Fungrim entry: bd7d8e

E_{4}^{3}\!\left(\tau\right) - E_{6}^{2}\!\left(\tau\right) = \frac{27}{4} {\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:

E_{4}^{3}\!\left(\tau\right) - E_{6}^{2}\!\left(\tau\right) = \frac{27}{4} {\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
`Pow`	${a}^{b}$	Power
`EisensteinE`	$E_{k}\!\left(\tau\right)$	Normalized Eisenstein series
`JacobiTheta`	$\theta_{j}\!\left(z , \tau\right)$	Jacobi theta function
`HH`	$\mathbb{H}$	Upper complex half-plane

Source code for this entry:

Entry(ID("bd7d8e"),
    Formula(Equal(Sub(Pow(EisensteinE(4, tau), 3), Pow(EisensteinE(6, tau), 2)), Mul(Div(27, 4), 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

Eisenstein series