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Fungrim entry: 60541a

RJ ⁣(0,y,z,w)3π2w(2yz+yw+zw)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(0,)  and  z(0,)  and  w(0,)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
CarlsonRJRJ ⁣(x,y,z,w)R_J\!\left(x, y, z, w\right) 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:
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)))))

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2021-03-15 19:12:00.328586 UTC