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Fungrim entry: 62eade

RG ⁣(0,y,z)πmax ⁣(y,z)4R_G\!\left(0, y, z\right) \le \frac{\pi \sqrt{\max\!\left(y, z\right)}}{4}
Assumptions:y[0,)  and  z[0,)y \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left[0, \infty\right)
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)
Fungrim symbol Notation Short description
CarlsonRGRG ⁣(x,y,z)R_G\!\left(x, y, z\right) Carlson symmetric elliptic integral of the second kind
Piπ\pi The constant pi (3.14...)
Sqrtz\sqrt{z} Principal square root
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Infinity\infty Positive infinity
Source code for this entry:
    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)))))

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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