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Fungrim entry: 7cc3d3

η ⁣(7i)=17(72+7+127+47)1/4η ⁣(i)\eta\!\left(7 i\right) = \frac{1}{\sqrt{7}} {\left(-\frac{7}{2} + \sqrt{7} + \frac{1}{2} \sqrt{-7 + 4 \sqrt{7}}\right)}^{1 / 4} \eta\!\left(i\right)
References:
  • https://math.stackexchange.com/questions/1334684/what-is-the-exact-value-of-eta6i/1334940
TeX:
\eta\!\left(7 i\right) = \frac{1}{\sqrt{7}} {\left(-\frac{7}{2} + \sqrt{7} + \frac{1}{2} \sqrt{-7 + 4 \sqrt{7}}\right)}^{1 / 4} \eta\!\left(i\right)
Definitions:
Fungrim symbol Notation Short description
DedekindEtaη ⁣(τ)\eta\!\left(\tau\right) Dedekind eta function
ConstIii Imaginary unit
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
Source code for this entry:
Entry(ID("7cc3d3"),
    Formula(Equal(DedekindEta(Mul(7, ConstI)), Mul(Mul(Div(1, Sqrt(7)), Pow(Add(Add(Neg(Div(7, 2)), Sqrt(7)), Mul(Div(1, 2), Sqrt(Add(-7, Mul(4, Sqrt(7)))))), Div(1, 4))), 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