \tau\right) \theta_{3}^{2}\!\left(0, \tau\right)}$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}$
TeX:
\theta_{4}\!\left(2 z , \tau\right) = \frac{\theta_{1}^{2}\!\left(z, \tau\right) \theta_{2}^{2}\!\left(z, \tau\right) + \theta_{3}^{2}\!\left(z, \tau\right) \theta_{4}^{2}\!\left(z, \tau\right)}{\theta_{4}\!\left(0 , \tau\right) \theta_{3}^{2}\!\left(0, \tau\right)}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
JacobiTheta$\theta_{j}\!\left(z , \tau\right)$ Jacobi theta function
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
HH$\mathbb{H}$ Upper complex half-plane
Source code for this entry:
Entry(ID("21dc98"),
Formula(Equal(JacobiTheta(4, Mul(2, z), tau), Div(Add(Mul(Pow(JacobiTheta(1, z, tau), 2), Pow(JacobiTheta(2, z, tau), 2)), Mul(Pow(JacobiTheta(3, z, tau), 2), Pow(JacobiTheta(4, z, tau), 2))), Mul(JacobiTheta(4, 0, tau), Pow(JacobiTheta(3, 0, tau), 2))))),
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.

2021-03-15 19:12:00.328586 UTC