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Fungrim entry: 66eb8b

θ1 ⁣(z,τ2)=2θ1 ⁣(z,τ)θ4 ⁣(z,τ)θ2 ⁣(0,τ2)\theta_{1}\!\left(z , \frac{\tau}{2}\right) = \frac{2 \theta_{1}\!\left(z , \tau\right) \theta_{4}\!\left(z , \tau\right)}{\theta_{2}\!\left(0 , \frac{\tau}{2}\right)}
Assumptions:zC  and  τHz \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}
\theta_{1}\!\left(z , \frac{\tau}{2}\right) = \frac{2 \theta_{1}\!\left(z , \tau\right) \theta_{4}\!\left(z , \tau\right)}{\theta_{2}\!\left(0 , \frac{\tau}{2}\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
CCC\mathbb{C} Complex numbers
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
    Formula(Equal(JacobiTheta(1, z, Div(tau, 2)), Div(Mul(Mul(2, JacobiTheta(1, z, tau)), JacobiTheta(4, z, tau)), JacobiTheta(2, 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.

2021-03-15 19:12:00.328586 UTC