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Fungrim entry: 278274

θ1 ⁣(0,τ)θ1 ⁣(0,τ)=θ2 ⁣(0,τ)θ2 ⁣(0,τ)+θ3 ⁣(0,τ)θ3 ⁣(0,τ)+θ4 ⁣(0,τ)θ4 ⁣(0,τ)\frac{\theta'''_{1}\!\left(0 , \tau\right)}{\theta'_{1}\!\left(0 , \tau\right)} = \frac{\theta''_{2}\!\left(0 , \tau\right)}{\theta_{2}\!\left(0 , \tau\right)} + \frac{\theta''_{3}\!\left(0 , \tau\right)}{\theta_{3}\!\left(0 , \tau\right)} + \frac{\theta''_{4}\!\left(0 , \tau\right)}{\theta_{4}\!\left(0 , \tau\right)}
Assumptions:τH\tau \in \mathbb{H}
TeX:
\frac{\theta'''_{1}\!\left(0 , \tau\right)}{\theta'_{1}\!\left(0 , \tau\right)} = \frac{\theta''_{2}\!\left(0 , \tau\right)}{\theta_{2}\!\left(0 , \tau\right)} + \frac{\theta''_{3}\!\left(0 , \tau\right)}{\theta_{3}\!\left(0 , \tau\right)} + \frac{\theta''_{4}\!\left(0 , \tau\right)}{\theta_{4}\!\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("278274"),
    Formula(Equal(Div(JacobiTheta(1, 0, tau, 3), JacobiTheta(1, 0, tau, 1)), Add(Add(Div(JacobiTheta(2, 0, tau, 2), JacobiTheta(2, 0, tau)), Div(JacobiTheta(3, 0, tau, 2), JacobiTheta(3, 0, tau))), Div(JacobiTheta(4, 0, tau, 2), JacobiTheta(4, 0, tau))))),
    Variables(tau),
    Assumptions(And(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.

2019-10-05 13:11:19.856591 UTC