Fungrim entry: fa8666

E(m) = \int_{0}^{1} \frac{\sqrt{1 - m {x}^{2}}}{\sqrt{1 - {x}^{2}}} \, dx

Assumptions:

m \in \mathbb{C}

TeX:

E(m) = \int_{0}^{1} \frac{\sqrt{1 - m {x}^{2}}}{\sqrt{1 - {x}^{2}}} \, 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
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("fa8666"),
    Formula(Equal(EllipticE(m), Integral(Div(Sqrt(Sub(1, Mul(m, Pow(x, 2)))), Sqrt(Sub(1, Pow(x, 2)))), For(x, 0, 1)))),
    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