Fungrim entry: 81f7db

F\!\left(\frac{-\pi}{2}, m\right) = -K(m)

Assumptions:

m \in \mathbb{C}

TeX:

F\!\left(\frac{-\pi}{2}, m\right) = -K(m)

m \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`IncompleteEllipticF`	$F\!\left(\phi, m\right)$	Legendre incomplete elliptic integral of the first kind
`Pi`	$\pi$	The constant pi (3.14...)
`EllipticK`	$K(m)$	Legendre complete elliptic integral of the first kind
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("81f7db"),
    Formula(Equal(IncompleteEllipticF(Div(Neg(Pi), 2), m), Neg(EllipticK(m)))),
    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