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Fungrim entry: 162ecf

ab≤agm⁡ ⁣(a,b)≤a+b2\sqrt{a b} \le \operatorname{agm}\!\left(a, b\right) \le \frac{a + b}{2}
Assumptions:a∈[0,∞)  and⁡  b∈[0,∞)a \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; b \in \left[0, \infty\right)
TeX:
\sqrt{a b} \le \operatorname{agm}\!\left(a, b\right) \le \frac{a + b}{2}

a \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; b \in \left[0, \infty\right)
Definitions:
Fungrim symbol Notation Short description
Sqrtz\sqrt{z} Principal square root
AGMagm⁡ ⁣(a,b)\operatorname{agm}\!\left(a, b\right) Arithmetic-geometric mean
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Infinity∞\infty Positive infinity
Source code for this entry:
Entry(ID("162ecf"),
    Formula(LessEqual(Sqrt(Mul(a, b)), AGM(a, b), Div(Add(a, b), 2))),
    Variables(a),
    Assumptions(And(Element(a, ClosedOpenInterval(0, Infinity)), Element(b, ClosedOpenInterval(0, Infinity)))))

Topics using this entry

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2021-03-15 19:12:00.328586 UTC