Fungrim entry: 087a7c

F\!\left(\operatorname{asin}\!\left(\frac{1}{\sqrt{m}}\right), m\right) = \frac{K\!\left(\frac{1}{m}\right)}{\sqrt{m}}

Assumptions:

m \in \mathbb{C} \setminus \left\{0\right\}

TeX:

F\!\left(\operatorname{asin}\!\left(\frac{1}{\sqrt{m}}\right), m\right) = \frac{K\!\left(\frac{1}{m}\right)}{\sqrt{m}}

m \in \mathbb{C} \setminus \left\{0\right\}

Definitions:

Fungrim symbol	Notation	Short description
`IncompleteEllipticF`	$F\!\left(\phi, m\right)$	Legendre incomplete elliptic integral of the first kind
`Sqrt`	$\sqrt{z}$	Principal square root
`EllipticK`	$K(m)$	Legendre complete elliptic integral of the first kind
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("087a7c"),
    Formula(Equal(IncompleteEllipticF(Asin(Div(1, Sqrt(m))), m), Div(EllipticK(Div(1, m)), Sqrt(m)))),
    Variables(m),
    Assumptions(Element(m, SetMinus(CC, Set(0)))))

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