Fungrim entry: 0e209c

R_F\!\left(0, y, z\right) \le \frac{1}{2 \sqrt{\max\!\left(y, z\right)}} \left(\pi + \left|\log\!\left(\frac{y}{z}\right)\right|\right)

Assumptions:

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

TeX:

R_F\!\left(0, y, z\right) \le \frac{1}{2 \sqrt{\max\!\left(y, z\right)}} \left(\pi + \left|\log\!\left(\frac{y}{z}\right)\right|\right)

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

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRF`	$R_F\!\left(x, y, z\right)$	Carlson symmetric elliptic integral of the first kind
`Sqrt`	$\sqrt{z}$	Principal square root
`Pi`	$\pi$	The constant pi (3.14...)
`Abs`	$\left\|z\right\|$	Absolute value
`Log`	$\log(z)$	Natural logarithm
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("0e209c"),
    Formula(LessEqual(CarlsonRF(0, y, z), Mul(Div(1, Mul(2, Sqrt(Max(y, z)))), Add(Pi, Abs(Log(Div(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