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Fungrim entry: 0fda1b

G6 ⁣(e2πi/3)=(Γ ⁣(13))188960π6G_{6}\!\left({e}^{2 \pi i / 3}\right) = \frac{{\left(\Gamma\!\left(\frac{1}{3}\right)\right)}^{18}}{8960 {\pi}^{6}}
TeX:
G_{6}\!\left({e}^{2 \pi i / 3}\right) = \frac{{\left(\Gamma\!\left(\frac{1}{3}\right)\right)}^{18}}{8960 {\pi}^{6}}
Definitions:
Fungrim symbol Notation Short description
EisensteinGGk ⁣(τ)G_{k}\!\left(\tau\right) Eisenstein series
Expez{e}^{z} Exponential function
ConstPiπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
Powab{a}^{b} Power
GammaFunctionΓ ⁣(z)\Gamma\!\left(z\right) Gamma function
Source code for this entry:
Entry(ID("0fda1b"),
    Formula(Equal(EisensteinG(6, Exp(Div(Mul(Mul(2, ConstPi), ConstI), 3))), Div(Pow(GammaFunction(Div(1, 3)), 18), Mul(8960, Pow(ConstPi, 6))))))

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

2019-09-22 15:43:45.410764 UTC