Fungrim entry: edcf6c

R_G\!\left(x, y, z\right) \ge \frac{\sqrt{x} + \sqrt{y} + \sqrt{z}}{3}

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) \ge \frac{\sqrt{x} + \sqrt{y} + \sqrt{z}}{3}

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
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("edcf6c"),
    Formula(GreaterEqual(CarlsonRG(x, y, z), Div(Add(Add(Sqrt(x), Sqrt(y)), Sqrt(z)), 3))),
    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

Carlson symmetric elliptic integrals