# Fungrim entry: 278274

$\frac{\theta'''_{1}\!\left(0 , \tau\right)}{\theta'_{1}\!\left(0 , \tau\right)} = \frac{\theta''_{2}\!\left(0 , \tau\right)}{\theta_{2}\!\left(0 , \tau\right)} + \frac{\theta''_{3}\!\left(0 , \tau\right)}{\theta_{3}\!\left(0 , \tau\right)} + \frac{\theta''_{4}\!\left(0 , \tau\right)}{\theta_{4}\!\left(0 , \tau\right)}$
Assumptions:$\tau \in \mathbb{H}$
TeX:
\frac{\theta'''_{1}\!\left(0 , \tau\right)}{\theta'_{1}\!\left(0 , \tau\right)} = \frac{\theta''_{2}\!\left(0 , \tau\right)}{\theta_{2}\!\left(0 , \tau\right)} + \frac{\theta''_{3}\!\left(0 , \tau\right)}{\theta_{3}\!\left(0 , \tau\right)} + \frac{\theta''_{4}\!\left(0 , \tau\right)}{\theta_{4}\!\left(0 , \tau\right)}

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
JacobiTheta$\theta_{j}\!\left(z , \tau\right)$ Jacobi theta function
HH$\mathbb{H}$ Upper complex half-plane
Source code for this entry:
Entry(ID("278274"),
Formula(Equal(Div(JacobiTheta(1, 0, tau, 3), JacobiTheta(1, 0, tau, 1)), Add(Add(Div(JacobiTheta(2, 0, tau, 2), JacobiTheta(2, 0, tau)), Div(JacobiTheta(3, 0, tau, 2), JacobiTheta(3, 0, tau))), Div(JacobiTheta(4, 0, tau, 2), JacobiTheta(4, 0, tau))))),
Variables(tau),
Assumptions(And(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.

2020-01-31 18:09:28.494564 UTC