# 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

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC