Fungrim entry: c38209

\left(a \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; b \in \left[0, \infty\right)\right) \;\implies\; \operatorname{agm}\!\left(a, b\right) \in \left[0, \infty\right)

TeX:

\left(a \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; b \in \left[0, \infty\right)\right) \;\implies\; \operatorname{agm}\!\left(a, b\right) \in \left[0, \infty\right)

Definitions:

Fungrim symbol	Notation	Short description
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval
`Infinity`	$\infty$	Positive infinity
`AGM`	$\operatorname{agm}\!\left(a, b\right)$	Arithmetic-geometric mean

Source code for this entry:

Entry(ID("c38209"),
    Formula(Implies(And(Element(a, ClosedOpenInterval(0, Infinity)), Element(b, ClosedOpenInterval(0, Infinity))), Element(AGM(a, b), ClosedOpenInterval(0, Infinity)))),
    Variables(a, b))

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