# Fungrim entry: e3e4c5

$\eta\!\left(\sqrt{3} i\right) = \frac{{3}^{1 / 8}}{{2}^{4 / 3}} \frac{{\left(\Gamma\!\left(\frac{1}{3}\right)\right)}^{3 / 2}}{\pi}$
References:
• https://math.stackexchange.com/questions/1334684/what-is-the-exact-value-of-eta6i/1334940
TeX:
\eta\!\left(\sqrt{3} i\right) = \frac{{3}^{1 / 8}}{{2}^{4 / 3}} \frac{{\left(\Gamma\!\left(\frac{1}{3}\right)\right)}^{3 / 2}}{\pi}
Definitions:
Fungrim symbol Notation Short description
DedekindEta$\eta(\tau)$ Dedekind eta function
Sqrt$\sqrt{z}$ Principal square root
ConstI$i$ Imaginary unit
Pow${a}^{b}$ Power
Gamma$\Gamma(z)$ Gamma function
Pi$\pi$ The constant pi (3.14...)
Source code for this entry:
Entry(ID("e3e4c5"),
Formula(Equal(DedekindEta(Mul(Sqrt(3), ConstI)), Mul(Div(Pow(3, Div(1, 8)), Pow(2, Div(4, 3))), Div(Pow(Gamma(Div(1, 3)), Div(3, 2)), Pi)))),
References("https://math.stackexchange.com/questions/1334684/what-is-the-exact-value-of-eta6i/1334940"))

## 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