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Fungrim entry: 204acd

η ⁣(e2πi/3)=eπi/2431/8(Γ ⁣(13))3/22π\eta\!\left({e}^{2 \pi i / 3}\right) = {e}^{-\pi i / 24} \frac{{3}^{1 / 8} {\left(\Gamma\!\left(\frac{1}{3}\right)\right)}^{3 / 2}}{2 \pi}
TeX:
\eta\!\left({e}^{2 \pi i / 3}\right) = {e}^{-\pi i / 24} \frac{{3}^{1 / 8} {\left(\Gamma\!\left(\frac{1}{3}\right)\right)}^{3 / 2}}{2 \pi}
Definitions:
Fungrim symbol Notation Short description
DedekindEtaη ⁣(τ)\eta\!\left(\tau\right) Dedekind eta function
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("204acd"),
    Formula(Equal(DedekindEta(Exp(Div(Mul(Mul(2, ConstPi), ConstI), 3))), Mul(Exp(Neg(Div(Mul(ConstPi, ConstI), 24))), Div(Mul(Pow(3, Div(1, 8)), Pow(GammaFunction(Div(1, 3)), Div(3, 2))), Mul(2, ConstPi))))))

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2019-08-19 14:38:23.809000 UTC