# Fungrim entry: e6d333

$\theta_{3}\!\left(z , \frac{\tau}{2}\right) = \frac{\theta_{4}^{2}\!\left(z, \tau\right) - \theta_{1}^{2}\!\left(z, \tau\right)}{\theta_{4}\!\left(0 , \frac{\tau}{2}\right)}$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}$
TeX:
\theta_{3}\!\left(z , \frac{\tau}{2}\right) = \frac{\theta_{4}^{2}\!\left(z, \tau\right) - \theta_{1}^{2}\!\left(z, \tau\right)}{\theta_{4}\!\left(0 , \frac{\tau}{2}\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("e6d333"),
Formula(Equal(JacobiTheta(3, z, Div(tau, 2)), Div(Sub(Pow(JacobiTheta(4, z, tau), 2), Pow(JacobiTheta(1, z, tau), 2)), JacobiTheta(4, 0, Div(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