# Fungrim entry: f12569

$\theta_{2}\!\left(2 z , 2 \tau\right) = \frac{\theta_{1}\!\left(\frac{1}{4} - z , \tau\right) \theta_{1}\!\left(\frac{1}{4} + z , \tau\right)}{\theta_{4}\!\left(0 , 2 \tau\right)}$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}$
TeX:
\theta_{2}\!\left(2 z , 2 \tau\right) = \frac{\theta_{1}\!\left(\frac{1}{4} - z , \tau\right) \theta_{1}\!\left(\frac{1}{4} + z , \tau\right)}{\theta_{4}\!\left(0 , 2 \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("f12569"),
Formula(Equal(JacobiTheta(2, Mul(2, z), Mul(2, tau)), Div(Mul(JacobiTheta(1, Sub(Div(1, 4), z), tau), JacobiTheta(1, Add(Div(1, 4), z), tau)), JacobiTheta(4, 0, Mul(2, 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