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Fungrim entry: 34e932

RD ⁣(x,y,z)(5x+y+3z)3R_D\!\left(x, y, z\right) \ge {\left(\frac{5}{\sqrt{x} + \sqrt{y} + 3 \sqrt{z}}\right)}^{3}
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_D\!\left(x, y, z\right) \ge {\left(\frac{5}{\sqrt{x} + \sqrt{y} + 3 \sqrt{z}}\right)}^{3}

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
CarlsonRDRD ⁣(x,y,z)R_D\!\left(x, y, z\right) Degenerate Carlson symmetric elliptic integral of the third kind
Powab{a}^{b} Power
Sqrtz\sqrt{z} Principal square root
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Infinity\infty Positive infinity
OpenInterval(a,b)\left(a, b\right) Open interval
Source code for this entry:
    Formula(GreaterEqual(CarlsonRD(x, y, z), Pow(Div(5, Add(Add(Sqrt(x), Sqrt(y)), Mul(3, Sqrt(z)))), 3))),
    Variables(x, y, z),
    Assumptions(And(Element(x, ClosedOpenInterval(0, Infinity)), Element(y, ClosedOpenInterval(0, Infinity)), Element(z, 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