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"))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-08-27 09:56:25.682319 UTC