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Fungrim entry: 737f2b

Fλ={τ:τH  and  ((Re(τ)(1,1)  and  min ⁣(τ12,z+12)>12)  or  Re(τ)=1  or  τ+12=12)}\mathcal{F}_{\lambda} = \left\{ \tau : \tau \in \mathbb{H} \;\mathbin{\operatorname{and}}\; \left(\left(\operatorname{Re}(\tau) \in \left(-1, 1\right) \;\mathbin{\operatorname{and}}\; \min\!\left(\left|\tau - \frac{1}{2}\right|, \left|z + \frac{1}{2}\right|\right) > \frac{1}{2}\right) \;\mathbin{\operatorname{or}}\; \operatorname{Re}(\tau) = -1 \;\mathbin{\operatorname{or}}\; \left|\tau + \frac{1}{2}\right| = \frac{1}{2}\right) \right\}
References:
  • J. M. Borwein and P. B. Borwein. Pi and the AGM. Wiley, New York, 1987. p. 113.
TeX:
\mathcal{F}_{\lambda} = \left\{ \tau : \tau \in \mathbb{H} \;\mathbin{\operatorname{and}}\; \left(\left(\operatorname{Re}(\tau) \in \left(-1, 1\right) \;\mathbin{\operatorname{and}}\; \min\!\left(\left|\tau - \frac{1}{2}\right|, \left|z + \frac{1}{2}\right|\right) > \frac{1}{2}\right) \;\mathbin{\operatorname{or}}\; \operatorname{Re}(\tau) = -1 \;\mathbin{\operatorname{or}}\; \left|\tau + \frac{1}{2}\right| = \frac{1}{2}\right) \right\}
Definitions:
Fungrim symbol Notation Short description
ModularLambdaFundamentalDomainFλ\mathcal{F}_{\lambda} Fundamental domain of the 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
Absz\left|z\right| Absolute value
Source code for this entry:
Entry(ID("737f2b"),
    Formula(Equal(ModularLambdaFundamentalDomain, Set(tau, For(tau), And(Element(tau, HH), Or(And(Element(Re(tau), OpenInterval(-1, 1)), Greater(Min(Abs(Sub(tau, Div(1, 2))), Abs(Add(z, Div(1, 2)))), Div(1, 2))), Equal(Re(tau), -1), Equal(Abs(Add(tau, Div(1, 2))), Div(1, 2))))))),
    References("J. M. Borwein and P. B. Borwein. Pi and the AGM. Wiley, New York, 1987. p. 113."))

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2021-03-15 19:12:00.328586 UTC