Fungrim entry: 204acd

\eta\!\left({e}^{2 \pi i / 3}\right) = {e}^{-\pi i / 24} \frac{{3}^{1 / 8} {\left(\Gamma\!\left(\frac{1}{3}\right)\right)}^{3 / 2}}{2 \pi}

TeX:

\eta\!\left({e}^{2 \pi i / 3}\right) = {e}^{-\pi i / 24} \frac{{3}^{1 / 8} {\left(\Gamma\!\left(\frac{1}{3}\right)\right)}^{3 / 2}}{2 \pi}

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
`Gamma`	$\Gamma(z)$	Gamma function

Source code for this entry:

Entry(ID("204acd"),
    Formula(Equal(DedekindEta(Exp(Div(Mul(Mul(2, Pi), ConstI), 3))), Mul(Exp(Neg(Div(Mul(Pi, ConstI), 24))), Div(Mul(Pow(3, Div(1, 8)), Pow(Gamma(Div(1, 3)), Div(3, 2))), Mul(2, Pi))))))

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