# Fungrim entry: ce2395

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

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; a \ne 0 \;\mathbin{\operatorname{and}}\; \frac{b}{a} \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("ce2395"),
Formula(Equal(AGM(a, b), Mul(a, AGM(1, Div(b, a))))),
Variables(a, b),
Assumptions(And(Element(a, CC), Element(b, CC), NotEqual(a, 0), NotElement(Div(b, a), 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