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Fungrim entry: 255142

RD ⁣(0,y,z)3π2z3y+y+zR_D\!\left(0, y, z\right) \ge \frac{3 \pi}{2 z \sqrt{3 y + y + z}}
Assumptions:y(0,)  and  z(0,)y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left(0, \infty\right)
R_D\!\left(0, y, z\right) \ge \frac{3 \pi}{2 z \sqrt{3 y + y + z}}

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
Piπ\pi The constant pi (3.14...)
Sqrtz\sqrt{z} Principal square root
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
Source code for this entry:
    Formula(GreaterEqual(CarlsonRD(0, y, z), Div(Mul(3, Pi), Mul(Mul(2, z), Sqrt(Add(Add(Mul(3, y), y), z)))))),
    Variables(y, z),
    Assumptions(And(Element(y, OpenInterval(0, Infinity)), Element(z, OpenInterval(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