Fungrim entry: 27b2c7

\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:

\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
`ComplexDerivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Complex derivative
`ModularLambda`	$\lambda(\tau)$	Modular lambda function
`Pi`	$\pi$	The constant pi (3.14...)
`ConstI`	$i$	Imaginary unit
`EisensteinE`	$E_{k}\!\left(\tau\right)$	Normalized Eisenstein series
`HH`	$\mathbb{H}$	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)))

Topics using this entry

Modular lambda function