Fungrim entry: 4b20ab

\left\{ \lambda(\tau) : \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, \operatorname{Re}(\tau) = -1 \right\} = \left(-\infty, 0\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 \mathbb{H} \,\mathbin{\operatorname{and}}\, \operatorname{Re}(\tau) = -1 \right\} = \left(-\infty, 0\right)

Definitions:

Fungrim symbol	Notation	Short description
`ModularLambda`	$\lambda(\tau)$	Modular lambda function
`HH`	$\mathbb{H}$	Upper complex half-plane
`Re`	$\operatorname{Re}(z)$	Real part
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("4b20ab"),
    Formula(Equal(Set(ModularLambda(tau), ForElement(tau, HH), Equal(Re(tau), -1)), OpenInterval(Neg(Infinity), 0))),
    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