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Fungrim entry: 166402

λ(τ)= ⁣(12(1+τ),τ) ⁣(τ2,τ) ⁣(12,τ) ⁣(τ2,τ)\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:τH\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
ModularLambdaλ(τ)\lambda(\tau) 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)))

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

2019-12-30 15:00:46.909060 UTC