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

Arithmetic-geometric mean

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