Fungrim home page

Fungrim entry: 0e209c

RF ⁣(0,y,z)12max ⁣(y,z)(π+log ⁣(yz))R_F\!\left(0, y, z\right) \le \frac{1}{2 \sqrt{\max\!\left(y, z\right)}} \left(\pi + \left|\log\!\left(\frac{y}{z}\right)\right|\right)
Assumptions:y(0,)  and  z(0,)y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left(0, \infty\right)
R_F\!\left(0, y, z\right) \le \frac{1}{2 \sqrt{\max\!\left(y, z\right)}} \left(\pi + \left|\log\!\left(\frac{y}{z}\right)\right|\right)

y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left(0, \infty\right)
Fungrim symbol Notation Short description
CarlsonRFRF ⁣(x,y,z)R_F\!\left(x, y, z\right) Carlson symmetric elliptic integral of the first kind
Sqrtz\sqrt{z} Principal square root
Piπ\pi The constant pi (3.14...)
Absz\left|z\right| Absolute value
Loglog(z)\log(z) Natural logarithm
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
Source code for this entry:
    Formula(LessEqual(CarlsonRF(0, y, z), Mul(Div(1, Mul(2, Sqrt(Max(y, z)))), Add(Pi, Abs(Log(Div(y, z))))))),
    Variables(y, z),
    Assumptions(And(Element(y, OpenInterval(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