Fungrim home page

Fungrim entry: cedcfc

j ⁣(τ)=32(θ28 ⁣(0,τ)+θ38 ⁣(0,τ)+θ48 ⁣(0,τ))3(θ2 ⁣(0,τ)θ3 ⁣(0,τ)θ4 ⁣(0,τ))8j\!\left(\tau\right) = \frac{32 {\left(\theta_{2}^{8}\!\left(0, \tau\right) + \theta_{3}^{8}\!\left(0, \tau\right) + \theta_{4}^{8}\!\left(0, \tau\right)\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(\theta_{2}^{8}\!\left(0, \tau\right) + \theta_{3}^{8}\!\left(0, \tau\right) + \theta_{4}^{8}\!\left(0, \tau\right)\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
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\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(JacobiTheta(2, 0, tau), 8), Pow(JacobiTheta(3, 0, tau), 8)), Pow(JacobiTheta(4, 0, tau), 8)), 3)), Pow(Mul(Mul(JacobiTheta(2, 0, tau), JacobiTheta(3, 0, tau)), JacobiTheta(4, 0, tau)), 8)))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

Topics using this entry

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