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Fungrim entry: 8e80c6

agm ⁣(1,b)=bagm ⁣(1,1b)\operatorname{agm}\!\left(1, b\right) = b \operatorname{agm}\!\left(1, \frac{1}{b}\right)
Assumptions:bC  and  b(,0]b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \notin \left(-\infty, 0\right]
\operatorname{agm}\!\left(1, b\right) = b \operatorname{agm}\!\left(1, \frac{1}{b}\right)

b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \notin \left(-\infty, 0\right]
Fungrim symbol Notation Short description
AGMagm ⁣(a,b)\operatorname{agm}\!\left(a, b\right) Arithmetic-geometric mean
CCC\mathbb{C} Complex numbers
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Infinity\infty Positive infinity
Source code for this entry:
    Formula(Equal(AGM(1, b), Mul(b, AGM(1, Div(1, b))))),
    Assumptions(And(Element(b, CC), NotElement(b, OpenClosedInterval(Neg(Infinity), 0)))))

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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