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Fungrim entry: cc579c

E4 ⁣(τ)=12(θ28 ⁣(0,τ)+θ38 ⁣(0,τ)+θ48 ⁣(0,τ))E_{4}\!\left(\tau\right) = \frac{1}{2} \left(\theta_{2}^{8}\!\left(0, \tau\right) + \theta_{3}^{8}\!\left(0, \tau\right) + \theta_{4}^{8}\!\left(0, \tau\right)\right)
Assumptions:τH\tau \in \mathbb{H}
E_{4}\!\left(\tau\right) = \frac{1}{2} \left(\theta_{2}^{8}\!\left(0, \tau\right) + \theta_{3}^{8}\!\left(0, \tau\right) + \theta_{4}^{8}\!\left(0, \tau\right)\right)

\tau \in \mathbb{H}
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:
    Formula(Equal(EisensteinE(4, tau), Mul(Div(1, 2), Add(Add(Pow(JacobiTheta(2, 0, tau), 8), Pow(JacobiTheta(3, 0, tau), 8)), Pow(JacobiTheta(4, 0, tau), 8))))),
    Assumptions(Element(tau, HH)))

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

2021-03-15 19:12:00.328586 UTC