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Fungrim entry: 8b825c

θ4 ⁣(2z,τ)=θ44 ⁣(z,τ)θ14 ⁣(z,τ)θ43 ⁣(0,τ)\theta_{4}\!\left(2 z , \tau\right) = \frac{\theta_{4}^{4}\!\left(z, \tau\right) - \theta_{1}^{4}\!\left(z, \tau\right)}{\theta_{4}^{3}\!\left(0, \tau\right)}
Assumptions:zC  and  τHz \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}
\theta_{4}\!\left(2 z , \tau\right) = \frac{\theta_{4}^{4}\!\left(z, \tau\right) - \theta_{1}^{4}\!\left(z, \tau\right)}{\theta_{4}^{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(4, Mul(2, z), tau), Div(Sub(Pow(JacobiTheta(4, z, tau), 4), Pow(JacobiTheta(1, z, tau), 4)), Pow(JacobiTheta(4, 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.

2021-03-15 19:12:00.328586 UTC