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Fungrim entry: 23ee29

∣agm⁡ ⁣(a,b)∣≤∣agm⁡ ⁣(∣a∣,∣b∣)∣\left|\operatorname{agm}\!\left(a, b\right)\right| \le \left|\operatorname{agm}\!\left(\left|a\right|, \left|b\right|\right)\right|
Assumptions:a∈C  and⁡  b∈Ca \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C}
TeX:
\left|\operatorname{agm}\!\left(a, b\right)\right| \le \left|\operatorname{agm}\!\left(\left|a\right|, \left|b\right|\right)\right|

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Abs∣z∣\left|z\right| Absolute value
AGMagm⁡ ⁣(a,b)\operatorname{agm}\!\left(a, b\right) Arithmetic-geometric mean
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("23ee29"),
    Formula(LessEqual(Abs(AGM(a, b)), Abs(AGM(Abs(a), Abs(b))))),
    Variables(a, b),
    Assumptions(And(Element(a, CC), Element(b, CC))))

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2021-03-15 19:12:00.328586 UTC