Fungrim entry: be2f32

\eta\!\left(8 i\right) = \frac{1}{{2}^{41 / 32}} \frac{{\left({2}^{1 / 4} - 1\right)}^{1 / 2}}{{\left(1 + \sqrt{2}\right)}^{1 / 8}} \eta(i)

References:

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

TeX:

\eta\!\left(8 i\right) = \frac{1}{{2}^{41 / 32}} \frac{{\left({2}^{1 / 4} - 1\right)}^{1 / 2}}{{\left(1 + \sqrt{2}\right)}^{1 / 8}} \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("be2f32"),
    Formula(Equal(DedekindEta(Mul(8, ConstI)), Mul(Mul(Div(1, Pow(2, Div(41, 32))), Div(Pow(Sub(Pow(2, Div(1, 4)), 1), Div(1, 2)), Pow(Add(1, Sqrt(2)), Div(1, 8)))), 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