Fungrim entry: ce2395

\operatorname{agm}\!\left(a, b\right) = a \operatorname{agm}\!\left(1, \frac{b}{a}\right)

Assumptions:

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; a \ne 0 \;\mathbin{\operatorname{and}}\; \frac{b}{a} \notin \left(-\infty, 0\right]

TeX:

\operatorname{agm}\!\left(a, b\right) = a \operatorname{agm}\!\left(1, \frac{b}{a}\right)

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; a \ne 0 \;\mathbin{\operatorname{and}}\; \frac{b}{a} \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("ce2395"),
    Formula(Equal(AGM(a, b), Mul(a, AGM(1, Div(b, a))))),
    Variables(a, b),
    Assumptions(And(Element(a, CC), Element(b, CC), NotEqual(a, 0), NotElement(Div(b, a), OpenClosedInterval(Neg(Infinity), 0)))))

Topics using this entry

Arithmetic-geometric mean