Fungrim entry: 9d84d8

\operatorname{agm}\!\left(1 + b, 1 - b\right) = \operatorname{agm}\!\left(1, \sqrt{1 - {b}^{2}}\right)

Assumptions:

b \in \mathbb{C}

TeX:

\operatorname{agm}\!\left(1 + b, 1 - b\right) = \operatorname{agm}\!\left(1, \sqrt{1 - {b}^{2}}\right)

b \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`AGM`	$\operatorname{agm}\!\left(a, b\right)$	Arithmetic-geometric mean
`Sqrt`	$\sqrt{z}$	Principal square root
`Pow`	${a}^{b}$	Power
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("9d84d8"),
    Formula(Equal(AGM(Add(1, b), Sub(1, b)), AGM(1, Sqrt(Sub(1, Pow(b, 2)))))),
    Variables(b),
    Assumptions(Element(b, CC)))

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