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Fungrim entry: 27b2c7

λ(τ)=πi3(E2 ⁣(τ2)+8E2 ⁣(2τ)6E2 ⁣(τ))λ(τ)\lambda'(\tau) = \frac{\pi i}{3} \left(E_{2}\!\left(\frac{\tau}{2}\right) + 8 E_{2}\!\left(2 \tau\right) - 6 E_{2}\!\left(\tau\right)\right) \lambda(\tau)
Assumptions:τH\tau \in \mathbb{H}
TeX:
\lambda'(\tau) = \frac{\pi i}{3} \left(E_{2}\!\left(\frac{\tau}{2}\right) + 8 E_{2}\!\left(2 \tau\right) - 6 E_{2}\!\left(\tau\right)\right) \lambda(\tau)

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
ComplexDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
ModularLambdaλ(τ)\lambda(\tau) Modular lambda function
Piπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
EisensteinEEk ⁣(τ)E_{k}\!\left(\tau\right) Normalized Eisenstein series
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("27b2c7"),
    Formula(Equal(ComplexDerivative(ModularLambda(tau), For(tau, tau)), Mul(Mul(Div(Mul(Pi, ConstI), 3), Sub(Add(EisensteinE(2, Div(tau, 2)), Mul(8, EisensteinE(2, Mul(2, tau)))), Mul(6, EisensteinE(2, tau)))), ModularLambda(tau)))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

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2019-12-30 15:00:46.909060 UTC