Fungrim entry: 62ffb3

\eta\!\left(6 i\right) = \frac{1}{{6}^{3 / 8}} {\left(\frac{5 - \sqrt{3}}{2} - \frac{{3}^{3 / 4}}{\sqrt{2}}\right)}^{1 / 6} \eta(i)

References:

https://math.stackexchange.com/questions/1334684/what-is-the-exact-value-of-eta6i/1334940

TeX:

\eta\!\left(6 i\right) = \frac{1}{{6}^{3 / 8}} {\left(\frac{5 - \sqrt{3}}{2} - \frac{{3}^{3 / 4}}{\sqrt{2}}\right)}^{1 / 6} \eta(i)

Definitions:

Fungrim symbol	Notation	Short description
`DedekindEta`	$\eta(\tau)$	Dedekind eta function
`ConstI`	$i$	Imaginary unit
`Pow`	${a}^{b}$	Power
`Sqrt`	$\sqrt{z}$	Principal square root

Source code for this entry:

Entry(ID("62ffb3"),
    Formula(Equal(DedekindEta(Mul(6, ConstI)), Mul(Mul(Div(1, Pow(6, Div(3, 8))), Pow(Sub(Div(Sub(5, Sqrt(3)), 2), Div(Pow(3, Div(3, 4)), Sqrt(2))), Div(1, 6))), DedekindEta(ConstI)))),
    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