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Fungrim entry: 07584a

RG ⁣(x,y,z)min ⁣(x+y+z3,x2+y2+z23xyz)R_G\!\left(x, y, z\right) \le \min\!\left(\sqrt{\frac{x + y + z}{3}}, \frac{{x}^{2} + {y}^{2} + {z}^{2}}{3 \sqrt{x y z}}\right)
Assumptions:x[0,)  and  y[0,)  and  z[0,)x \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left[0, \infty\right)
R_G\!\left(x, y, z\right) \le \min\!\left(\sqrt{\frac{x + y + z}{3}}, \frac{{x}^{2} + {y}^{2} + {z}^{2}}{3 \sqrt{x y z}}\right)

x \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left[0, \infty\right)
Fungrim symbol Notation Short description
CarlsonRGRG ⁣(x,y,z)R_G\!\left(x, y, z\right) Carlson symmetric elliptic integral of the second kind
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Infinity\infty Positive infinity
Source code for this entry:
    Formula(LessEqual(CarlsonRG(x, y, z), Min(Sqrt(Div(Add(Add(x, y), z), 3)), Div(Add(Add(Pow(x, 2), Pow(y, 2)), Pow(z, 2)), Mul(3, Sqrt(Mul(Mul(x, y), z))))))),
    Variables(x, y, z),
    Assumptions(And(Element(x, ClosedOpenInterval(0, Infinity)), Element(y, ClosedOpenInterval(0, Infinity)), Element(z, ClosedOpenInterval(0, Infinity)))))

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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