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Fungrim entry: 664b4c

j ⁣(τ)=((η ⁣(τ)η ⁣(2τ))8+28(η ⁣(2τ)η ⁣(τ))16)3j\!\left(\tau\right) = {\left({\left(\frac{\eta\!\left(\tau\right)}{\eta\!\left(2 \tau\right)}\right)}^{8} + {2}^{8} {\left(\frac{\eta\!\left(2 \tau\right)}{\eta\!\left(\tau\right)}\right)}^{16}\right)}^{3}
Assumptions:τH\tau \in \mathbb{H}
TeX:
j\!\left(\tau\right) = {\left({\left(\frac{\eta\!\left(\tau\right)}{\eta\!\left(2 \tau\right)}\right)}^{8} + {2}^{8} {\left(\frac{\eta\!\left(2 \tau\right)}{\eta\!\left(\tau\right)}\right)}^{16}\right)}^{3}

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
ModularJj ⁣(τ)j\!\left(\tau\right) Modular j-invariant
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("664b4c"),
    Formula(Equal(ModularJ(tau), Pow(Add(Pow(Div(DedekindEta(tau), DedekindEta(Mul(2, tau))), 8), Mul(Pow(2, 8), Pow(Div(DedekindEta(Mul(2, tau)), DedekindEta(tau)), 16))), 3))),
    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.

2019-09-20 18:07:53.062439 UTC