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Fungrim entry: a9c825

θ2 ⁣(0,τ)=2η2 ⁣(2τ)η ⁣(τ)\theta_{2}\!\left(0 , \tau\right) = \frac{2 \eta^{2}\!\left(2 \tau\right)}{\eta\!\left(\tau\right)}
Assumptions:τH\tau \in \mathbb{H}
TeX:
\theta_{2}\!\left(0 , \tau\right) = \frac{2 \eta^{2}\!\left(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("a9c825"),
    Formula(Equal(JacobiTheta(2, 0, tau), Div(Mul(2, Pow(DedekindEta(Mul(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.

2019-09-19 20:12:49.583742 UTC