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Fungrim entry: 476642

θ3 ⁣(0,τ2)θ4 ⁣(0,τ2)=θ42 ⁣(0,τ)\theta_{3}\!\left(0 , \frac{\tau}{2}\right) \theta_{4}\!\left(0 , \frac{\tau}{2}\right) = \theta_{4}^{2}\!\left(0, \tau\right)
Assumptions:τ∈H\tau \in \mathbb{H}
TeX:
\theta_{3}\!\left(0 , \frac{\tau}{2}\right) \theta_{4}\!\left(0 , \frac{\tau}{2}\right) = \theta_{4}^{2}\!\left(0, \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
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("476642"),
    Formula(Equal(Mul(JacobiTheta(3, 0, Div(tau, 2)), JacobiTheta(4, 0, Div(tau, 2))), Pow(JacobiTheta(4, 0, tau), 2))),
    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.

2021-03-15 19:12:00.328586 UTC