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Fungrim entry: 5a3ebf

θ14 ⁣(z,τ)θ24 ⁣(z,τ)=θ44 ⁣(z,τ)θ34 ⁣(z,τ)\theta_{1}^{4}\!\left(z, \tau\right) - \theta_{2}^{4}\!\left(z, \tau\right) = \theta_{4}^{4}\!\left(z, \tau\right) - \theta_{3}^{4}\!\left(z, \tau\right)
Assumptions:zC  and  τHz \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}
\theta_{1}^{4}\!\left(z, \tau\right) - \theta_{2}^{4}\!\left(z, \tau\right) = \theta_{4}^{4}\!\left(z, \tau\right) - \theta_{3}^{4}\!\left(z, \tau\right)

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}
Fungrim symbol Notation Short description
Powab{a}^{b} Power
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
CCC\mathbb{C} Complex numbers
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
    Formula(Equal(Sub(Pow(JacobiTheta(1, z, tau), 4), Pow(JacobiTheta(2, z, tau), 4)), Sub(Pow(JacobiTheta(4, z, tau), 4), Pow(JacobiTheta(3, z, tau), 4)))),
    Variables(z, tau),
    Assumptions(And(Element(z, CC), 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