Fungrim entry: a14442

E\!\left(\frac{\pi k}{2}, m\right) = k E(m)

Assumptions:

m \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}

TeX:

E\!\left(\frac{\pi k}{2}, m\right) = k E(m)

m \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}

Definitions:

Fungrim symbol	Notation	Short description
`IncompleteEllipticE`	$E\!\left(\phi, m\right)$	Legendre incomplete elliptic integral of the second kind
`Pi`	$\pi$	The constant pi (3.14...)
`EllipticE`	$E(m)$	Legendre complete elliptic integral of the second kind
`CC`	$\mathbb{C}$	Complex numbers
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("a14442"),
    Formula(Equal(IncompleteEllipticE(Div(Mul(Pi, k), 2), m), Mul(k, EllipticE(m)))),
    Variables(m, k),
    Assumptions(And(Element(m, CC), Element(k, ZZ))))

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