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Fungrim entry: e3e4c5

η ⁣(3i)=31/824/3(Γ ⁣(13))3/2π\eta\!\left(\sqrt{3} i\right) = \frac{{3}^{1 / 8}}{{2}^{4 / 3}} \frac{{\left(\Gamma\!\left(\frac{1}{3}\right)\right)}^{3 / 2}}{\pi}
References:
  • https://math.stackexchange.com/questions/1334684/what-is-the-exact-value-of-eta6i/1334940
TeX:
\eta\!\left(\sqrt{3} i\right) = \frac{{3}^{1 / 8}}{{2}^{4 / 3}} \frac{{\left(\Gamma\!\left(\frac{1}{3}\right)\right)}^{3 / 2}}{\pi}
Definitions:
Fungrim symbol Notation Short description
DedekindEtaη ⁣(τ)\eta\!\left(\tau\right) Dedekind eta function
Sqrtz\sqrt{z} Principal square root
ConstIii Imaginary unit
Powab{a}^{b} Power
GammaFunctionΓ ⁣(z)\Gamma\!\left(z\right) Gamma function
ConstPiπ\pi The constant pi (3.14...)
Source code for this entry:
Entry(ID("e3e4c5"),
    Formula(Equal(DedekindEta(Mul(Sqrt(3), ConstI)), Mul(Div(Pow(3, Div(1, 8)), Pow(2, Div(4, 3))), Div(Pow(GammaFunction(Div(1, 3)), Div(3, 2)), ConstPi)))),
    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