# Fungrim entry: a1a3d4

$\eta\!\left(\tau + \frac{1}{2}\right) = {e}^{\pi i / 24} \frac{\eta^{3}\!\left(2 \tau\right)}{\eta(\tau) \eta\!\left(4 \tau\right)}$
Assumptions:$\tau \in \mathbb{H}$
TeX:
\eta\!\left(\tau + \frac{1}{2}\right) = {e}^{\pi i / 24} \frac{\eta^{3}\!\left(2 \tau\right)}{\eta(\tau) \eta\!\left(4 \tau\right)}

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
DedekindEta$\eta(\tau)$ Dedekind eta function
Exp${e}^{z}$ Exponential function
Pi$\pi$ The constant pi (3.14...)
ConstI$i$ Imaginary unit
Pow${a}^{b}$ Power
HH$\mathbb{H}$ Upper complex half-plane
Source code for this entry:
Entry(ID("a1a3d4"),
Formula(Equal(DedekindEta(Add(tau, Div(1, 2))), Mul(Exp(Div(Mul(Pi, ConstI), 24)), Div(Pow(DedekindEta(Mul(2, tau)), 3), Mul(DedekindEta(tau), DedekindEta(Mul(4, tau))))))),
Variables(tau),
Assumptions(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