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Fungrim entry: 20d581

θ3 ⁣(2z,τ)=θ14 ⁣(z,τ)+θ34 ⁣(z,τ)θ33 ⁣(0,τ)\theta_{3}\!\left(2 z , \tau\right) = \frac{\theta_{1}^{4}\!\left(z, \tau\right) + \theta_{3}^{4}\!\left(z, \tau\right)}{\theta_{3}^{3}\!\left(0, \tau\right)}
Assumptions:zCandτHz \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}
\theta_{3}\!\left(2 z , \tau\right) = \frac{\theta_{1}^{4}\!\left(z, \tau\right) + \theta_{3}^{4}\!\left(z, \tau\right)}{\theta_{3}^{3}\!\left(0, \tau\right)}

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \tau \in \mathbb{H}
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:
    Formula(Equal(JacobiTheta(3, Mul(2, z), tau), Div(Add(Pow(JacobiTheta(1, z, tau), 4), Pow(JacobiTheta(3, z, tau), 4)), Pow(JacobiTheta(3, 0, tau), 3)))),
    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.

2020-01-31 18:09:28.494564 UTC