Fungrim entry: 255142

R_D\!\left(0, y, z\right) \ge \frac{3 \pi}{2 z \sqrt{3 y + y + z}}

Assumptions:

y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left(0, \infty\right)

TeX:

R_D\!\left(0, y, z\right) \ge \frac{3 \pi}{2 z \sqrt{3 y + y + z}}

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
`Pi`	$\pi$	The constant pi (3.14...)
`Sqrt`	$\sqrt{z}$	Principal square root
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("255142"),
    Formula(GreaterEqual(CarlsonRD(0, y, z), Div(Mul(3, Pi), Mul(Mul(2, z), Sqrt(Add(Add(Mul(3, y), y), z)))))),
    Variables(y, z),
    Assumptions(And(Element(y, OpenInterval(0, Infinity)), Element(z, OpenInterval(0, Infinity)))))

Topics using this entry

Carlson symmetric elliptic integrals