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Fungrim entry: c18c95

λ(τ)=2iπ(ζ ⁣(12,τ2)+8ζ ⁣(12,2τ)6ζ ⁣(12,τ))λ ⁣(τ)\lambda'(\tau) = \frac{2 i}{\pi} \left(\zeta\!\left(\frac{1}{2}, \frac{\tau}{2}\right) + 8 \zeta\!\left(\frac{1}{2}, 2 \tau\right) - 6 \zeta\!\left(\frac{1}{2}, \tau\right)\right) \lambda\!\left(\tau\right)
Assumptions:τH\tau \in \mathbb{H}
TeX:
\lambda'(\tau) = \frac{2 i}{\pi} \left(\zeta\!\left(\frac{1}{2}, \frac{\tau}{2}\right) + 8 \zeta\!\left(\frac{1}{2}, 2 \tau\right) - 6 \zeta\!\left(\frac{1}{2}, \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
ConstIii Imaginary unit
ConstPiπ\pi The constant pi (3.14...)
WeierstrassZetaζ ⁣(z,τ)\zeta\!\left(z, \tau\right) Weierstrass zeta function
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("c18c95"),
    Formula(Equal(Derivative(ModularLambda(tau), tau, tau), Mul(Mul(Div(Mul(2, ConstI), ConstPi), Sub(Add(WeierstrassZeta(Div(1, 2), Div(tau, 2)), Mul(8, WeierstrassZeta(Div(1, 2), Mul(2, tau)))), Mul(6, WeierstrassZeta(Div(1, 2), tau)))), ModularLambda(tau)))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

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2019-09-19 20:12:49.583742 UTC