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Fungrim entry: 4b20ab

{λ(τ):τHandRe(τ)=1}=(,0)\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
ModularLambdaλ(τ)\lambda(\tau) Modular lambda function
HHH\mathbb{H} Upper complex half-plane
ReRe(z)\operatorname{Re}(z) Real part
OpenInterval(a,b)\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."))

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2021-03-15 19:12:00.328586 UTC