Fungrim home page

Fungrim entry: 9d84d8

agm ⁣(1+b,1b)=agm ⁣(1,1b2)\operatorname{agm}\!\left(1 + b, 1 - b\right) = \operatorname{agm}\!\left(1, \sqrt{1 - {b}^{2}}\right)
Assumptions:bCb \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
AGMagm ⁣(a,b)\operatorname{agm}\!\left(a, b\right) Arithmetic-geometric mean
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
CCC\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

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