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Fungrim entry: c3d8c2

2θ32 ⁣(0,2τ)=θ32 ⁣(0,τ)+θ42 ⁣(0,τ)2 \theta_{3}^{2}\!\left(0, 2 \tau\right) = \theta_{3}^{2}\!\left(0, \tau\right) + \theta_{4}^{2}\!\left(0, \tau\right)
Assumptions:τH\tau \in \mathbb{H}
TeX:
2 \theta_{3}^{2}\!\left(0, 2 \tau\right) = \theta_{3}^{2}\!\left(0, \tau\right) + \theta_{4}^{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("c3d8c2"),
    Formula(Equal(Mul(2, Pow(JacobiTheta(3, 0, Mul(2, tau)), 2)), Add(Pow(JacobiTheta(3, 0, tau), 2), Pow(JacobiTheta(4, 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.

2019-09-20 18:07:53.062439 UTC