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BesselJ




Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselJ[nu,z] > Identities > Recurrence identities > Distant neighbors > Increasing





http://functions.wolfram.com/03.01.17.0007.01









  


  








Input Form





BesselJ[\[Nu], z] == (1/z^2) ((-z^2 + 4 (1 + \[Nu]) (2 + \[Nu])) BesselJ[2 + \[Nu], z] - 2 z (1 + \[Nu]) BesselJ[3 + \[Nu], z])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["BesselJ", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", SuperscriptBox["z", "2"]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["z", "2"]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "\[Nu]"]], ")"]]]]]], ")"]], " ", RowBox[List["BesselJ", "[", RowBox[List[RowBox[List["2", "+", "\[Nu]"]], ",", "z"]], "]"]]]], "-", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]], " ", RowBox[List["BesselJ", "[", RowBox[List[RowBox[List["3", "+", "\[Nu]"]], ",", "z"]], "]"]]]]]], ")"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mi> J </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> J </mi> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> J </mi> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 3 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> BesselJ </ci> <ci> &#957; </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <ci> BesselJ </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> BesselJ </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 3 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BesselJ", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["z", "2"]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "\[Nu]"]], ")"]]]]]], ")"]], " ", RowBox[List["BesselJ", "[", RowBox[List[RowBox[List["2", "+", "\[Nu]"]], ",", "z"]], "]"]]]], "-", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]], " ", RowBox[List["BesselJ", "[", RowBox[List[RowBox[List["3", "+", "\[Nu]"]], ",", "z"]], "]"]]]]]], SuperscriptBox["z", "2"]]]]]]


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





2002-12-18