Fungrim entry: 830dd4

\left\{ \lambda(\tau) : \tau \in \operatorname{Interior}(\mathcal{F}_{\lambda}) \right\} = \mathbb{C} \setminus \left(\left(-\infty, 0\right] \cup \left[1, \infty\right)\right)

This mapping is one-to-one.

References:

J. M. Borwein and P. B. Borwein. Pi and the AGM. Wiley, New York, 1987. p. 118.

TeX:

\left\{ \lambda(\tau) : \tau \in \operatorname{Interior}(\mathcal{F}_{\lambda}) \right\} = \mathbb{C} \setminus \left(\left(-\infty, 0\right] \cup \left[1, \infty\right)\right)

Definitions:

Fungrim symbol	Notation	Short description
`ModularLambda`	$\lambda(\tau)$	Modular lambda function
`ModularLambdaFundamentalDomain`	$\mathcal{F}_{\lambda}$	Fundamental domain of the modular lambda function
`CC`	$\mathbb{C}$	Complex numbers
`OpenClosedInterval`	$\left(a, b\right]$	Open-closed interval
`Infinity`	$\infty$	Positive infinity
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval

Source code for this entry:

Entry(ID("830dd4"),
    Formula(Equal(Set(ModularLambda(tau), ForElement(tau, Interior(ModularLambdaFundamentalDomain))), SetMinus(CC, Parentheses(Union(OpenClosedInterval(Neg(Infinity), 0), ClosedOpenInterval(1, Infinity)))))),
    Description("This mapping is one-to-one."),
    References("J. M. Borwein and P. B. Borwein. Pi and the AGM. Wiley, New York, 1987. p. 118."))

Topics using this entry

Modular lambda function