Fungrim entry: 978287

R_C\!\left(x, y\right) \ge \frac{3}{\sqrt{x} + 2 \sqrt{y}}

Assumptions:

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

TeX:

R_C\!\left(x, y\right) \ge \frac{3}{\sqrt{x} + 2 \sqrt{y}}

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

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRC`	$R_C\!\left(x, y\right)$	Degenerate Carlson symmetric elliptic integral of the first kind
`Sqrt`	$\sqrt{z}$	Principal square root
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval
`Infinity`	$\infty$	Positive infinity
`OpenInterval`	$\left(a, b\right)$	Open interval

Source code for this entry:

Entry(ID("978287"),
    Formula(GreaterEqual(CarlsonRC(x, y), Div(3, Add(Sqrt(x), Mul(2, Sqrt(y)))))),
    Variables(x, y),
    Assumptions(And(Element(x, ClosedOpenInterval(0, Infinity)), Element(y, 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