Fungrim entry: 2e40b8

R_F\!\left(0, y, z\right) \ge \frac{2 \log(2)}{\sqrt{\max\!\left(y, z\right)}}

Assumptions:

y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left(0, \infty\right)

TeX:

R_F\!\left(0, y, z\right) \ge \frac{2 \log(2)}{\sqrt{\max\!\left(y, z\right)}}

y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left(0, \infty\right)

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRF`	$R_F\!\left(x, y, z\right)$	Carlson symmetric elliptic integral of the first kind
`Log`	$\log(z)$	Natural logarithm
`Sqrt`	$\sqrt{z}$	Principal square root
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("2e40b8"),
    Formula(GreaterEqual(CarlsonRF(0, y, z), Div(Mul(2, Log(2)), Sqrt(Max(y, z))))),
    Variables(y, z),
    Assumptions(And(Element(y, OpenInterval(0, Infinity)), Element(z, OpenInterval(0, Infinity)))))

Topics using this entry

Carlson symmetric elliptic integrals

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