# Fungrim entry: 166402

$\lambda(\tau) = \frac{\wp\!\left(\frac{1}{2} \left(1 + \tau\right), \tau\right) - \wp\!\left(\frac{\tau}{2}, \tau\right)}{\wp\!\left(\frac{1}{2}, \tau\right) - \wp\!\left(\frac{\tau}{2}, \tau\right)}$
Assumptions:$\tau \in \mathbb{H}$
TeX:
\lambda(\tau) = \frac{\wp\!\left(\frac{1}{2} \left(1 + \tau\right), \tau\right) - \wp\!\left(\frac{\tau}{2}, \tau\right)}{\wp\!\left(\frac{1}{2}, \tau\right) - \wp\!\left(\frac{\tau}{2}, \tau\right)}

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
ModularLambda$\lambda(\tau)$ Modular lambda function
WeierstrassP$\wp\!\left(z, \tau\right)$ Weierstrass elliptic function
HH$\mathbb{H}$ Upper complex half-plane
Source code for this entry:
Entry(ID("166402"),
Formula(Equal(ModularLambda(tau), Div(Sub(WeierstrassP(Mul(Div(1, 2), Add(1, tau)), tau), WeierstrassP(Div(tau, 2), tau)), Sub(WeierstrassP(Div(1, 2), tau), WeierstrassP(Div(tau, 2), 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