# Fungrim entry: 66efb8

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

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; w \in \tau \;\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("66efb8"),
Formula(Equal(Mul(Mul(JacobiTheta(3, Add(z, w), tau), JacobiTheta(3, Sub(z, w), tau)), Pow(JacobiTheta(2, 0, tau), 2)), Add(Mul(Pow(JacobiTheta(3, z, tau), 2), Pow(JacobiTheta(2, w, tau), 2)), Mul(Pow(JacobiTheta(4, z, tau), 2), Pow(JacobiTheta(1, w, tau), 2))), Add(Mul(Pow(JacobiTheta(2, z, tau), 2), Pow(JacobiTheta(3, w, tau), 2)), Mul(Pow(JacobiTheta(1, z, tau), 2), Pow(JacobiTheta(4, w, tau), 2))))),
Variables(z, w, tau),
Assumptions(And(Element(z, CC), Element(w, tau), 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