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Fungrim entry: 6d2880

E8 ⁣(τ)=12(θ216 ⁣(0,τ)+θ316 ⁣(0,τ)+θ416 ⁣(0,τ))E_{8}\!\left(\tau\right) = \frac{1}{2} \left(\theta_{2}^{16}\!\left(0, \tau\right) + \theta_{3}^{16}\!\left(0, \tau\right) + \theta_{4}^{16}\!\left(0, \tau\right)\right)
Assumptions:τ∈H\tau \in \mathbb{H}
TeX:
E_{8}\!\left(\tau\right) = \frac{1}{2} \left(\theta_{2}^{16}\!\left(0, \tau\right) + \theta_{3}^{16}\!\left(0, \tau\right) + \theta_{4}^{16}\!\left(0, \tau\right)\right)

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
EisensteinEEk ⁣(τ)E_{k}\!\left(\tau\right) Normalized Eisenstein series
Powab{a}^{b} Power
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("6d2880"),
    Formula(Equal(EisensteinE(8, tau), Mul(Div(1, 2), Add(Add(Pow(JacobiTheta(2, 0, tau), 16), Pow(JacobiTheta(3, 0, tau), 16)), Pow(JacobiTheta(4, 0, tau), 16))))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

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2021-03-15 19:12:00.328586 UTC