Fungrim entry: 033d39

\frac{1}{\lambda(\tau)} = \frac{1}{16} \frac{\eta^{8}\!\left(\frac{\tau}{2}\right)}{\eta^{8}\!\left(2 \tau\right)} + 1

Assumptions:

\tau \in \mathbb{H}

TeX:

\frac{1}{\lambda(\tau)} = \frac{1}{16} \frac{\eta^{8}\!\left(\frac{\tau}{2}\right)}{\eta^{8}\!\left(2 \tau\right)} + 1

\tau \in \mathbb{H}

Definitions:

Fungrim symbol	Notation	Short description
`ModularLambda`	$\lambda(\tau)$	Modular lambda function
`Pow`	${a}^{b}$	Power
`DedekindEta`	$\eta(\tau)$	Dedekind eta function
`HH`	$\mathbb{H}$	Upper complex half-plane

Source code for this entry:

Entry(ID("033d39"),
    Formula(Equal(Div(1, ModularLambda(tau)), Add(Mul(Div(1, 16), Div(Pow(DedekindEta(Div(tau, 2)), 8), Pow(DedekindEta(Mul(2, tau)), 8))), 1))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

Topics using this entry

Modular lambda function

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