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Fungrim entry: f14471

θ42 ⁣(0,2τ)=θ3 ⁣(0,τ)θ4 ⁣(0,τ)\theta_{4}^{2}\!\left(0, 2 \tau\right) = \theta_{3}\!\left(0 , \tau\right) \theta_{4}\!\left(0 , \tau\right)
Assumptions:τH\tau \in \mathbb{H}
TeX:
\theta_{4}^{2}\!\left(0, 2 \tau\right) = \theta_{3}\!\left(0 , \tau\right) \theta_{4}\!\left(0 , \tau\right)

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
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("f14471"),
    Formula(Equal(Pow(JacobiTheta(4, 0, Mul(2, tau)), 2), Mul(JacobiTheta(3, 0, tau), JacobiTheta(4, 0, tau)))),
    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.

2019-09-22 15:43:45.410764 UTC