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Fungrim entry: 95e508

θ4 ⁣(z,τ2)=θ32 ⁣(z,τ)θ22 ⁣(z,τ)θ4 ⁣(0,τ2)\theta_{4}\!\left(z , \frac{\tau}{2}\right) = \frac{\theta_{3}^{2}\!\left(z, \tau\right) - \theta_{2}^{2}\!\left(z, \tau\right)}{\theta_{4}\!\left(0 , \frac{\tau}{2}\right)}
Assumptions:zCandτHz \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}
TeX:
\theta_{4}\!\left(z , \frac{\tau}{2}\right) = \frac{\theta_{3}^{2}\!\left(z, \tau\right) - \theta_{2}^{2}\!\left(z, \tau\right)}{\theta_{4}\!\left(0 , \frac{\tau}{2}\right)}

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \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
CCC\mathbb{C} Complex numbers
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("95e508"),
    Formula(Equal(JacobiTheta(4, z, Div(tau, 2)), Div(Sub(Pow(JacobiTheta(3, z, tau), 2), Pow(JacobiTheta(2, z, tau), 2)), JacobiTheta(4, 0, Div(tau, 2))))),
    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.

2019-12-11 23:01:54.699850 UTC