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

Dedekind eta function

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