# Fungrim entry: 6dda7a

$R_D\!\left(x, y, z\right) + R_D\!\left(y, z, x\right) + R_D\!\left(z, x, y\right) = \frac{3}{\sqrt{x} \sqrt{y} \sqrt{z}}$
Assumptions:$x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; x \ne 0 \;\mathbin{\operatorname{and}}\; y \ne 0$
Alternative assumptions:$z \ne 0$
TeX:
R_D\!\left(x, y, z\right) + R_D\!\left(y, z, x\right) + R_D\!\left(z, x, y\right) = \frac{3}{\sqrt{x} \sqrt{y} \sqrt{z}}

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; x \ne 0 \;\mathbin{\operatorname{and}}\; y \ne 0

z \ne 0
Definitions:
Fungrim symbol Notation Short description
CarlsonRD$R_D\!\left(x, y, z\right)$ Degenerate Carlson symmetric elliptic integral of the third kind
Sqrt$\sqrt{z}$ Principal square root
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("6dda7a"),
Formula(Equal(Add(Add(CarlsonRD(x, y, z), CarlsonRD(y, z, x)), CarlsonRD(z, x, y)), Div(3, Mul(Mul(Sqrt(x), Sqrt(y)), Sqrt(z))))),
Variables(x, y, z),
Assumptions(And(Element(x, CC), Element(y, CC), Element(z, CC), NotEqual(x, 0), NotEqual(y, 0)), NotEqual(z, 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