Fungrim home page

Fungrim entry: 166402

λ ⁣(τ)= ⁣(12(1+τ),τ) ⁣(τ2,τ) ⁣(12,τ) ⁣(τ2,τ)\lambda\!\left(\tau\right) = \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:τH\tau \in \mathbb{H}
TeX:
\lambda\!\left(\tau\right) = \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
ModularLambdaλ ⁣(τ)\lambda\!\left(\tau\right) Modular lambda function
WeierstrassP ⁣(z,τ)\wp\!\left(z, \tau\right) Weierstrass elliptic function
HHH\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.

2019-09-15 11:00:55.020619 UTC