Fungrim entry: a4e47f

R_J\!\left(x, y, z, w\right) \le {\left(x y z {w}^{2}\right)}^{-3 / 10}

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

TeX:

R_J\!\left(x, y, z, w\right) \le {\left(x y z {w}^{2}\right)}^{-3 / 10}

x \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; 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
`Pow`	${a}^{b}$	Power
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("a4e47f"),
    Formula(LessEqual(CarlsonRJ(x, y, z, w), Pow(Mul(Mul(Mul(x, y), z), Pow(w, 2)), Neg(Div(3, 10))))),
    Variables(x, y, z, w),
    Assumptions(And(Element(x, OpenInterval(0, Infinity)), Element(y, OpenInterval(0, Infinity)), Element(z, OpenInterval(0, Infinity)), Element(w, OpenInterval(0, Infinity)))))

Topics using this entry

Carlson symmetric elliptic integrals