# Fungrim entry: c03f78

$R_F\!\left(x, y, z\right) \le \frac{1}{{\left(x y z\right)}^{1 / 6}}$
Assumptions:$x \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left(0, \infty\right)$
References:
• https://dlmf.nist.gov/19.24
TeX:
R_F\!\left(x, y, z\right) \le \frac{1}{{\left(x y z\right)}^{1 / 6}}

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
CarlsonRF$R_F\!\left(x, y, z\right)$ Carlson symmetric elliptic integral of the first kind
Pow${a}^{b}$ Power
OpenInterval$\left(a, b\right)$ Open interval
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("c03f78"),
Formula(LessEqual(CarlsonRF(x, y, z), Div(1, Pow(Mul(Mul(x, y), z), Div(1, 6))))),
Variables(x, y, z),
Assumptions(And(Element(x, OpenInterval(0, Infinity)), Element(y, OpenInterval(0, Infinity)), Element(z, OpenInterval(0, Infinity)))),
References("https://dlmf.nist.gov/19.24"))

## 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