Bessel function of the first kind: Inequalities (formula 03.01.29.0002)

BesselJ

$Mathematica Notation$

Bessel-Type Functions

BesselJ[nu,z]

Inequalities

http://functions.wolfram.com/03.01.29.0002.01

Input Form

Abs[BesselJ[\[Nu], z]] <= 1/Sqrt[2] /; \[Nu] >= 1

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Abs", "[", RowBox[List["BesselJ", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "]"]], "\[LessEqual]", FractionBox["1", SqrtBox["2"]]]], "/;", RowBox[List["\[Nu]", "\[GreaterEqual]", "1"]]]]]]

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> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mrow> <msub> <mi> J </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mo> ≤ </mo> <mfrac> <mn> 1 </mn> <msqrt> <mn> 2 </mn> </msqrt> </mfrac> </mrow> <mo> /; </mo> <mrow> <mi> ν </mi> <mo> ≥ </mo> <mn> 1 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <leq /> <apply> <abs /> <apply> <ci> BesselJ </ci> <ci> ν </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <geq /> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2001-10-29