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http://functions.wolfram.com/03.01.29.0004.01
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Abs[BesselJ[\[Nu], z]] <= Abs[((z/2)^\[Nu] E^Abs[Im[z]])/Gamma[\[Nu] + 1]] /;
\[Nu] >= -(1/2)
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Abs", "[", RowBox[List["BesselJ", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "]"]], "\[LessEqual]", RowBox[List["Abs", "[", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["z", "2"], ")"]], "\[Nu]"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["Abs", "[", RowBox[List["Im", "[", "z", "]"]], "]"]]]]], RowBox[List["Gamma", "[", RowBox[List["\[Nu]", "+", "1"]], "]"]]], "]"]]]], "/;", RowBox[List["\[Nu]", "\[GreaterEqual]", RowBox[List["-", FractionBox["1", "2"]]]]]]]]]
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<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> x </mi> <mo> ) </mo> </mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mo> ≤ </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mi> x </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> ν </mi> </msup> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> </msup> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> ν </mi> <mo> ≥ </mo> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> <mo> ∧ </mo> <mrow> <mi> x </mi> <mo> > </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <leq /> <apply> <abs /> <apply> <ci> BesselJ </ci> <ci> ν </ci> <ci> x </ci> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <ci> x </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <ci> ν </ci> </apply> <apply> <power /> <exponentiale /> <apply> <abs /> <apply> <imaginary /> <ci> x </ci> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <geq /> <ci> ν </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <gt /> <ci> x </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Abs", "[", RowBox[List["BesselJ", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "]"]], "\[LessEqual]", RowBox[List["Abs", "[", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["z", "2"], ")"]], "\[Nu]"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["Abs", "[", RowBox[List["Im", "[", "z", "]"]], "]"]]]]], RowBox[List["Gamma", "[", RowBox[List["\[Nu]", "+", "1"]], "]"]]], "]"]]]], "/;", RowBox[List["\[Nu]", "\[GreaterEqual]", RowBox[List["-", FractionBox["1", "2"]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
