# Fungrim entry: d60119

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

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; c \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left(a = 0 \;\mathbin{\operatorname{or}}\; b = 0 \;\mathbin{\operatorname{or}}\; c = 0 \;\mathbin{\operatorname{or}}\; \frac{b}{a} \notin \left(-\infty, 0\right]\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("d60119"),
Formula(Equal(AGM(Mul(c, a), Mul(c, b)), Mul(c, AGM(a, b)))),
Variables(a, b, c),
Assumptions(And(Element(a, CC), Element(b, CC), Element(c, CC), Or(Equal(a, 0), Equal(b, 0), Equal(c, 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