Fungrim entry: 34e932

R_D\!\left(x, y, z\right) \ge {\left(\frac{5}{\sqrt{x} + \sqrt{y} + 3 \sqrt{z}}\right)}^{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_D\!\left(x, y, z\right) \ge {\left(\frac{5}{\sqrt{x} + \sqrt{y} + 3 \sqrt{z}}\right)}^{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
`CarlsonRD`	$R_D\!\left(x, y, z\right)$	Degenerate Carlson symmetric elliptic integral of the third kind
`Pow`	${a}^{b}$	Power
`Sqrt`	$\sqrt{z}$	Principal square root
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval
`Infinity`	$\infty$	Positive infinity
`OpenInterval`	$\left(a, b\right)$	Open interval

Source code for this entry:

Entry(ID("34e932"),
    Formula(GreaterEqual(CarlsonRD(x, y, z), Pow(Div(5, Add(Add(Sqrt(x), Sqrt(y)), Mul(3, Sqrt(z)))), 3))),
    Variables(x, y, z),
    Assumptions(And(Element(x, ClosedOpenInterval(0, Infinity)), Element(y, ClosedOpenInterval(0, Infinity)), Element(z, OpenInterval(0, Infinity)))))

Topics using this entry

Carlson symmetric elliptic integrals