Fungrim entry: 688efb

R_C\!\left(x, y\right) \le \frac{1}{{\left(x {y}^{2}\right)}^{1 / 6}}

Assumptions:

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

TeX:

R_C\!\left(x, y\right) \le \frac{1}{{\left(x {y}^{2}\right)}^{1 / 6}}

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
`Pow`	${a}^{b}$	Power
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("688efb"),
    Formula(LessEqual(CarlsonRC(x, y), Div(1, Pow(Mul(x, Pow(y, 2)), Div(1, 6))))),
    Variables(x, y),
    Assumptions(And(Element(x, OpenInterval(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