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# Fungrim entry: 95e508

$\theta_{4}\!\left(z , \frac{\tau}{2}\right) = \frac{\theta_{3}^{2}\!\left(z, \tau\right) - \theta_{2}^{2}\!\left(z, \tau\right)}{\theta_{4}\!\left(0 , \frac{\tau}{2}\right)}$
Assumptions:$z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}$
TeX:
\theta_{4}\!\left(z , \frac{\tau}{2}\right) = \frac{\theta_{3}^{2}\!\left(z, \tau\right) - \theta_{2}^{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("95e508"),
Formula(Equal(JacobiTheta(4, z, Div(tau, 2)), Div(Sub(Pow(JacobiTheta(3, z, tau), 2), Pow(JacobiTheta(2, 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.

2019-09-22 15:43:45.410764 UTC