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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
ComplexDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
ModularJj(τ)j(\tau) Modular j-invariant
Piπ\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(\tau) Dedekind eta function
HHH\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))))

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2020-01-31 18:09:28.494564 UTC