Fungrim entry: e15f43

K(m) = \frac{\pi}{2 \operatorname{agm}\!\left(1, \sqrt{1 - m}\right)}

Assumptions:

m \in \mathbb{C}

TeX:

K(m) = \frac{\pi}{2 \operatorname{agm}\!\left(1, \sqrt{1 - m}\right)}

m \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`EllipticK`	$K(m)$	Legendre complete elliptic integral of the first kind
`Pi`	$\pi$	The constant pi (3.14...)
`AGM`	$\operatorname{agm}\!\left(a, b\right)$	Arithmetic-geometric mean
`Sqrt`	$\sqrt{z}$	Principal square root
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("e15f43"),
    Formula(Equal(EllipticK(m), Div(Pi, Mul(2, AGM(1, Sqrt(Sub(1, m))))))),
    Variables(m),
    Assumptions(Element(m, CC)))

Topics using this entry

2021-03-15 19:12:00.328586 UTC