Fungrim home page

Fungrim entry: ea1d58

agm ⁣(a,b)=bagm ⁣(1,ab)\operatorname{agm}\!\left(a, b\right) = b \operatorname{agm}\!\left(1, \frac{a}{b}\right)
Assumptions:aC  and  bC  and  b0  and  ab(,0]a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \ne 0 \;\mathbin{\operatorname{and}}\; \frac{a}{b} \notin \left(-\infty, 0\right]
\operatorname{agm}\!\left(a, b\right) = b \operatorname{agm}\!\left(1, \frac{a}{b}\right)

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \ne 0 \;\mathbin{\operatorname{and}}\; \frac{a}{b} \notin \left(-\infty, 0\right]
Fungrim symbol Notation Short description
AGMagm ⁣(a,b)\operatorname{agm}\!\left(a, b\right) Arithmetic-geometric mean
CCC\mathbb{C} Complex numbers
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Infinity\infty Positive infinity
Source code for this entry:
    Formula(Equal(AGM(a, b), Mul(b, AGM(1, Div(a, b))))),
    Variables(a, b),
    Assumptions(And(Element(a, CC), Element(b, CC), NotEqual(b, 0), NotElement(Div(a, b), 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