# 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

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC