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Fungrim entry: a0a1ee

θ2 ⁣(2z,4τ)=θ3 ⁣(z,τ)−θ4 ⁣(z,τ)2\theta_{2}\!\left(2 z , 4 \tau\right) = \frac{\theta_{3}\!\left(z , \tau\right) - \theta_{4}\!\left(z , \tau\right)}{2}
Assumptions:z∈C  and⁡  τ∈Hz \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \tau \in \mathbb{H}
TeX:
\theta_{2}\!\left(2 z , 4 \tau\right) = \frac{\theta_{3}\!\left(z , \tau\right) - \theta_{4}\!\left(z , \tau\right)}{2}

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
CCC\mathbb{C} Complex numbers
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("a0a1ee"),
    Formula(Equal(JacobiTheta(2, Mul(2, z), Mul(4, tau)), Div(Sub(JacobiTheta(3, z, tau), JacobiTheta(4, z, 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