Fungrim entry: 62eade

R_G\!\left(0, y, z\right) \le \frac{\pi \sqrt{\max\!\left(y, z\right)}}{4}

Assumptions:

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

TeX:

R_G\!\left(0, y, z\right) \le \frac{\pi \sqrt{\max\!\left(y, z\right)}}{4}

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

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRG`	$R_G\!\left(x, y, z\right)$	Carlson symmetric elliptic integral of the second kind
`Pi`	$\pi$	The constant pi (3.14...)
`Sqrt`	$\sqrt{z}$	Principal square root
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("62eade"),
    Formula(LessEqual(CarlsonRG(0, y, z), Div(Mul(Pi, Sqrt(Max(y, z))), 4))),
    Variables(y, z),
    Assumptions(And(Element(y, ClosedOpenInterval(0, Infinity)), Element(z, ClosedOpenInterval(0, Infinity)))))

Topics using this entry

Carlson symmetric elliptic integrals