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Fungrim entry: 9a2054

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

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
Powab{a}^{b} Power
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("9a2054"),
    Formula(Equal(Mul(Mul(2, JacobiTheta(2, 0, Mul(2, tau))), JacobiTheta(3, 0, Mul(2, tau))), Pow(JacobiTheta(2, 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.

2019-09-19 20:12:49.583742 UTC