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Fungrim entry: 737805

η ⁣(τ)=eπiτ/12θ3 ⁣(τ+12,3τ)\eta\!\left(\tau\right) = {e}^{\pi i \tau / 12} \theta_{3}\!\left(\frac{\tau + 1}{2} , 3 \tau\right)
Assumptions:τH\tau \in \mathbb{H}
\eta\!\left(\tau\right) = {e}^{\pi i \tau / 12} \theta_{3}\!\left(\frac{\tau + 1}{2} , 3 \tau\right)

\tau \in \mathbb{H}
Fungrim symbol Notation Short description
DedekindEtaη ⁣(τ)\eta\!\left(\tau\right) Dedekind eta function
Expez{e}^{z} Exponential function
ConstPiπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
    Formula(Equal(DedekindEta(tau), Mul(Exp(Div(Mul(Mul(ConstPi, ConstI), tau), 12)), JacobiTheta(3, Div(Add(tau, 1), 2), Mul(3, tau))))),
    Assumptions(Element(tau, HH)))

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2019-08-19 14:38:23.809000 UTC