# Fungrim entry: e4315f

$\left\{ \lambda\!\left(\tau\right) : \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, \left|\tau + \frac{1}{2}\right| = \frac{1}{2} \right\} = \left(1, \infty\right)$
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\!\left(\tau\right) : \tau \in \mathbb{H} \,\mathbin{\operatorname{and}}\, \left|\tau + \frac{1}{2}\right| = \frac{1}{2} \right\} = \left(1, \infty\right)
Definitions:
Fungrim symbol Notation Short description
SetBuilder$\left\{ f\!\left(x\right) : P\!\left(x\right) \right\}$ Set comprehension
ModularLambda$\lambda\!\left(\tau\right)$ Modular lambda function
HH$\mathbb{H}$ Upper complex half-plane
Abs$\left|z\right|$ Absolute value
OpenInterval$\left(a, b\right)$ Open interval
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("e4315f"),
Formula(Equal(SetBuilder(ModularLambda(tau), tau, And(Element(tau, HH), Equal(Abs(Add(tau, Div(1, 2))), Div(1, 2)))), OpenInterval(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

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-15 11:00:55.020619 UTC