# 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

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