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

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