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Fungrim entry: 557b19

θ2 ⁣(0,τ)θ3 ⁣(0,τ)θ4 ⁣(0,τ)=2η3 ⁣(τ)\theta_{2}\!\left(0 , \tau\right) \theta_{3}\!\left(0 , \tau\right) \theta_{4}\!\left(0 , \tau\right) = 2 \eta^{3}\!\left(\tau\right)
Assumptions:τH\tau \in \mathbb{H}
TeX:
\theta_{2}\!\left(0 , \tau\right) \theta_{3}\!\left(0 , \tau\right) \theta_{4}\!\left(0 , \tau\right) = 2 \eta^{3}\!\left(\tau\right)

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
Powab{a}^{b} Power
DedekindEtaη ⁣(τ)\eta\!\left(\tau\right) Dedekind eta function
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("557b19"),
    Formula(Equal(Mul(Mul(JacobiTheta(2, 0, tau), JacobiTheta(3, 0, tau)), JacobiTheta(4, 0, tau)), Mul(2, Pow(DedekindEta(tau), 3)))),
    Variables(tau),
    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.

2019-09-19 20:12:49.583742 UTC