Fungrim entry: c18c95

\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(\tau)

Assumptions:

\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(\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
`ConstI`	$i$	Imaginary unit
`Pi`	$\pi$	The constant pi (3.14...)
`WeierstrassZeta`	$\zeta\!\left(z, \tau\right)$	Weierstrass zeta function
`HH`	$\mathbb{H}$	Upper complex half-plane

Source code for this entry:

Entry(ID("c18c95"),
    Formula(Equal(ComplexDerivative(ModularLambda(tau), For(tau, tau)), Mul(Mul(Div(Mul(2, ConstI), Pi), 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)))

Topics using this entry

Modular lambda function