# Fungrim entry: f29729

$R_F\!\left(x, y, z\right) = R_F\!\left(x, z, y\right) = R_F\!\left(y, x, z\right) = R_F\!\left(y, z, x\right) = R_F\!\left(z, x, y\right) = R_F\!\left(z, y, x\right)$
Assumptions:$x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}$
TeX:
R_F\!\left(x, y, z\right) = R_F\!\left(x, z, y\right) = R_F\!\left(y, x, z\right) = R_F\!\left(y, z, x\right) = R_F\!\left(z, x, y\right) = R_F\!\left(z, y, x\right)

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
CarlsonRF$R_F\!\left(x, y, z\right)$ Carlson symmetric elliptic integral of the first kind
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("f29729"),
Formula(Equal(CarlsonRF(x, y, z), CarlsonRF(x, z, y), CarlsonRF(y, x, z), CarlsonRF(y, z, x), CarlsonRF(z, x, y), CarlsonRF(z, y, x))),
Variables(x, y, z),
Assumptions(And(Element(x, CC), Element(y, CC), Element(z, CC))))

## 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