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Fungrim entry: cedcfc

j ⁣(τ)=32((θ2 ⁣(0,τ))8+(θ3 ⁣(0,τ))8+(θ4 ⁣(0,τ))8)3(θ2 ⁣(0,τ)θ3 ⁣(0,τ)θ4 ⁣(0,τ))8j\!\left(\tau\right) = \frac{32 {\left({\left(\theta_2\!\left(0, \tau\right)\right)}^{8} + {\left(\theta_3\!\left(0, \tau\right)\right)}^{8} + {\left(\theta_4\!\left(0, \tau\right)\right)}^{8}\right)}^{3}}{{\left(\theta_2\!\left(0, \tau\right) \theta_3\!\left(0, \tau\right) \theta_4\!\left(0, \tau\right)\right)}^{8}}
Assumptions:τH\tau \in \mathbb{H}
TeX:
j\!\left(\tau\right) = \frac{32 {\left({\left(\theta_2\!\left(0, \tau\right)\right)}^{8} + {\left(\theta_3\!\left(0, \tau\right)\right)}^{8} + {\left(\theta_4\!\left(0, \tau\right)\right)}^{8}\right)}^{3}}{{\left(\theta_2\!\left(0, \tau\right) \theta_3\!\left(0, \tau\right) \theta_4\!\left(0, \tau\right)\right)}^{8}}

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
ModularJj ⁣(τ)j\!\left(\tau\right) Modular j-invariant
Powab{a}^{b} Power
JacobiTheta2θ2 ⁣(z,τ)\theta_2\!\left(z, \tau\right) Jacobi theta function
JacobiTheta3θ3 ⁣(z,τ)\theta_3\!\left(z, \tau\right) Jacobi theta function
JacobiTheta4θ4 ⁣(z,τ)\theta_4\!\left(z, \tau\right) Jacobi theta function
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("cedcfc"),
    Formula(Equal(ModularJ(tau), Div(Mul(32, Pow(Add(Add(Pow(JacobiTheta2(0, tau), 8), Pow(JacobiTheta3(0, tau), 8)), Pow(JacobiTheta4(0, tau), 8)), 3)), Pow(Mul(Mul(JacobiTheta2(0, tau), JacobiTheta3(0, tau)), JacobiTheta4(0, tau)), 8)))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

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2019-06-18 07:49:59.356594 UTC