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Fungrim entry: f2e28a

θ1 ⁣(0,τ)=πθ2 ⁣(0,τ)θ3 ⁣(0,τ)θ4 ⁣(0,τ)\theta'_{1}\!\left(0 , \tau\right) = \pi \theta_{2}\!\left(0 , \tau\right) \theta_{3}\!\left(0 , \tau\right) \theta_{4}\!\left(0 , \tau\right)
Assumptions:τH\tau \in \mathbb{H}
TeX:
\theta'_{1}\!\left(0 , \tau\right) = \pi \theta_{2}\!\left(0 , \tau\right) \theta_{3}\!\left(0 , \tau\right) \theta_{4}\!\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
ConstPiπ\pi The constant pi (3.14...)
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("f2e28a"),
    Formula(Equal(JacobiTheta(1, 0, tau, 1), Mul(Mul(Mul(ConstPi, JacobiTheta(2, 0, tau)), JacobiTheta(3, 0, tau)), JacobiTheta(4, 0, tau)))),
    Variables(tau),
    Assumptions(And(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.

2019-10-05 13:11:19.856591 UTC