Hyperbolic cosine integral: Inequalities (formula 01.20.29.0002)

Cosh

$Mathematica Notation$

Elementary Functions

Cosh[z]

Inequalities

http://functions.wolfram.com/01.20.29.0002.01

Input Form

Cosh[x] >= Abs[Cos[x]] /; Element[x, Reals]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Cosh", "[", "x", "]"]], "\[GreaterEqual]", RowBox[List["Abs", "[", RowBox[List["Cos", "[", "x", "]"]], "]"]]]], "/;", RowBox[List["x", "\[Element]", "Reals"]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> ≥ </mo> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> x </mi> <mo> ∈ </mo> <semantics> <mi> ℝ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalR]", Function[Reals]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <geq /> <apply> <cosh /> <ci> x </ci> </apply> <apply> <abs /> <apply> <cos /> <ci> x </ci> </apply> </apply> </apply> <apply> <in /> <ci> x </ci> <reals /> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Date Added to functions.wolfram.com (modification date)

2001-10-29