Fungrim entry: 190843

E(m) = \int_{0}^{\pi / 2} \sqrt{1 - m \sin^{2}\!\left(x\right)} \, dx

Assumptions:

m \in \mathbb{C}

TeX:

E(m) = \int_{0}^{\pi / 2} \sqrt{1 - m \sin^{2}\!\left(x\right)} \, dx

m \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`EllipticE`	$E(m)$	Legendre complete elliptic integral of the second kind
`Integral`	$\int_{a}^{b} f(x) \, dx$	Integral
`Sqrt`	$\sqrt{z}$	Principal square root
`Pow`	${a}^{b}$	Power
`Sin`	$\sin(z)$	Sine
`Pi`	$\pi$	The constant pi (3.14...)
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("190843"),
    Formula(Equal(EllipticE(m), Integral(Sqrt(Sub(1, Mul(m, Pow(Sin(x), 2)))), For(x, 0, Div(Pi, 2))))),
    Variables(m),
    Assumptions(Element(m, CC)))

Topics using this entry

Legendre elliptic integrals

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