Fungrim entry: 60541a

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

Assumptions:

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

TeX:

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

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

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRJ`	$R_J\!\left(x, y, z, w\right)$	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("60541a"),
    Formula(GreaterEqual(CarlsonRJ(0, y, z, w), Div(Mul(3, Pi), Mul(2, Sqrt(Mul(w, Add(Add(Mul(Mul(2, y), z), Mul(y, w)), Mul(z, w)))))))),
    Variables(y, z, w),
    Assumptions(And(Element(y, OpenInterval(0, Infinity)), Element(z, OpenInterval(0, Infinity)), Element(w, OpenInterval(0, Infinity)))))

Topics using this entry

Carlson symmetric elliptic integrals