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Fungrim entry: 46f244

2θ1 ⁣(0,2τ)θ4 ⁣(0,2τ)=θ1 ⁣(0,τ)θ2 ⁣(0,τ)2 \theta'_{1}\!\left(0 , 2 \tau\right) \theta_{4}\!\left(0 , 2 \tau\right) = \theta'_{1}\!\left(0 , \tau\right) \theta_{2}\!\left(0 , \tau\right)
Assumptions:τH\tau \in \mathbb{H}
TeX:
2 \theta'_{1}\!\left(0 , 2 \tau\right) \theta_{4}\!\left(0 , 2 \tau\right) = \theta'_{1}\!\left(0 , \tau\right) \theta_{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
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("46f244"),
    Formula(Equal(Mul(Mul(2, JacobiTheta(1, 0, Mul(2, tau), 1)), JacobiTheta(4, 0, Mul(2, tau))), Mul(JacobiTheta(1, 0, tau, 1), JacobiTheta(2, 0, tau)))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

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2021-03-15 19:12:00.328586 UTC