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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\!\left(\tau\right)
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\!\left(\tau\right)

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
Derivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Derivative
ModularLambdaλ ⁣(τ)\lambda\!\left(\tau\right) Modular lambda function
ConstPiπ\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(Derivative(ModularLambda(tau), tau, tau), Mul(Mul(Div(Mul(ConstPi, 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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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-15 11:00:55.020619 UTC