Fungrim entry: 903962

\frac{\lambda(\tau)}{\lambda(\tau) - 1} = -\frac{\theta_{2}^{4}\!\left(0, \tau\right)}{\theta_{4}^{4}\!\left(0, \tau\right)}

Assumptions:

\tau \in \mathbb{H}

TeX:

\frac{\lambda(\tau)}{\lambda(\tau) - 1} = -\frac{\theta_{2}^{4}\!\left(0, \tau\right)}{\theta_{4}^{4}\!\left(0, \tau\right)}

\tau \in \mathbb{H}

Definitions:

Fungrim symbol	Notation	Short description
`ModularLambda`	$\lambda(\tau)$	Modular lambda function
`Pow`	${a}^{b}$	Power
`JacobiTheta`	$\theta_{j}\!\left(z , \tau\right)$	Jacobi theta function
`HH`	$\mathbb{H}$	Upper complex half-plane

Source code for this entry:

Entry(ID("903962"),
    Formula(Equal(Div(ModularLambda(tau), Sub(ModularLambda(tau), 1)), Neg(Div(Pow(JacobiTheta(2, 0, tau), 4), Pow(JacobiTheta(4, 0, tau), 4))))),
    Variables(tau),
    Assumptions(Element(tau, HH)))

Topics using this entry

Jacobi theta functions
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