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Fungrim entry: 59fd23

θ22 ⁣(0,τ2)=2θ2 ⁣(0,τ)θ3 ⁣(0,τ)\theta_{2}^{2}\!\left(0, \frac{\tau}{2}\right) = 2 \theta_{2}\!\left(0 , \tau\right) \theta_{3}\!\left(0 , \tau\right)
Assumptions:τH\tau \in \mathbb{H}
TeX:
\theta_{2}^{2}\!\left(0, \frac{\tau}{2}\right) = 2 \theta_{2}\!\left(0 , \tau\right) \theta_{3}\!\left(0 , \tau\right)

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
Powab{a}^{b} Power
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("59fd23"),
    Formula(Equal(Pow(JacobiTheta(2, 0, Div(tau, 2)), 2), Mul(Mul(2, JacobiTheta(2, 0, tau)), JacobiTheta(3, 0, tau)))),
    Variables(tau),
    Assumptions(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.

2019-09-20 18:07:53.062439 UTC