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Fungrim entry: dbf388

G2 ⁣(τ)=4πiη(τ)η(τ)G_{2}\!\left(\tau\right) = -4 \pi i \frac{\eta'(\tau)}{\eta(\tau)}
Assumptions:τH\tau \in \mathbb{H}
G_{2}\!\left(\tau\right) = -4 \pi i \frac{\eta'(\tau)}{\eta(\tau)}

\tau \in \mathbb{H}
Fungrim symbol Notation Short description
EisensteinGGk ⁣(τ)G_{k}\!\left(\tau\right) Eisenstein series
Piπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
ComplexDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
DedekindEtaη(τ)\eta(\tau) Dedekind eta function
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
    Formula(Equal(EisensteinG(2, tau), Neg(Mul(Mul(Mul(4, Pi), ConstI), Div(ComplexDerivative(DedekindEta(tau), For(tau, tau)), DedekindEta(tau)))))),
    Assumptions(Element(tau, HH)))

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2021-03-15 19:12:00.328586 UTC