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# Fungrim entry: 8e80c6

$\operatorname{agm}\!\left(1, b\right) = b \operatorname{agm}\!\left(1, \frac{1}{b}\right)$
Assumptions:$b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \notin \left(-\infty, 0\right]$
TeX:
\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]
Definitions:
Fungrim symbol Notation Short description
AGM$\operatorname{agm}\!\left(a, b\right)$ Arithmetic-geometric mean
CC$\mathbb{C}$ Complex numbers
OpenClosedInterval$\left(a, b\right]$ Open-closed interval
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("8e80c6"),
Formula(Equal(AGM(1, b), Mul(b, AGM(1, Div(1, b))))),
Variables(b),
Assumptions(And(Element(b, CC), NotElement(b, OpenClosedInterval(Neg(Infinity), 0)))))

## Topics using this entry

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