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Fungrim entry: 62ffb3

η ⁣(6i)=163/8(53233/42)1/6η ⁣(i)\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\!\left(i\right)
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\!\left(i\right)
Definitions:
Fungrim symbol Notation Short description
DedekindEtaη ⁣(τ)\eta\!\left(\tau\right) Dedekind eta function
ConstIii Imaginary unit
Powab{a}^{b} Power
Sqrtz\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"))

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

2019-08-19 14:38:23.809000 UTC