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Fungrim entry: e4315f

{λ ⁣(τ):τHandτ+12=12}=(1,)\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{f ⁣(x):P ⁣(x)}\left\{ f\!\left(x\right) : P\!\left(x\right) \right\} Set comprehension
ModularLambdaλ ⁣(τ)\lambda\!\left(\tau\right) Modular lambda function
HHH\mathbb{H} Upper complex half-plane
Absz\left|z\right| Absolute value
OpenInterval(a,b)\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."))

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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