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Fungrim entry: c38209

(a[0,)  and  b[0,))        agm ⁣(a,b)[0,)\left(a \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; b \in \left[0, \infty\right)\right) \;\implies\; \operatorname{agm}\!\left(a, b\right) \in \left[0, \infty\right)
\left(a \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; b \in \left[0, \infty\right)\right) \;\implies\; \operatorname{agm}\!\left(a, b\right) \in \left[0, \infty\right)
Fungrim symbol Notation Short description
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Infinity\infty Positive infinity
AGMagm ⁣(a,b)\operatorname{agm}\!\left(a, b\right) Arithmetic-geometric mean
Source code for this entry:
    Formula(Implies(And(Element(a, ClosedOpenInterval(0, Infinity)), Element(b, ClosedOpenInterval(0, Infinity))), Element(AGM(a, b), ClosedOpenInterval(0, Infinity)))),
    Variables(a, b))

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

2021-03-15 19:12:00.328586 UTC