Fungrim entry: f0f53b

j'(\tau) = -2 \pi i \frac{E_{14}\!\left(\tau\right)}{\eta^{24}\!\left(\tau\right)}

Assumptions:

\tau \in \mathbb{H}

TeX:

j'(\tau) = -2 \pi i \frac{E_{14}\!\left(\tau\right)}{\eta^{24}\!\left(\tau\right)}

\tau \in \mathbb{H}

Definitions:

Fungrim symbol	Notation	Short description
`ComplexDerivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Complex derivative
`ModularJ`	$j(\tau)$	Modular j-invariant
`Pi`	$\pi$	The constant pi (3.14...)
`ConstI`	$i$	Imaginary unit
`EisensteinE`	$E_{k}\!\left(\tau\right)$	Normalized Eisenstein series
`Pow`	${a}^{b}$	Power
`DedekindEta`	$\eta(\tau)$	Dedekind eta function
`HH`	$\mathbb{H}$	Upper complex half-plane

Source code for this entry:

Entry(ID("f0f53b"),
    Formula(Equal(ComplexDerivative(ModularJ(tau), For(tau, tau)), Mul(Neg(Mul(Mul(2, Pi), ConstI)), Div(EisensteinE(14, tau), Pow(DedekindEta(tau), 24))))),
    Variables(tau),
    Assumptions(And(Element(tau, HH))))

Topics using this entry

Modular j-invariant

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC