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Fungrim entry: f0f53b

j(τ)=2πiE14 ⁣(τ)η24 ⁣(τ)j'(\tau) = -2 \pi i \frac{E_{14}\!\left(\tau\right)}{\eta^{24}\!\left(\tau\right)}
Assumptions:τH\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
Derivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Derivative
ModularJj ⁣(τ)j\!\left(\tau\right) Modular j-invariant
ConstPiπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
EisensteinEEk ⁣(τ)E_{k}\!\left(\tau\right) Normalized Eisenstein series
Powab{a}^{b} Power
DedekindEtaη ⁣(τ)\eta\!\left(\tau\right) Dedekind eta function
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("f0f53b"),
    Formula(Equal(Derivative(ModularJ(tau), tau, tau), Mul(Neg(Mul(Mul(2, ConstPi), ConstI)), Div(EisensteinE(14, tau), Pow(DedekindEta(tau), 24))))),
    Variables(tau),
    Assumptions(And(Element(tau, HH))))

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

2019-09-20 18:07:53.062439 UTC