Fungrim entry: 8e5c81

E\!\left(\overline{m}\right) = \overline{E(m)}

Assumptions:

m \in \mathbb{C} \setminus \left(1, \infty\right)

TeX:

E\!\left(\overline{m}\right) = \overline{E(m)}

m \in \mathbb{C} \setminus \left(1, \infty\right)

Definitions:

Fungrim symbol	Notation	Short description
`EllipticE`	$E(m)$	Legendre complete elliptic integral of the second kind
`Conjugate`	$\overline{z}$	Complex conjugate
`CC`	$\mathbb{C}$	Complex numbers
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("8e5c81"),
    Formula(Equal(EllipticE(Conjugate(m)), Conjugate(EllipticE(m)))),
    Variables(m),
    Assumptions(Element(m, SetMinus(CC, OpenInterval(1, Infinity)))))

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