# Fungrim entry: 8e6189

$R_F\!\left(x, y, z\right) = R_F\!\left(\frac{x + \lambda}{4}, \frac{y + \lambda}{4}, \frac{z + \lambda}{4}\right)\; \text{ where } \lambda = \sqrt{x} \sqrt{y} + \sqrt{y} \sqrt{z} + \sqrt{x} \sqrt{z}$
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(\frac{x + \lambda}{4}, \frac{y + \lambda}{4}, \frac{z + \lambda}{4}\right)\; \text{ where } \lambda = \sqrt{x} \sqrt{y} + \sqrt{y} \sqrt{z} + \sqrt{x} \sqrt{z}

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
Sqrt$\sqrt{z}$ Principal square root
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("8e6189"),
Assumptions(And(Element(x, CC), Element(y, CC), Element(z, CC))))