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Fungrim entry: 04d3a6

1λ ⁣(τ)=θ44 ⁣(0,τ)θ34 ⁣(0,τ)1 - \lambda\!\left(\tau\right) = \frac{\theta_{4}^{4}\!\left(0, \tau\right)}{\theta_{3}^{4}\!\left(0, \tau\right)}
Assumptions:τH\tau \in \mathbb{H}
TeX:
1 - \lambda\!\left(\tau\right) = \frac{\theta_{4}^{4}\!\left(0, \tau\right)}{\theta_{3}^{4}\!\left(0, \tau\right)}

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
ModularLambdaλ ⁣(τ)\lambda\!\left(\tau\right) Modular lambda function
Powab{a}^{b} Power
JacobiThetaθj ⁣(z,τ)\theta_{j}\!\left(z , \tau\right) Jacobi theta function
HHH\mathbb{H} Upper complex half-plane
Source code for this entry:
Entry(ID("04d3a6"),
    Formula(Equal(Sub(1, ModularLambda(tau)), Div(Pow(JacobiTheta(4, 0, tau), 4), Pow(JacobiTheta(3, 0, tau), 4)))),
    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.

2019-09-16 21:17:18.797188 UTC