Fungrim entry: cedcfc

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}}

Assumptions:

\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
`ModularJ`	$j\!\left(\tau\right)$	Modular j-invariant
`Pow`	${a}^{b}$	Power
`JacobiTheta2`	$\theta_2\!\left(z, \tau\right)$	Jacobi theta function
`JacobiTheta3`	$\theta_3\!\left(z, \tau\right)$	Jacobi theta function
`JacobiTheta4`	$\theta_4\!\left(z, \tau\right)$	Jacobi theta function
`HH`	$\mathbb{H}$	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)))

Topics using this entry

Modular j-invariant