# Fungrim entry: 07584a

$R_G\!\left(x, y, z\right) \le \min\!\left(\sqrt{\frac{x + y + z}{3}}, \frac{{x}^{2} + {y}^{2} + {z}^{2}}{3 \sqrt{x y z}}\right)$
Assumptions:$x \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left[0, \infty\right)$
TeX:
R_G\!\left(x, y, z\right) \le \min\!\left(\sqrt{\frac{x + y + z}{3}}, \frac{{x}^{2} + {y}^{2} + {z}^{2}}{3 \sqrt{x y z}}\right)

x \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left[0, \infty\right)
Definitions:
Fungrim symbol Notation Short description
CarlsonRG$R_G\!\left(x, y, z\right)$ Carlson symmetric elliptic integral of the second kind
Sqrt$\sqrt{z}$ Principal square root
Pow${a}^{b}$ Power
ClosedOpenInterval$\left[a, b\right)$ Closed-open interval
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("07584a"),
Formula(LessEqual(CarlsonRG(x, y, z), Min(Sqrt(Div(Add(Add(x, y), z), 3)), Div(Add(Add(Pow(x, 2), Pow(y, 2)), Pow(z, 2)), Mul(3, Sqrt(Mul(Mul(x, y), z))))))),
Variables(x, y, z),
Assumptions(And(Element(x, ClosedOpenInterval(0, Infinity)), Element(y, ClosedOpenInterval(0, Infinity)), Element(z, ClosedOpenInterval(0, Infinity)))))

## 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