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Fungrim entry: 46c021

agm⁡ ⁣(1,b)=b+12agm⁡ ⁣(1,2bb+1)\operatorname{agm}\!\left(1, b\right) = \frac{b + 1}{2} \operatorname{agm}\!\left(1, \frac{2 \sqrt{b}}{b + 1}\right)
Assumptions:b∈Cb \in \mathbb{C}
TeX:
\operatorname{agm}\!\left(1, b\right) = \frac{b + 1}{2} \operatorname{agm}\!\left(1, \frac{2 \sqrt{b}}{b + 1}\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
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("46c021"),
    Formula(Equal(AGM(1, b), Mul(Div(Add(b, 1), 2), AGM(1, Div(Mul(2, Sqrt(b)), Add(b, 1)))))),
    Variables(b),
    Assumptions(Element(b, CC)))

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2021-03-15 19:12:00.328586 UTC