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Fungrim entry: de7918

θ32 ⁣(0,τ2)=θ22 ⁣(0,τ)+θ32 ⁣(0,τ)\theta_{3}^{2}\!\left(0, \frac{\tau}{2}\right) = \theta_{2}^{2}\!\left(0, \tau\right) + \theta_{3}^{2}\!\left(0, \tau\right)
Assumptions:τ∈H\tau \in \mathbb{H}
TeX:
\theta_{3}^{2}\!\left(0, \frac{\tau}{2}\right) = \theta_{2}^{2}\!\left(0, \tau\right) + \theta_{3}^{2}\!\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("de7918"),
    Formula(Equal(Pow(JacobiTheta(3, 0, Div(tau, 2)), 2), Add(Pow(JacobiTheta(2, 0, tau), 2), Pow(JacobiTheta(3, 0, tau), 2)))),
    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.

2021-03-15 19:12:00.328586 UTC