# Fungrim entry: 60541a

$R_J\!\left(0, y, z, w\right) \ge \frac{3 \pi}{2 \sqrt{w \left(2 y z + y w + z w\right)}}$
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) \ge \frac{3 \pi}{2 \sqrt{w \left(2 y z + y w + z w\right)}}

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...)
Sqrt$\sqrt{z}$ Principal square root
OpenInterval$\left(a, b\right)$ Open interval
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("60541a"),
Formula(GreaterEqual(CarlsonRJ(0, y, z, w), Div(Mul(3, Pi), Mul(2, Sqrt(Mul(w, Add(Add(Mul(Mul(2, y), z), Mul(y, w)), Mul(z, w)))))))),
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

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