Fungrim home page

Fungrim entry: add3ea

RJ ⁣(0,y,z,w)3π4(yzw2)3/8R_J\!\left(0, y, z, w\right) \le \frac{3 \pi}{4} {\left(y z {w}^{2}\right)}^{-3 / 8}
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)
R_J\!\left(0, y, z, w\right) \le \frac{3 \pi}{4} {\left(y z {w}^{2}\right)}^{-3 / 8}

y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; w \in \left(0, \infty\right)
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...)
Powab{a}^{b} Power
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
Source code for this entry:
    Formula(LessEqual(CarlsonRJ(0, y, z, w), Mul(Div(Mul(3, Pi), 4), Pow(Mul(Mul(y, z), Pow(w, 2)), Neg(Div(3, 8)))))),
    Variables(y, z, w),
    Assumptions(And(Element(y, OpenInterval(0, Infinity)), Element(z, OpenInterval(0, Infinity)), Element(w, 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