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Fungrim entry: 9448f2

θ4 ⁣(0,τ)=η2 ⁣(12τ)η ⁣(τ)\theta_{4}\!\left(0 , \tau\right) = \frac{\eta^{2}\!\left(\frac{1}{2} \tau\right)}{\eta\!\left(\tau\right)}
Assumptions:τH\tau \in \mathbb{H}
TeX:
\theta_{4}\!\left(0 , \tau\right) = \frac{\eta^{2}\!\left(\frac{1}{2} \tau\right)}{\eta\!\left(\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
DedekindEtaη ⁣(τ)\eta\!\left(\tau\right) Dedekind eta function
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("9448f2"),
    Formula(Equal(JacobiTheta(4, 0, tau), Div(Pow(DedekindEta(Mul(Div(1, 2), tau)), 2), DedekindEta(tau)))),
    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.

2019-09-22 15:43:45.410764 UTC