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Fungrim entry: 10f3b2

E6 ⁣(τ)=12(θ312 ⁣(0,τ)+θ412 ⁣(0,τ)3θ28 ⁣(0,τ)(θ34 ⁣(0,τ)+θ44 ⁣(0,τ)))E_{6}\!\left(\tau\right) = \frac{1}{2} \left(\theta_{3}^{12}\!\left(0, \tau\right) + \theta_{4}^{12}\!\left(0, \tau\right) - 3 \theta_{2}^{8}\!\left(0, \tau\right) \left(\theta_{3}^{4}\!\left(0, \tau\right) + \theta_{4}^{4}\!\left(0, \tau\right)\right)\right)
Assumptions:τH\tau \in \mathbb{H}
TeX:
E_{6}\!\left(\tau\right) = \frac{1}{2} \left(\theta_{3}^{12}\!\left(0, \tau\right) + \theta_{4}^{12}\!\left(0, \tau\right) - 3 \theta_{2}^{8}\!\left(0, \tau\right) \left(\theta_{3}^{4}\!\left(0, \tau\right) + \theta_{4}^{4}\!\left(0, \tau\right)\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("10f3b2"),
    Formula(Equal(EisensteinE(6, tau), Mul(Div(1, 2), Sub(Add(Pow(JacobiTheta(3, 0, tau), 12), Pow(JacobiTheta(4, 0, tau), 12)), Mul(Mul(3, Pow(JacobiTheta(2, 0, tau), 8)), Add(Pow(JacobiTheta(3, 0, tau), 4), Pow(JacobiTheta(4, 0, tau), 4))))))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

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2019-10-05 13:11:19.856591 UTC