Fungrim entry: add3ea

R_J\!\left(0, y, z, w\right) \le \frac{3 \pi}{4} {\left(y z {w}^{2}\right)}^{-3 / 8}

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) \le \frac{3 \pi}{4} {\left(y z {w}^{2}\right)}^{-3 / 8}

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...)
`Pow`	${a}^{b}$	Power
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("add3ea"),
    Formula(LessEqual(CarlsonRJ(0, y, z, w), Mul(Div(Mul(3, Pi), 4), Pow(Mul(Mul(y, z), Pow(w, 2)), Neg(Div(3, 8)))))),
    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