# Fungrim entry: afabeb

$F\!\left(\frac{\pi k}{2}, m\right) = k K(m)$
Assumptions:$m \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; \left(k \ne 0 \;\mathbin{\operatorname{or}}\; m \ne 1\right)$
TeX:
F\!\left(\frac{\pi k}{2}, m\right) = k K(m)

m \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; \left(k \ne 0 \;\mathbin{\operatorname{or}}\; m \ne 1\right)
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
ZZ$\mathbb{Z}$ Integers
Source code for this entry:
Entry(ID("afabeb"),
Formula(Equal(IncompleteEllipticF(Div(Mul(Pi, k), 2), m), Mul(k, EllipticK(m)))),
Variables(m, k),
Assumptions(And(Element(m, CC), Element(k, ZZ), Or(NotEqual(k, 0), NotEqual(m, 1)))))

## 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