# Fungrim entry: a255e1

$\theta_{2}\!\left(4 z , 4 \tau\right) = \frac{\theta_{2}\!\left(\frac{1}{8} - z , \tau\right) \theta_{2}\!\left(\frac{1}{8} + z , \tau\right) \theta_{2}\!\left(\frac{3}{8} - z , \tau\right) \theta_{2}\!\left(\frac{3}{8} + z , \tau\right)}{\theta_{3}\!\left(0 , \tau\right) \theta_{4}\!\left(0 , \tau\right) \theta_{3}\!\left(\frac{1}{4} , \tau\right)}$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}$
TeX:
\theta_{2}\!\left(4 z , 4 \tau\right) = \frac{\theta_{2}\!\left(\frac{1}{8} - z , \tau\right) \theta_{2}\!\left(\frac{1}{8} + z , \tau\right) \theta_{2}\!\left(\frac{3}{8} - z , \tau\right) \theta_{2}\!\left(\frac{3}{8} + z , \tau\right)}{\theta_{3}\!\left(0 , \tau\right) \theta_{4}\!\left(0 , \tau\right) \theta_{3}\!\left(\frac{1}{4} , \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
CC$\mathbb{C}$ Complex numbers
HH$\mathbb{H}$ Upper complex half-plane
Source code for this entry:
Entry(ID("a255e1"),
Formula(Equal(JacobiTheta(2, Mul(4, z), Mul(4, tau)), Div(Mul(Mul(Mul(JacobiTheta(2, Sub(Div(1, 8), z), tau), JacobiTheta(2, Add(Div(1, 8), z), tau)), JacobiTheta(2, Sub(Div(3, 8), z), tau)), JacobiTheta(2, Add(Div(3, 8), z), tau)), Mul(Mul(JacobiTheta(3, 0, tau), JacobiTheta(4, 0, tau)), JacobiTheta(3, Div(1, 4), tau))))),
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