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Fungrim entry: 85b2ff

θ3 ⁣(0,τ)=η2 ⁣(12(τ+1))η ⁣(τ+1)\theta_{3}\!\left(0 , \tau\right) = \frac{\eta^{2}\!\left(\frac{1}{2} \left(\tau + 1\right)\right)}{\eta\!\left(\tau + 1\right)}
Assumptions:τH\tau \in \mathbb{H}
TeX:
\theta_{3}\!\left(0 , \tau\right) = \frac{\eta^{2}\!\left(\frac{1}{2} \left(\tau + 1\right)\right)}{\eta\!\left(\tau + 1\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("85b2ff"),
    Formula(Equal(JacobiTheta(3, 0, tau), Div(Pow(DedekindEta(Mul(Div(1, 2), Add(tau, 1))), 2), DedekindEta(Add(tau, 1))))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

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2019-09-20 18:07:53.062439 UTC