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Fungrim entry: 6c71c0

E6 ⁣(e2πi/3)=27(Γ ⁣(13))18512π12E_{6}\!\left({e}^{2 \pi i / 3}\right) = \frac{27 {\left(\Gamma\!\left(\frac{1}{3}\right)\right)}^{18}}{512 {\pi}^{12}}
TeX:
E_{6}\!\left({e}^{2 \pi i / 3}\right) = \frac{27 {\left(\Gamma\!\left(\frac{1}{3}\right)\right)}^{18}}{512 {\pi}^{12}}
Definitions:
Fungrim symbol Notation Short description
EisensteinEEk ⁣(τ)E_{k}\!\left(\tau\right) Normalized 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("6c71c0"),
    Formula(Equal(EisensteinE(6, Exp(Div(Mul(Mul(2, ConstPi), ConstI), 3))), Div(Mul(27, Pow(GammaFunction(Div(1, 3)), 18)), Mul(512, Pow(ConstPi, 12))))))

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2019-09-19 20:12:49.583742 UTC