# Fungrim entry: 20d581

$\theta_{3}\!\left(2 z , \tau\right) = \frac{\theta_{1}^{4}\!\left(z, \tau\right) + \theta_{3}^{4}\!\left(z, \tau\right)}{\theta_{3}^{3}\!\left(0, \tau\right)}$
Assumptions:$z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}$
TeX:
\theta_{3}\!\left(2 z , \tau\right) = \frac{\theta_{1}^{4}\!\left(z, \tau\right) + \theta_{3}^{4}\!\left(z, \tau\right)}{\theta_{3}^{3}\!\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("20d581"),
Formula(Equal(JacobiTheta(3, Mul(2, z), tau), Div(Add(Pow(JacobiTheta(1, z, tau), 4), Pow(JacobiTheta(3, z, tau), 4)), Pow(JacobiTheta(3, 0, tau), 3)))),
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